font=9pt font=footnotesize

11institutetext: retired, formerly Università degli Studi di Milano

W

??

??

# E. Amaldi, C. Dilworth, G.P.S. Occhialini on F.G. Houtermans

Pasquale Tucci

###### Abstract

In the Occhialini-Dilworth Archives of the University of Milan are preserved
four typescripts by E. Amaldi, dealing with F.G. Houtermans, German physicist,
who fled to the USSR to escape the Nazis. During a Stalinist purge he was
arrested. The typescripts were sent to the two Milanese physicists so that
they might give a judgement. G.S. Occhialini and C. Dilworth, in fact, had
personally met Houtermans in 1934 and in 1950. The scenario is that of the
role of nuclear physicists during the WW2. The exchange of letters between
Amaldi and the two Milanese physicists will be analysed in order to identify
possible influences on Amaldi. I will highlight Dilworth’s contribution, which
found room in a chapter of Amaldi’s biography of Houtermans.

††issue: ??

##  1 Introducion: Amaldi’s typescripts111When a person is mentioned for the
first time throughout the paper, I give the following information: full name
and surname and, in round brackets, year of birth and, if any, year of death.
When I’m unable to give the year of death I digit four “?”. When the person is
alive I digit four “.”. Thereafter, the person is mentioned only by her/his
surname.

In the Occhialini-Dilworth Archives333Occhialini-Dilworth Archives are kept in
the BICF, library of Biology, Computer Science, Chemistry, Physics of the
University of Milan. For the history of Occhialini-Dilworth Archives see [4]
are kept 4 typescripts, as well as several letters, sent to Constance
Charlotte Dilworth (1924-2004) (Connie for her friends) and Giuseppe Paolo
Stanislao Occhialini (1907-1993) (Beppo for his friends) by Edoardo Amaldi
(1908-1989).444For an historical reconstruction of Occhialini’s life see [5].
For Dilworth’s life see[6].

The first 155-page typescript, in English, dating back to the early 80s of the
1900,[1] sent to Dilworth and to Occhialini around the year 1984,555In the
Occhialini-Dilworth Archives I did not find Amaldi’s accompanying letter so
I’m unable to say when the typescript was sent. I assume that Amaldi sent his
typescript around 1984-’85 as the comments of both Occhialini and Dilworth are
dated November 1985.  is divided into a Preamble and 22 chapters whose titles
are the same as those of the book of E. Amaldi The adventurous life of
Friedrich Georg Houtermans, Physicist (1903-1966),666Amaldi could not find a
publisher willing to publish his text. Among others, Dilworth also tried to
find a publisher after intervening on the text to make it more fluent.[7];[8]
posthumously published for the first time in 1998[2] and in 2012.[3] At the
end of the typescript are inserted:

  * a)

a “List of publications by F.G. Houtermans (edited by his collaborators of the
University of Bern)” featuring 135 items. In the edition published in 2012, 97
items are listed, to which the editors added another 38 items;

  * b)

a “Bibliography” (actually Notes + Bibliography) including 110 items.

The second 102-pages typescript, dated “October 1987”, in Einglish, is
entitled The adventurous life of Friedrich Georg Houtermans, physicist
(1903-1966). [9] The title, the division into chapters and their titles were
identical to those of Amaldi’s book published in 2012. The List of Houtermans’
publications and the Notes + Bibliography are missing. 164 numerical
references to footnotes are in the typescript, but their text is missing.777In
the published book in 1998 and 2012 the Notes and Bibliography are inserted at
the end of each chapter. In a note Amaldi provided the list of people to whom
he had sent the typescript. [3], p. XIII

The typescript was annotated by Dilworth who, however, limited herself to the
correction of English. In addition she sent by letter to Amaldi some comments.
[10]

The third typescript, identical to the second, is not annotated. It includes
the List of publications by Houtermans (135 items) and Notes+Bibliography (89
items).

The fourth typescript was sent by E. Amaldi on November 23th, 1987. [11] It
consisted of 5 sheets ranging from pages 132 to 136 and its title was: “22 -
Why we recall him”. It was the twenty-second chapter with the title “Why we
remember it” of the book posthumously published. The chapter was sent to two
Milanese physicists to check the parts that concerned them, asking
specifically Dilworth for integrating it.

Amaldi, therefore, completed the first draft of Houterman’s biography in the
early ‘80s. In a letter sent to Charlotte Riefenstahl (1899-1993) (Schnax for
her friends),888A biography of Riefenstahl, based on many autobiographical
material and from other sources, can be found in [14], pp. 30-99. the first
wife of Houtermans, dated July 29th, 1981, Amaldi attached “… the draft of the
Section 8 to 19 of Fritz Biography”. [12] He continued to work on the
Houtermans’ biography until at least on October 1987.

The inspiration to write it, as told by the author himself, came from the film
“The Confession”, directed by Costa-Gravas, taken from the book by Artur
Gerard London “The confession”. [13] Both the film and the book had to deal
with the misadventures of London (1915-1986), a member of the Czechoslovak
Communist Party, imprisoned in Prague in 1957 on suspicion of deviationism and
accused of having contacts with state enemies. Amaldi associated the story of
London with that one of Friedrich Georg Houtermans (1903-1966), a German
physicist who had experienced similar misadventures in the USSR, where he had
voluntarily gone to escape the Nazi dictatorship and to contribute to the
construction of a freer and fairer society. Amaldi had known the German
physicist personally around 1950.

On November 23th, 1979, Amaldi asked Dilworth for Notes of her conversation
with Houtermans in Brussels. [15] In the letter Amaldi stated that he was
writing Houtermans’ biography and that he was quite ahead.

Amaldi’s book, posthumously published, was based on the draft dated “October
1987”. The editors of the edition of 2012 S. Braccini, A. Ereditato and P.
Scampoli added to the text two interviews with Peter Karl Ferdinand Grieder
(1928-????) and Johannes Geiss (1926-2020), a paper by F.G. Houtermans, V.
Fomin, L. Shubnikov “Formation of Heavy Hydrogen Nuclei from Protons and
Neutrons” (translated from Ukrainian) and a brief biography of Amaldi. The
editors limited themselves to update some biographical data and to insert
several images, having been lost the original pictures selected by the author.

Amaldi’s book, namely the draft dated “October 1987”, published for the first
time by Gianni Battimelli & Giovanni Paoloni [2].999In it some notes are
incomplete. In the brief introduction to the text, the two editors
contextualize the historical as well as the physical interests of Amaldi. [2],
pp. 475-476

Amaldi’s book, together with that one of Victor Yakovlevich Frenkel
(1930-1997), published in Russian in 1997, but largely unnoticed, [16], p. X,
and in English in 2015[17], are the most complete biographies of the German
physicist.101010There are also several other papers that deal in a synthetic
way with the misadventures of F.G. Houtermans and with his contributions to
the physics. It is worth underlining the paper of Lanfranco Belloni
(1944-2017), where several papers and books in Russian on F.G. Houtermans are
quoted.[19] Sources for Houtermans’ biography were provided to both Frenkel
and Amaldi by Charlotte Riefenstahl. Frenkel, moreover, had the chance to
consult archival material, including secret documents, made available by the
FSB, the successor of the KGB. The FSB archives were made public only for a
short period of time after USSR collapse.[18], p. 1 In addition to the KGB
archives, consulted thanks to Žores Ivanovič Alfërov (1930-2019), Nobel Prize
in Physics in 2000, Frenkel was able to consult material kept in the State
Archives of Potsdam, in the former DDR.[19]

As Amaldi wrote in the published text “The adventurous life … ” Charlotte
Riefenstahl, had given him:

  * a)

26 pages manuscript she had written for her children about the family of
Houtermans;

  * b)

“And he was always right”, typewritten pages dated September 1948;

  * c)

21 typewritten pages written after Houterman’s death;

  * d)

7 typewritten pages circulated among a few friends in 1981.[3], p. 3

##  2 Who was Houtermans?

Friedrich George Houtermans, Fritz or Fisl for his friends, physicist, lived
in a particularly troubled period of world history, experiencing first-hand
the Nazi wickedness and the cruelty of Stalin’s purges.

Houtermans was an excellent physicist trained from 1922 to 1927, in the middle
of the Weimar republic, in the University of Göttingen, one of the three
outstanding centres of German mathematical and physical tradition together
with Berlin and Munich.111111A description of Göttingen Scientific environment
can be found both in Amaldi’s and in Frenkel’s biography of Houtermans.[3],
pp. 11-15;[17], pp. 99-106  At that time the University of Göttingen had in
its staff the mathematicians David Hilbert (1862-1943), Richard Courant
(1888-1972), Emmy Noether (1882-1935), Herman Weyl (1885-1955). At the
Institute of physics Max Born (1882-1970) had the chair of Theoretical Physics
and several younger theoreticians spent months or years working in Göttingen:
Werner Heisenberg (1901-1976), Wolfgang Pauli (1900-1958), Enrico Fermi
(1901-1954), Giancarlo Wick (1909-1992), Robert Oppenheimer (1904-1967), Paul
Adrien Maurice Dirac (1902-1984), Vladimir Aleksandrovich Fock (1898-1974),
Victor Weisskopf (1908-2002), Léon Rosenfeld (1904-1974).

George Gamow (1904-1968) arrived from Berlin in 1928. He and Houtermans wrote
a paper inspired by Gamow’s paper on the theory of emission of alpha-particles
from radioactive nuclei. They collaborated on an extension of Gamow’s theory
of alpha decay of elements like uranium and thorium, which involved quantum
mechanical tunneling or barrier penetration.

In 1929 Robert d’Escourt Atkinson (1898-1982) (then visiting Göttingen), and
Houtermans turned Gamow’s idea around and considered tunneling as a way of
assembling complex atoms, thereby arriving at much of the essence of the
proton–proton chain put forward in 1939 by Hans Bethe (1908-2005), Nobel Prize
1967 for this work.[20] At the end of his studies Houtermans got a job at the
Technische Hochschule in Berlin-Charlottenburg.

Also in Berlin Houtermans found a rich scientific environment, “an impressive
collection of scientific talents belonging to four or five different research
institutions.”[3], pp. 17-21. In 1929 Atkinson and Houtermans published a more
complete and systematic treatment of the theory of the alpha decay of heavy
nuclei and used their formula for computing from the experimental values of
the energy of the emitted alpha-particle and of the decay constant the radius
and height of the potential barrier for each single nucleus of the uranium-
radium family.[3], p. 18

At about the same time they tackled a completely new problem: that of the
formation of elements in stars with production of energy. Atkinson and
Houtermans computed the probability per unit time of nuclear capture in light
nuclei not of alpha particles but of protons under the conditions expected at
the centre of a star. For heavy nuclei the probability of proton capture
turned out to be exceedingly small, but for light elements, assuming a
collision radius of 4 10-13 cm, they obtained half lives ranging from 8 s in
^4_2He to 109 years for ^10_20Ne. Then they proceeded to estimate from
phenomenological arguments the probability for a proton remaining bound in the
nucleus through the emission of its excess energy by radiation.[3], p. 19

From a detailed analysis of the capture of protons by light nuclei they
concluded that processes of this kind can provide the mechanism not only for
the formation of light elements, but also for supplying the energy required
for maintaining over the ages the emission of radiation from the stars. The
authors discussed their paper with Gamow before publication. The results are
very close to those given afterwards, as Gamow pointed out some years
later.[3], p. 19

In 1932 Houtermans wrote a paper together with Werner Schulze on the electron
microscope. Their paper is considered as the first to have introduced the
Louis De Broglie (1892-1987) wave length of the electron as the important
physical quantity that should be considered in connection with the resolving
power of the electron microscope.[3], p. 19

A member of the German Communist Party,[17], p. 141 Houtermans fled Germany to
escape Nazism and emigrated to England in 1933 with his wife Charlotte and
with their daughter Giovanna (Bamsi for their friends). Fisl and Schnax had
married few years before, in 1930, with Wolfgang Pauli (1900-1958) and Rudolf
Peierls (1907-1995) as witnesses, during a boat trip in the Caucasus organized
for the participants to a physics conference in Odessa.

Charlotte had received her doctorate in physics in 1927 under the physical
chemist Gustav Heinrich Tammann (1861-1938) at the University of Göttingen
where Houtermans had also received his doctorate in the 1927, under James
Frank (1882-1964), Nobel prize in physics for the 1925.

In 1935 Alexandr Leipunskii (1903-1972) invited Houtermans to work at the
Ukrainian Physico-Technical Institute in Kharkov, then in the URSS, although
some their friends, among them Pauli, had warned not to go. But their hate of
the Nazi regime and their hopes on the Soviet regime prevailed. There they
hoped to realize their ideals of freedom.

At the time the Institute was one of the country’s leading physics centres and
there Houtermans carried out physics researches in Leipunskii’s laboratory.
Fritz became a good friend of Lev Davidovič Landau (1908-1968) who was used to
say: “If you have a question of nuclear physics, ask Fritz.”[21], p. 32

But despite his hate for the Nazis, his knowledge of nuclear physics, his
ability to collaborate with colleagues, he became a victim of Stalin’s purges
and, accused of being a spy in the pay of the Nazis, was put in prison in
1937. All communications to and from the outside world were interrupted and he
was forced to confess to being a Trotskyist plotter and a German spy.[16], p.
XI He hoped that his confession, extracted under torture, would avoid
reprisals against his family, who, however, had managed to escape from the
USSR.[16], p. XI

But there is never an end to the worst. As Houtermans himself recounted in
Russian Purge … , written by Beck and Godin, 121212Beck and Godin are the
pesudonims used by Houtermans and Kostantin Feododdovitch Shteppa (1896-1958)
to hide themselves. They had been in the USSR prison in the same cell. The
real authors were discovered by Frenkel in the 1991. [17], p. 267. Indeed
Amaldi had been the first to know the real authors of the Russian Purge … as
he begun to meet Houtermans rather frequently around the 1950.[3], p. XI.  “In
March [1940] I was … asked to sign paper … that I would agree to do secret
work for the USSR abroad. This I signed … otherwise one would be kept
indefinitively.”[22]

Houtermanns was handed over to the Gestapo and put in prison, this time in
Germany. Finally on July 16th 1940 he was set free thanks to Max von Laue
(1879-1960), Nobel prize winner in physics for the 1914. With the help of von
Laue and Carl Friedrich von Weizsäcker (1912-2007), Houtermans obtained a
position in January 1941 at a private laboratory directed by Manfred von
Ardenne (1907-1997) in Lichterfelde, near Berlin.

Here, in August 1941, Houtermans wrote a report,131313Two pages of the 1941
Report were translated in Italian and you can find them in the Occhialini-
Dilworth Archives.[24] The original paper of Houtermans, in German, was
attached by Powers to his letter to Dilworth.[25] for internal use of the
Laboratory, in which he hypothesized the production of energy by means of a
chain reaction based on the fission of heavy elements. The paper was published
two years later in a magazine of the “Deutsche Reichpost”.[23] Von Ardenne, in
fact, had sent the paper to Wilhelm Ohnesoge, Reich Ministry of Posts. Copies
of the report were sent to participants in the Uranverein, launched in 1939:
it was attended, at different times, by Walter Bothe (1891-1957), Kurt Diebner
(1905-1964), Otto Hahn (1879-1968), Fritz Strassmann (1902-1980), Hans Geiger
(1882-1945), C.F. Weizsäcker and W. Heisenberg, along with some others.[17],
p. 234

In the report, about 30 typewritten pages long, Houtermans discussed the
possibility of producing energy by means of nuclear chain-reactions based on
the fission of heavy elements. It was divided in seven sections dealing with:

(1) the general point of view;

(2) the processes in competition with fission which can produce an undesired
reduction of the neutron density;

(3) the chain reaction based on fission produced by fast neutrons;

(4) the chain reactions based on the use of thermal neutrons;

(5) the possibility of realizing a nuclear chain reaction with thermal
neutrons;

(6) the chain reaction in the case of a finite volume of the system;

(7) the meaning of a chain reaction at low temperature as a source of neutrons
and a device for producing nuclear transmutations. The author quoted from the
beginning the theory of nuclear fission published in 1939 by Niels Bohr
(1885-1962) and John Archibald Wheeler (1911-2008)[26] as well as the
experimental papers by the Paris and Columbia University groups concerning the
emission of secondary neutrons in fission [3], p. 77, footnote 7.

The most interesting points of Houtermans’ paper were, according to Amaldi:

a) the conjecture derived from the theory of nuclear fission that the nuclide
of mass number 239 and atomic number Z = 94 (called by its discoverers
plutonium: ^239_94Pu) should undergo fission even with slow neutrons;

(b) the impossibility of a chain reaction with fast neutrons using ordinary
uranium (^238U 99.3%; ^235U 0.7% );

(c) the advantage as a fissionable material of the new nuclide (^239Pu) with
respect to ^238U because the use of the latter requires the separation of this
rather rare isotope from the about one hundred times more abundant ^238U;

(d) the possibility of constructing a bomb based on nuclear chain reaction;

(e) the possibility of constructing what today is called a fast breeder
reactor as the most rational procedure for the exploitation of nuclear energy
and the only one which allows the utilization of the whole energy content of
natural uranium. Amaldi acknowledged the extreme originality of the paper. If
the paper did not produce the effects that could be deduced from it, it is due
to the fact that it was not been sent “to the upper political authorities and
the strategic command where it would have triggered a greater interest …
.”[3], p. 76

The influence that Houtermans’ paper on the German atomic bomb program was one
of the two points of discussion, after the war, when some physicists posed the
problem of Houtermans’ rehabilitation from the accusation of having aided the
Nazis.

The other controversial point was Houtermans’ return in October 1941 to the
Nazi-conquered Kharkov as the representative of the German government in the
Luftwaffe uniform-clad.[17], pp. 250-258 As we will see, Houtermans, when in
1950 had a long discussion with Occhialini at Gamow’s home141414“My late
husband told me that he and Houtermans met for the first time after the war at
a conference of the Royal Society in 1950. Then, among others, were invited to
the house of a colleague and there they got into a corner and “had it out”
about the Kharkov affair.”[28] and after with Dilworth in Brussels, denied
that he had worn the Nazi uniform. Dilworth quoted Houtermans: “They will tell
you I went to Karkhov in uniform. It is not true.”[27]151515In Frenkel’s book
many pages are dedicated to Houtermans’ return to Kharkov. [17], pp. 248-266
The author’s goal was to dismiss any suspicion of Houtermans’ collaboration
with the Nazis. The thesis, based on various documents and testimonies, was
that he wanted to save his former colleagues and laboratory equipment. A
thesis supported by Occhialini and Dilworth after their meeting with the
German physicist in the 1950, as we will see shortly. Amaldi, in his biography
of Houtermans, made his own the thesis of those who justified the behaviour of
the German physicist.

##  3 Houtermans’ meetings with Occhialini

Occhialini first met Houtermans in 1933 in Cambridge (UK). Houtermans, being a
member of the Communist Party, banned after the Reichestag fire of February
27th, 1933 by a fanatic communist, had decided to flee Germany with his
family. Hitler had just been appointed chancellor on January 1933. As
Occhialini will recall in his Memories written in 1992/’93, he had settled
with Houtermans a “very warm affectionate relationship, based on my unreserved
admiration for his brilliance, his political attitude, his knowledge of
physics and the originality of his ideas, founded in German culture.” [29], p.
66.

In 1938, in one of his periodic returns from Brasil, Occhialini met Charlotte
Riefenstahl, the first wife of Houtermans, who told him of the tragedy of the
imprisonment of her husband.[29], pp. 66-67. 161616Occhialini’s first reaction
was to think that it had been his brilliance that had ruined him, that he had
talked too much. Houtermans’ wife denied all that but Occhialini nevertheless
continued to have “… an uncomfortable sensation, the idea that his wit had
brought him to commit indiscretions”.

In that occasion Charlotte asked whether Beppo could meet Frédéric Joliot
(1900-1958) in Paris in order to use the influence of the French physicist on
Soviet authorities to help her husband. Beppo met Joliot, as the he told in
his Memoirs [29], p. 67, and as Charlotte Riefenstahl reported in a letter to
Occhialini dated August 5th, 1938: “Something should come out of this, I have
such a feeling as if this project of yours might work. Thanks
Peppino!”.[30]171717Riefenstahl’s letter, as well as that of July 7th, 1938
and that of December 12th, 1938, are entirely transcribed in the thesis of
Mattia Verzeroli, Degree in Physics at the University of Milan, Academic year
2018-2019, Supervisor prof. Leonardo Gariboldi and Co-supervisor prof. Massimo
Lazzazoni.

Indeed Joliot, together with his wife Irène Curie (1897-1956) and Jean Perrin
(1870-1942), all three Nobel laureates, sent a telegram to the State Attorney
General of USSR and to Stalin. Moreover they sent a long letter to the
Attorney General and to Stalin through the Soviet Ambassador in Paris. In the
letter they asked the release from prison of Houtermans and Alexander
Weissberg (1901-1964)181818Weissberg was the founder of the Soviet Journal of
Physics. Like Houtermans he was the victim of a Stalinist purge and suffered a
fate very similar to that of Houtermans: imprisoned and handed over to the
Gestapo in a prisoner exchange. on behalf of their “old friendship with the
Soviet Union”.191919The telegram and the letter were firstly published in [2],
p. 622 and pp. 623-624, and in [3]. pp. 46-47. Moreover the text of the
telegram and of the letter was sent by Charlotte Riefenstahl to Occhialini in
a letter dated July 7th, 1938.

The letter from Joliot, Curie and Perrin was not followed up favorably, as the
relationships between the USSR and the French government had deteriorated.
Charlotte Reifensthal wrote to Occhialini in a letter dated December 12th,
1938: “Are you going to stop at the Collège de France in Paris? Do send me a
card in case you are going there. How are you? I have no news, I am very sorry
to say.”

Only at the end of the war did Occhialini hear of the exchange of Houtermans
between the Russians and the Gestapo, and of Houtermans’ visit to the
laboratory of Kharkov.

Occhialini met again Houtermans in 1950. Both had been invited to dinner by
Gamow. There Occhialini had a long conversation eye to eye with Fisl. At the
end of the conversation he was completely convinced. Fisl had changed: in 1933
Beppo had met a teenager but now he had become a man. I asked few questions,
he explained everything very clearly, his affection for URSS, his indignation
for the injustice of the Government who had sent him back to Germany as a Nazi
spy, the danger of his situation in Germany and his rescue by von Ardenne and
Heisenberg, his brotherly feeling for his Russian colleagues, in particular
Leipunskii and his desire to help them which led to his return to Kharkov to
help people who might need it. This was the hard point of the discussion.
Anti-nazi Germans I had encountered in previous years at Bristol had warned me
that Russian colleagues asked about this episode had evaded the question.
After this conversation, a dead friend resuscitated had come into my life
never more.[29], p. 67

Following the clarification Occhialini invited Houtermans to Brussels to meet
Ezra Edgard Picciotto (1921-????)202020Amaldi provided brief biographical
informations about Picciotto. Ezra Edgard Picciotto (Italian citizen b. in
Istanbul, Turkey, 1921) has studied in Brussels, where he became “Docteur ès
Sciences” of the Université Libre in 1952. He made most of his carrier at the
same University, except for a number of study periods spent at foreign
institutions. His research activity refers to the geochemistry of stable and
radioactive isotopes in rocks, ocean and atmosphere. In the period 1957 to
1966, Picciotto concentrated his work on the chemistry of Antarctic ices,
taking part in a number of Belgian and American expeditions to the Antartic.
He likes to remind that his orientation and formation as a chemist was
influenced by Irène Curie and mostly by Giuseppe Occhialini and Friedrich
Houtermans.[3] p. 126 and, having to go to Brazil for a UNESCO mission, he
proposed Houtermans to replace him.

At the end of the meeting, however, Occhialini had the impression that the
problem of the Kharkov incident remained. “I feel still the need, not to
excuse but to understand him, and also to understand the intelligent people
who condemned him.” According to Occhialini A very witty person is in an
unstable equilibrium. He is as it were, a moralist and the intellectual does
not forgive a moralist who errs. The wit, who may be called
Triboulet212121Nicolas Ferrial (1479-1536) known as Triboulet was a jester for
Louis XII and Francis I. https://en.wikipedia.org/wiki/Triboulet consulted on
July 12, 2023 or Oscar Wilde (1854-1900) can be victim of his public when he
commits an error. [I already said that the man of 1950 was different from the
of 1934.]

On the other hand although wit has a component of wisdom, when it expressed
not in writing but verbally, it can be considered as denoting
irresponsibility. One laughs freely at satires on others, not on oneself. I
never heard anyone complaining at being hurt by Houthermans wit, but people
with Communist sympathies seemed to have found it natural to suppose that a
sense of humour tolerated in England should cause him difficulties in USSR.
That has been denied by both Fisl and Schnax, who were so alone to the danger
of too open speech that they talked of certain things to each other only in
bed, under the sheets.[29], pp. 68-69

##  4 Houtermans’ meeting with Dilworth

Occhialini and Dilworth met Houtermans in Brussels, few months after London
meeting of Occhialini. This time Dilworth was present. The reasons for the
meeting were described by Dilworth in a letter to Amaldi [31] who had asked
Connie to search through her papers for notes on the conversation she had had
with Houtermans in Brussels.[15] Occhialini had informed Belgian colleagues of
his willing to invite Houtermans to Brussels, at his research group. But his
colleagues were still very sensitive on the subject of war-time
collaborations, had heard various rumours about Houtermans: that he had been a
Nazi spy in Russia and had collaborated in the German war-effort, and in
particular in atomic bomb research. In order to be able to defend him, Beppo
started asking questions, lost patience, went off to a cinema and left Connie
to carry out a “third degree”. In the same letter Dilworth thanked Amaldi for
the Touschek article[31]222222Amaldi’s Touschek biography is also published
in[2], pp. 505-591. Moreover she added some verses she had written after
Touschek’s death.232323 Bruno Touschek
I met you first in Gottingen, shortly after the war, young, but old in knowing
of death and its endless chore. Each for our separate reason, we took the road
to Italy to work with welcoming friends, in a spirit that was free.
From Rome to Milan without money or map is a long way to go
In a small car dodging round great lorries caught in the snow.
But we met and laughed so often when the wine circled free,
We met and mourned to gather friends like Houtermans and Pauli.
We grew older, each in his …., and learnt to suffer life,
But you never gave up the struggle, as I did, not bearing strife.
Then I heard you died in Innsbruck, the day that I was there
And I searched your soul in Innsbruck, knowing I must find it there.
You come to die in Innsbruck, home to the land you knew,
(Should I feel death’s breath on my back, I would home to where I grew.)
To a brook that gently falls by sweet flowers, singing
Through green grass waving to the echo of church bells ringing.
Far from the sunburnt hills where the red grape grows,
Far from the bitter joy that the red wine knows.
Softly you laid your head on a pillow of down,
Softly you met your dead, surrendering your crown.
So to the last you carried a flag with no trace of blood
In a battle without trumpets for a truth not bespattered with mud.
Old Europe died with you, for me and some others,
With the last lingering regrets for a world that called us brothers.

As Dilworth will recall in a letter to Thomas Powers (1940-….) in 1989,
Occhialini had lost patience because in their conversation Houtermans told him
that he had deposited, at the post-office of Charlottetown, a claim for a
patent for the plutonium idea. “It was this that made my husband so angry that
he went to the cinema and left me to carry on the interrogation. Houtermans
assured him that to deposit it at the post-office was equivalent to burying
it.”[ManuscriptofadraftofaLetterofDilworthtoPowerspriorto19891115] Amaldi
considered rumors Houternans’ deposit, at the Post Office in Berlin-
Charlottenburg, of the application for a patent of a fissionable device of
military interest.[3], p. 102 Frenkel didn’t mention this rumour in his long
discussion of 1941 Houtermans’ report.[17], pp. 227-236

Dilworth highlighted, in the letter to Powers, as her report of her “third
degree” with Houtermans was lacking of Houtermans’ comments: This bald summary
does not contain the typical Houtermans comment which made his account
convincing. For instance, I remember he explained to me that to deposit a
report in the Ministry of Posts was perfectly safe, for such was the internal
division and petty war between departments in the Nazi bureaucracy, it would
never reached the group which was doing real research on the bomb. In fact, it
appears he was right, but only Fisl could be so sure of his knowledge of the
Kafkian complexity of bureaucracy to do such a thing to ensure his scientific
priority. This sort of background to the summary is, I am afraid, lost except
in my memory.

The conversation between Houtermans and Dilworth continued, and eventually
Dilworth became convinced of Houtermans’ good faith. Dilworth had taken notes
during the conversation and based on them she wrote 16-point notes. They
represent one of the few first and direct witnesses of Houtermans’ defense
against prosecution about his supposed and controversial collaboration with
Nazism.242424Dilworth’s Notes
1\. Houtermans was in Gestapo prison in February 1940;
2\. He was released the end of July through the intervention of Laue;
3\. Under police supervision as for enemy aliens, not allowed to work in State
Institutes or Universities;
4\. Was found a job by Laue as research physicist in an industrial firm making
cyclotrons generators counters etc. under Von Ardenne;
5\. Police supervision gradually relaxed as for enemy aliens but travelling
restricted;
6\. Work at Von Ardenne fully published except one paper;
7\. Spring 1941 Von Ardenne asked Houtermans for a paper on the possibility of
a chain reaction;
8\. The paper was finished in August 1941, based entirely on published work,
mainly on a paper by Zeldovitch and Chariton 1940 in a Russian Journal;
9\. The content of this paper was:
a. No chain reaction possible with fats neutrons from ordinary Uranium;
b. Possibility of a thermal pile with carbon beryllium or heavy water;
c. Influence of Doppler effect on chain reaction;
d. Possibility of a breeding pile producing Plutonium, if the number of
neutrons per fission of U is greater than 2, which was not known to
Houtermans. This was all highly hypothetical since Houtermans did not know:
a. Capture cross section by U;
b. Resonance cross section for U, so Houtermans thought that a pile would have
to be run at low temperature about —100°C;
c. The fact that Plutonium would show thermal fission was highly hypothetical,
only derived from Bohr Wheeler considerations;
10\. This paper was given to Von Ardenne who passed it to the Research
Department of the Post Ministry, which at that time was not coordinated with
the official Uranverein;
11\. Houtermans did not tell his friend Heisenberg about the contents of this
paper which remained unread by any competent physicist until after the general
coordination of nuclear research in 1944;
12\. Houtermans discussed the paper with two friends Suess and Jensen who were
in the Uranium project. He knew them to be anti-Nazi, having been introduced
to Jensen by Rompe his friend since 1932;
13\. Suess is mentioned by initial as having assisted the Allies by giving
information to the Norwegian heavy water engineers in a book by one of them
about the role of the heavy water plant in the war. This can be checked;
14\. In automn 1941 Houtermans asked Weizsäcker whom he took at that time to
be a anti-nazi whom he knew to be going to visit Bohr to tell Bohr the whole
position of the Uranium project in Germany and to get absolution for the part
played by German physicists in nuclear research since there was no danger of
it being used in the war;
15\. Neither Weizsäcker nor Heisenberg did so;
16\. Houtermans hearing of this through Suess who had met Moller, commissioned
Jensen to do the same on behalf of himself Suess and Houtermans on his visit
to Bohr in 1942.[31]

The points 8., 9., 12., 14., deserve attention.
In the point 8. Houtermans, as Dilworth reported, based his paper on that one
of two Russian scientists: a) Yakov Borisovich Zeldovich (1914-1987) played an
important role in the development of Soviet nuclear and thermonuclear weapons.
b) Yulii Borisovich Khariton (1904-1996) directed the Soviet nuclear program
for many years.[17], pp. 222-223 On the contribution of Zeldovich and Khariton
to nuclear physics see[32].

In the point 9. Dilworth described the content of Houtermans’ article “Zur
Frage … ”[23]. In it Dilworth pointed out that the paper was based on
published work and was highly hypothetical because Houtermans didn’t know

a. the capture cross section by U;

b. the resonanace cross section by U;

c. the fact that Plutonium would show thermal fission was highly hypothetical,
only derived from Bohr Wheeler considerations.

Dilworth argued that the paper would have been of little practical use, giving
substance to the thesis that Houtermans did not give any aid to the German war
effort.

In the point 12. Dilworth wrote that Houtermans had communicated the contents
of his paper to Hans E. Suess (1909-1993)252525Suess was an expert on heavy
water and a scientific advisor to Norsk Hydro, the Norwegian plant in Vemork,
producing hydrogen by electrolyzing water and as a by-product of heavy
water.[35] and Hans Jensen (1907-1973)262626He worked with Paul Harteck
(1902-1985) on heavy water. In the 1942 he talked to Bohr about his researches
in Germany. who were in the Uranium project and that he knew them as anti-
Nazi, having been introduced to Jensen by Robert Rompe (1905-1993), his friend
since 1932.

In the point 14. Dilworth reported that in autumn 1941 Houtermans had asked
Weizsäcker, considered at that time to be a anti-Nazi, whom he knew to be
going to visit Bohr, to tell to Danish physicist the whole position of the
Uranium project in Germany and to get absolution for the role played by German
physicists in nuclear research since there was no danger of it being used in
the war.

Ultimately, Dilworth’s impression from the conversation with Houtermans about
his 1941 paper was one of complete innocence and that his anti-Nazism was
fully proven.

I do not know what transpired these discussions, but Fisl remained in Brussels
and started a very positive collaboration with Picciotto on “plombiologia”,
i.e. geophysical dating by means of lead isotopes. Later, he, Fisl, was
offered a chair in the University of Berne, where he created an extremely
vital centre on geophysical data, carried on by his pupil Geiss.[33]

While the points taken during the conversation were lost, the Notes were found
by Dilworth and were sent to Amaldi in 1980.[31]

She sent her Notes also to Thomas Powers, journalist, who was writing a book
about Heisenberg.[34] with the premise of taking “into account my age - at the
time $\sim$ 26 years - and my consequent ingenuity.”[33]

##  5 Occhialini’s comments to Amaldi’s Biography of Houtermans

Occhialini annotated the first Amaldi’s typescript in several parts. In
general, Beppo’s aim was to highlight or confirm Amaldi’s statements. Few of
them, however, - they can be counted on the fingers of one hand - showed
different points of view.

For example, in chapter 13 entitled “A few other physicist’s political
troubles” Amaldi recalled the story of Pjotr Leonidovich Kapitza (1894-1984)
whom he and Emilio Segré (1905-1989) had met in 1934 at the Cavendish and Mond
Laboratories in Cambridge (UK). As it is known, when in 1934 Kapitza went to
the USSR to participate in the Mendelee’ff Congress, organized on the occasion
of the centenary of the Russian chemist, he did not receive the passport for
the return and the direction of a new laboratory was offered to him. Amaldi
wrote: When, in 1978, Leonidovich Kapitza was awarded the Nobel Prize for his
discovery of superfluidity, all physicists throughout the world were very
happy to see the recognition of his outstanding piece of work which emerges
from a full life devoted, with great success, to the progress of science. But
everybody that had the great luck of meeting him or at least of knowing some
detail about his life, was also satisfied or even moved, that such a
recognition was given to a person endowed of such extraordinary values.[1]

Occhialini underlined “extraordinary human values” and added: Era difficile ma
la trasposizione del periodo 1934 dopo il 1937 è faticoso.272727Translation:
It was difficult but the transposition of the period 1934 after 1937 is
tiring. See also his behavior at the Sakharov trial at the USSR Academy.
Occhialini was referring to the following episode: when in 1980282828The
Decree of the Presidium of the USSR Supreme Soviet is dated January 8th, 1980.
Andrej Sakharov (1921-1989) was stripped of the title of Hero of Socialist
Labor and of all his state awards and exiled, from 1980 to 1986, to Gorki (now
Nizhny Novgorod), a city then off limits to foreigners by decision of the
authorities, Kapitsa was asked to intervene but, as Sakharov wrote in his
Memoirs, “ … like our other “celebrities”, he did nothing.”[36], p.
517,292929A. Marchenko wrote “An open letter to Acedemician P.L. Kapitsa”
dated March 1, 1980 asking him an active intervention in defense of Sakharov,
but even this appeal was not followed up.[37], pp. 31-37.

On the other hand, Sakharov credited Kapitsa with not having signed, in 1973,
a letter in which about fifty academics accused him of having carried out
actions alien to Soviet scientists.[36], p. 303, p. 517.

There is again a long comment by both Occhialini and Dilworth on Houtermans’
moving letter to his mother published by Amaldi in chapter 14 entitled
“Finally out of prison”. Dilworth commented: “Sarebbe certo interessante di
conoscere più lettere di Fisl che certamente esistono e che potrebbero trovare
posto in una biografia. C. D.”303030Translation: It would certainly be
interesting to know more letters of Fisl that certainly exist and that could
find a place in a biography. C. D. (My transaltion P.T.)

Occhialini wrote: La lettera prova qualche cosa di più che l’attaccamento alla
famiglia. È un documento culturale impressionante e vorrei vedere le altre
perché costituiscono la definizione del secondo Houtermans che mi ha colpito
dopo la guerra per la maturazione prodotta dalla prigionia (Heine again
(protestante + ebreo)). Mostra come il “wit e il senso of humour” vengono dal
profondo e fa desiderare di leggere ancora di queste lettere con una
traduzione inglese perfetta. Da notare l’assenza di self
pity.313131Translation: The letter shows something more than attachment to
family. It is an impressive cultural document and I would like to see the
others because they constitute the definition of the second Houtermans that
struck me after the war for the maturation produced by imprisonment (Heine
again (Protestant + Jew)). It shows how the “wit and sense of humour” come
from deep inside and makes you want to read more of these letters with a
perfect English translation. Note the absence of self pity.(My transaltion
P.T.)

Amaldi left the chapter unchanged in the final published version of
Houtermans’ biography. It is very likely that the copy commented by Occhialini
was not sent to Amaldi. Instead, Amaldi received from Occhialini two
handwritten sheets with various considerations.[38] For he who lives more than
one life more than one death must die” (O.W., citato a Memoria,
prob[abilmente] sbagliato.323232Wilde: “For he who lives than one / More
deaths than one must die.”[39] After listing the small deaths of Houtermans
Occhialini continued: La crisi più grave è la $3^{a}$ come ho capito una sera
a Londra ($\sim$ 1950) che ha marcato la nostra riconciliazione (non c’eravamo
incontrati più dal 1934). Non è stata da parte mia un adattamento, sono
rimasto convinto, anche perchè ricordavo (Schnax 31 Dic 1938 - 1 Gennaio in
Londra) che il solo fatto di essere stato arrestato era un peccato per la
sinistra europea.333333The most serious crisis is the $3^{a}$ as I understood
one evening in London ($\sim$ 1950) that marked our reconciliation (we had not
met since 1934). It was not an adaptation on my part, I remained convinced,
also because I remembered (Schnax 31 Dec 1938 - 1 January in London) that the
mere fact of being arrested was a shame for the European left. (My transaltion
P.T.) Two notes concerned Houtermans’ return to Kharkov. Fisl denied that he
went into Nazi uniforms and that he had a military cap.

##  6 Dilworth’s comments to Amaldi’s biography of Houtermans

Dilworth listed 6 points where she disagreed with Amaldi. [10] The fifth point
was interesting. Dilworth argued that Fisl’s security that his paper of 1941
would remain buried stemmed from his theory of “Baumaschology”, according to
which an official document can be used for any end except the one for which it
was issued. And he gave the example of a free pass for a train journey which
will not accepted by the station ticket office but may be used to get petrol
off the ration.

The most important part of Dilworth’s considerations, however, dealt with the
question why we remember Houtermans. It is worth quoting this part in full
because it was almost entirely inserted by Amaldi in the chapter “Why we
recall him”. As an individual but also as a representative of a culture that
is lost. The latter is what he had in common with Bruno Tousheck
(1921-1978).343434Amaldi published a Touschek’s biography two years after the
death of the Austrian scientist. [40]. Amaldi’s Touschek biography is also
published in[2], pp. 505-591. Both were essentially ’Mittel Europa’, Germanic
in the best sense, of the anarchist breed; in revolt against the Prussian
element, and against bureaucracy. Individualist, romantic, but with a
crystalline cynicism with regard to any form of fanaticism: enthusiastic and
in love with life, but life of the city. You cannot imagine either of them
planting cabbages. That both were hard drinkers is indicative of the
melancholy that underlies ebullience.

Professionally, both were much better than their work, their intelligence was
at least equal to the most successful of the contemporaries. The lack of
success was in part due to being in the wrong place at the wrong time.

Houtermans was an innocent, of the tribe of Peter Pan. His refusal, to grow
up, to become serious, was the basis of his charm. On the other hand, as all
Peter pans, he never understood women. His four marriages, three wives and
many children do not denote the profligate but rather a child seeking the road
to the Never Never Land.

Part of this was his warmth and generosity. He may have lied, betrayed and
twisted truth to feed his vanity, but he was not mean. He had no ideal, but
was idealistic in the sense that he did not live for today or tomorrow. He
lived in the stream of history, egoistic but not egocentric, that his culture
forbade. Above all, life was a great joke, a continuous laugh against the
lumpen-bourgeoisie.

They don’t make them like that anymore. That’s why we remember him.[10]

Amaldi pointed out that the letter that had been sent by Connie was very
interesting and he wanted to quote in full a long passage contained in it.[41]

Both the content and the date of Connie’s letter were confirmed by a Beppo’s
letter to Amaldi of November 8, 1985, in Italian.[38] Beppo wrote that he went
to Rome for a meeting of GIFCO (Gruppo Italiano di Fisica Cosmica) and wanted
to personally give Connie’s synthetic notes on Houtermans, but Amaldi was not
in the Institute. In addition to being interesting for the clarification, the
letter is moving because in it Beppo confessed his melancholy: Ho vissuto uno
di questi periodi crepuscolari. Gli ultimi mesi sono saturi di scomparse di
amici, viaggi per tentare di arrivare in tempo a salutarli per l’ultima volta,
visita e lettere per tentare di consolare famigliari, notti di incubi e
rimorsi.

Sto emergendo dalla crisi e nelle prossime settimane ti manderò l’estratto di
varie dozzine di pagine di divagazioni sopra Fisl.

Se, a causa del ritardo non c’è + posto fammelo sapere con dolcezza. 353535“I
lived one of these crepuscolar periods. The last few months have been
saturated with disappearances of friends, trips to try to arrive in time to
say goodbye for the last time, visits and letters to try to comfort family,
nights of nightmares and remorse.
I am emerging from the crisis and in the coming weeks I will send you the
extract of several dozen pages of digressions above Fisl.
If, due to the delay there is no + place let me know sweetly.” (My
translation. P.T.)

Occhialini expressed the same mood in a letter to his brother in 1981: “Milano
mi fa paura, e Genova è per me troppo triste.”363636“Milan scares me, and
Genoa is too sad for me.” (My translation. P.T.) Remembering the death of his
friend Touschek he wrote to Amaldi:

… questa morte risuscitando le memorie di Pauli e di Houtermans ha chiuso
tanto del passato della fisica che sono rimasto con gli occhi che volevano
guardare altrove. Mi sono concentrato nel futuro di questo pezzo di terra [la
sua casa in Toscana] cercando di scacciare i fantasmi. 373737“… this death
resurrecting the memories of Pauli and Houtermans closed so much of the past
of physics that I remained with eyes that wanted to look elsewhere.” (My
translation. P.T.)

Quotations were reported by Agnese Mandrino in the Foreword to the Inventory
of the Occhialini-Dilworth Archives compiled in the years 1998-2000.[42]

In 1992 Dilworth, probably under the pressure of writing the Memoirs,[29] came
back to Houtermans’ biography of Amaldi. In the Archives Occhialini-Dilworth
seven unpublished sheets of Dilworth’s manuscript are kept.[43] The sheets
deal with different themes and some sheets have been lost. So some Dilworth’s
considerations are interrupted. Nevertheless, they are very interesting
because they offer us Dilworth’s thought in all its complexity. They are
undated, but a reference to Giorgio Salvini (1920-2015)[44] places the
manuscripts after the publication date of Salvini’s paper. In them Dilworth
aimed to analyze what Amaldi had written on Touschek and Houtermans splitting
her reflections in three points:
1\. Critique of Amaldi Method;
2\. Explanation of re-presentation;
3\. Historical background.

As regards to the point 1. Dilworth wrote that Amaldi was not an historian and
presented mostly personal memoirs with little verification from documents and
rarely confronted with other testimonials. But this could not be considered a
defect because it had the advantage of vivacity, “… lightening Amaldi’s
pedantic style. As a physicist he couples to the personal drama, long
explanations of the personal activity. This is valid approach in that
necessary but indigestible to the common reader.[43], sheet 1

As regards to the point 2. Dilworth highlighted how in order to overcome the
difficulties of the original text the editor had taken some liberties with it.
As regards to the point 3. Dilworth remembered that once when they were
talking about his essay on Houtermans she asked Amaldi why he choose two such
subjects, Touschek and Houtermans (at that time Dilworth was not aware of
Amaldi’s essay on Majorana).
Amaldi replied that it was because he did not understand them. According to
Dilworth, that he did not, is part of the fascination of these attempts. Here
she quoted Salvini, who remembered Amaldi’s “exemplary cold rationality” and
Dilworth commented: This puzzled rationality, seeking to understand intuitive
imaginative characters is the essential theme of this book. It underscores the
complexity of characters attracted to what the general public is led to
believe as the cold objective attitude to science. In truth, nothing is rarer
in the profession. The personality of Amaldi which comes through his writings
is far from typical.[43], sheet 2 What did Majorana, Houtermans and Touscek
have in common? Why Amaldi wrote their biography? According to Dilworth the
three physicist had in common the passion for their work. And it was the very
passion which destroyed them, the same passion which helped Houtermans to
survive four years of prison of the KGB.383838Indeed Dilworth claimed that
Houtermans was in Soviet prison for seven years. But this is an imprecise
recollection. In Amaldi’s careful, objective, (though uncritical) account of
the lives of his personages there are tantalising glimpses of a Europe which
is being fast forgotten (Houtermans, in post-world-war I was part of the Adler
group (so also was the wife of Pauli, Franca). It was the time of the Weimar
Republic, of the“Berlin Diaries of Christopher Isherwood
(1904-1986)393939Berlin is portrayed by Isherwood during this chaotic interwar
period as a carnival of debauchery and despair inhabited by desperate people
who are unaware of the national catastrophe that awaits them.
$https://en.wikipedia.org/wiki/The_{B}erlin_{S}toriesconsultedinJuly11th,2023$
and in USA of the tragedy of Sacco e Vanzetti.[43], sheet 6

Finally, Dilworth emphasized the “esprit de corps” of the scientific
community: Von Laue helped Houermans to find a job after his imprisonment in
Russia and Germany.

Arnold Sommerfeld (1868-1951) helped Touschek to move from Vienna to Hamburg
where Jensen and Wilhelm Lenz (1888-1957), strictly related to Sommerfeld,
could be trusted in supporting Touschek in his semi-clandestine life in
Germany, where his Jewish origin was not as easily detectable as it had been
in Vienna.[45]

Perrin and Joliot, at the time of their action in support of Houtermans were
not in danger, but still their letters showed that the community took its
responsibilities very seriously.

##  7 Conclusions

Unlike Amaldi who wrote a book with the goal of reconstructing historically
the adventurous life of Houtermans, Dilworth and Occhialini didn’t have such a
goal, although Dilworth claimed to have “dabbled in History of Science” after
her retirement.[DraftofaletterofDilworthtoPowersundatedafter19890418]
Considerations of the two Milanese physicists on Houtermans, in fact, are
scattered through a wide range of notes, not intended for printing, and in
private letters.

Nevertheless it is possible to identify quite clearly three different ways of
analysing the figure of Houtermans, although they had in common the intent to
free Houtermans from the shameful accusation of having helped the German war
effort during World War II.

In a manuscript Dilworth reported that she had asked Amaldi why he had taken
an interest in Houtermans and Touschek, the Roman physicist replied “because I
did not understand them”. And immediately afterwards Dilworth reported
Salvini’s judgment on rational behavior of Amaldi who, evidently, judged
Houtermans’ behavior irrational. Amaldi observed in Houtermns two completely
contradictory personalities: from on the one hand the physical and objective
side of which Amaldi appreciated his numerous and profound papers; on the
other hand, the subjective side with behaviours incomprehensible to the Roman
physicist: Houtermans had married four times and twice with the same person;
the first time he had suddenly married Charlotte during a boat trip organized
during a conference in Odessa; he had gone to Russia despite the misgivings of
many of his friends including Pauli; he had returned to Kharkov in Nazi
uniform ans so on. In general, Amaldi also found incomprehensible that a good
physicist, in a valid institution as the Ukrainian Physico-Technical
Instritute in Kharkov, in a nation chosen because Houtermans hated Nazism,
could be persecuted.

Dilworth and Occhialini, on the other hand, appreciated Houtermans as
physicist but they tried to understand Houtermans’ personality.

Occhialini, as well as Dilworth, didn’t want to reconstruct historically the
events of Houtermans’ life. Beppo was convinced of Houtermns’ innocence not on
the basis of documentation but on the basis of what Houtermans told him as
justification in the long meeting at Gamow’s house. Occhialini felt that
Houtermans had been too wit and that if this characteristic was appreciated in
Germany or England it could create problems for him in Russia, although in
conversation with Charlotte Riefenstahl, Houterman’s first and third wife, she
had excluded this possibility.

According to Occhialini wit has a component of wisdom, when it expressed not
in writing but verbally, it can be considered as denoting irresponsibility.
People with Communist sympathies found it natural to suppose that a sense of
humour tolerated in England should cause him difficulties in USSR.

However, Occhialini’s proposal to offer Houtermans the possibility of
replacing him on the occasion of his trip to Brazil on behalf of UNESCO was
decisive for Houtermans’ complete rehabilitation. And no less decisive for
Houtermans was Occhialini’s ability to convince his fellow physicists of
Houtermans’ innocense.

Dilworth claimed that Houtermans was an eternal Peter Pan. His refusal, to
grow up, to become serious, was the basis of his charm. And while Occhialini
claimed that between 1934, the date of their first meeting, and 1950
Houtermans had become an adult, for Dilworth, instead, Houtermans had remained
an eternal child.

According to Dilworth, as all Peter pans, he never understood women. His four
marriages, three wives and many children do not denote the profligate but
rather a child seeking the road to the Never Never Land.

However according to Dilworth he may have lied, betrayed and twisted truth to
feed his vanity, but he was not mean. Life was a great joke, a continuous
laugh against the lumpen-bourgeoisie.

Dilworth pointed out that individuals such as Houtermans or Touscheck were the
last specimens of a species that died together with the Weimar Republic.

Houtermans’ strong passion for physics, and science in general, allowed
Houtermans to withstand four years of imprisonment. But Houterman as all
brilliant physicists, who strongly claim the priority of an important
discovery, in 1941 handed von Ardenne a document that could have terrible
consequences.

But Dilworth, not forgetting that she was a physicist and, analysing the
physical content of the 1941 report, drew the conclusion that it could not
have practical consequences, since too much relevant data was missing.
Although she admitted that in the 1941 report Houtermans spoke explicitly of a
war use of a possible product of his research.

Dilworth and Occhialini were prompted by Amaldi to rethink the Houtermans
affair as a couple decades after they had played an important role in
dispelling any doubts about Houtermans’ innocence.

In conclusion, a conviction is common to the three interpretations of
Houtermans: his innocence.

## Acknowledgment

I warmly thank Doct. Daniela Martella, Librarian of the BICF, Università degli
Studi di Milano, and Doct. Flavia Safina, BICF, for their assistance in
consulting the Occhialini-Dilworth Archives as well as Doct. Antonella
Cotugno, Archivist and Librarian of the Library and Archive of the Physics
department of the University of Rome, for her assistance in consulting Amaldi
Archives.
A very special thanks goes to Prof. Gianni Battimelli who was of fundamental
help in guiding me among the sheets and the papers of Amaldi Archives.

## References

  * [1] Edoardo Amaldi Dattiloscritto The adventurous life of Friedrich Georg Houtermans, physicist (1903-1966) (Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano, early 80s).
  * [2] Giovanni Battimelli & Giovanni Paoloni “Prominent Personalities in 20th Century Physics” in Battimelli, Giovanni & Paoloni, Giovanni (eds.) (1998). 20th century physics: essays and recollections. A selection of historical writings by Edoardo Amaldi (World Scientific, Singapore-New Jersey-London-Hong Kong 1998), pp. 475-476.
  * [3] Edoardo Amaldi The adventurous life of Friedrich Georg Houtermans, Physicist (1903-1966) in Saverio Braccini & Antonio Ereditato and Paola Scampoli eds The adventurous life of Friedrich Georg Houtermans, Physicist (1903-1966) (Springer, Heidelberg-New York-Dordrecht-London 2012).
  * [4] Etra Occhialini & Pasquale Tucci “The Occhialini-Dilworth Archives” in Pietro Redondi & Giorgio Sironi & Pasquale Tucci and Guido Vegni (eds)The Scientific Legacy of Beppo Occhialini (Società Italiana di Fisica, Bologna - Springer, Berlin 2006).
  * [5] Leonardo Gariboldi Giuseppe Paolo Stanislao Occhialini (1907-1993). A Short Biography in Pietro Redondi & Giorgio Sironi & Pasquale Tucci and Guido Vegni (eds) The Scientific Legacy of Beppo Occhialini (Società Italiana di Fisica, Bologna - Springer, Berlin 2006).
  * [6] Leonardo Gariboldi “Constance Charlotte Dilworth, Streatham (Londra) 5 febbraio 1924) - Firenze 16 maggio 2004” Il Nuovo Saggiatore 20(3-4)16-212004
  * [7] Constance Dilworth Letter of Dilworth to Rufus Neal 19920825 (Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano).
  * [8] Constance Dilworth Letter of Dilworth to Laurie Mark Brown 19920820 (Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano).
  * [9] Edoardo Amaldi Dattiloscritto The adventurous life of Friedrich Georg Houtermans, physicist (1903-1966) (Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano, 1987).
  * [10] Constance Dilworth Letter of Dilworth to Amaldi 19851107 (Dipartimento di Fisica, Università Roma “La Sapienza”, Fondo Edoardo Amaldi, Subfondo Archivio Amaldi eredi (AAE), primo e secondo versamento, Serie 9, scatola 72, fasc. 1).
  * [11] Edoardo Amaldi Dattiloscritto 22 - Why recall him (Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano, 23.11.1987).
  * [12] Edoardo Amaldi Letter of Amaldi to Charlotte Riefenstahl 19812906 Dipartimento di Fisica, Università Roma “La Sapienza”, Fondo Edoardo Amaldi, Subfondo Archivio Amaldi eredi (AAE), primo e secondo versamento, Serie 9, scatola 72, fasc. 1).
  * [13] Artur Gerard London The confession (Morrow, New York 1970).
  * [14] Misha Shifman “Ascent: Charlotte Houtermans’ life and destiny” in Shifman, Misha (ed) Standing together in troubled times (World Scientific, Singapore 2017), pp. 31-99.
  * [15] Edoardo Amaldi Letter of Amaldi to Dilworth 19791123 (Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano).
  * [16] Misha Shifman “Preface” in Shifman, Misha (ed) Physics in a mad world. Houtermans Golfhand (World Scientific, Singapore 2015), pp. IX-XIV.
  * [17] Victor Frenkel “Houtermans” in Shifman, Misha (ed) Physics in a mad world. Houtermans Golfhand (World Scientific, Singapore 2015), pp. 86-386.
  * [18] Misha Shifman “Introduction” in Shifman, Misha (ed) Physics in a mad world. Houtermans Golfhand (World Scientific, Singapore 2015), pp. 1-85.
  * [19] Lanfranco Belloni “Un fisico europeo: Houtermans” Quaderni di Storia della Fisica 917-382001
  * [20] Michael Meo “Houtermans, Friedrich Georg” in Thomas Hockey (Editor-in-Chief) Biographical Encyclopedia of Astronomers, Second Edition (Springer, Heidelberg-Dordrecht-London 2014), pp. 530-531.
  * [21] Iosif B. Khriplovich “The Eventful Life of Fritz Houtermans” Physics Today29(7)29-371992
  * [22] Beck F. & Godin W. Russian Purge and the Extraction of Confession (Hurst & Blackett Ltd, London-New York-Melbourne-Sydney-Cape Town 1951).
  * [23] Friedrich George Houtermans “Zur Frage der Auslösung von Kern-Kettenreaktionen” Sonderhefte der Forschungsanstalt der Deutschen Reichspost, Abteilung für Kernphysik Oktober 1943115-1451943
  * [24] “Ma infine un apparato… ” Two pages translated in Italian, after 19891115, of the 1941 Report of Houtermans, published in 1943 (Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano).
  * [25] Thomas Powers Letter of Powers to Dilworth 19891115 (Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano).
  * [26] Niels Bohr, J.A. Wheeler “The Mechanism of Nuclear Fission” Physical Review56426-4501939
  * [27] Constance Dilworth Draft of a Letter of Dilworth to Rose after 19930722(Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano).
  * [28] Constance Dilworth Draft of the Letter of Dilworth to Rose after 19950205 (Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano).
  * [29] Leonardo Gariboldi, Pasquale Tucci “Occhialini’s Memoirs” Giornale di Fisica (Supplemento)631-732022
  * [30] Charlotte Riefenstahl Letter of Riefenstahl to Occhialini 19380508(Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano).
  * [31] Constance Dilworth Letter of Dilworth to Amaldi 19800725 (Dipartimento di Fisica, Università Roma “La Sapienza”, Fondo Edoardo Amaldi, Subfondo Archivio Amaldi eredi (AAE), primo e secondo versamento, Serie 9, scatola 72, fasc. 1)).
  * [32] Ostriker (ed) “Selected works of Yakov Borisovich Zeldovich” Vol II Particles, Nuclei, and the Universe” in J.P. Ostriker Selected works of Yakov Borisovich Zeldovich” Vol II Particles, Nuclei, and the Universe (Princeton University Press, Princeton 1993), pp. 1-27.
  * [33] Constance Dilworth Draft of a Letter of Dilworth to Powers prior to 19890418 (Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano).
  * [34] Thomas Powers Heisenberg’s war. The secret history of the German bomb (Knopf, New York 1993).
  * [35] Heinrich Waenke; James R. Arnold Hans E. Suess 1909–1993 (The National Academies Press, Washington D.C. 2005).
  * [36] Andrei Sakharov Memoirs (Vintage Books, New York 1992).
  * [37] Anatoly Marchenko “An open letter to Academician P.L. Kapitsa” in Alexander Babyonyshev (Ed) On Sakharov (Vintage books, New York 1982), pp. 31-37.
  * [38] Giuseppe Occhialini Letter of Occhialini to Amaldi 19851108 (Dipartimento di Fisica, Università Roma “La Sapienza”, Fondo Edoardo Amaldi, Subfondo Archivio Amaldi eredi (AAE), primo e secondo versamento, Serie 9, scatola 72, fasc. 1).
  * [39] Oscar Wilde “The Ballad of Reading Gaol” in Smithers, Leonard (ed) The Ballad of Reading Gaol. By C.3.3 (The Chiswick Press for Smithers, London 1898), pp. 1-31.
  * [40] Edoardo Amaldi The Bruno Touschek legacy (Vienna 1921-Innsbruck 1978) (CERN, Geneva 1981).
  * [41] Constance Dilworth Letter of Amaldi to Dilworth 19871123 (Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano).
  * [42] Agnese Mandrino “Inventario dell’Archivio Occhialini-Dilworth” 1998-2000.
  * [43] Constance Dilworth Seven sheets undated, after 1992 (Archivio Occhialini-Dilworth, BICF, Università degli Studi di Milano).
  * [44] Giorgio Salvini “Edoardo Amaldi (5 September 1908-5 December 1989)” Proceedings of the American Philosophical Society133(3)424-4291992
  * [45] Luisa Bonolis & Giulia Pancheri “Bruno Touschek: particle physicist and father of the $e^{+}e^{-}$ collider” The European Physical Journal H361-612011


# Linear-in-Complexity Computational Strategies for Modeling and Dosimetry at
TeraHertz

###### Abstract

This work presents a fast direct solver strategy allowing full-wave modeling
and dosimetry at terahertz (THz) frequencies. The novel scheme leverages a
preconditioned combined field integral equation together with a regularizer
for its elliptic spectrum to enable its compression into a non-hierarchical
skeleton, invertible in quasi-linear complexity. Numerical results will show
the effectiveness of the new scheme in a realistic skin modeling scenario.

###### Index Terms:

integral equations, dosimetry, terahertz, fast solver

Linear-in-Complexity Computational Strategies for Modeling and Dosimetry at
TeraHertz

Viviana Giunzioni${}^{(\ref{org1})}$, Giuseppe Ciacco${}^{(\ref{org1})}$,
Clément Henry${}^{(\ref{org2})}$, Adrien Merlini${}^{(\ref{org2})}$, and
Francesco P. Andriulli${}^{(\ref{org1})}$

(1) Department of Electronics and Telecommunications, Politecnico di Torino,
Italy

(2) Microwaves Department, IMT Atlantique, Brest, France

##  I Introduction

With the technological advances in THz technology, a growing number of
interdisciplinary applications in the THz range have emerged and gained
popularity in the last two decades within areas ranging from security, to
communications, or biomedicine [1]. As the impact of THz devices in our
societies grows, accurately assessing the effects of THz waves on the human
body gains crucial importance [2]. Hence the need for exposure analyses that
aim at quantifying the amount of energy absorbed by biological tissues subject
to electromagnetic radiations [3].

Preliminary dosimetry assessments are a fundamental phase during the design of
THz equipments, to guarantee their compliance with the limits on the power
absorbed by human tissues set by international agencies [4]. Exposure
measurements are often challenging to perform, especially in the near field,
but this challenge can be, in part, sidestepped by reliable and accurate
numerical dosimetric assessments, when they are within reach. However
numerical modeling at THz also comes with its own set of complications.

On the one hand, many of the solvers proposed in the literature employ
approximations of the Maxwell’s system, suitable to the high frequency regime
considered, or apply geometrical simplification to make use of proper analytic
solutions. However, application of these approximations can degrade the
solution accuracy, and potentially compromise the reliability of the
dosimetric analyses. On the other hand, full-wave models leverage the original
Maxwell system and can be applied to arbitrarily complex geometries, but the
higher computational costs incurred can become prohibitive. In addition, they
suffer from numerical issues, such as ill-conditioning or spurious resonances
at high frequencies [5] that need to be handled to obtain reliable results.

We propose here a novel full-wave approach, well suited to modeling reflection
and absorption of THz waves by biological samples. Being a fast direct
solution strategy, this approach allows for the efficient solution of the THz
problems for multiple exposures at once, with a complexity which grows only
quasi-linearly with the number of unknowns, that is, with increasing
frequency. This is obtained by first defining a proper set of boundary
integral equations and leveraging a tailored preconditioning scheme, resulting
in a well-conditioned system of linear equations freed from spurious
resonances. This formulation is then coupled with a recently proposed fast
inversion strategy [6], that relies on the compression of the elliptic
spectrum of the boundary operator into a rank-deficient skeleton form and on
the use of the Woodbury matrix identity [7].

##  II Background and Notation

Dosimetry analyzes aim at assessing the amount of energy absorbed by the human
body when exposed to an electromagnetic radiation. This estimation can be
performed by numerically simulating the response of the biological tissue to
the impinging field through a full-wave electromagnetic solver. In this work
we employ the two-dimensional approximation, that assumes tha invariance of
the geometries and field along an axis $\hat{\veg z}$. This lends itself well
to the case under study given the large dimensions of some body parts compared
to THz wavelengths. However, this approximation is not suited to modeling all
body parts.

Based on the representation theorem [8], different boundary integral equations
(BIEs) can be set up to numerically model the time-harmonic electromagnetic
scattering and absorption of a penetrable body. Given a two-dimensional domain
$\Omega$ with boundary $\Gamma\coloneqq\uppartial\Omega$ characterized by the
outgoing normal field $\hat{\veg n}$, the boundary integral operators [8]

$\displaystyle\left(\mathcal{S}_{k}^{\Gamma}\psi\right)(\veg{r})$
$\displaystyle\left(\mathcal{D}_{k}^{\Gamma}\psi\right)(\veg{r})$
$\displaystyle\coloneqq\mathrm{p.v.}\int_{\Gamma}\uppartial_{\veg{n}^{\prime}}G_{k}(\veg{r}-\veg{r}^{\prime})\psi(\veg{r}^{\prime})\dd
S(\veg{r}^{\prime})\,,$ (1)
$\displaystyle\left(\mathcal{D}^{*\Gamma}_{k}\psi\right)(\veg{r})$
$\displaystyle\coloneqq\mathrm{p.v.}\int_{\Gamma}\uppartial_{\veg{n}}G_{k}(\veg{r}-\veg{r}^{\prime})\psi(\veg{r}^{\prime})\dd
S(\veg{r}^{\prime})\,,$ (2)
$\displaystyle\left(\mathcal{N}_{k}^{\Gamma}\psi\right)(\veg{r})$
$\displaystyle\coloneqq-\mathrm{f.p.}\int_{\Gamma}\uppartial_{\veg{n}}\uppartial_{\veg{n}^{\prime}}G_{k}(\veg{r}-\veg{r}^{\prime})\psi(\veg{r}^{\prime})\dd
S(\veg{r}^{\prime})\,,$ (3)

which are respectively the single layer, double layer, adjoint double layer,
and hypersingular operator, constitute the building blocks of any of these
formulations. The notations p.v. and f.p. indicate the Cauchy principal value
and the Hadamard finite part. We denote by $G_{k}$ the two-dimensional Green’s
function in free-space

$G_{k}(\veg{r}-\veg{r}^{\prime})=-\frac{j}{4}H_{0}^{(2)}\left(k||\veg{r}-\veg{r}^{\prime}||\right)\,,$
(4)

where $H_{0}^{(2)}$ is the Hankel function of the second kind with order zero
as defined in [9].

Moreover, numerical exposure assessments also require the a priori definition
of a realistic model of the tissue under study, both in terms of geometry and
dielectric permittivity. Research on THz external dosimetry is often focused
on the skin [3, 10], as THz impinging field is absorbed by this organ.
Different geometrical models of the skin have been proposed [11] to accurately
reproduce the human anatomy. They usually aim at modeling the stratification
of compartments with different physical properties, such as the stratum
corneum, the epidermis, and the dermis layers, sometimes even modeling
anisotropies and depth-varying water percentage [11], at the cost of
increasing model complexity. For the sake of simplicity, in this work we
employ a single-dielectric model. Following the double Debye model [12], the
permittivity of the skin as a function of the frequency is modeled as

$\epsilon_{r}(\omega)=\epsilon_{\infty}+\frac{\epsilon_{s}-\epsilon_{2}}{1+j\omega\tau_{1}}+\frac{\epsilon_{2}-\epsilon_{\infty}}{1+j\omega\tau_{2}}\,,$
(5)

with parameters $\epsilon_{\infty}=$ 3, $\epsilon_{s}=$ 60, $\epsilon_{2}=$
3.6, $\tau_{1}=$ 10ps, and $\tau_{2}=$ 0.2ps [13]. The validity of this
approximation has been demonstrated in previous works [14], which however have
also highlighted a limitation of the model when applied to dry skin and, in
general, to tissues characterized by low water contents.

##  III Fast Direct Solver Strategy for THz Dosimetry

We propose here a fast direct solver strategy for modeling the electromagnetic
response of a biological tissue of boundary $\Gamma_{s}$ to an excitation
realized by means of a metallic body of boundary $\Gamma_{m}$. It is based on
a composite formulation made up of the combined field integral equation (CFIE)
for perfect electric conductor (PEC) materials [15] and of the Poggio-Miller-
Chang-Harrington-Wu-Tsai (PMCHWT) equation for penetrable media [16]. As is
sometimes done in the literature, we assume that the coupling terms between
the metallic and the dielectric objects can be neglected [17, 18]. In the case
where both objects (i.e., the metallic and the dielectric ones) are subject to
a TM polarized field, the resulting system of integral equations is given in
eqn:integraleq at the bottom of the page. Similar results can be found for
different polarizations.

$\begin{cases}\mathcal{S}_{k_{0}}^{\Gamma_{m}}j_{z,m}(\veg
r)+\left(\frac{1}{2}\mathcal{I}+\mathcal{D}^{*\Gamma_{m}}_{k_{0}}\right)j_{z,m}(\veg
r)=\frac{1}{jk_{0}\eta}E_{z}^{\text{inc},m}(\veg r)+H_{t}^{\text{inc},m}(\veg
r),&\text{$\veg r\in\Gamma_{m}$}\\\
\left(-jk_{0}\eta_{0}\mathcal{S}_{k_{0}}^{\Gamma_{s}}-jk_{1}\eta_{1}\mathcal{S}_{k_{1}}^{\Gamma_{s}}\right)j_{z,s}(\veg
r)+\left(\mathcal{D}_{k_{0}}^{\Gamma_{s}}+\mathcal{D}_{k_{1}}^{\Gamma_{s}}\right)m_{t,s}(\veg
r)=E_{z}^{\text{inc},s}(\veg r),&\text{$\veg r\in\Gamma_{s}$}\\\
-\left(\mathcal{D}_{k_{0}}^{*\Gamma_{s}}+\mathcal{D}_{k_{1}}^{*\Gamma_{s}}\right)j_{z,s}(\veg
r)+\left(-1/(jk_{0}\eta_{0})\mathcal{N}_{k_{0}}^{\Gamma_{s}}-1/(jk_{1}\eta_{1})\mathcal{N}_{k_{1}}^{\Gamma_{s}}\right)m_{t,s}(\veg
r)=H_{t}^{\text{inc},s}(\veg r),&\text{$\veg r\in\Gamma_{s}$}\end{cases}$ (7)

In these equations, we denote by the subscript 0 the quantities related to the
exterior medium, which can be assumed to be the air, and by the subscript 1
the ones related to the interior, penetrable, medium. The exterior and
interior wavenumbers are denoted as $k_{0}=\omega\sqrt{\epsilon_{0}\mu_{0}}$
and $k_{1}=\omega\sqrt{\epsilon_{1}\mu_{1}}$, while
$\eta_{0/1}=\sqrt{\mu_{0/1}/\epsilon_{0/1}}$ are the characteristic impedances
of the exterior or interior medium. $(E^{\text{inc},m},H^{\text{inc},m})$ and
$(E^{\text{inc},s},H^{\text{inc},s})$ are the electromagnetic fields incident
over $\Gamma_{m}$ and $\Gamma_{s}$ respectively, further separated into the
transversal and longitudinal components, denoted by t and z. In the following,
we will denote by the subscripts m and s quantities related to $\Gamma_{m}$
and $\Gamma_{s}$ respectively.

The unknowns in eqn:integraleq are the surface equivalent currents defined on
the metallic and dielectric boundaries. They are of electric type only in the
former case, $j_{z,m}$, and of both electric and magnetic type in the latter,
$j_{z,s}$ and $m_{t,s}$. In particular, by superimposing the radiation
provided by these currents, it is possible to retrieve the scattered
electromagnetic field, to be summed to the incident field in order to
determine the resulting electric and magnetic fields everywhere and, in
particular, inside the biological sample.

The application of a Galerkin discretization scheme, based on the
approximation of the unknown currents as linear combinations of $N_{m/s}$
piecewise linear basis functions $\lambda_{i}(\veg r)$ defined on a mesh of
the boundary $\Gamma_{m/s}$, as
$j_{z,m/s}\simeq\sum_{i=1}^{N_{m/s}}(\vec{j}_{z,m/s})_{i}\lambda_{i}$ and
$m_{t,s}\simeq\sum_{i=1}^{N_{m/s}}(\vec{m}_{t,s})_{i}\lambda_{i}$, results in
the linear system of equations

$\begin{pmatrix}\mat C&\vec{0}&\vec{0}\\\ \vec{0}&\mat P_{11}&\mat P_{12}\\\
\vec{0}&\mat P_{21}&\mat P_{22}\end{pmatrix}\begin{pmatrix}\vec{j}_{z,m}\\\
\vec{j}_{z,s}\\\
\vec{m}_{t,s}\end{pmatrix}=\begin{pmatrix}\vec{e}_{z,m}/(jk_{0}\eta_{0})+\vec{h}_{t,m}\\\
\vec{e}_{z,s}\\\ \vec{h}_{t,s}\end{pmatrix}\,.$ (8)

In the above system,

$\displaystyle(\vec{e}_{z,m/s})_{i}$
$\displaystyle=\left(\lambda_{i},E_{z}^{\text{inc},m/s}\right)_{L^{2}(\Gamma_{s/m})}\quad$
(9) $\displaystyle(\vec{h}_{t,m/s})_{i}$
$\displaystyle=\left(\lambda_{i},H_{t}^{\text{inc},m/s}\right)_{L^{2}(\Gamma_{s/m})}\,,$
(10)

and the matrices $\mat C$, $\mat P_{11}$, $\mat P_{12}$, $\mat P_{21}$, and
$\mat P_{22}$ are defined as

$\displaystyle\mat C$
$\displaystyle=\mat{S}_{k_{0}}^{\Gamma_{m}}+\frac{1}{2}\mat{G}^{\Gamma_{m}}+\mat{D}^{*\Gamma_{m}}_{k_{0}}$
(11) $\displaystyle\mat P_{11}$
$\displaystyle=-jk_{0}\eta_{0}\mat{S}_{k_{0}}^{\Gamma_{s}}-jk_{1}\eta_{1}\mat{S}_{k_{1}}^{\Gamma_{s}}$
(12) $\displaystyle\mat P_{12}$
$\displaystyle=\mat{D}_{k_{0}}^{\Gamma_{s}}+\mat{D}_{k_{1}}^{\Gamma_{s}}$ (13)
$\displaystyle\mat P_{21}$
$\displaystyle=-\left(\mat{D}_{k_{0}}^{*\Gamma_{s}}+\mat{D}_{k_{1}}^{*\Gamma_{s}}\right)$
(14) $\displaystyle\mat P_{22}$
$\displaystyle=-1/(jk_{0}\eta_{0})\mat{N}_{k_{0}}^{\Gamma_{s}}-1/(jk_{1}\eta_{1})\mat{N}_{k_{1}}^{\Gamma_{s}}\,,$
(15)

where we have used the generic notation $(\mat
O_{k}^{\Gamma})_{i}j=\left(\lambda_{i},\mathcal{O}_{k}^{\Gamma}\lambda_{j}\right)_{L^{2}(\Gamma)}$,
where $\mathcal{O}$ stands for one of
$\\{\mathcal{S},\mathcal{D},\mathcal{D}^{*},\mathcal{N}\\}$. The gram matrix
$\mat G^{\Gamma}$ is obtained as $(\mat
G^{\Gamma})_{ij}=(\lambda_{i},\lambda_{j})_{L^{2}(\Gamma)}$.

As a consequence of the fact that the metallic radiator is electrically much
larger than the biological sample under study, a significantly higher number
of basis functions is required for the discretization of the unknown currents
on its boundary $\Gamma_{m}$ (following the Nyquist sampling principle).
Hence, we infer that the numerical solution of the linear system resulting
from the discretization of the CFIE is the bottleneck, in terms of time and
memory required, towards the solution of the entire system (8), both directly
or iteratively. To alleviate this computational burden, we propose here to
extend the Calderón preconditioned scheme presented in [19, 6] for $\mat C$
and to extend the fast direct solver tailored for the resulting well-
conditioned operator recently proposed in [6]. In particular, we define the
Calderón stabilized operator matrix as

$\displaystyle\mat C_{p}\coloneqq\,\,$
$\displaystyle\mat{N}_{\tilde{k}_{0}}^{\Gamma_{m}}\left(\mat{G}^{\Gamma_{m}}\right)^{-1}\mat{S}_{k_{0}}^{\Gamma_{m}}+$
$\displaystyle\left(\frac{1}{2}\mat{G}^{\Gamma_{m}}-\mat{D}^{*\Gamma_{m}}_{\tilde{k}_{0}}\right)\left(\mat{G}^{\Gamma_{m}}\right)^{-1}\left(\frac{1}{2}\mat{G}^{\Gamma_{m}}+\mat{D}^{*\Gamma_{m}}_{k_{0}}\right)\,$
(16)

where, following the approach introduced in [20], $\tilde{k}_{0}\coloneqq
k_{0}-j0.4k_{0}^{1/3}a^{-2/3}$, with $a$ evaluated as a suitable average of
the radius of curvature along $\Gamma_{m}$. Then, following the procedure
described in [6], we express $\mat C_{p}$ as the sum $\mat C_{p}=\mat
C_{p,\text{c}}+\mat C_{p,\text{ext}}$, where $\mat C_{p,\text{c}}$ is the
circular counterpart of $\mat C_{p}$ discretized over an equi-perimeter
circular boundary. We employ at this point an adaptive randomized algorithm,
such as the one presented in [21], to compute a skeleton form of $\mat
C_{p,\text{ext}}$ as

$\mat C_{p,\text{ext}}=\mat C_{p}-\mat C_{p,\text{c}}\simeq\mat U\mat
V^{\T}\,.$ (17)

Given the spectral properties of matrix $\mat C_{p,\text{ext}}$, the rank of
the skeleton $\mat U\mat V^{\T}$ grows only approximately as $k_{0}^{1/3}$
toward the high frequency limit. As a consequence, by applying a proper
acceleration technique such as the fast multiple method (FMM) [22], the
solution of the system, for any number of right hand sides, can be obtained
efficiently, in quasi-linear complexity, by directly evaluating the inverse
[7]

$\mat C_{p}^{-1}=\mat C_{p,\text{c}}^{-1}-\mat C_{p,\text{c}}^{-1}\mat
U\left(\mat I+\mat V^{\T}\mat C_{p,\text{c}}^{-1}\mat U\right)^{-1}\mat
V^{\T}\mat C_{p,\text{c}}^{-1}\,.$ (18)

In particular, after noticing that all operations involving circulant matrices
are computed rapidly via the use of the fast Fourier transform (FFT)
algorithm, we recognize that the complexity of evaluating (18) scales in
frequency approximately as $k_{0}^{4/3}$, with an overhead complexity with
respect to the linear one determined by the skeleton rank increase.

##  IV Numerical results

In this section, we first aim at assessing the efficiency of the fast direct
solver. The rank of the skeleton form $\mat U\mat V^{\T}$ is the key parameter
to observe, as it directly determines the computational complexity of the
method, affecting both time and memory required. The first geometry analyzed
is the ellipse. Figure 1 shows the rank of the skeleton of the operator, for
both TE and TM formulations, evaluated over an ellipse with aspect ratio 1.5
and perimeter 2$\pi$ m. Secondarily, we have considered an airfoil geometry,
resulting from the application of the Joukowsky conformal mapping from the
circle, with perimeter 2$\pi$ m (fig:wing_rank). In both cases, we observe
that the rank grows less than linearly with frequency and tends to stabilize
to the expected behaviour of $k_{0}^{1/3}$ in the high frequency limit.
Consistently, the compression time (i.e., the time required for the skeleton
evaluation), dominating the overall inversion time, scales quasi-linearly, as
shown in tab:time.

Then, we applied the solver to the evaluation of the electromagnetic
scattering from a skin sample (fig:skinfield). In particular, we considered an
ellipse of perimeter approximately of 5.85mm excited by a time-harmonic field
at the frequency of 1THz. We employed the double Debye model (eqn:debye) to
approximate the permittivity of the skin, corresponding to a penetration
length of approximately 62.

Figure 1: Rank of the skeleton form $\mat U\mat V^{\T}$ evaluated over an
ellipse with aspect ratio 1.5 and perimeter 2$\pi$ m as a function of the
free-space wavenumber $k_{0}$.

Figure 2: Rank of the skeleton form $\mat U\mat V^{\T}$ evaluated over an airfoil with perimeter 2$\pi$ m as a function of the free-space wavenumber $k_{0}$. $N$ |  $k_{0}$ [rad/m] | compr. time [s] | eri
---|---|---|---
15011 | 833.91 | 59.33 | -
30021 | 1667.8 | 129.6 | 1.13
45032 | 2501.7 | 210.2 | 1.19
TABLE I: Compression time required to evaluate the skeleton form $\mat U\mat
V^{\T}$ evaluated over an ellipse with aspect ratio 1.5 and perimeter 2$\pi$ m
at different frequencies, corresponding to different numbers of unknowns $N$,
and experimental rate of increase (eri). The simulations have been performed
on 25 parallel processes.

Figure 3: Magnitude of the longitudinal electric field scattered by the skin
given a TM plane-wave excitation at the frequency of 1THz impinging at an
angle of -1/5$\pi$.

##  V Conclusion

This paper presented a fast direct solver strategy for full-wave modeling and
dosimetry at terahertz frequencies. This has been obtained by leveraging a
preconditioned version of the combined field integral equation, free of
spurious high-frequency resonances, and a suitable compression technique for
its elliptic spectrum, resulting in an operator matrix invertible in quasi-
linear complexity. The direct nature of the solver makes its use convenient to
solve multiple sources problems, where the scatterer response to many
different exposures should be analyzed, as it can be the case in dosimetry
studies.

## Acknowledgment

The work of this paper has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation
programme (grant agreement No 724846, project 321), from the Horizon Europe
Research and innovation programme under the EIC Pathfinder grant agreement n°
101046748 (project CEREBRO), and from the ANR Labex CominLabs under the
project “CYCLE”.

## References

  * [1] X. Chen, H. Lindley-Hatcher, R. Stantchev, J. Wang, K. Li, A. Hernandez Serrano, Z. Taylor, E. Castro-Camus, and E. Pickwell-MacPherson, “Terahertz (THz) biophotonics technology: Instrumentation, techniques, and biomedical applications,” _Chemical Physics Reviews_ , vol. 3, no. 1, p. 011311, Mar. 2022.
  * [2] O. P. Cherkasova, D. S. Serdyukov, A. S. Ratushnyak, E. F. Nemova, E. N. Kozlov, Yu. V. Shidlovskii, K. I. Zaytsev, and V. V. Tuchin, “Effects of terahertz radiation on living cells: A review,” _Optics and Spectroscopy_ , vol. 128, no. 6, pp. 855–866, Jun. 2020.
  * [3] S. Alekseev, A. Radzievsky, M. Logani, and M. Ziskin, “Millimeter wave dosimetry of human skin,” _Bioelectromagnetics_ , vol. 29, no. 1, pp. 65–70, Jan. 2008.
  * [4] ICNIRP, “Guidelines for limiting exposure to electromagnetic fields (100 kHz to 300 GHz),” _Health Physics_ , vol. 118, no. 5, pp. 483–524, May 2020.
  * [5] S. Adrian, A. Dely, D. Consoli, A. Merlini, and F. Andriulli, “Electromagnetic integral equations: Insights in conditioning and preconditioning,” _IEEE Open Journal of Antennas and Propagation_ , vol. 2, pp. 1143–1174, 2021.
  * [6] D. Consoli, C. Henry, A. Dély, L. Rahmouni, J. Ortiz G., T. Chhim, S. Adrian, A. Merlini, and F. Andriulli, “On the fast direct solution of a preconditioned electromagnetic integral equation,” Apr. 2022.
  * [7] H. V. Henderson and S. R. Searle, “On deriving the inverse of a sum of matrices,” _SIAM Review_ , vol. 23, no. 1, pp. 53–60, Jan. 1981.
  * [8] J. Nédélec, _Acoustic and Electromagnetic Equations_ , ser. Applied Mathematical Sciences, J. E. Marsden and L. Sirovich, Eds. New York, NY: Springer New York, 2001, vol. 144.
  * [9] F. W. J. Olver and National Institute of Standards and Technology, Eds., _NIST Handbook of Mathematical Functions_. Cambridge: Cambridge Univ. Press [u.a.], 2010.
  * [10] Z. Haider, Y. Le Drean, G. Sacco, D. Nikolayev, R. Sauleau, and M. Zhadobov, “High-resolution model of human skin appendages for electromagnetic dosimetry at millimeter waves,” _IEEE Journal of Microwaves_ , vol. 2, no. 1, pp. 214–227, Jan. 2022.
  * [11] J. Wang, H. Lindley-Hatcher, X. Chen, and E. Pickwell-MacPherson, “THz sensing of human skin: A review of skin modeling approaches,” _Sensors_ , vol. 21, no. 11, p. 3624, May 2021.
  * [12] J. T. Kindt and C. A. Schmuttenmaer, “Far-infrared dielectric properties of polar liquids probed by femtosecond terahertz pulse spectroscopy,” _The Journal of Physical Chemistry_ , vol. 100, no. 24, pp. 10 373–10 379, Jan. 1996.
  * [13] E. Pickwell, B. E. Cole, A. J. Fitzgerald, V. P. Wallace, and M. Pepper, “Simulation of terahertz pulse propagation in biological systems,” _Applied Physics Letters_ , vol. 84, no. 12, pp. 2190–2192, Mar. 2004.
  * [14] E. Pickwell, B. E. Cole, A. J. Fitzgerald, M. Pepper, and V. P. Wallace, “ _In Vivo_ study of human skin using pulsed terahertz radiation,” _Physics in Medicine and Biology_ , vol. 49, no. 9, pp. 1595–1607, May 2004.
  * [15] J. Mavtz and R. Harrington, “H-field, E-field, and combined field solutions for conducting body of revolution,” _Archiv Elektronik Übertragungstechnik_ , vol. 32, pp. 157–164, 1978.
  * [16] A. Poggio and E. Miller, “Integral equation solutions of three-dimensional scattering problems,” in _Computer Techniques for Electromagnetics_. Elsevier, 1973, pp. 159–264.
  * [17] M. Ziane, R. Sauleau, and M. Zhadobov, “Antenna/body coupling in the near-field at 60 GHz: Impact on the absorbed power density,” _Applied Sciences_ , vol. 10, no. 21, p. 7392, Oct. 2020.
  * [18] G. Sacco, D. Nikolayev, R. Sauleau, and M. Zhadobov, “Antenna/human body coupling in 5G millimeter-wave bands: Do age and clothing matter?” _IEEE Journal of Microwaves_ , vol. 1, no. 2, pp. 593–600, Apr. 2021.
  * [19] F. Andriulli, I. Bogaert, and K. Cools, “On the high frequency behavior and stabilization of a preconditioned and resonance-free formulation,” in _2015 International Conference on Electromagnetics in Advanced Applications (ICEAA)_. Torino, Italy: IEEE, Sep. 2015, pp. 1321–1324.
  * [20] M. Darbas, “Generalized combined field integral equations for the iterative solution of the three-dimensional Maxwell equations,” _Applied Mathematics Letters_ , vol. 19, no. 8, pp. 834–839, Aug. 2006.
  * [21] N. Halko, P. G. Martinsson, and J. A. Tropp, “Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions,” _SIAM Review_ , vol. 53, no. 2, pp. 217–288, Jan. 2011.
  * [22] R. Coifman, V. Rokhlin, and S. Wandzura, “The fast multipole method for the wave equation: A pedestrian prescription,” _IEEE Antennas and Propagation Magazine_ , vol. 35, no. 3, pp. 7–12, Jun. 1993.