Present address: ]Institut für Kernphysik, Technische Universität Darmstadt,
D-64289 Darmstadt, Germany

Present address: ]LPC Caen, ENSICAEN, Université de Caen Normandie,
CNRS/IN2P3, F-14050 Caen Cedex, France Present address: ]Institut für
Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
Present address: ] Department of Physics, University of York, Heslington, York
YO10 5DD, United Kingdom Present address: ]Institut für Kernphysik, Technische
Universität Darmstadt, D-64289 Darmstadt, Germany

# Quasi-free Neutron Knockout Reaction Reveals a Small $s$-orbital Component
in the Borromean Nucleus 17B

Z. H. Yang<EMAIL_ADDRESS>Research Center for Nuclear Physics (RCNP),
Osaka University, 10-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan  RIKEN
Nishina Center, Hirosawa 2-1, Wako, Saitama 351-0198, Japan  Y. Kubota  [
RIKEN Nishina Center, Hirosawa 2-1, Wako, Saitama 351-0198, Japan  Center for
Nuclear Study, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, Japan
A. Corsi  Département de Physique Nucléaire, IRFU, CEA, Université Paris-
Saclay, F-91191 Gif-sur-Yvette, France  K. Yoshida  Advanced Science Research
Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan  X.-X. Sun
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics,
Chinese Academy of Sciences, Beijing 100190, China  School of Physical
Sciences, University of Chinese Academy of Sciences, Beijing 100049, China  J.
G. Li  School of Physics and State Key Laboratory of Nuclear Physics and
Technology, Peking University, Beijing 100871, China  M. Kimura  Department of
Physics, Hokkaido University, Sapporo 060-0810, Japan  Nuclear Reaction Data
Centre, Hokkaido University, Sapporo 060-0810, Japan  Research Center for
Nuclear Physics (RCNP), Osaka University, 10-1 Mihogaoka, Ibaraki, Osaka
567-0047, Japan  N. Michel  Institute of Modern Physics, Chinese Academy of
Sciences, Lanzhou 730000, China  School of Nuclear Science and Technology,
University of Chinese Academy of Sciences, Beijing 100049, China  K. Ogata
Research Center for Nuclear Physics (RCNP), Osaka University, 10-1 Mihogaoka,
Ibaraki, Osaka 567-0047, Japan  Department of Physics, Osaka City University,
Osaka 558-8585, Japan  C. X. Yuan  Sino-French Institute of Nuclear
Engineering and Technology, Sun Yat-Sen University, Zhuhai, 519082, Guangdong,
China  Q. Yuan  School of Physics and State Key Laboratory of Nuclear Physics
and Technology, Peking University, Beijing 100871, China  G. Authelet
Département de Physique Nucléaire, IRFU, CEA, Université Paris-Saclay, F-91191
Gif-sur-Yvette, France  H. Baba  RIKEN Nishina Center, Hirosawa 2-1, Wako,
Saitama 351-0198, Japan  C. Caesar  Institut für Kernphysik, Technische
Universität Darmstadt, D-64289 Darmstadt, Germany  D. Calvet  Département de
Physique Nucléaire, IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-
Yvette, France  A. Delbart  Département de Physique Nucléaire, IRFU, CEA,
Université Paris-Saclay, F-91191 Gif-sur-Yvette, France  M. Dozono  Center for
Nuclear Study, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, Japan
J. Feng  School of Physics and State Key Laboratory of Nuclear Physics and
Technology, Peking University, Beijing 100871, China  F. Flavigny  [  IPN
Orsay, Université Paris Sud, IN2P3-CNRS, F-91406 Orsay Cedex, France  J.-M.
Gheller  Département de Physique Nucléaire, IRFU, CEA, Université Paris-
Saclay, F-91191 Gif-sur-Yvette, France  J. Gibelin  LPC Caen, ENSICAEN,
Université de Caen Normandie, CNRS/IN2P3, F-14050 Caen Cedex, France  A.
Giganon  Département de Physique Nucléaire, IRFU, CEA, Université Paris-
Saclay, F-91191 Gif-sur-Yvette, France  A. Gillibert  Département de Physique
Nucléaire, IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
K. Hasegawa  Department of Physics, Tohoku University, Aramaki Aza-Aoba 6-3,
Aoba, Sendai, Miyagi 980-8578, Japan  T. Isobe  RIKEN Nishina Center, Hirosawa
2-1, Wako, Saitama 351-0198, Japan  Y. Kanaya  Department of Applied Physics,
University of Miyazaki, Gakuen-Kibanadai-Nishi 1-1, Miyazaki 889-2192, Japan
S. Kawakami  Department of Applied Physics, University of Miyazaki, Gakuen-
Kibanadai-Nishi 1-1, Miyazaki 889-2192, Japan  D. Kim  Center for Exotic
Nuclear Studies, Institute for Basic Science, Daejeon 34126, Republic of Korea
Y. Kiyokawa  Center for Nuclear Study, University of Tokyo, Hongo 7-3-1,
Bunkyo, Tokyo 113-0033, Japan  M. Kobayashi  Center for Nuclear Study,
University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, Japan  N. Kobayashi
Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo
113-0033, Japan  T. Kobayashi  Department of Physics, Tohoku University,
Aramaki Aza-Aoba 6-3, Aoba, Sendai, Miyagi 980-8578, Japan  Y. Kondo
Department of Physics, Tokyo Institute of Technology, 2-12-1 O-Okayama,
Meguro, Tokyo 152-8551, Japan  Z. Korkulu  Center for Exotic Nuclear Studies,
Institute for Basic Science, Daejeon 34126, Republic of Korea  Institute for
Nuclear Research, Hungarian Academy of Sciences (MTA Atomki), P.O. Box 51,
H-4001 Debrecen, Hungary  S. Koyama  Department of Physics, University of
Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, Japan  V. Lapoux  Département de
Physique Nucléaire, IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-
Yvette, France  Y. Maeda  Department of Applied Physics, University of
Miyazaki, Gakuen-Kibanadai-Nishi 1-1, Miyazaki 889-2192, Japan  F. M. Marqués
LPC Caen, ENSICAEN, Université de Caen Normandie, CNRS/IN2P3, F-14050 Caen
Cedex, France  T. Motobayashi  RIKEN Nishina Center, Hirosawa 2-1, Wako,
Saitama 351-0198, Japan  T. Miyazaki  Department of Physics, University of
Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, Japan  T. Nakamura  Department of
Physics, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro, Tokyo
152-8551, Japan  N. Nakatsuka  Department of Physics, Kyoto University,
Kitashirakawa, Sakyo, Kyoto 606-8502, Japan  Y. Nishio  Department of Physics,
Kyushu University, Nishi, Fukuoka 819-0395, Japan  A. Obertelli  [
Département de Physique Nucléaire, IRFU, CEA, Université Paris-Saclay, F-91191
Gif-sur-Yvette, France  A. Ohkura  Department of Physics, Kyushu University,
Nishi, Fukuoka 819-0395, Japan  N. A. Orr  LPC Caen, ENSICAEN, Université de
Caen Normandie, CNRS/IN2P3, F-14050 Caen Cedex, France  S. Ota  Center for
Nuclear Study, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, Japan
H. Otsu  RIKEN Nishina Center, Hirosawa 2-1, Wako, Saitama 351-0198, Japan  T.
Ozaki  Department of Physics, Tokyo Institute of Technology, 2-12-1 O-Okayama,
Meguro, Tokyo 152-8551, Japan  V. Panin  RIKEN Nishina Center, Hirosawa 2-1,
Wako, Saitama 351-0198, Japan  S. Paschalis  [  Institut für Kernphysik,
Technische Universität Darmstadt, D-64289 Darmstadt, Germany  E. C. Pollacco
Département de Physique Nucléaire, IRFU, CEA, Université Paris-Saclay, F-91191
Gif-sur-Yvette, France  S. Reichert  Physik Department, Technische Universität
München, D-85748 Garching, Germany  J.-Y. Roussé  Département de Physique
Nucléaire, IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
A. T. Saito  Department of Physics, Tokyo Institute of Technology, 2-12-1
O-Okayama, Meguro, Tokyo 152-8551, Japan  S. Sakaguchi  Department of Physics,
Kyushu University, Nishi, Fukuoka 819-0395, Japan  M. Sako  RIKEN Nishina
Center, Hirosawa 2-1, Wako, Saitama 351-0198, Japan  C. Santamaria
Département de Physique Nucléaire, IRFU, CEA, Université Paris-Saclay, F-91191
Gif-sur-Yvette, France  M. Sasano  RIKEN Nishina Center, Hirosawa 2-1, Wako,
Saitama 351-0198, Japan  H. Sato  RIKEN Nishina Center, Hirosawa 2-1, Wako,
Saitama 351-0198, Japan  M. Shikata  Department of Physics, Tokyo Institute of
Technology, 2-12-1 O-Okayama, Meguro, Tokyo 152-8551, Japan  Y. Shimizu  RIKEN
Nishina Center, Hirosawa 2-1, Wako, Saitama 351-0198, Japan  Y. Shindo
Department of Physics, Kyushu University, Nishi, Fukuoka 819-0395, Japan  L.
Stuhl  Center for Exotic Nuclear Studies, Institute for Basic Science, Daejeon
34126, Republic of Korea  RIKEN Nishina Center, Hirosawa 2-1, Wako, Saitama
351-0198, Japan  T. Sumikama  Department of Physics, Tohoku University,
Aramaki Aza-Aoba 6-3, Aoba, Sendai, Miyagi 980-8578, Japan  Y. L. Sun  [
Département de Physique Nucléaire, IRFU, CEA, Université Paris-Saclay, F-91191
Gif-sur-Yvette, France  M. Tabata  Department of Physics, Kyushu University,
Nishi, Fukuoka 819-0395, Japan  Y. Togano  Department of Physics, Tokyo
Institute of Technology, 2-12-1 O-Okayama, Meguro, Tokyo 152-8551, Japan
Department of Physics, Rikkyo University, 3-34-1, Nishi-Ikebukuro, Toshima,
Tokyo 171-8501, Japan  J. Tsubota  Department of Physics, Tokyo Institute of
Technology, 2-12-1 O-Okayama, Meguro, Tokyo 152-8551, Japan  F. R. Xu  School
of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking
University, Beijing 100871, China  J. Yasuda  Department of Physics, Kyushu
University, Nishi, Fukuoka 819-0395, Japan  K. Yoneda  RIKEN Nishina Center,
Hirosawa 2-1, Wako, Saitama 351-0198, Japan  J. Zenihiro  RIKEN Nishina
Center, Hirosawa 2-1, Wako, Saitama 351-0198, Japan  S.-G. Zhou  CAS Key
Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese
Academy of Sciences, Beijing 100190, China  School of Physical Sciences,
University of Chinese Academy of Sciences, Beijing 100049, China  W. Zuo
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000,
China  School of Nuclear Science and Technology, University of Chinese Academy
of Sciences, Beijing 100049, China  T. Uesaka  RIKEN Nishina Center, Hirosawa
2-1, Wako, Saitama 351-0198, Japan  Cluster for Pioneering Research, RIKEN,
Hirosawa 2-1, Wako, Saitama 351-0198, Japan

###### Abstract

A kinematically complete quasi-free $(p,pn)$ experiment in inverse kinematics
was performed to study the structure of the Borromean nucleus 17B, which had
long been considered to have neutron halo. By analyzing the momentum
distributions and exclusive cross sections, we obtained the spectroscopic
factors for $1s_{1/2}$ and $0d_{5/2}$ orbitals, and a surprisingly small
percentage of 9(2)$\%$ was determined for $1s_{1/2}$. Our finding of such a
small $1s_{1/2}$ component and the halo features reported in prior experiments
can be explained by the deformed relativistic Hartree-Bogoliubov theory in
continuum, revealing a definite but not dominant neutron halo in 17B. The
present work gives the smallest $s$\- or $p$-orbital component among known
nuclei exhibiting halo features, and implies that the dominant occupation of
$s$ or $p$ orbitals is not a prerequisite for the occurrence of neutron halo.

###### pacs:

21.60.Gx, 25.60.Gc, 25.70.Ef, 25.70.Mn

Along an isotopic chain, with increasing neutron number the nuclei gradually
lose binding as the dripline (the limit of nuclear existence) is approached
[1, 2]. When occupying the $s$ or $p$ orbital, the least bound neutrons of
near-dripline nuclei can tunnel far out into the “classically forbidden”
region, and a novel phenomenon—the neutron halo—occurs [3, 4, 5, 6, 7, 8, 9,
10]. It is a prime example of the emergent simplicity in nuclear many-body
systems on top of the complexity of interactions among the constituent
nucleons [11, 13, 12, 14].

In the context of halo, of particular interest are nuclei with a 2$n$-halo
structure, which generally exhibit a Borromean character without any bound
binary subsystems [4, 5, 6, 7, 8, 9]. Recently, $2n$-halo structure was
reported in 22C and 29F from the large matter radius [15, 16, 17] and in 19B
from the enhanced electric dipole strength measurements [18]. It has been of
great interest to search for new 2$n$-halo systems [8] and new halo features
such as the core-halo shape decoupling [19, 20, 21] and the Efimov state [22,
23]. Meanwhile, it is also important to have comprehensive investigation of
the structure of a variety of nuclei with both well- and less-developed halos,
particularly using transfer or knockout reactions, to reach a detailed
understanding of 2$n$ halo [6, 7, 9, 8]. Such measurements have so far only
been made for light systems with a well-developed 2$n$ halo, 6He [24, 25, 26],
11Li [27, 28, 29, 30, 34, 31, 32, 33], 14Be [35, 36, 34, 37, 38]. In all these
cases, the valence neutrons dominantly occupy $p$ and $s$ orbitals. This
naturally raises the question whether the dominant occupation of $s$ or $p$
orbitals is universal for $2n$-halo nuclei and should thus be a criterion to
identify 2$n$-halo systems [6, 7]. On the other hand, recent theoretical
calculations show that a slight $s$-wave tail should be sufficient for the
occurrence of $2n$ halo in very weakly bound neutron-rich systems [39].

In this Letter, we report the observation of a surprisingly small $s$-orbital
component in the Borromean nucleus 17B, which has long been considered as a
2$n$-halo system [8]. Halo features in 17B have already been reported—the
large matter radius [41, 40], the narrow momentum distribution of 15B [42],
and the thick neutron surface [43], but the $s$-orbital percentage has
hitherto not been directly measured. Using a 15B+$n$+$n$ 3-body model with 15B
being an inert and spherical core, a large $s$-orbital percentage was deduced
from the matter radius and the 15B momentum distribution—36(19)$\%$ [41],
69(20)$\%$ [42], 50(10)$\%$ [44], 53(21)$\%$ [45]. However, Estradé et al.
found its neutron skin thickness did not fit in with such a 3-body picture
bearing out a dominant $s$-orbital component [43]. The large $s$-orbital
percentage in the neighboring isotopes—14B (64$\%$ $\sim$ 89$\%$) [46, 47,
48], 15B ($\sim$63$\%$) [47], 18B [49], and 19B ($\sim$35$\%$) [18]—also makes
the $s$-orbital percentage in 17B an intriguing question.

In the present work, we have achieved the first direct measurement of the
$s$-orbital percentage in 17B using the quasi-free $(p,pn)$ reaction in
inverse kinematics. This study concerns a kinematically complete measurement,
which was made possible by combining the high-intensity beams provided by the
Radioactive Isotope Beam Factory of RIKEN Nishina Center and the state-of-the-
art detector instruments including the vertex-tracking liquid hydrogen target
MINOS [50], in-beam $\gamma$-ray spectrometer DALI2 [51], and the SAMURAI
spectrometer [52, 53, 54].

Experiment.— Secondary 17B beams ($\sim$1.4${\times}$104 $pps$, $\sim$277
MeV/nucleon) were produced from the fragmentation of 48Ca at 345 MeV/nucleon
and prepared using the BigRIPS fragment separator [55, 56]. They were then
tracked onto the 150 mm-thick MINOS target [50] using two multi-wire drift
chambers. At the target region, we placed a $\gamma$-ray detector array
constructed with 68 NaI crystals of DALI2 [51], a recoil-proton spectrometer
composted of a multi-wire drift chamber and a plastic scintillator array, and
the recoil-neutron detector array WINDS [57]. The charged fragments and decay
neutrons were detected by SAMURAI [52, 53] and NEBULA [54]. The relative
energy $E_{\rm rel}$ of the unbound nucleus 16B was reconstructed from the
momenta of 15B and the decay neutron, with a resolution (FWHM) of
$\sim$0.45$\sqrt{E_{\rm rel}}$ (in MeV). When 15B is in an excited state, the
energy of 16B ($E_{\rm d}$) with respect to the 15B$(g.s.)+n$ threshold can be
obtained as the sum of $E_{\rm rel}$ and the excitation energy of 15B.
Population of excited 15B fragments was reported in a prior breakup experiment
of 17B [58]. Details of the setup can be found in [38, 33, 32].

Quasi-free $(p,pn)$.—We first confirmed the quasi-free $(p,pn)$ process by
checking the kinematical correlation between recoil protons and recoil
neutrons [38, 60, 59]. The correlation between the polar angles, $\theta_{p}$
and $\theta_{n}$, agrees nicely with the kinematical simulation (Fig. 1(a)).

The kinematically complete measurement allows us to reconstruct the momentum
of the recoil neutron from momentum conservation without detecting it, which
largely enhances the statistics. The corresponding angular correlation is
presented in Fig. 1(b). The correlation locus gets broadened relative to panel
(a), but follows well the expected correlation pattern of quasi-free $(p,pn)$.

Gamma-coincidence.—The Doppler-shift-corrected $\gamma$-ray spectrum in
coincidence with 16B ($E_{\rm rel}\leq$ 5 MeV) is shown in Fig. 1(c). It is
well fitted using the response functions of two known $\gamma$ rays, 1327 keV
and 1407 keV from 15B excited states [61, 58, 62], and a two-exponential
background ($\chi^{2}/ndf$=1.4). For each $\gamma$ ray, the response function
was obtained from Geant4 simulations considering the realistic setup and the
resolution of each crystal. The inset shows the $\gamma$-gated $E_{\rm rel}$
spectrum after correcting for the $\gamma$ efficiency ($\sim$12$\%$), in
comparison to the inclusive one. Obviously, the core-excited component is
small (within $\sim$5$\%$), and thus neglected when fitting the $E_{\rm rel}$
spectrum (see below). 16B states from $\gamma$-coincident analysis [63] are
presented in Table 1.

Figure 1: Angular correlation between recoil protons and neutrons for events
with recoil neutrons detected by WINDS (a) and reconstructed from momentum
conservation (b). The black line indicates the kinematical simulation assuming
quasi-free $(p,pn)$ off 17B. (c) Doppler-corrected $\gamma$-ray spectrum,
fitted using two $\gamma$ rays (1327 keV and 1407 keV) and a two-exponential
background. The inset presents the $\gamma$-gated $E_{\rm rel}$ spectrum,
together with the inclusive one for comparison.

$E_{\rm rel}$ spectrum of 16B.—For 17B with $N$=12, the knocked-out neutron
should mainly come from 1$\emph{s}_{1/2}$ and 0$\emph{d}_{5/2}$ orbitals. The
small contribution from $p$-wave orbitals was confirmed by checking the
angular correlation [28]. Ignoring higher-lying 0$\emph{d}_{3/2}$ is justified
by the theoretical calculations we employed (see below).

We first checked the $E_{\rm rel}$ spectrum gated by the momentum ($P$) of the
knocked-out neutron to disentangle states populated by 1$\emph{s}_{1/2}$ and
0$\emph{d}_{5/2}$ knockout. The $E_{\rm rel}$ spectra gated by 0 MeV/$c$ $\leq
P\leq 60$ MeV/$c$ (selective for 1$\emph{s}_{1/2}$) and 60 MeV/$c$ $\leq P\leq
160$ MeV/$c$ (selective for 0$\emph{d}_{5/2}$) are shown in Fig. 2(a),
together with the inclusive one for comparison. All the spectra are normalized
according to the peak at $\sim$0, since it is 3- associated purely with
0$\emph{d}_{5/2}$ (see below). Its $d$-wave character has also been
established in [64]. To enhance the visibility, in Fig. 2(b) we presented the
ratio of the $P$-gated spectrum to the inclusive one. Obviously, the prominent
peak at $\sim$1 MeV in Fig. 2(a) is mainly from 0$\emph{d}_{5/2}$ knockout.
Meanwhile, the red histogram in Fig. 2(b) clearly shows two
1$\emph{s}_{1/2}$-associated states, one at $\sim$0.2 MeV and another broad
bump at 1$\sim$4 MeV.

Figure 2: (a)16B $E_{\rm rel}$ spectra gated by 0 MeV/$c$ $\leq P\leq 60$
MeV/$c$ (red) and 60 MeV/$c$ $\leq P\leq 160$ MeV/$c$ (blue) in comparison to
the inclusive one (black). (b) Ratios of the momentum-gated spectrum to the
inclusive one. The grey dashed line, with a constant value of 1, stands for
the scenario that the entire spectrum is associated with knockout of
0$\emph{d}_{5/2}$ neutrons. (c) The fitting with a sum of four resonances. The
inset is a zoom-in view of the 0-1 MeV region.

Hence, the $E_{\rm rel}$ spectrum was fitted using four resonances, after
taking into account the experimental acceptance and resolutions. The states at
$\sim$0.04 MeV and $\sim$1 MeV were described with $d$-wave Breit-Wigner line
shapes and the other two with $s$-wave line shapes [65]. Since the intrinsic
width of the $\sim$0.04-MeV state is much smaller than the experimental
resolution, it was fixed to 1 keV in the fitting, and an upper limit of
$\sim$20 keV was estimated. The results are presented in Fig. 2(c) and Table
1. Errors of the resonance parameters include both statistical and systematic
errors, the latter being dominated by the effect of the fitting range. The
0.046(3)-MeV state agrees with prior reports [64, 49, 66], but the resonant
energy is refined; meanwhile, the inset of Fig. 1(c) clearly shows that it is
associated with 15B$(g.s.)$. The 2.38(8)-MeV state observed in the
$\gamma$-coincident analysis also agrees well with the reported state at
2.40(7) MeV [66].

Table 1:  Summary of 16B states and experimental spectroscopic factors
($S_{\rm exp}$). The experimental ($\sigma_{\rm exp}$) and theoretical single-
particle cross sections ($\sigma_{\rm th}$) are the integrated value over the
detector coverage. $S_{\rm exp}$ is defined as $S_{\rm exp}=\sigma_{\rm
exp}/\sigma_{\rm th}$.

_$E_{\rm x}(^{15}$_ B) [MeV] | _$E_{\rm rel}$_ [MeV] | _$\Gamma_{\rm r}$_ [MeV] | _$E_{\rm d}$_ [MeV] a | $J^{\pi}$ | $n$ orbital | _$\sigma_{\rm exp}$_ [mb] | _$\sigma_{\rm th}$_ [mb] | _$S_{\rm exp}$_
---|---|---|---|---|---|---|---|---
0 | 0.046(3) |  $<$ 0.02 | 0.046(3) | $3^{-}$ | $0d_{5/2}$ | 0.0639(6) | 0.199 | 0.32(4)
0 | 0.183(6) | 0.44(7) | 0.183(6) | $2^{-}$ | $0d_{5/2}$ | 0.041(5) | 0.196 | 0.21(3)
$1s_{1/2}$ | 0.007(2) | 0.329 | 0.02(1)
0 | 1.08(6) | 0.5(2) | 1.08(6) | $4^{-}$ | $0d_{5/2}$ | 0.18(2) | 0.181 | 0.97(14)
0 | 2.8(1) | 1.8(3) | 2.8(1) | $1^{-}$/ $2^{-}$ | $0d_{5/2}$ | 0.14(2) | 0.160 | 0.87(14)
$1s_{1/2}$ | 0.054(9) | 0.243 | 0.22(4)
1.33 | 1.05(8) | 0.3(2) | 2.38(8) | $(3^{-})$ | $0d_{5/2}$ | 0.009(3) | 0.164 | 0.06(2)
1.33 | 2.4(2) | 0.4(3) |  3.7(2)b | $(3^{-}$/ $4^{-}$) | $0d_{5/2}$ | 0.011(4) | 0.154 | 0.07(3)
2.73 | 0.9(3) | 0.5(2)
2.73 | 2.1(1) |  $<$ 0.5 | 4.8(1) |  $(3^{-}$/ $4^{-}$) | $0d_{5/2}$ | 0.003(2) | 0.144 | 0.02(1)
|  $1s_{1/2}$ spectroscopic factor percentage |  9(2) $\%$

  * a

$E_{\rm d}$=$E_{\rm rel}$+$E_{\rm x}$(15B).

  * b

Taken as the weighted average of the results of the two decay channels.

Results and Discussions.—In Fig. 3, we compare the level scheme of 16B to
theoretical calculations: $(i)$ Shell model (SM) calculation with YSOX
interactions, considering the reduction of $sd$-shell $n$-$n$ interactions by
a factor of 0.75 [67, 68, 69, 70, 71]. $(ii)$ Valence-space in-medium
similarity renormalization group (VS-IMSRG) calculation [72] using the
optimized chiral effective field theory interaction at next-to-next-to-leading
order [73] in Hartree-Fock basis with 15 major harmonic-oscillator shells
($\hbar\omega$ = 24 MeV). $(iii)$ Antisymmetrized molecular dynamics plus
generator coordinate method (AMD) calculation using the Gogny D1S interaction
[43, 74]. $(iv)$ Gamow shell model (GSM) calculation with a 10He core [75, 76,
77]. All partial waves up to $l$ = 3 were included for the valence neutrons,
while $\emph{p}_{3/2}$ and $\emph{p}_{1/2}$ basis states were included for the
well-bound valence protons. For the two-body force we adopted the Minnesota
force [78], and the one-body force was modeled with a Woods-Saxon potential
with the potential parameters adjusted to reproduce the separation energies
and low-lying states of 14B and 15B.

Figure 3: Observed 16B states compared to Gamow shell model (GSM), valence-
space in-medium similarity renormalization group (VS-IMSRG), antisymmetrized
molecular dynamics (AMD), and shell model (SM) calculations. The
$1n$-separation energies are shown in the parentheses (in MeV).

Given that the spin-parity ($J^{\pi}$) of 17B$(g.s)$ is $3/2^{-}$, $J^{\pi}$
of the two $1s_{1/2}$-associated states (0.183 MeV, 2.8 MeV) should be either
$1^{-}$ or $2^{-}$, while the other two non-$1s_{1/2}$ states should be more
likely $3^{-}$ or $4^{-}$. Tentative assignments of $J^{\pi}$ can thus be
made, as shown in Fig. 3. Though predicted as the ground state by SM, AMD, and
VS-IMSRG, 0- should be safely excluded for the 0.046 MeV state, because of the
small spectroscopic factors ($<$0.03) predicted by these models.

In order to analyze the momentum distribution of the knocked-out neutron and
extract the $0d_{5/2}$ and $1s_{1/2}$ spectroscopic factors in 17B, we carried
out the distorted-wave impulse approximation (DWIA) calculation [79]. This
model has recently been applied in several $(p,pn)$ and $(p,2p)$ experiments
[32, 33, 80, 81, 82, 83, 84, 85, 86]. The single-particle wave function and
the nuclear density were obtained using the Bohr-Mottelson potential [87]. The
optical potentials for the distorted waves in the initial and final channels
were constructed with the microscopic folding model [88] using the Melbourne
g-matrix interaction [89] with the spin-orbit component disregarded. For the
$p$-$n$ interaction, the Franey-Love effective interaction [90] was adopted.
DWIA calculations were performed separately for all reaction channels listed
in Table 1, taking into account $E_{\rm d}$ of 16B.

Figure 4 shows the transverse momentum ($P_{\rm x}$) distributions, together
with DWIA calculated curves for $1s_{1/2}$ and $0d_{5/2}$ knockout after
folding in the experimental resolution (FWHM) of 45 MeV/$c$. For the 0.046-MeV
state (0 MeV $\leq E_{\rm rel}\leq 0.1$ MeV) and the 1.08-MeV state (0.9 MeV
$\leq E_{\rm rel}\leq 1.3$ MeV), the data can be well reproduced by a pure
$0d_{5/2}$ component, in line with the above $J^{\pi}$ assignment of $3^{-}$
and $4^{-}$.

For the 0.183-MeV state (0.25 MeV $\leq E_{\rm rel}\leq 0.45$ MeV) and the
2.8-MeV state (2.5 MeV $\leq E_{\rm rel}\leq 3.5$ MeV), we performed the
minimum-$\chi^{2}$ fitting using a combination of $1s_{1/2}$ and $0d_{5/2}$. A
$1s_{1/2}$ fraction of $14(4)\%$ and $28(3)\%$ was obtained, respectively. The
errors include both the statistical and systematic errors, the latter being
dominated by DWIA and the $E_{\rm rel}$ gate for the data. For the 2.8-MeV
state, the same $1s_{1/2}$ fraction is obtained when gating on the left
($29(2)\%$) or right half ($28(2)\%$) of the $E_{\rm rel}$ peak in the
analysis, providing further evidence that it is a singlet rather than a
doublet.

For $\gamma$-coincident 16B states, the $P_{\rm x}$ distributions are all in
agreement with knockout of 0$d_{5/2}$ neutrons from 17B [63]. This naturally
leads to a $J^{\pi}$ of $3^{-}$ or $4^{-}$ , as shown in Fig. 3. The
contribution of the 14B+$2n$ channel is very small ($\sim$5 $\%$) and thus not
included in Table 1, and the $P_{\rm x}$ distribution is consistent with
$0d_{5/2}$ knockout.

Figure 4: Transverse momentum ($P_{\rm x}$) distributions for different 16B
states. The vertical error bars stand for the statistical error, while the
horizontal for the bin size. In (a) and (b), DWIA calculated curves for
knockout of $1s_{1/2}$ (red-dashed) and $0d_{5/2}$ (black-dotted) neutrons are
normalized to the peak of the experimental spectrum; in (c) and (d), the blue-
solid curves represent the fitting with a combination of $1s_{1/2}$ (red-
dashed) and $0d_{5/2}$ (black-dotted). All DWIA curves have been convoluted
with the experimental resolution.

We then deduced the exclusive cross sections ($\sigma_{\rm exp}$), as
tabulated in Table 1. For the 0.183-MeV and 2.8-MeV states, the $1s_{1/2}$
fraction determined above has been used. The experimental spectroscopic factor
($S_{\rm exp}$) is obtained by dividing $\sigma_{\rm exp}$ with the
theoretical cross section for a unit spectroscopic factor ($\sigma_{\rm th}$)
from DWIA. Both $\sigma_{\rm exp}$ and $\sigma_{\rm th}$ are the integrated
cross sections over the detector coverage
($35^{\circ}<\theta_{p}<55^{\circ}$). We have incorporated the experimental
conditions into DWIA to facilitate the direct comparison of $\sigma_{\rm exp}$
and $\sigma_{\rm th}$ [63]. The errors quoted are the combined statistical and
systematic errors. For the 0.046-MeV and 1.08-MeV states, the systematic error
of $\sigma_{\rm exp}$ is dominated by the correction of detector efficiencies
(9$\%$). For the 0.183-MeV and 2.8-MeV states, the uncertainty of the
$1s_{1/2}$ fraction has also been considered. For $S_{\rm exp}$, the
uncertainty on $\sigma_{\rm th}$ (within 10$\%$) has further been included,
estimated by varying the potential parameters and $E_{\rm d}$ of 16B in the
DWIA calculation.

The total spectroscopic factors for $1s_{1/2}$ ($S_{s}$ = 0.24(4)) and
$0d_{5/2}$ ($S_{d}$ = 2.53(21)) are obtained by summing up the $S_{\rm exp}$
for $1s_{1/2}$ and $0d_{5/2}$ respectively in Table 1, and a $1s_{1/2}$
spectroscopic factor percentage of 9(2)$\%$ is thus deduced from the ratio of
$S_{s}$ and $S_{s}$ \+ $S_{d}$. As shown in Fig. 3, some 16B states are not
observed in the current quasi-free $(p,pn)$ experiment, indicating that these
states should have very small spectroscopic factors in 17B; their effect on
$S_{s}$ and the $1s_{1/2}$ spectroscopic factor percentage is negligible
compared to the errors quoted above. Note that the 1.08-MeV state could be a
doublet of two closely located states, given its relatively large width. But
such possibility will not affect our conclusion—a small $1s_{1/2}$ component
in 17B, since the $P_{\rm x}$ distribution in Fig. 4(b) clearly shows it is
populated (almost) purely by $0d_{5/2}$ knockout. Following the conventional
picture for “$2n$-halo nuclei” [6], one may expect a 15B+2$n$ structure for
17B [41, 42, 44, 45], and the $1s_{1/2}$ spectroscopic factor percentage of
9(2)% thus leads to a percentage of only 9(2)% for the halo-relevant
$(1s_{1/2})^{2}$ configuration. As discussed by Estradé et al. [43], 17B may
be better described in a 13B+4$n$ model, and our result would then lead to a
percentage of $\sim$18$\%$ for the halo-relevant
$(1s_{1/2})^{2}(0d_{5/2})^{2}$ configuration, which is also small.

However, prior experiments indeed consistently point to the formation of halo
in 17B [41, 40, 42, 44, 43], which seems to suggest a predominant $s$ orbital
component ($\sim$$50\%$) [41, 40, 42, 44, 45] in accordance with the
conventional picture of “$2n$-halo nuclei”—an inert core plus two spatially
decoupled valence neutrons [6]. To understand this seeming discrepancy, we
compared our result to theoretical predictions obtained by summing up the
$1s_{1/2}$ and $0d_{5/2}$ spectroscopic factors of states shown in Fig. 3. The
$1s_{1/2}$ percentage is largely overestimated by SM ($25\%$), VS-IMSRG
($26\%$), and GSM ($45\%$). For SM and GSM, we have also checked that the
result is not sensitive to the one-body Hamiltonian of $1s_{1/2}$. This may
suggest significant impact of deformation or other many-body effects, which
can not be sufficiently considered within the shell-model framework. A small
$1s_{1/2}$ percentage of $5\%$ is provided by AMD, which is based on the
nucleonic degrees of freedom and also predicts a large prolate deformation in
17B ($\beta$ = 0.4). But the $1s_{1/2}$ percentage is significantly
underestimated by AMD, mainly due to the use of Gaussian wave functions [91].

We then resort to the deformed relativistic Hartree-Bogoliubov theory in
continuum (DRHBc) [19, 93, 92, 20, 94, 95], which self-consistently considers
weak binding, deformation, and pairing-induced continuum coupling. We used the
effective interaction PK1 [96] and a density-dependent zero-range pairing
force [20]. The neutron and matter radius [43], deformation [62, 97], and
$S_{2n}$ [98] of 17B are well reproduced [63]. DRHBc provides a small
$1s_{1/2}$ orbital percentage of 14$\%$ for the valence neutrons, close to the
experimental result of 9(2)$\%$. Meanwhile, the neutron density distribution
shows a slight but definite low-density tail extending into large radial
distances [63], indicating a weak halo component in 17B. Hence, the neutron
halo exists in 17B as reported in prior experiments [41, 40, 42, 44, 43], but
not as the dominant structure component.

Summary.—We have measured the $0d_{5/2}$ and $1s_{1/2}$ spectroscopic factors
in 17B using the quasi-free $(p,pn)$ reaction in inverse kinematics. A small
spectroscopic factor percentage of 9(2)$\%$ was determined for the $1s_{1/2}$
orbital. Our result thus reveals a surprisingly small $s$-orbital component in
17B whether it is described in a simple 15B+2$n$ model or more properly in a
13B+4$n$ model. Our finding of such a small $1s_{1/2}$ component and the halo
features in 17B reported in prior experiments [41, 40, 42, 44, 43] can be well
explained by DRHBc, revealing a definite but not dominant halo component in
17B. The present work gives the smallest $s$\- or $p$-orbital component among
known nuclei exhibiting halo features, and implies that the dominant
occupation of $s$ or $p$ orbitals is not a prerequisite for the occurrence of
neutron halo. In weakly bound neutron-rich nuclei, as long as $s$ or $p$
orbitals around the Fermi surface are occupied by the least bound neutrons
with an appreciable strength, the halo naturally occurs and coexists with
other non-halo configurations [4, 6, 7, 8, 9]. The halo component, whether or
not dominant, results in a distinctive diffused surface, and thus manifests
itself in reactions sensitive to the surface properties [6, 7, 8, 9].

###### Acknowledgements.

We would like to thank the RIBF accelerator staff for the primary beam
delivery and the BigRIPS team for their efforts in preparing the secondary
beams. Z. H. Y. acknowledges fruitful discussions with C.L. Bai, J. Casal, Y.
Sato, T.T. Sun, and S.M. Wang, and the support from the Foreign Postdoctoral
Researcher program of RIKEN. This work has been supported by the European
Research Council through the ERC Grant No. MINOS-25856; the JSPS KAKENHI
Grants No. JP16K05352, No. JP18H05404, and No. JP16H02179; the National
Natural Science Foundation of China under Grants No. 11525524, No. 11835001,
No. 11921006, No. 11975282, No. 11435014, No. 11775316, and No. 11961141004;
the Strategic Priority Research Program of Chinese Academy of Sciences, Grant
No. XDB34000000; the Institute for Basic Science (IBS-R031-D1). The
computation of this work was partly supported by the HPC Cluster of ITP-CAS
and the Supercomputing Center, CNIC of CAS.

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