###  O.7 Lemmas

######  Lemma O.7.1.

Let $G=(V,E)$ be a directed tree rooted at $r\in V$, and suppose
$u,u^{\prime},v\in V$ are such that the following conditions hold:

  1. (i)

$u\neq v$

  2. (ii)

$u$ is not a descendant of $v$

  3. (iii)

$(u^{\prime},v)\in E$.

Let $G^{\prime}$ be the directed graph obtained from $G$ by deleting the edge
$(u^{\prime},v)$ and adding the edge $(u,v)$, that is,
$G^{\prime}=(V,(E\setminus\\{(u^{\prime},v)\\})\cup\\{(u,v)\\})$. Then
$G^{\prime}$ is a directed tree rooted at $r$.

###### Proof.

We show that for any vertex $w$, there is a unique path in $G^{\prime}$ from
$r$ to $w$.

First, suppose $w$ is not a descendant of $v$ in $G^{\prime}$. Then $w$ is not
a descendant of $v$ in $G$, since the set of descendants of $v$ is the same in
$G$ and $G^{\prime}$. Thus no path from $r$ to $w$ in either $G$ or
$G^{\prime}$ passes through $v$; consequently, no path from $r$ to $w$ in
either $G$ or $G^{\prime}$ contains either of the edges $(u^{\prime}v)$ or
$(u,v)$. Thus, a sequence of vertices $r=x_{0},\ x_{1},\ \ldots,\ x_{n}=w$ is
a path in $G^{\prime}$ if and only if it is a path in $G$. Since there is a
unique path from $r$ to $w$ in $G$, it follows that there is a unique path
from $r$ to $w$ in $G^{\prime}$.

Next, suppose $w$ is a descendant of $v$ in $G^{\prime}$ (and hence also in
$G$). Because $u^{\prime}$ is the only in-neighbor of $v$ in $G$, it follows
that $u$ is the only in-neighbor of $v$ in $G^{\prime}$. Thus, every path from
$r$ to $w$ in $G^{\prime}$ is the concatenation of a path from $r$ to $u$ with
a path from $v$ to $w$. But since $u$ is not a descendant of $v$ in $G$ (hence
neither in $G^{\prime}$), there is a unique path from $r$ to $u$ in
$G^{\prime}$, by the above paragraph. And of course, there is a unique path
from $v$ to $w$ in $G$, hence also in $G^{\prime}$ since the subtrees rooted
at $v$ are the same. Therefore there is a unique path from $v$ to $w$ in
$G^{\prime}$. ∎


2022 186 07 September

Neutron emission in UPC Pb–Pb at $\mathrm{\sqrt{s_{\mathrm{NN}}}=5.02}$ TeV

ALICE Collaboration††thanks: See Appendix A for the list of collaboration
members ALICE Collaboration

In ultraperipheral collisions (UPCs) of relativistic nuclei without overlap of
nuclear densities, the two nuclei are excited by the Lorentz-contracted
Coulomb fields of their collision partners. In these UPCs, the typical nuclear
excitation energy is below a few tens of MeV, and a small number of nucleons
are emitted in electromagnetic dissociation (EMD) of primary nuclei, in
contrast to complete nuclear fragmentation in hadronic interactions. The cross
sections of emission of given numbers of neutrons in UPCs of 208Pb nuclei at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV were measured with the neutron zero degree
calorimeters (ZDCs) of the ALICE detector at the LHC, exploiting a similar
technique to that used in previous studies performed at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. In addition, the cross sections for the
exclusive emission of one, two, three, four, and five forward neutrons in the
EMD, not accompanied by the emission of forward protons, and thus mostly
corresponding to the production of 207,206,205,204,203Pb, respectively, were
measured for the first time. The predictions from the available models
describe the measured cross sections well. These cross sections can be used
for evaluating the impact of secondary nuclei on the LHC components, in
particular, on superconducting magnets, and also provide useful input for the
design of the Future Circular Collider (FCC-hh).

##  1 Introduction

Studies of collisions of ultrarelativistic nuclei typically focus on the
participant zone where the nuclei overlap and the quark–gluon plasma (QGP), a
state of matter where quarks and gluons are free, can be created [1]. This is
the domain where hot and dense matter is produced due to the enormous
collision energy of the participating nucleons. At the same time, a domain of
cold nuclear matter is expected to coexist with the participant zone in
peripheral collisions. It is represented by spectator nucleons, which mainly
preserve the velocity of the initial nuclei and travel forward. Measurements
at the CERN Super Proton Synchrotron (SPS) [2] have shown that some of the
spectator nucleons remain bound in nuclear fragments produced in peripheral
collisions of ultrarelativistic 208Pb nuclei with a beam energy of 158 GeV per
nucleon with a lead target. At this energy heavy spectator fragments were also
detected in interactions of 208Pb nuclei with various target nuclei [3]. This
was explained by a modest excitation of spectator matter in peripheral
collisions [3].

In ultraperipheral collisions (UPCs) of relativistic heavy ions without
nuclear overlap the colliding nuclei can be considered entirely as spectators.
While their geometrical overlap is excluded because the collision impact
parameter exceeds the sum of the nuclear radii, nuclei are still excited by
the Lorentz-contracted Coulomb fields of their collision partners. In
comparison to hadronic nucleus–nucleus collisions, electromagnetic excitation
is a rather soft process that results in the electromagnetic dissociation
(EMD) of primary nuclei with the emission of just a few nucleons [4].

Large EMD cross sections for the emission of one, two and three forward
neutrons have been reported by the ALICE Collaboration [5] for UPCs of 208Pb
nuclei at a centre-of-mass energy per nucleon pair
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV at the Large Hadron Collider (LHC). EMD
products retain beam rapidity similarly to spectators from hadronic
nucleus–nucleus collisions. The EMD of 208Pb nuclei contributes significantly
to the decay of the beam intensity [6] and produces various secondary nuclei
in all four interaction points (ALICE, ATLAS, CMS and LHCb) of the LHC [7].
Certain secondary nuclei with their charge-to-mass ratio close to 208Pb
(principally 207Pb) can travel for long distances around the collider rings
because their magnetic rigidity is close to that of 208Pb and they may
potentially be lost in superconducting magnets [7, 8]. With a proper set-up of
the collimation system, most of these secondary nuclei are intercepted
efficiently by the off-momentum collimators and the dispersion suppressor
sections around the LHC experiments. A dominant source of beam loss in the
latter regions is the process of bound-free $\mathrm{e}^{+}\mathrm{e}^{-}$
pair production in UPCs with the electron capture by 208Pb [7, 8].

The methods to study fragmentation of projectile nuclei at multi-GeV or TeV
collision energies differ significantly from those used at much lower
collision energies. In the latter case, fragments of projectiles with an
initial energy of hundreds of MeV per nucleon are emitted at large angles with
respect to the beam axis, so that their spread permits complete identification
of projectile fragments using, among others, scintillator hodoscopes and time-
of-flight detectors [9, 10]. In particular, the multi-fragment break-up of
spectator matter has been investigated at intermediate collision energies [9].

In contrast, the detection of projectile fragments in experiments at
ultrarelativistic energies exceeding tens of GeV per nucleon is harder. It is
difficult to separate these fragments from beam nuclei because they are
emitted at very small angles with respect to the beam axis. For example,
projectile fragments were intercepted by imposing an external magnetic field
and placing fragment detectors far from the interaction point [2]. High
resolution nuclear emulsions [11] and solid-state track detectors made of CR39
plastic [12] have also been employed to study fragmentation of
ultrarelativistic nuclei. The charge distributions of fragments have been
measured [11, 12] in a wide range of charges of secondary nuclei, but nuclear
emulsions and stacks of CR39 remained insensitive to spectator neutrons.
Measurements of the charge-changing cross sections for lead and indium nuclei
at an energy of 158 GeV per nucleon were performed with multiple-sampling
ionisation chambers in Refs. [3] and [13], respectively, also without
detecting forward neutrons.

It should be emphasised that, to date, the production of charged spectator
fragments has not been studied, neither at RHIC nor at the LHC. There exist
only two proposals for future experiments to detect charged fragments in
collider experiments, in particular, by means of a centrality detector at RHIC
[14] and by the ATLAS Forward Proton detectors at the LHC [15]. The ALICE
experiment already has a unique possibility to detect forward protons as well
as neutrons with its neutron and proton zero degree calorimeters (ZDCs) [16,
17, 18].

According to the RELDIS [19, 20, 4] and FLUKA [21] models, the production of
various secondary nuclei is expected in EMD of 208Pb at the LHC. It is
impossible to identify masses and charges of secondary nuclei at the LHC and
thus directly measure the cross sections of production of specific nuclides.
However, the cross sections of production of 207,206,205,204,203Pb are closely
related to the cross sections to emit one, two, three, four, and five
neutrons, respectively, in the absence of proton emission.

The aim of the present work is twofold. Firstly, to determine the cross
sections of neutron emission in EMD of heavy nuclei at the highest collision
energy available in accelerator experiments. Various models [4, 21, 22, 23]
that are used to calculate neutron emission in EMD can be tested with these
new data. Secondly, to measure the cross sections of emission of 1, 2, …, 5
neutrons without protons, to be used as approximations of the cross sections
of production of 207,206,205,204,203Pb. The validity of this approximation is
studied by means of the RELDIS model.

In Sec. 2 the ALICE ZDCs are briefly described. In Sec. 3 the data sample and
the adopted trigger configuration are presented. Section 4 describes the
methods of fitting ZDC energy spectra, and the corrections for detection
efficiency and acceptance that provided the measured cross sections presented
in Sec. 5. In Sec. 6, on the basis of the RELDIS model, the neutron emission
without protons in EMD of 208Pb is associated with the production of secondary
lead nuclei. Finally, conclusions and outlook are given in Sec. 7.

##  2 Experimental set-up

A detailed description of the ALICE experiment can be found in Ref. [24]. In
the following, only the detectors relevant for the measurements discussed in
this paper will be described. Two identical systems of hadronic calorimeters
are placed on both sides (C and A) of the nominal interaction point (IP),
112.5 m away from the IP along the beam direction, see Fig. 1 for the
placement on the side A. The neutron (ZNC and ZNA) and proton (ZPC and ZPA)
calorimeters [16, 17, 18] were denoted as ZN and ZP, respectively. The letter
C(A) was assigned to the corresponding calorimeter because it intercepts the
forward nucleons emitted by nuclei of the clockwise (anticlockwise) beam 1(2).
Each ZDC is segmented into four towers. Half the optical fibres uniformly
distributed in the calorimeter are read out by four tower photomultipliers
(PMTs) and the other half are read out by a single fifth photomultiplier (PMC)
common to all towers. Thus, there exist two options to obtain the energy
deposited in the ZDC, either from the sum of signals in all PMTs (including
PMC), or from the signal in the PMC alone.

Figure 1: Colour online: Simplified layout with respect to the ALICE
interaction point (IP2) (not to scale) of the neutron (ZN), proton (ZP), and
two electromagnetic (ZEM) calorimeters. The approximate positions of a dipole
magnet (D1) and quadruple magnets (Q1, Q2, and Q3) are also shown. A view
towards the forward surface of the ZN and ZP (A–A) shows typical distributions
of entry points of forward nucleons obtained in Monte Carlo modelling. The
longitudinal dimensions of ZN and ZP are shown in a simplified three-
dimensional (3D) scheme.

ZNC and ZNA are placed at zero degrees with respect to the neutron flight path
from the IP to detect neutral forward particles at pseudorapidities
$|\eta|>8.8$. ZPC and ZPA detect forward protons guided to these calorimeters
by the LHC magnet system. Two small electromagnetic calorimeters (ZEM1 and
ZEM2) are placed only on the side A, at 7.5 m from the IP, see Fig. 1,
covering the pseudorapidity range $4.8\leq\eta\leq 5.7$ [18] and two intervals
$-16^{\circ}<\phi<16^{\circ}$ and $164^{\circ}<\phi<196^{\circ}$ of azimuthal
angle. Technical characteristics of the hadronic neutron (ZN), proton (ZP),
and electromagnetic (ZEM) calorimeters are summarised in Table 1.

Table 1: Technical characteristics of the hadronic neutron (ZN), proton (ZP), and electromagnetic (ZEM) calorimeters. | ZN | ZP | ZEM
---|---|---|---
Dimensions (cm3) | $7.04\times 7.04\times 100$ | $12\times 22.4\times 150$ | $7\times 7\times 20.6$
Absorber material | W alloy | brass | lead
$\rho_{\mathrm{absorber}}$ (g/cm3) | 17.61 | 8.48 | 11.34
Length (in $\lambda_{\mathrm{I}}$ units ) | 8.7 | 8.2 | 1.1
Length (in $X_{\mathrm{0}}$ units ) | 251 | 100 | 35.4
Filling ratio | 1/22 | 1/65 | 1/22
Fibre spacing (mm) | 1.6 | 4 | –
Fibre diameter (mm) | 0.365 | 0.550 | 0.550
Fibre tilted at (deg) | 0 | 0 | 45

##  3 Data sample

Data on 208Pb–208Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV collected
by ALICE in 2018 were analysed. Special runs for the EMD cross section
measurement with reduced instantaneous luminosity and, consequently, with
reduced event pile-up were considered. For these runs the average number of
hadronic inelastic interactions per bunch crossing $\mu_{\mathrm{inel}}\sim
1.3\times 10^{-4}$ was about 10 times lower than during the ALICE standard
physics runs. Events were triggered requiring a signal over threshold either
in ZNC or in ZNA. This condition is referred to as the ZED trigger and it is
sensitive to one-sided EMD events with neutrons emitted either towards the C
or A sides, as well as to EMD and hadronic events with neutrons emitted on
both sides. It is customary (see, e.g. Ref. [5]) to define as single EMD
events those with at least one neutron emitted in EMD processes, and as mutual
EMD events those with at least one neutron emitted per side in EMD processes,
so that mutual EMD events are a subset of single EMD events.

Using the ZDC timing information, only events corresponding to interactions
happening at the nominal bunch crossing were selected, thus rejecting
collisions between the beam and residual gas in the beam pipe, and collisions
involving nuclei circulating outside the nominal bunch slots. The total number
of selected events amounts to ${N_{\mathrm{tot}}}=2.050\times 10^{6}$. The ZED
trigger cross section $\sigma_{\mathrm{ZED}}$ was measured in a van der Meer
(vdM) scan [25] and found to be $\sigma_{\mathrm{ZED}}=420.5\pm 10.1$ b [26].

The triggered events were classified into electromagnetic and hadronic events
according to the signals of the forward calorimeters ZEM1 and ZEM2. Events
with a signal in either ZEM were tagged as hadronic and rejected, leaving a
sample of ${N^{\mathrm{EMD}}}_{\mathrm{tot}}=2.009\times 10^{6}$ single or
mutual EMD event candidates. However, as follows from the modelling of
particle emission in UPCs of 208Pb at the LHC [19], in a small fraction of EMD
events, protons and pions are emitted at $|\eta|\leq 6$. Detection of these
particles by one of the ZEMs may lead to the rejection of EMD events due to
the ZEM veto condition. Therefore, it is necessary to estimate the efficiency
of the ZEM veto to select electromagnetic events.

Let the numbers of single EMD, mutual EMD and hadronic events be denoted as
$s$, $m$ and $h$, respectively. The number of detected events with neutrons,
say, only on side C is defined as $s-m+h\zeta_{hnm}={\cal N}_{1}$. In this
equation a small fraction $\zeta_{hnm}$ of hadronic non-mutual events with the
emission of forward neutrons only on one side is taken into account. The
number of events with neutrons only on side C, but obtained without signal in
ZEM is calculated as
$s\varepsilon-m\varepsilon_{m}+h\zeta_{hnm}\varepsilon_{h}={\cal N}_{2}$. Here
the fractions of single EMD, mutual EMD, and hadronic events, which survive
the ZEM veto, are denoted as $\varepsilon$, $\varepsilon_{m}$, and
$\varepsilon_{h}$, respectively. The condition that neutrons are detected only
on side C can be released, thus providing the equations: $s+h={\cal N}_{3}$
and $s\varepsilon+h\varepsilon_{h}={\cal N}_{4}$, without and with the ZEM
veto, respectively. In Ref. [5] a small value $\varepsilon_{h}=0.076$ was
reported on the basis of HIJING modelling. According to the AAMCC model [27],
the fraction of hadronic events with 1–5 forward neutrons on a given side, but
without neutrons on the other side, is calculated as $\zeta_{hnm}=0.003$. As
estimated with the RELDIS and AAMCC models, for each of the 1n–5n channels,
the relation $s\gg h$ is valid, and consequently, $s\gg h\varepsilon_{h}$.
Because of the dominance of single EMD events over mutual EMD events, the
relations $s-m\gg h\zeta_{hnm}$ and $s\varepsilon-m\varepsilon_{m}\gg
h\zeta_{hnm}$ are also valid and the hadronic contribution can be neglected in
all four equations for each neutron multiplicity with the solution
$\varepsilon={\cal N}_{4}/{\cal N}_{3}$ and $\varepsilon_{m}=({\cal
N}_{4}-{\cal N}_{2})/({\cal N}_{3}-{\cal N}_{1})$.

The resulting $\varepsilon_{i}$ for each neutron multiplicity $i=1,2,\dots 5$
for events with less than 6 neutrons and for events with any number of
neutrons (Xn) are given in Table 2 together with their uncertainties
calculated following Ref. [28] assuming a uniform prior. The values of
$\varepsilon_{i}$ estimated on both sides exceed 99%. As can be also seen from
Table 2, there is a trend that the higher the neutron multiplicity, the higher
the fraction of EMD events lost due to the ZEM veto. Hereafter, events with
zero, one, two, …, six neutrons are denoted as 0n, 1n, 2n, …, 6n events. Less
than 0.125% of 1n events are lost due to the ZEM veto, but up to 1% for 5n.
This is explained by the fact that EMD products associated with high neutron
multiplicity events are emitted at larger angles and in some rare cases can
hit ZEM. Nevertheless, the efficiency of selecting EMD events by imposing the
ZEM veto remains extremely high ($>99.8$%) for the 1n–5n channels. The values
of $\varepsilon_{i}$ listed in Table 2 were used to correct the numbers of
detected events ${n_{i}}$, of each neutron multiplicity $i$n, for the
efficiency of the ZEM veto to select EMD events.

Table 2: Efficiency of the ZEM veto to select electromagnetic events with a given neutron multiplicity and for events with any number of neutrons, estimated from the data collected with and without the ZEM veto for the sides C and A. Neutron |  $\varepsilon_{i}$ (%)
---|---
multiplicity $i$n | Side C | Side A
1n | $99.875\pm 0.005$ | $99.902\pm 0.005$
2n | $99.766\pm 0.014$ | $99.819\pm 0.013$
3n | $99.457\pm 0.039$ | $99.349\pm 0.042$
4n | $99.479\pm 0.043$ | $99.321\pm 0.049$
5n | $99.368\pm 0.050$ | $99.025\pm 0.064$
total 1n–5n | $99.802\pm 0.005$ | $99.806\pm 0.005$
total Xn | $96.722\pm 0.017$ | $96.117\pm 0.019$

The emission of neutrons in the EMD of one or both colliding nuclei can be
accompanied by two-photon interactions
$\gamma\gamma\rightarrow\mathrm{e}^{+}\mathrm{e}^{-}$ in the same UPC event.
This process was considered in Ref. [29] for mutual EMD. By modelling with
STARlight [30] dilepton production and neutron emission on one side, the
energy distributions of $\mathrm{e}^{+}$ and $\mathrm{e}^{-}$ within the
acceptance of the ZEM were calculated. The probability to obtain leptons with
energy above the ZEM veto threshold of about 10 GeV was found to be
negligible.

##  4 Analysis

###  4.1 Collection, calibration and fit of ZDC energy spectra

In the present work the ZDC energy spectra collected with the PMC were used to
obtain the neutron emission cross sections. These spectra were calibrated to
satisfy as precisely as possible two main criteria: (1) the pedestal peak is
centred at zero energy; (2) the distance between consecutive peaks amounts to
the beam energy $E_{0}=2510$ GeV per nucleon.

The numbers of detected events $n_{i}$ for each neutron multiplicity class
$i$n were extracted by fitting the calibrated distributions of energy $E$
deposited in ZN using the $\chi^{2}$ fit method. The fitting procedures were
validated with Run 1 data in Ref. [5]. The fitting function $F(E)$ is the sum
of six Gaussians corresponding to up to six detected neutrons

$F(E)=\sum_{i=1}^{6}G_{i}(E)=\sum_{i=1}^{6}\frac{n_{i}}{\sqrt{2\pi}\sigma_{i}}\
\mathrm{e}^{-\frac{(E-\mu_{i})^{2}}{2\sigma_{i}^{2}}}.$ (1)

The Gaussian $G_{i}(E)$ represents the $i$-th peak and it is characterised by
the mean value $\mu_{i}$, the standard deviation $\sigma_{i}$ and the
normalisation constant $n_{i}$, which denotes the number of detected events
with $i$ neutrons. Because of the large widths of the peaks corresponding to
neutron multiplicities larger than 5 in the neutron spectra, it was not
possible to identify unambiguously the numbers of events with six or more
neutrons. Though the 6n peak is not well defined, it is still used to improve
fit results for 1, 2, …, 5 neutrons. The values of $\mu_{1}$, $\sigma_{1}$,
and $n_{1}$ for the first nucleon peak were considered as free parameters.
Despite the expected exact correspondence of $\mu_{1}$ to $E_{0}$, some
variations of $\mu_{1}$ in the course of the fitting procedure were allowed
within a $\pm 10$% deviation from $E_{0}$. In addition, the value of
$\sigma_{1}$ was constrained to be between $0.1\times E_{0}$ and $0.5\times
E_{0}$ to improve the fit quality. These conditions make it possible to
account for imperfect ZDC calibration. The parameters of the Gaussians
describing the two-, three-, four-, five-, and six-nucleon peaks were also
restricted: $\mu_{i}$ varied within $\pm 20$% around $i\times\mu_{1}$ while
$\sigma_{i}$ varied from $\sigma_{1}$ to $\sqrt{i}\sigma_{1}$. The numbers of
detected events $n_{i}$ in each peak were introduced as free parameters of the
fit. As described below, after taking into account the
acceptance$\times$efficiency of the ZDCs, corrected numbers of events $N_{i}$
were finally obtained from $n_{i}$.

The distributions of energy deposited by forward EMD neutrons in ZNC and ZNA
are shown in Fig. 2. These distributions were obtained for events with at
least one neutron registered either in ZNC (Fig. 2, left) or in ZNA (Fig. 2,
right), surviving the ZEM veto. As seen from this figure, the spectra
collected on the C and A sides are very similar. These spectra were fitted
with the functions given by Eq. (1). The yields of 1n, 2n, …, 5n EMD events
were extracted from these spectra and used to calculate the cross section of
emission of given numbers of neutrons along with any number of forward
protons, as described in Sec. 5.1.

Figure 2: Colour online: distributions of energy in ZNC (left) and ZNA (right)
from EMD events (histograms) and resulting fit functions (solid curves)
representing the sum of Gaussians. The Gaussians representing 1n peaks are
shown by dashed curves.

###  4.2 Correction for detection efficiency and acceptance of neutron and
proton ZDCs

Some of the forward nucleons are lost on their way to the ZDCs due to the
limited ZDC acceptance and scattering on various components of the LHC, in
particular, on injection collimators, beam pipes, recombination chamber, and
in air. Also, a peripheral impact of some nucleons on the calorimeter is
responsible for an increased shower leakage leading to reduced energy
deposited in the ZDCs. Because of such effects, the distributions of energy
deposited in the ZDCs are distorted, particularly in events with a high
nucleon multiplicity. For example, either one or two nucleons can be lost in a
three-nucleon event. As a result, the three-nucleon event can be
misidentified, respectively, as a two-nucleon or as a one-nucleon event. The
probability to obtain a fake one-nucleon event will be different in two- and
three-nucleon events. This suggests the need to calculate the efficiency of
event detection separately for each multiplicity class, as demonstrated in
Ref. [31].

The acceptance$\times$efficiency correction factors
$f_{i{\mathrm{n}}}=N^{\mathrm{MC}}_{i}/n^{\mathrm{MC}}_{i}$ were calculated
for ZNC and ZNA and, for the study of neutron emission without protons, also
for ZPC and ZPA. In a realistic Monte Carlo simulation of the ALICE apparatus,
and after transporting neutrons generated with RELDIS, the number of generated
events $N^{\mathrm{MC}}_{i}$ and the number of events $n^{\mathrm{MC}}_{i}$
registered in ZDC were calculated for each neutron multiplicity class $i$n.
RELDIS has been validated with data on neutron emission in EMD of 208Pb at the
LHC [5] and at lower collision energies [32]. The acceptance$\times$efficiency
correction factors calculated for the channels with the emission of zero, one,
two, three, four, and five neutrons, possibly along with other particles, are
given in Table 3. The values of $f_{i{\mathrm{n}}}$ were obtained by two
different methods described below, and the simple averages $f_{i{\mathrm{n}}}$
were applied to raw data, as explained in Sec. 4.3. The first method was based
on counting nucleons crossing the front area of each ZDC, while in the second
method simulated ZDC energy spectra were fitted by the functions given by Eq.
(1). Finally, in both methods the numbers of events of each multiplicity $i$n
generated by RELDIS were divided by the numbers of detected events to obtain
the correction factors. The difference between the results of the two methods
divided by $\sqrt{2}$ is considered as the systematic uncertainty for the
final average correction factors. These factors are given in Table 3 together
with their combined statistical and systematic uncertainties. As seen from
this table, most of the obtained $f_{i{\mathrm{n}}}$ values exceed unity,
because the loss of EMD neutrons in a channel of a certain multiplicity is not
compensated by the migration of events from less frequent channels of higher
multiplicity induced by the loss of one or two neutrons. In contrast,
according to RELDIS, only in 3.2% of EMD events neutrons are not emitted, but
the 0n channel is filled with events of different neutron multiplicity when
all neutrons are lost. This explains a noticeable correction of
$f_{0{\mathrm{n}}}\approx 0.3$ for the 0n channel.

When considering neutron emission without associated proton emission,
additional correction factors for the proton ZDC, $f_{0{\mathrm{p}}}$, were
applied to the raw yields. Hereafter, events with zero protons are denoted as
0p events. These correction factors were calculated with the same two methods
as for the neutron ZDC resulting in the average values of $0.848\pm 0.015$ and
$0.852\pm 0.018$ for ZPC and ZPA, respectively. In general, results from MC
simulations are consistent with results of the probabilistic model of Ref.
[31] with the probability $p_{\mathrm{n}}=0.9$ to detect a neutron in ZN and
with $p_{\mathrm{p}}=0.55$ to detect a proton in ZP.

Table 3: Acceptance$\times$efficiency correction factors for detecting neutrons in ZNC and ZNA and their estimated uncertainties. Neutron | Average of two methods
---|---
multiplicity | $f_{i{\mathrm{n}}}$
$i$n | ZNC | ZNA
0n | 0.286 $\pm$ 0.126 | 0.302 $\pm$ 0.097
1n | 1.064 $\pm$ 0.031 | 1.064 $\pm$ 0.030
2n | 1.092 $\pm$ 0.024 | 1.010 $\pm$ 0.095
3n | 1.057 $\pm$ 0.032 | 1.066 $\pm$ 0.020
4n | 1.001 $\pm$ 0.046 | 0.962 $\pm$ 0.094
5n | 0.907 $\pm$ 0.132 | 0.917 $\pm$ 0.104

###  4.3 Determination of neutron emission cross sections

The cross sections for specific EMD channels $\sigma(i{\mathrm{n}})$ with a
given number of neutrons $i$ and an arbitrary number of protons were obtained
by combining $\sigma_{\mathrm{ZED}}$ introduced in Sec. 3 and ${n_{i}}$ from
the fit functions given by Eq. (1). The cross sections were measured
separately on the C and A sides by ZNC and ZNA, respectively. After the signal
extraction, the corrections for the efficiency of the ZEM veto
$\varepsilon_{i}$ introduced in Sec. 4.1 and for the ZDC efficiency and
acceptance, $f_{i{\mathrm{n}}}$, Sec. 4.2, were applied:

$\sigma(i{\mathrm{n}})=\sigma_{\mathrm{ZED}}\frac{N_{i}}{N_{\mathrm{tot}}}=\sigma_{\mathrm{ZED}}\frac{n_{i}}{N_{\mathrm{tot}}}\frac{f_{i{\mathrm{n}}}}{\varepsilon_{i}}=\sigma_{\mathrm{ZED}}\frac{n_{i}}{N_{\mathrm{tot}}}F_{i\mathrm{n}}\
.$ (2)

Here $N_{i}$ is a corrected number of events with given neutron multiplicity
$i$, $N_{\mathrm{tot}}$ is the total number of ZED trigger events defined in
Sec. 3, and $F_{i\mathrm{n}}$ is the resulting correction factor. The cross
sections of specific EMD channels $\sigma(i{\mathrm{n}},{\mathrm{0p}})$ with
given number of neutrons $i$ and without protons on the side C or A were
obtained in the same way, but with the additional correction factors
$f_{0{\mathrm{p}}}$ for the efficiency of registration of 0p events in ZPC and
ZPA, respectively:

$\sigma(i{\mathrm{n}},\mathrm{0p})=\sigma_{\mathrm{ZED}}\frac{N_{i}}{N_{\mathrm{tot}}}=\sigma_{\mathrm{ZED}}\frac{n_{i}}{N_{\mathrm{tot}}}\frac{f_{i{\mathrm{n}}}f_{0{\mathrm{p}}}}{\varepsilon_{i}}=\sigma_{\mathrm{ZED}}\frac{n_{i}}{N_{\mathrm{tot}}}F_{i\mathrm{n},0\mathrm{p}}\
.$ (3)

Here $F_{i\mathrm{n},0\mathrm{p}}$ is the resulting correction factor as in
Eq. (2), but for 0p events. Because of the very large number of collected ZED
trigger events, the uncertainty of $N_{\mathrm{tot}}$ is negligible. The
statistical uncertainties of $n_{i}$ originate from the uncertainties on the
numbers of events found by the fit procedure. The systematic uncertainties of
$n_{i}$ were estimated from a variation of the fit procedure by considering
the difference in $n_{i}$ obtained with the nominal and double bin size. Only
systematic uncertainties were considered for $F_{i\mathrm{n}}$ and
$F_{i\mathrm{n},0\mathrm{p}}$. Following Ref. [26], the relative systematic
uncertainty of $\sigma_{\mathrm{ZED}}$ was taken as $2.4$%, resulting from the
vdM scan analysis.

The final cross sections were obtained as the average between the measurements
performed on the sides C and A from the event numbers and resulting correction
factors introduced in Eqs. (2) and (3):

$\bar{\sigma}=\frac{\sigma^{\mathrm{C}}+\sigma^{\mathrm{A}}}{2}=\sigma_{\mathrm{ZED}}\frac{n^{\mathrm{C}}F^{\mathrm{C}}+n^{\mathrm{A}}F^{\mathrm{A}}}{2N_{\mathrm{tot}}}\
\ .$ (4)

The contributions to the relative systematic uncertainties of $\bar{\sigma}$
were propagated from the systematic uncertainties on each side as summarised
in Table 4. These uncertainties were calculated separately for the cross
sections of neutron emission accompanied by an arbitrary number of protons
(Yp, including zero protons) and without proton emission (0p).

Table 4: Relative systematic uncertainties of the cross sections of emission of given numbers of neutrons $i$ accompanied by an arbitrary number of protons (Yp, including zero protons) and without protons (0p), in UPCs of 208Pb nuclei at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. Each uncertainty is calculated for the average of the cross sections measured on the sides C and A. Source | Relative uncertainty (%)
---|---
1n | 2n | 3n | 4n | 5n
Yp $|$ 0p | Yp $|$ 0p | Yp $|$ 0p | Yp $|$ 0p | Yp $|$ 0p
Fitting procedure | 0.55 $|$ 0.55 | 0.32 $|$ 0.29 | 0.83 $|$ 0.72 | 0.73 $|$ 0.67 | 1.14 $|$ 1.01
ZDC+ZEM efficiency | 2.03 $|$ 2.45 | 4.68 $|$ 4.88 | 1.78 $|$ 2.25 | 5.35 $|$ 5.52 | 9.26 $|$ 9.36
$\sigma_{\mathrm{ZED}}$ determination | 2.4
from vdM scan
Total | 3.19 $|$ 3.47 | 5.27 $|$ 5.45 | 3.10 $|$ 3.37 | 5.91 $|$ 6.05 | 9.63 $|$ 9.72

In these measurements, the pile-up of EMD events was lower with respect to the
previous ALICE measurements of the EMD cross sections [5]. Nevertheless, the
uncertainty due to the residual pile-up of EMD events was also addressed. The
main issue with the pile-up is to count two 1n events as a 2n event. For these
runs the average number of hadronic inelastic interactions per bunch crossing
$\mu_{\mathrm{inel}}$ was about $1.3\times 10^{-4}$. The same value, but
calculated for 1n emission in EMD is
$\mu_{\mathrm{1n}}=\mu_{\mathrm{inel}}\times(\sigma_{\mathrm{1n}}/\sigma_{\mathrm{had}})=1.8\times
10^{-3}$, where $\sigma_{\mathrm{1n}}=108$ b is calculated with RELDIS and
$\sigma_{\mathrm{had}}=7.67\pm 0.25$ b is the inelastic hadronic interaction
cross section measured in Ref. [26]. With
$\sigma_{\mathrm{2n}}/\sigma_{\mathrm{1n}}\approx 0.24$, also estimated with
RELDIS, the relation $\mu_{\mathrm{2n}}\approx 0.24\times\mu_{\mathrm{1n}}$ is
obtained. Following the Poisson distribution, the ratio of the probabilities
to obtain two 1n events in the same bunch crossing $p(2,\mu_{\mathrm{1n}})$
and to have one 2n event $p(1,\mu_{\mathrm{2n}})$ is

$\frac{p(2,\mu_{\mathrm{1n}})}{p(1,\mu_{\mathrm{2n}})}=\frac{\mu^{2}_{\mathrm{1n}}\exp(-\mu_{\mathrm{1n}})}{2\mu_{\mathrm{2n}}\exp(-\mu_{\mathrm{2n}})}=\frac{\mu_{\mathrm{1n}}}{0.48}\exp(-0.76\mu_{\mathrm{1n}})\approx
0.004\ .$ (5)

One can conclude that the pile-up effect of 0.4% for 2n emission can be
neglected in view of the total $\approx 5$% uncertainty for this channel
reported in Table 4.

##  5 Results

###  5.1 Cross sections of emission of given numbers of neutrons

The EMD cross sections $\sigma(i{\mathrm{n}})$ for 1n, 2n, 3n, 4n, and 5n
emission accompanied by an arbitrary number of forward protons (including zero
protons) were measured separately on the C and A sides. They are listed in
Table 5. In order to obtain these cross sections, EMD events were selected by
applying a veto on ZEM, as described in Section 3. The cross sections given in
Table 5 were corrected for the ZDC and ZEM efficiency separately for each side
as described in Sec. 4.2. As seen, the cross sections measured on the side C
are slightly larger compared to those on the side A. However, the side C and A
cross sections are in most cases consistent, because this difference is within
the uncorrelated uncertainty of the side A cross section. As follows from
Table 4, the main contribution to the systematic uncertainties of the cross
sections is due to the uncertainties of the corrections for ZDC and ZEM
efficiency.

The average $\sigma(i{\mathrm{n}})$ between the C and A sides were calculated
for each neutron multiplicity $i$ according to Eq. (4). The resulting
$\sigma(i{\mathrm{n}})$ are given in Table 5 with their statistical and
systematic uncertainties propagated from the uncertainties on each side, which
were considered as uncorrelated, except for the contribution from the vdM scan
uncertainty, which is fully correlated between the C and A sides. The
differences between the cross sections obtained on the sides C and A depend on
the chosen method to calculate the ZDC efficiency, with the exception of 1n
channel, so the uncertainties on the efficiency can justify the difference
between the cross sections on the C and A sides. On the basis of this finding,
the difference between C and A sides divided by $\sqrt{2}$ was considered as
an additional uncertainty only for the average 1n cross section.

In Table 5 the measured cross sections are compared with results of the RELDIS
[4] and $\mathrm{n^{O}_{O}n}$ [23] models. Both models are based on the
Weizsäcker–Williams method to calculate the cross sections of neutron emission
in EMD of nuclei by considering the respective photonuclear reactions induced
by equivalent photons. RELDIS simulates nuclear reactions induced by
Weizsäcker–Williams photons on 208Pb by means of the intranuclear cascade
model of photonuclear reactions with the subsequent de-excitation of residual
nuclei via neutron evaporation and other processes [33]. A phenomenological
approximation for the total photoabsorption cross section on 208Pb is used as
an input to RELDIS together with calculated relative contributions of various
final states to obtain the absolute values of $\sigma(i{\mathrm{n}})$ and
$\sigma(i{\mathrm{n}},{\mathrm{0p}})$. A similar phenomenological
approximation of the total photoabsorption cross section is also used in
$\mathrm{n^{O}_{O}n}$. In this event generator the calculations of probability
of a given neutron emission channel are based on approximations of partial
photoneutron cross sections measured on 208Pb below 140 MeV and extrapolated
to higher photon energies [23]. Only neutron emission events can be generated
with $\mathrm{n^{O}_{O}n}$, but the 0n EMD cross section of 6.85 b
corresponding to 3.2% of EMD events with the emission of other particles
without neutrons was calculated with RELDIS.

The uncertainties of RELDIS results ($\approx 5$%) given in Table 5 stem from
the uncertainty of the phenomenological approximation of the total
photoabsorption cross section on 208Pb used by this model. As shown in Ref.
[20], the uncertainties of the calculations of specific neutron emission
channels (1n, 2n) in absorption of low energy photons are typically as high as
7%. Another source of uncertainties is connected to the estimations of unknown
total nuclear photoabsorption cross section at high photon energies ($>60$
GeV) from the measured total $\gamma\mathrm{p}$ cross sections taking into
account nuclear shadowing. As evaluated recently [34], the total EMD cross
sections calculated with different high-energy approximations for 208Pb–208Pb
collisions at the LHC differ by $\approx 2$%. Similar uncertainties of
$\approx$ 2–4% were attributed to the measured total cross section of the
absorption of real intermediate energy photons (0.5–2.6 GeV) by natPb [35].
The total EMD cross section is the sum of the contributions of processes
induced by Weizsäcker–Williams photons from the above-mentioned energy
domains. Therefore, the combined error of $\approx 5$% is attributed to the
cross sections calculated with RELDIS also for each individual neutron
emission channel in Table 5. The uncertainty of 2% also applies to the cross
sections calculated with $\mathrm{n^{O}_{O}n}$ because of the uncertainties of
the approximation of the total photoabsorption cross section on 208Pb.

The sum of the measured 1n–5n cross sections amounts to $151.5\pm 0.2\pm 4.7$
b, and it is within $2\sigma$ in agreement with the same sum calculated with
RELDIS as $159.8\pm 5.6$ b, see Table 5. The 1n–5n sum calculated with
$\mathrm{n^{O}_{O}n}$ as $143.1\pm 2.2$ b is lower. In general, the measured
sum is in the middle between the models. The total single EMD cross section
for neutron emission can be simply estimated from the cross sections measured
in Ref. [26] as $(\sigma_{\mathrm{ZED}}-\sigma_{\mathrm{had}})/2=206.4$ b
assuming 100% efficiency of the ZED trigger. It is in good agreement with the
corresponding cross section of $204.6\pm 7.1$ b calculated with RELDIS. As
seen, the measurements and calculations demonstrate dominant contributions of
73% and 78%, respectively, of 1n–5n channels to the EMD of 208Pb leading to
neutron emission.

Table 5: Cross sections of emission of one, two, three, four and five neutrons along with an arbitrary number of protons in EMD of 208Pb at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV measured on the C and A sides and their average along with their statistical and systematic uncertainties. Cross sections calculated with RELDIS [4] and $\mathrm{n^{O}_{O}n}$ [23] are given for comparison. The sum of 1n–5n cross sections is presented in the last row. The uncertainties of the measurements are reported in the order $\pm$ (stat.) $\pm$ (syst.).  ZN |  $\sigma(i{\mathrm{n}})$ (b) | $\sigma(i{\mathrm{n}})$ | $\sigma^{\mathrm{RELDIS}}(i{\mathrm{n}})$ | $\sigma^{\mathrm{n^{O}_{O}n}}(i{\mathrm{n}})$
---|---|---|---|---
Side C | Side A | (b) | (b) | (b)
1n | $109.7\pm 0.1\pm 4.2$ | $107.2\pm 0.1\pm 4.1$ | $108.4\pm 0.1\pm 3.9$ | $108.0\pm 5.4$ | $103.7\pm 2.1$
2n | $25.8\pm 0.1\pm 0.8$ | $24.1\pm 0.1\pm 2.3$ | $25.0\pm 0.1\pm 1.3$ | $25.9\pm 1.3$ | $23.6\pm 0.5$
3n | $7.97\pm 0.07\pm 0.33$ | $7.94\pm 0.04\pm 0.25$ | $7.95\pm 0.04\pm 0.25$ | $11.4\pm 0.6$ | $6.3\pm 0.1$
4n | $5.73\pm 0.04\pm 0.30$ | $5.56\pm 0.04\pm 0.56$ | $5.65\pm 0.03\pm 0.33$ | $7.8\pm 0.4$ | $4.8\pm 0.1$
5n | $4.61\pm 0.04\pm 0.68$ | $4.47\pm 0.04\pm 0.52$ | $4.54\pm 0.03\pm 0.44$ | $6.3\pm 0.3$ | $4.7\pm 0.1$
1n–5n |  |  | $151.5\pm 0.2\pm 4.7$ | $159.8\pm 5.6$ | $143.1\pm 2.2$
Figure 3: Colour online: measured (points) and calculated with RELDIS [4]
(solid-line histogram) and $\mathrm{n^{O}_{O}n}$ [23] (dashed-line histogram)
cross sections of emission of given numbers of neutrons $i$ in UPCs of 208Pb
nuclei at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. Combined statistical and
systematic uncertainties of the measurements are presented.

The measured cross sections are also shown in Fig. 3 together with results of
the models. As seen, the cross sections of 1n- and 2n-emission calculated with
RELDIS and $\mathrm{n^{O}_{O}n}$ agree with the measured ones. On the other
hand, the measured 3n and 4n cross sections are overestimated by RELDIS and
underestimated by $\mathrm{n^{O}_{O}n}$. At the same time, the 5n cross
section is described very well by $\mathrm{n^{O}_{O}n}$, but overestimated by
RELDIS. One can note that the models agree well with respect to the 1n and 2n
cross sections, but differ for higher neutron multiplicities. This indicates
the importance of 3n, 4n, and 5n measurements for tuning the parameters of the
models mentioned above.

###  5.2 Comparison with previous ALICE results

Previous ALICE results on neutron emission in EMD were reported in Ref. [5]
for 208Pb–208Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. Events were
required to have a signal in one of the two ZN and no signal in the other one,
so events of symmetric emission, such as those occurring in hadronic and
mutual EMD were rejected, and the sample contained single but not mutual EMD
events. The ZEM veto was not used to suppress hadronic events. With this
selection the fractions of 1n, 2n, and 3n events were determined in Ref. [5].
Following the same selection, the spectra in ZNC and ZNA for single minus
mutual EMD process were obtained also in the present work at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV without the ZEM veto described in Sec. 3.

The fractions of 1n-, 2n-, 3n-, and 4n-events over the total number of events
without neutrons on the opposite side $N_{\mathrm{one\mbox{-}side}}$ are
listed in Table 6. These fractions were extracted from ZNC and ZNA spectra and
were corrected for ZNC and ZNA acceptance as described in Sec. 4.2. The
measurements are compared with RELDIS results given in the same table. The
previous ALICE results for 208Pb–208Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV [5] are also given together with RELDIS
results for this collision energy.

Table 6: Fractions (in %) of EMD events with given numbers of neutrons but without neutrons on the opposite side measured and calculated for 208Pb–208Pb UPCs at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV [5] and $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. The uncertainties of the measurements are given in the order $\pm$ (stat.) $\pm$ (syst.). Single minus |  $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV [5] |  $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV
---|---|---
mutual | Experiment | RELDIS | Experiment | RELDIS
${N_{1}}/{N_{\mathrm{one\mbox{-}side}}}$ | $51.5\pm 0.4\pm 0.2$ | $54.2\pm 2.4$ | $52.4\pm 0.1\pm 1.3$ | $51.3\pm 2.3$
${N_{2}}/{N_{\mathrm{one\mbox{-}side}}}$ | $11.6\pm 0.3\pm 0.5$ | $12.7\pm 0.8$ | $11.94\pm 0.03\pm 0.56$ | $12.2\pm 0.8$
${N_{3}}/{N_{\mathrm{one\mbox{-}side}}}$ | $3.6\pm 0.2\pm 0.2$ | $5.4\pm 0.7$ | $3.74\pm 0.02\pm 0.07$ | $5.4\pm 0.7$
${N_{4}}/{N_{\mathrm{one\mbox{-}side}}}$ |  |  | $2.66\pm 0.01\pm 0.14$ | $3.7\pm 0.5$

As seen from Table 6, similar fractions of 1n, 2n, and 3n events are measured
at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV [5] and $\sqrt{s_{\mathrm{NN}}}=5.02$
TeV. The dominance of 1n emission is evident at both collision energies. The
measured 1n and 2n fractions are in very good agreement with RELDIS. A slight
reduction of calculated 1n events is seen at higher energy because of the
redistribution of events in favour of higher multiplicities. This can be
explained by a higher average equivalent photon energy at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. However, such a subtle effect cannot be
traced with confidence because of measurement and modelling uncertainties,
which were calculated as described in Sec. 4.3.

###  5.3 Emission of neutrons without protons

In order to measure the cross section for 1n, 2n, …, 5n emission without
proton emission (0p), the energy spectra in ZNC and ZNA were obtained for
events not having a signal in the respective ZP. Measured cross sections of
1n-, 2n-, 3n-, 4n-, and 5n-emission without protons are given in Table 7
together with RELDIS results. As can be seen, the cross sections measured on
side C are systematically slightly larger than on side A, but the difference
remains within the uncorrelated uncertainty of side A cross sections for all
neutron multiplicities. The cross sections were calculated with Eq. (3) from
the numbers of events ${n_{i}}$ of each neutron multiplicity $i$n obtained
from the fit of spectra with the functions given by Eq. (1). In this case of
0p measurements, the numbers of true events of each multiplicity ${N_{i}}$
were obtained by correcting for the efficiency of ZNC and ZNA and also for
protons undetected in ZPC and ZPA, as described in Sec. 4.2. Statistical and
systematic uncertainties were calculated as described in Sections 4.3 and 5.1.
Contributions to the total systematic uncertainties are presented in Table 4.

The measured cross sections of 1n, 2n, …, 5n emission not accompanied by
protons, shown in Table 7, are lower than the cross sections of 1n, 2n,.. 5n
emission along with other particles presented in Table 5. This difference is
larger for 4n and 5n channels because protons are emitted more frequently at
higher equivalent photon energies associated with multineutron events. With
the exception of 5n emission, the measured 0p cross sections are lower than
the cross sections calculated with RELDIS. Nevertheless, the agreement between
the measurements and calculations for 0p cross sections is better than for Yp
cross sections presented in Table 5.

The sum of the measured 0p cross sections from 1n to 5n is estimated as
$126.0\pm 0.2\pm 4.1$ b. It is also listed in Table 7 for comparison with
RELDIS. This sum of 0p cross sections provides a dominant ($\approx 83$%)
contribution to the sum of Yp cross sections $151.5\pm 0.2\pm 4.7$ b given in
Table 5. In other words, only $\approx 17$% of 1n–5n events are accompanied by
the emission of protons.

Table 7: Cross sections of emission of one, two, three, four and five neutrons without protons on the same side in the EMD of 208Pb at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, measured on the C and A sides, and their average along with their statistical and systematic uncertainties. Cross sections calculated with RELDIS are given for comparison. The sum of 1n–5n cross sections is presented in the last row. The uncertainties of the measurements are given in the order $\pm$ (stat.) $\pm$ (syst.). ZN | ZP |  $\sigma(i{\mathrm{n}},{\mathrm{0p}})$ (b) | $\sigma(i{\mathrm{n}},{\mathrm{0p}})$ (b) | $\sigma^{\mathrm{RELDIS}}(i{\mathrm{n}},{\mathrm{0p}})$ (b)
---|---|---|---|---
Side C | Side A
1n | 0p | $92.6\pm 0.1\pm 3.9$ | $90.9\pm 0.1\pm 4.0$ | $91.8\pm 0.1\pm 3.4\ \ \ \ $ | $104.1\pm 5.2$
2n | $21.4\pm 0.1\pm 0.8$ | $20.0\pm 0.1\pm 2.0$ | $20.7\pm 0.1\pm 1.1$ | $21.9\pm 1.1$
3n | $6.14\pm 0.07\pm 0.28$ | $6.21\pm 0.04\pm 0.24$ | $6.17\pm 0.04\pm 0.21$ | $7.59\pm 0.38$
4n | $4.21\pm 0.04\pm 0.23$ | $4.08\pm 0.04\pm 0.42$ | $4.15\pm 0.03\pm 0.25$ | $4.29\pm 0.22$
5n | $3.16\pm 0.04\pm 0.47$ | $3.08\pm 0.03\pm 0.36$ | $3.12\pm 0.03\pm 0.30$ | $2.95\pm 0.15$
1n–5n |  |  |  | $126.0\pm 0.2\pm 4.1$ | $140.8\pm 5.3$

The measured 0p neutron emission cross sections are shown in Fig. 4 and
compared with RELDIS results for the same cross sections and also with the
calculated cross sections to produce specific secondary nuclei:
207,206,205,204,203Pb. According to RELDIS, the cross section of the
production of 207Pb, is almost the same as (1n,0p) cross section, while the
cross sections of production of 206Pb and 205Pb are smaller than (2n,0p) and
(3n,0p) cross sections only by 3% and 10%, respectively. According to this
model, the calculated 0p cross sections of emission of four, five, six, and
seven neutrons can be considered as upper limits for the cross sections of
production of 204,203,202,201Pb, respectively. The difference is due to the
emission of additional particles, e.g. protons and/or charged $\pi$ mesons,
which leave residual nuclei other than Pb, as explained in Sec. 6.

Figure 4: Colour online: measured cross sections of emission of given numbers
of neutrons $i$ in UPCs of 208Pb nuclei at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV
without proton emission (points) and the cross sections calculated with RELDIS
[4] (solid-line histogram). Calculated cross sections to produce specific
secondary nuclei, 207,206,205,204,203,202,201Pb, are presented by the dash-
dotted histogram marked by nuclide symbols. Combined statistical and
systematic uncertainties of the measurements are presented.

##  6 Discussion

The measured cross sections $\sigma(i{\mathrm{n}})$ of neutron emission
accompanied by an arbitrary number of protons in EMD can be used to validate
various EMD models. The cross sections of neutron emission
$\sigma(i{\mathrm{n}},{\mathrm{0p}})$ without protons were also measured.
Because of the absence of proton emission, these cross sections can be
associated with the production of 207Pb, 206Pb, 205Pb, 204Pb, and 203Pb as
secondary nuclei in EMD of 208Pb.

In order to test this association, the RELDIS event generator, validated with
data on neutron emission [32, 5] and production of secondary nuclei [3] in EMD
of 208Pb at lower collision energies, was used. In each simulated event
$\Delta A=A_{\mathrm{res}}+N_{\mathrm{n}}+N_{\mathrm{p}}-208$ and $\Delta
Z=Z_{\mathrm{res}}+N_{\mathrm{p}}-82$ were calculated from the mass number
$A_{\mathrm{res}}$ and charge $Z_{\mathrm{res}}$ of the heaviest residual
nucleus and the numbers of emitted neutrons $N_{\mathrm{n}}$ and protons
$N_{\mathrm{p}}$. The calculated probability distributions to obtain $\Delta
A$ and $\Delta Z$ in events with a given $N_{\mathrm{n}}$ are presented in
Fig. 5. As seen from this figure, in RELDIS simulations the probabilities to
obtain 1n, 2n, …, 5n events with $\Delta A=0$ or $\Delta Z=0$ among all EMD
events are within the range of 3–50%. However, the probability of 1n, 2n, …,
5n events with $\Delta A<0$ or $|\Delta Z|>0$ is well below 1%.

Two examples of such rare events are presented in the following. The first one
is represented by the excitation of an intranuclear neutron with its
conversion to a proton:
$\gamma{\mathrm{n}}\rightarrow\Delta^{\mathrm{o}}\rightarrow{\mathrm{p}}+\pi^{-}$.
In the case of the undetected $\pi^{-}$ escaping the nucleus, the total charge
of the system, including emitted nucleons, differs from 82: $\Delta Z=1$. In
Ref. [36] the production of 83Bi from 158A GeV 82Pb nuclei in their
ultraperipheral collisions with different targets has been explained by the
production of $\pi^{-}$. In the second example, the products of the
fragmentation contain an undetected $\alpha$-particle in addition to nucleons:
$\Delta A=-4$. In Ref. [37] a similar reaction of the emission of
$\alpha$-particles from 197Au induced by bremsstrahlung photons was
investigated.

Figure 5: Colour online: Probability, calculated with RELDIS (in %), of the
difference $\Delta A$ between the sum of the mass number of the most heavy
residual nucleus and the numbers of emitted nucleons and $A$ of the initial
208Pb (left) and probability (in %) of the difference $\Delta Z$ between the
sum of the charge of the most heavy residual nucleus and the number of emitted
protons and $Z$ of 208Pb (right) plotted as functions of $N_{\mathrm{n}}$ in
each event.

One can conclude from Fig. 5 that, according to RELDIS, in the majority of
1n–5n EMD events ${\Delta A=0}$ and ${\Delta Z=0}$, and it is sufficient to
measure $N_{\mathrm{n}}$ and $N_{\mathrm{p}}$ for evaluating
$A_{\mathrm{res}}$ and $Z_{\mathrm{res}}$. The dominance of ${\Delta A=0}$ and
${\Delta Z=0}$ events is explained by a rather modest excitation energy per
nucleon $E^{\star}/A$ delivered in the absorption of Weizsäcker–Williams
photons by 208Pb. This was demonstrated in Ref. [33] where $\langle
E^{\star}/A\rangle$ were calculated for photospallation of natPb by real
photons with energies from 20 MeV to 4 GeV. As found in Ref. [33], $\langle
E^{\star}/A\rangle$ is typically below 1 MeV. This suggests the creation of an
excited single heavy nuclear residue as a result of the emission of free
neutrons and protons during the intranuclear cascade. Such an excited nucleus
would evaporate few nucleons and possibly undergo nuclear fission [33] rather
than a multi-fragment break-up which becomes possible only at $E^{\star}/A>3$
MeV [38]. For example, the decay of the giant dipole resonance in 208Pb with
$E^{\star}=\mbox{7--20}$ MeV mostly produces one neutron [39]. According to
RELDIS [20], the production of two neutrons is ten times less frequent in EMD
of 208Pb in this interval of $E^{\star}$. The residual nuclei, 207Pb or 206Pb,
can be distinguished by detecting the number of emitted neutrons.

The contribution of electromagnetically induced fission of 208Pb in UPCs can
also be estimated with RELDIS. The fission process violates the condition
$\Delta A=0$ and $\Delta Z=0$, but its calculated probability at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV is as low as 0.6%. The EM fission
probability for 158A GeV 208Pb projectiles on Pb target is calculated with
RELDIS as 0.18%. It is of the same order as the fission probabilities of 0.66%
and 0.75% measured at the CERN SPS in Refs. [40] and [41], respectively. One
can conclude that both theory and experiment indicate fission probabilities
below 1%. This process can be safely neglected in favour of the creation of a
single residual nucleus and several nucleons in EMD of 208Pb.

##  7 Conclusions and outlook

The cross sections for emission of given numbers of forward neutrons in EMD of
208Pb nuclei in ultraperipheral collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$
TeV have been measured with the ALICE neutron zero degree calorimeters. The
fractions of 1n, 2n, and 3n events were measured at the highest 208Pb–208Pb
collision energy available so far in accelerator experiments. These fractions
were found to be similar to those measured at $\sqrt{s_{\mathrm{NN}}}=2.76$
TeV. The predictions from the RELDIS [4] and $\mathrm{n^{O}_{O}n}$ [23] models
describe well the measured cross sections, in particular, for low neutron
multiplicities. These measurements are important for the extraction of the
contributions of high- and low-energy photons from coherent vector meson
photoproduction measurements accompanied by neutron emission [42, 43].

The cross sections of EMD events with the emission of exactly one, two, three,
four, and five neutrons and without emission of protons have been measured.
According to the RELDIS model, in EMD a single heavy residual nucleus is
typically produced after the emission of several nucleons. The probability of
nuclear fission in EMD is estimated to be below 1%. Therefore, the EMD events
of 1n, 2n, 3n, 4n, and 5n emission without protons can be associated with the
production of 207Pb, 206Pb, 205Pb, 204Pb, and 203Pb, respectively. In other
words, the measured neutron emission cross sections can be considered as upper
limits for the respective isotope production cross sections.

Since the charge-to-mass ratio of 207Pb remains close to 208Pb, these
frequently produced secondary nuclei emerge from the interaction points and
propagate in the field of the LHC magnets on dispersive trajectories in the
vicinity of the primary beam [7]. The collider collimation system is adjusted
to intercept them (off-momentum collimators around Point 3 of LHC) to avoid
the risk of beam dumps or quenches of superconducting magnets [44, 7, 8, 45].
The moderate fluxes of 206Pb nuclei may hit the beam pipe closer to the
interaction points. The smaller fluxes of 205,204,…Pb generated in the
collisions are lost at the start of the dispersion suppressor or taken up by
physics debris absorbers and do not present any risks in collider operation.

A good quantitative understanding of the cross sections and fluxes of these
nuclei provides valuable input for evaluating luminosity decay and beam losses
in the design of the Future Circular Collider (FCC-hh) [46]. They also
increase confidence in similar calculations for interactions of beam nuclei
with carbon and other materials in the collimation systems of the LHC and FCC
[8].

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020¿2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and University Politehnica of Bucharest, Romania; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSTDA), Thailand Science Research and Innovation (TSRI) and National Science, Research and Innovation Fund (NSRF), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. In addition, individual groups or members have received support from: Marie Skłodowska Curie, European Research Council, Strong 2020 - Horizon 2020 (grant nos. 950692, 824093, 896850), European Union; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland; Programa de Apoyos para la Superación del Personal Académico, UNAM, Mexico.

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##  Appendix A The ALICE Collaboration

S. Acharya 124, D. Adamová 86, A. Adler69, G. Aglieri Rinella 32, M. Agnello
29, N. Agrawal 50, Z. Ahammed 131, S. Ahmad 15, S.U. Ahn 70, I. Ahuja 37, A.
Akindinov 139, M. Al-Turany 97, D. Aleksandrov 139, B. Alessandro 55, H.M.
Alfanda 6, R. Alfaro Molina 66, B. Ali 15, Y. Ali13, A. Alici 25, N.
Alizadehvandchali 113, A. Alkin 32, J. Alme 20, G. Alocco 51, T. Alt 63, I.
Altsybeev 139, M.N. Anaam 6, C. Andrei 45, A. Andronic 134, V. Anguelov 94, F.
Antinori 53, P. Antonioli 50, C. Anuj 15, N. Apadula 74, L. Aphecetche 103, H.
Appelshäuser 63, C. Arata 73, S. Arcelli 25, M. Aresti 51, R. Arnaldi 55, I.C.
Arsene 19, M. Arslandok 136, A. Augustinus 32, R. Averbeck 97, M.D. Azmi 15,
A. Badalà 52, Y.W. Baek 40, X. Bai 117, R. Bailhache 63, Y. Bailung 47, R.
Bala 91, A. Balbino 29, A. Baldisseri 127, B. Balis 2, D. Banerjee 4, Z. Banoo
91, R. Barbera 26, F. Barile 31, L. Barioglio 95, M. Barlou78, G.G. Barnaföldi
135, L.S. Barnby 85, V. Barret 124, L. Barreto 109, C. Bartels 116, K. Barth
32, E. Bartsch 63, F. Baruffaldi 27, N. Bastid 124, S. Basu 75, G. Batigne
103, D. Battistini 95, B. Batyunya 140, D. Bauri46, J.L. Bazo Alba 101, I.G.
Bearden 83, C. Beattie 136, P. Becht 97, D. Behera 47, I. Belikov 126, A.D.C.
Bell Hechavarria 134, F. Bellini 25, R. Bellwied 113, S. Belokurova 139, V.
Belyaev 139, G. Bencedi 135, S. Beole 24, A. Bercuci 45, Y. Berdnikov 139, A.
Berdnikova 94, L. Bergmann 94, M.G. Besoiu 62, L. Betev 32, P.P. Bhaduri 131,
A. Bhasin 91, M.A. Bhat 4, B. Bhattacharjee 41, L. Bianchi 24, N. Bianchi 48,
J. Bielčík 35, J. Bielčíková 86, J. Biernat 106, A.P. Bigot 126, A. Bilandzic
95, G. Biro 135, S. Biswas 4, N. Bize 103, J.T. Blair 107, D. Blau 139, M.B.
Blidaru 97, N. Bluhme38, C. Blume 63, G. Boca 21,54, F. Bock 87, T. Bodova 20,
A. Bogdanov139, S. Boi 22, J. Bok 57, L. Boldizsár 135, A. Bolozdynya 139, M.
Bombara 37, P.M. Bond 32, G. Bonomi 130,54, H. Borel 127, A. Borissov 139,
A.G. Borquez Carcamo 94, H. Bossi 136, E. Botta 24, Y.E.M. Bouziani 63, L.
Bratrud 63, P. Braun-Munzinger 97, M. Bregant 109, M. Broz 35, G.E. Bruno
96,31, M.D. Buckland 116, D. Budnikov 139, H. Buesching 63, S. Bufalino 29, O.
Bugnon103, P. Buhler 102, Z. Buthelezi 67,120, J.B. Butt13, S.A. Bysiak106, M.
Cai 6, H. Caines 136, A. Caliva 97, E. Calvo Villar 101, J.M.M. Camacho 108,
P. Camerini 23, F.D.M. Canedo 109, M. Carabas 123, A.A. Carballo 32, F.
Carnesecchi 32, R. Caron 125, J. Castillo Castellanos 127, F. Catalano 24,29,
C. Ceballos Sanchez 140, I. Chakaberia 74, P. Chakraborty 46, S. Chandra 131,
S. Chapeland 32, M. Chartier 116, S. Chattopadhyay 131, S. Chattopadhyay 99,
T.G. Chavez 44, T. Cheng 97,6, C. Cheshkov 125, B. Cheynis 125, V. Chibante
Barroso 32, D.D. Chinellato 110, E.S. Chizzali II,95, J. Cho 57, S. Cho 57, P.
Chochula 32, P. Christakoglou 84, C.H. Christensen 83, P. Christiansen 75, T.
Chujo 122, M. Ciacco 29, C. Cicalo 51, L. Cifarelli 25, F. Cindolo 50, M.R.
Ciupek97, G. ClaiIII,50, F. Colamaria 49, J.S. Colburn100, D. Colella 96,31,
M. Colocci 32, M. Concas IV,55, G. Conesa Balbastre 73, Z. Conesa del Valle
72, G. Contin 23, J.G. Contreras 35, M.L. Coquet 127, T.M. CormierI,87, P.
Cortese 129,55, M.R. Cosentino 111, F. Costa 32, S. Costanza 21,54, J.
Crkovská 94, P. Crochet 124, R. Cruz-Torres 74, E. Cuautle64, P. Cui 6, L.
Cunqueiro87, A. Dainese 53, M.C. Danisch 94, A. Danu 62, P. Das 80, P. Das 4,
S. Das 4, A.R. Dash 134, S. Dash 46, A. De Caro 28, G. de Cataldo 49, J. de
Cuveland38, A. De Falco 22, D. De Gruttola 28, N. De Marco 55, C. De Martin
23, S. De Pasquale 28, S. Deb 47, R.J. Debski 2, K.R. Deja132, R. Del Grande
95, L. Dello Stritto 28, W. Deng 6, P. Dhankher 18, D. Di Bari 31, A. Di Mauro
32, R.A. Diaz 140,7, T. Dietel 112, Y. Ding 125,6, R. Divià 32, D.U. Dixit 18,
Ø. Djuvsland20, U. Dmitrieva 139, A. Dobrin 62, B. Dönigus 63, A.K. Dubey 131,
J.M. Dubinski132, A. Dubla 97, S. Dudi 90, P. Dupieux 124, M. Durkac105, N.
Dzalaiova12, T.M. Eder 134, R.J. Ehlers 87, V.N. Eikeland20, F. Eisenhut 63,
D. Elia 49, B. Erazmus 103, F. Ercolessi 25, F. Erhardt 89, M.R. Ersdal20, B.
Espagnon 72, G. Eulisse 32, D. Evans 100, S. Evdokimov 139, L. Fabbietti 95,
M. Faggin 27, J. Faivre 73, F. Fan 6, W. Fan 74, A. Fantoni 48, M. Fasel 87,
P. Fecchio29, A. Feliciello 55, G. Feofilov 139, A. Fernández Téllez 44, M.B.
Ferrer 32, A. Ferrero 127, C. Ferrero 55, A. Ferretti 24, V.J.G. Feuillard 94,
V. Filova35, D. Finogeev 139, F.M. Fionda 51, F. Flor 113, A.N. Flores 107, S.
Foertsch 67, I. Fokin 94, S. Fokin 139, E. Fragiacomo 56, E. Frajna 135, U.
Fuchs 32, N. Funicello 28, C. Furget 73, A. Furs 139, T. Fusayasu 98, J.J.
Gaardhøje 83, M. Gagliardi 24, A.M. Gago 101, C.D. Galvan 108, D.R.
Gangadharan 113, P. Ganoti 78, C. Garabatos 97, J.R.A. Garcia 44, E. Garcia-
Solis 9, K. Garg 103, C. Gargiulo 32, A. Garibli81, K. Garner134, P. Gasik 97,
A. Gautam 115, M.B. Gay Ducati 65, M. Germain 103, C. Ghosh131, S.K. Ghosh4,
M. Giacalone 25, P. Giubellino 97,55, P. Giubilato 27, A.M.C. Glaenzer 127, P.
Glässel 94, E. Glimos119, D.J.Q. Goh76, V. Gonzalez 133, L.H. González-Trueba
66, M. Gorgon 2, S. Gotovac33, V. Grabski 66, L.K. Graczykowski 132, E. Grecka
86, A. Grelli 58, C. Grigoras 32, V. Grigoriev 139, S. Grigoryan 140,1, F.
Grosa 32, J.F. Grosse-Oetringhaus 32, R. Grosso 97, D. Grund 35, G.G.
Guardiano 110, R. Guernane 73, M. Guilbaud 103, K. Gulbrandsen 83, T. Gundem
63, T. Gunji 121, W. Guo 6, A. Gupta 91, R. Gupta 91, S.P. Guzman 44, L.
Gyulai 135, M.K. Habib97, C. Hadjidakis 72, H. Hamagaki 76, A. Hamdi 74, M.
Hamid6, Y. Han 137, R. Hannigan 107, M.R. Haque 132, J.W. Harris 136, A.
Harton 9, H. Hassan 87, D. Hatzifotiadou 50, P. Hauer 42, L.B. Havener 136,
S.T. Heckel 95, E. Hellbär 97, H. Helstrup 34, M. Hemmer 63, T. Herman 35, G.
Herrera Corral 8, F. Herrmann134, S. Herrmann 125, K.F. Hetland 34, B. Heybeck
63, H. Hillemanns 32, C. Hills 116, B. Hippolyte 126, B. Hofman 58, B.
Hohlweger 84, J. Honermann 134, G.H. Hong 137, M. Horst 95, A. Horzyk 2, R.
Hosokawa14, Y. Hou 6, P. Hristov 32, C. Hughes 119, P. Huhn63, L.M. Huhta 114,
C.V. Hulse 72, T.J. Humanic 88, H. Hushnud99, A. Hutson 113, D. Hutter 38,
J.P. Iddon 116, R. Ilkaev139, H. Ilyas 13, M. Inaba 122, G.M. Innocenti 32, M.
Ippolitov 139, A. Isakov 86, T. Isidori 115, M.S. Islam 99, M. Ivanov12, M.
Ivanov 97, V. Ivanov 139, V. Izucheev139, M. Jablonski 2, B. Jacak 74, N.
Jacazio 32, P.M. Jacobs 74, S. Jadlovska105, J. Jadlovsky105, S. Jaelani 82,
L. Jaffe38, C. Jahnke110, M.J. Jakubowska 132, M.A. Janik 132, T. Janson69, M.
Jercic89, A.A.P. Jimenez 64, F. Jonas 87, P.G. Jones100, J.M. Jowett 32,97, J.
Jung 63, M. Jung 63, A. Junique 32, A. Jusko 100, M.J. Kabus 32,132, J.
Kaewjai104, P. Kalinak 59, A.S. Kalteyer 97, A. Kalweit 32, V. Kaplin 139, A.
Karasu Uysal 71, D. Karatovic 89, O. Karavichev 139, T. Karavicheva 139, P.
Karczmarczyk 132, E. Karpechev 139, V. Kashyap80, U. Kebschull 69, R. Keidel
138, D.L.D. Keijdener58, M. Keil 32, B. Ketzer 42, A.M. Khan 6, S. Khan 15, A.
Khanzadeev 139, Y. Kharlov 139, A. Khatun 15, A. Khuntia 106, B. Kileng 34, B.
Kim 16, C. Kim 16, D.J. Kim 114, E.J. Kim 68, J. Kim 137, J.S. Kim 40, J. Kim
94, J. Kim 68, M. Kim 18,94, S. Kim 17, T. Kim 137, K. Kimura 92, S. Kirsch
63, I. Kisel 38, S. Kiselev 139, A. Kisiel 132, J.P. Kitowski 2, J.L. Klay 5,
J. Klein 32, S. Klein 74, C. Klein-Bösing 134, M. Kleiner 63, T. Klemenz 95,
A. Kluge 32, A.G. Knospe 113, C. Kobdaj 104, T. Kollegger97, A. Kondratyev
140, E. Kondratyuk 139, J. Konig 63, S.A. Konigstorfer 95, P.J. Konopka 32, G.
Kornakov 132, S.D. Koryciak 2, A. Kotliarov 86, V. Kovalenko 139, M. Kowalski
106, V. Kozhuharov 36, I. Králik 59, A. Kravčáková 37, L. Kreis97, M. Krivda
100,59, F. Krizek 86, K. Krizkova Gajdosova 35, M. Kroesen 94, M. Krüger 63,
D.M. Krupova 35, E. Kryshen 139, V. Kučera 32, C. Kuhn 126, P.G. Kuijer 84, T.
Kumaoka122, D. Kumar131, L. Kumar 90, N. Kumar90, S. Kumar 31, S. Kundu 32, P.
Kurashvili 79, A. Kurepin 139, A.B. Kurepin 139, S. Kushpil 86, J. Kvapil 100,
M.J. Kweon 57, J.Y. Kwon 57, Y. Kwon 137, S.L. La Pointe 38, P. La Rocca 26,
Y.S. Lai74, A. Lakrathok104, M. Lamanna 32, R. Langoy 118, P. Larionov 32, E.
Laudi 32, L. Lautner 32,95, R. Lavicka 102, T. Lazareva 139, R. Lea 130,54, G.
Legras 134, J. Lehrbach 38, R.C. Lemmon 85, I. León Monzón 108, M.M. Lesch 95,
E.D. Lesser 18, M. Lettrich95, P. Lévai 135, X. Li10, X.L. Li6, J. Lien 118,
R. Lietava 100, B. Lim 24,16, S.H. Lim 16, V. Lindenstruth 38, A. Lindner45,
C. Lippmann 97, A. Liu 18, D.H. Liu 6, J. Liu 116, I.M. Lofnes 20, C. Loizides
87, P. Loncar 33, J.A. Lopez 94, X. Lopez 124, E. López Torres 7, P. Lu
97,117, J.R. Luhder 134, M. Lunardon 27, G. Luparello 56, Y.G. Ma 39, A.
Maevskaya139, M. Mager 32, T. Mahmoud42, A. Maire 126, M.V. Makariev 36, M.
Malaev 139, G. Malfattore 25, N.M. Malik 91, Q.W. Malik19, S.K. Malik 91, L.
Malinina VII,140, D. Mal’Kevich 139, D. Mallick 80, N. Mallick 47, G.
Mandaglio 30,52, V. Manko 139, F. Manso 124, V. Manzari 49, Y. Mao 6, G.V.
Margagliotti 23, A. Margotti 50, A. Marín 97, C. Markert 107, P. Martinengo
32, J.L. Martinez113, M.I. Martínez 44, G. Martínez García 103, S. Masciocchi
97, M. Masera 24, A. Masoni 51, L. Massacrier 72, A. Mastroserio 128,49, A.M.
Mathis 95, O. Matonoha 75, P.F.T. Matuoka109, A. Matyja 106, C. Mayer 106,
A.L. Mazuecos 32, F. Mazzaschi 24, M. Mazzilli 32, J.E. Mdhluli 120, A.F.
Mechler63, Y. Melikyan 139, A. Menchaca-Rocha 66, E. Meninno 102,28, A.S.
Menon 113, M. Meres 12, S. Mhlanga112,67, Y. Miake122, L. Micheletti 55, L.C.
Migliorin125, D.L. Mihaylov 95, K. Mikhaylov 140,139, A.N. Mishra 135, D.
Miśkowiec 97, A. Modak 4, A.P. Mohanty 58, B. Mohanty 80, M. Mohisin Khan
V,15, M.A. Molander 43, Z. Moravcova 83, C. Mordasini 95, D.A. Moreira De
Godoy 134, I. Morozov 139, A. Morsch 32, T. Mrnjavac 32, V. Muccifora 48, S.
Muhuri 131, J.D. Mulligan 74, A. Mulliri22, M.G. Munhoz 109, R.H. Munzer 63,
H. Murakami 121, S. Murray 112, L. Musa 32, J. Musinsky 59, J.W. Myrcha 132,
B. Naik 120, A.I. Nambrath 18, B.K. Nandi46, R. Nania 50, E. Nappi 49, A.F.
Nassirpour 75, A. Nath 94, C. Nattrass 119, M.N. Naydenov 36, A. Neagu19, A.
Negru123, L. Nellen 64, S.V. Nesbo34, G. Neskovic 38, D. Nesterov 139, B.S.
Nielsen 83, E.G. Nielsen 83, S. Nikolaev 139, S. Nikulin 139, V. Nikulin 139,
F. Noferini 50, S. Noh 11, P. Nomokonov 140, J. Norman 116, N. Novitzky 122,
P. Nowakowski 132, A. Nyanin 139, J. Nystrand 20, M. Ogino 76, A. Ohlson 75,
V.A. Okorokov 139, J. Oleniacz 132, A.C. Oliveira Da Silva 119, M.H. Oliver
136, A. Onnerstad 114, C. Oppedisano 55, A. Ortiz Velasquez 64, A.
Oskarsson75, J. Otwinowski 106, M. Oya92, K. Oyama 76, Y. Pachmayer 94, S.
Padhan 46, D. Pagano 130,54, G. Paić 64, A. Palasciano 49, S. Panebianco 127,
H. Park 122, J. Park 57, J.E. Parkkila 32, R.N. Patra91, B. Paul 22, H. Pei 6,
T. Peitzmann 58, X. Peng 6, M. Pennisi 24, L.G. Pereira 65, H. Pereira Da
Costa 127, D. Peresunko 139, G.M. Perez 7, S. Perrin 127, Y. Pestov139, V.
Petráček 35, V. Petrov 139, M. Petrovici 45, R.P. Pezzi 103,65, S. Piano 56,
M. Pikna 12, P. Pillot 103, O. Pinazza 50,32, L. Pinsky113, C. Pinto 95, S.
Pisano 48, M. Płoskoń 74, M. Planinic89, F. Pliquett63, M.G. Poghosyan 87, S.
Politano 29, N. Poljak 89, A. Pop 45, S. Porteboeuf-Houssais 124, J. Porter
74, V. Pozdniakov 140, K.K. Pradhan 47, S.K. Prasad 4, S. Prasad 47, R.
Preghenella 50, F. Prino 55, C.A. Pruneau 133, I. Pshenichnov 139, M. Puccio
32, S. Pucillo 24, Z. Pugelova105, S. Qiu 84, L. Quaglia 24, R.E. Quishpe113,
S. Ragoni 14,100, A. Rakotozafindrabe 127, L. Ramello 129,55, F. Rami 126,
S.A.R. Ramirez 44, T.A. Rancien73, M. Rasa 26, S.S. Räsänen 43, R. Rath 50,47,
M.P. Rauch 20, I. Ravasenga 84, K.F. Read 87,119, C. Reckziegel 111, A.R.
Redelbach 38, K. Redlich VI,79, A. Rehman20, F. Reidt 32, H.A. Reme-Ness 34,
Z. Rescakova37, K. Reygers 94, A. Riabov 139, V. Riabov 139, R. Ricci 28, T.
Richert75, M. Richter 19, A.A. Riedel 95, W. Riegler 32, F. Riggi 26, C.
Ristea 62, M. Rodríguez Cahuantzi 44, K. Røed 19, R. Rogalev 139, E. Rogochaya
140, T.S. Rogoschinski 63, D. Rohr 32, D. Röhrich 20, P.F. Rojas44, S. Rojas
Torres 35, P.S. Rokita 132, G. Romanenko 140, F. Ronchetti 48, A. Rosano
30,52, E.D. Rosas64, A. Rossi 53, A. Roy 47, P. Roy99, S. Roy46, N. Rubini 25,
O.V. Rueda 113,75, D. Ruggiano 132, R. Rui 23, B. Rumyantsev140, P.G. Russek
2, R. Russo 84, A. Rustamov 81, E. Ryabinkin 139, Y. Ryabov 139, A. Rybicki
106, H. Rytkonen 114, W. Rzesa 132, O.A.M. Saarimaki 43, R. Sadek 103, S.
Sadhu 31, S. Sadovsky 139, J. Saetre 20, K. Šafařík 35, S.K. Saha 4, S. Saha
80, B. Sahoo 46, R. Sahoo 47, S. Sahoo60, D. Sahu 47, P.K. Sahu 60, J. Saini
131, K. Sajdakova37, S. Sakai 122, M.P. Salvan 97, S. Sambyal 91, I. Sanna
32,95, T.B. Saramela109, D. Sarkar 133, N. Sarkar131, P. Sarma41, V. Sarritzu
22, V.M. Sarti 95, M.H.P. Sas 136, J. Schambach 87, H.S. Scheid 63, C. Schiaua
45, R. Schicker 94, A. Schmah94, C. Schmidt 97, H.R. Schmidt93, M.O. Schmidt
32, M. Schmidt93, N.V. Schmidt 87, A.R. Schmier 119, R. Schotter 126, A.
Schröter 38, J. Schukraft 32, K. Schwarz97, K. Schweda 97, G. Scioli 25, E.
Scomparin 55, J.E. Seger 14, Y. Sekiguchi121, D. Sekihata 121, I. Selyuzhenkov
97,139, S. Senyukov 126, J.J. Seo 57, D. Serebryakov 139, L. Šerkšnytė 95, A.
Sevcenco 62, T.J. Shaba 67, A. Shabetai 103, R. Shahoyan32, A. Shangaraev 139,
A. Sharma90, D. Sharma 46, H. Sharma 106, M. Sharma 91, N. Sharma90, S. Sharma
76, S. Sharma 91, U. Sharma 91, A. Shatat 72, O. Sheibani113, K. Shigaki 92,
M. Shimomura77, J. Shin11, S. Shirinkin 139, Q. Shou 39, Y. Sibiriak 139, S.
Siddhanta 51, T. Siemiarczuk 79, T.F. Silva 109, D. Silvermyr 75, T.
Simantathammakul104, R. Simeonov 36, B. Singh91, B. Singh 95, R. Singh 80, R.
Singh 91, R. Singh 47, S. Singh 15, V.K. Singh 131, V. Singhal 131, T. Sinha
99, B. Sitar 12, M. Sitta 129,55, T.B. Skaali19, G. Skorodumovs 94, M.
Slupecki 43, N. Smirnov 136, R.J.M. Snellings 58, E.H. Solheim 19, J. Song
113, A. Songmoolnak104, F. Soramel 27, R. Spijkers 84, I. Sputowska 106, J.
Staa 75, J. Stachel 94, I. Stan 62, P.J. Steffanic 119, S.F. Stiefelmaier 94,
D. Stocco 103, I. Storehaug 19, P. Stratmann 134, S. Strazzi 25, C.P.
Stylianidis84, A.A.P. Suaide 109, C. Suire 72, M. Sukhanov 139, M. Suljic 32,
R. Sultanov 139, V. Sumberia 91, S. Sumowidagdo 82, S. Swain60, I. Szarka 12,
U. Tabassam13, S.F. Taghavi 95, G. Taillepied 97, J. Takahashi 110, G.J.
Tambave 20, S. Tang 124,6, Z. Tang 117, J.D. Tapia Takaki 115, N. Tapus123,
L.A. Tarasovicova 134, M.G. Tarzila 45, G.F. Tassielli 31, A. Tauro 32, A.
Telesca 32, L. Terlizzi 24, C. Terrevoli 113, G. Tersimonov3, S. Thakur 4, D.
Thomas 107, A. Tikhonov 139, A.R. Timmins 113, M. Tkacik105, T. Tkacik 105, A.
Toia 63, R. Tokumoto92, N. Topilskaya 139, M. Toppi 48, F. Torales-Acosta18,
T. Tork 72, A.G. Torres Ramos 31, A. Trifiró 30,52, A.S. Triolo 30,52, S.
Tripathy 50, T. Tripathy 46, S. Trogolo 32, V. Trubnikov 3, W.H. Trzaska 114,
T.P. Trzcinski 132, R. Turrisi 53, T.S. Tveter 19, K. Ullaland 20, B. Ulukutlu
95, A. Uras 125, M. Urioni 54,130, G.L. Usai 22, M. Vala37, N. Valle 21, S.
Vallero 55, L.V.R. van Doremalen58, M. van Leeuwen 84, C.A. van Veen 94,
R.J.G. van Weelden 84, P. Vande Vyvre 32, D. Varga 135, Z. Varga 135, M.
Varga-Kofarago 135, M. Vasileiou 78, A. Vasiliev 139, O. Vázquez Doce 48, V.
Vechernin 139, E. Vercellin 24, S. Vergara Limón44, L. Vermunt 97, R. Vértesi
135, M. Verweij 58, L. Vickovic33, Z. Vilakazi120, O. Villalobos Baillie 100,
G. Vino 49, A. Vinogradov 139, T. Virgili 28, V. Vislavicius83, A. Vodopyanov
140, B. Volkel 32, M.A. Völkl 94, K. Voloshin139, S.A. Voloshin 133, G. Volpe
31, B. von Haller 32, I. Vorobyev 95, N. Vozniuk 139, J. Vrláková 37, B.
Wagner20, C. Wang 39, D. Wang39, A. Wegrzynek 32, F.T. Weiglhofer38, S.C.
Wenzel 32, J.P. Wessels 134, S.L. Weyhmiller 136, J. Wiechula 63, J. Wikne 19,
G. Wilk 79, J. Wilkinson 97, G.A. Willems 134, B. Windelband94, M. Winn 127,
J.R. Wright 107, W. Wu39, Y. Wu 117, R. Xu 6, A. Yadav 42, A.K. Yadav 131, S.
Yalcin 71, Y. Yamaguchi92, K. Yamakawa92, S. Yang20, S. Yano 92, Z. Yin 6,
I.-K. Yoo 16, J.H. Yoon 57, S. Yuan20, A. Yuncu 94, V. Zaccolo 23, C. Zampolli
32, H.J.C. Zanoli58, F. Zanone 94, N. Zardoshti 32,100, A. Zarochentsev 139,
P. Závada 61, N. Zaviyalov139, M. Zhalov 139, B. Zhang 6, L. Zhang 39, S.
Zhang 39, X. Zhang 6, Y. Zhang117, Z. Zhang 6, M. Zhao 10, V. Zherebchevskii
139, Y. Zhi10, N. Zhigareva139, D. Zhou 6, Y. Zhou 83, J. Zhu 97,6, Y. Zhu6,
G. ZinovjevI,3, S.C. Zugravel 55, N. Zurlo 130,54

## Affiliation Notes

I Deceased
II Also at: Max-Planck-Institut für Physik, Munich, Germany
III Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
IV Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
V Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
VI Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
VII Also at: An institution covered by a cooperation agreement with CERN

## Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia
2 AGH University of Science and Technology, Cracow, Poland
3 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine
4 Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India
5 California Polytechnic State University, San Luis Obispo, California, United
States
6 Central China Normal University, Wuhan, China
7 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba
8 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and
Mérida, Mexico
9 Chicago State University, Chicago, Illinois, United States
10 China Institute of Atomic Energy, Beijing, China
11 Chungbuk National University, Cheongju, Republic of Korea
12 Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovak Republic
13 COMSATS University Islamabad, Islamabad, Pakistan
14 Creighton University, Omaha, Nebraska, United States
15 Department of Physics, Aligarh Muslim University, Aligarh, India
16 Department of Physics, Pusan National University, Pusan, Republic of Korea
17 Department of Physics, Sejong University, Seoul, Republic of Korea
18 Department of Physics, University of California, Berkeley, California,
United States
19 Department of Physics, University of Oslo, Oslo, Norway
20 Department of Physics and Technology, University of Bergen, Bergen, Norway
21 Dipartimento di Fisica, Università di Pavia, Pavia, Italy
22 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy
23 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy
24 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy
25 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy
26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy
27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy
28 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy
29 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy
30 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy
31 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy
32 European Organization for Nuclear Research (CERN), Geneva, Switzerland
33 Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia
34 Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway
35 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic
36 Faculty of Physics, Sofia University, Sofia, Bulgaria
37 Faculty of Science, P.J. Šafárik University, Košice, Slovak Republic
38 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany
39 Fudan University, Shanghai, China
40 Gangneung-Wonju National University, Gangneung, Republic of Korea
41 Gauhati University, Department of Physics, Guwahati, India
42 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany
43 Helsinki Institute of Physics (HIP), Helsinki, Finland
44 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico
45 Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania
46 Indian Institute of Technology Bombay (IIT), Mumbai, India
47 Indian Institute of Technology Indore, Indore, India
48 INFN, Laboratori Nazionali di Frascati, Frascati, Italy
49 INFN, Sezione di Bari, Bari, Italy
50 INFN, Sezione di Bologna, Bologna, Italy
51 INFN, Sezione di Cagliari, Cagliari, Italy
52 INFN, Sezione di Catania, Catania, Italy
53 INFN, Sezione di Padova, Padova, Italy
54 INFN, Sezione di Pavia, Pavia, Italy
55 INFN, Sezione di Torino, Turin, Italy
56 INFN, Sezione di Trieste, Trieste, Italy
57 Inha University, Incheon, Republic of Korea
58 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht
University/Nikhef, Utrecht, Netherlands
59 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovak Republic
60 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India
61 Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic
62 Institute of Space Science (ISS), Bucharest, Romania
63 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany
64 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico
65 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil
66 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico
67 iThemba LABS, National Research Foundation, Somerset West, South Africa
68 Jeonbuk National University, Jeonju, Republic of Korea
69 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany
70 Korea Institute of Science and Technology Information, Daejeon, Republic of
Korea
71 KTO Karatay University, Konya, Turkey
72 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France
73 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France
74 Lawrence Berkeley National Laboratory, Berkeley, California, United States
75 Lund University Department of Physics, Division of Particle Physics, Lund,
Sweden
76 Nagasaki Institute of Applied Science, Nagasaki, Japan
77 Nara Women’s University (NWU), Nara, Japan
78 National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece
79 National Centre for Nuclear Research, Warsaw, Poland
80 National Institute of Science Education and Research, Homi Bhabha National
Institute, Jatni, India
81 National Nuclear Research Center, Baku, Azerbaijan
82 National Research and Innovation Agency - BRIN, Jakarta, Indonesia
83 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
84 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands
85 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom
86 Nuclear Physics Institute of the Czech Academy of Sciences, Husinec-Řež,
Czech Republic
87 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
88 Ohio State University, Columbus, Ohio, United States
89 Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia
90 Physics Department, Panjab University, Chandigarh, India
91 Physics Department, University of Jammu, Jammu, India
92 Physics Program and International Institute for Sustainability with Knotted
Chiral Meta Matter (SKCM2), Hiroshima University, Hiroshima, Japan
93 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany
94 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
95 Physik Department, Technische Universität München, Munich, Germany
96 Politecnico di Bari and Sezione INFN, Bari, Italy
97 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Darmstadt, Germany
98 Saga University, Saga, Japan
99 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata,
India
100 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom
101 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru
102 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
103 SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France
104 Suranaree University of Technology, Nakhon Ratchasima, Thailand
105 Technical University of Košice, Košice, Slovak Republic
106 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland
107 The University of Texas at Austin, Austin, Texas, United States
108 Universidad Autónoma de Sinaloa, Culiacán, Mexico
109 Universidade de São Paulo (USP), São Paulo, Brazil
110 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
111 Universidade Federal do ABC, Santo Andre, Brazil
112 University of Cape Town, Cape Town, South Africa
113 University of Houston, Houston, Texas, United States
114 University of Jyväskylä, Jyväskylä, Finland
115 University of Kansas, Lawrence, Kansas, United States
116 University of Liverpool, Liverpool, United Kingdom
117 University of Science and Technology of China, Hefei, China
118 University of South-Eastern Norway, Kongsberg, Norway
119 University of Tennessee, Knoxville, Tennessee, United States
120 University of the Witwatersrand, Johannesburg, South Africa
121 University of Tokyo, Tokyo, Japan
122 University of Tsukuba, Tsukuba, Japan
123 University Politehnica of Bucharest, Bucharest, Romania
124 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
125 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de
Lyon, Lyon, France
126 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France,
Strasbourg, France
127 Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment
de Physique Nucléaire (DPhN), Saclay, France
128 Università degli Studi di Foggia, Foggia, Italy
129 Università del Piemonte Orientale, Vercelli, Italy
130 Università di Brescia, Brescia, Italy
131 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata,
India
132 Warsaw University of Technology, Warsaw, Poland
133 Wayne State University, Detroit, Michigan, United States
134 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany
135 Wigner Research Centre for Physics, Budapest, Hungary
136 Yale University, New Haven, Connecticut, United States
137 Yonsei University, Seoul, Republic of Korea
138 Zentrum für Technologie und Transfer (ZTT), Worms, Germany
139 Affiliated with an institute covered by a cooperation agreement with CERN
140 Affiliated with an international laboratory covered by a cooperation
agreement with CERN.