Quasi-free Neutron Knockout Reaction Reveals a Small s-orbital Component in the Borromean Nucleus ^{17}B
Z. H. Yang, Y. Kubota, A. Corsi, K. Yoshida, X.-X. Sun, J. G. Li, M. Kimura, N. Michel, K. Ogata, C. X. Yuan, Q. Yuan, G. Authelet, H. Baba, C. Caesar, D. Calvet, A. Delbart, M. Dozono, J. Feng, F. Flavigny, J.-M. Gheller, J. Gibelin, A. Giganon, A. Gillibert, K. Hasegawa, T. Isobe, Y. Kanaya, S. Kawakami, D. Kim, Y. Kiyokawa, M. Kobayashi, N. Kobayashi, T. Kobayashi, Y. Kondo, Z. Korkulu, S. Koyama, V. Lapoux, Y. Maeda, F. M. Marqes, T. Motobayashi, T. Miyazaki, T. Nakamura, N. Nakatsuka, Y. Nishio, A. Obertelli, y A. Ohkura, N. A. Orr, S. Ota, H. Otsu, T. Ozaki, V. Panin, S. Paschalis, E. C. Pollacco, S. Reichert, J.-Y. Rousse, A. T. Saito, S. Sakaguchi, M. Sako, C. Santamaria, 4 M. Sasano, H. Sato, M. Shikata, Y. Shimizu, Y. Shindo, L. Stuhl, T. Sumikama, Y. L. Sun, M. Tabata, Y. Togano, J. Tsubota, F. R. Xu, J. Yasuda, K. Yoneda, J. Zenihiro, S.-G. Zhou, W. Zuo, T. Uesaka
QQuasi-free Neutron Knockout Reaction Reveals a Small s -orbital Component in theBorromean Nucleus B Z. H. Yang,
1, 2, ∗ Y. Kubota,
2, 3, † A. Corsi, K. Yoshida, X.-X. Sun,
6, 7
J. G. Li, M. Kimura,
9, 10, 1
N. Michel,
11, 12
K. Ogata,
1, 13
C. X. Yuan, Q. Yuan, G. Authelet, H. Baba, C. Caesar, D. Calvet, A. Delbart, M. Dozono, J. Feng, F. Flavigny, ‡ J.-M. Gheller, J. Gibelin, A. Giganon, A. Gillibert, K. Hasegawa, T. Isobe, Y. Kanaya, S. Kawakami, D. Kim, Y. Kiyokawa, M. Kobayashi, N. Kobayashi, T. Kobayashi, Y. Kondo, Z. Korkulu,
20, 23
S. Koyama, V. Lapoux, Y. Maeda, F. M. Marqu´es, T. Motobayashi, T. Miyazaki, T. Nakamura, N. Nakatsuka, Y. Nishio, A. Obertelli, † A. Ohkura, N. A. Orr, S. Ota, H. Otsu, T. Ozaki, V. Panin, S. Paschalis, § E. C. Pollacco, S. Reichert, J.-Y. Rouss´e, A. T. Saito, S. Sakaguchi, M. Sako, C. Santamaria, M. Sasano, H. Sato, M. Shikata, Y. Shimizu, Y. Shindo, L. Stuhl,
20, 2
T. Sumikama, Y. L. Sun, † M. Tabata, Y. Togano,
22, 27
J. Tsubota, F. R. Xu, J. Yasuda, K. Yoneda, J. Zenihiro, S.-G. Zhou,
6, 7
W. Zuo,
11, 12 and T. Uesaka
2, 28 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 Center for Nuclear Study, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, Japan D´epartement de Physique Nucl´eaire, IRFU, CEA, Universit´e Paris-Saclay, F-91191 Gif-sur-Yvette, France Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan CAS Key Laboratory of Theoretical Physics, Institute of TheoreticalPhysics, Chinese Academy of Sciences, Beijing 100190, China School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China Department of Physics, Hokkaido University, Sapporo 060-0810, Japan Nuclear Reaction Data Centre, Hokkaido University, Sapporo 060-0810, Japan 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 Department of Physics, Osaka City University, Osaka 558-8585, Japan Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai, 519082, Guangdong, China Institut f¨ur Kernphysik, Technische Universit¨at Darmstadt, D-64289 Darmstadt, Germany IPN Orsay, Universit´e Paris Sud, IN2P3-CNRS, F-91406 Orsay Cedex, France LPC Caen, ENSICAEN, Universit´e de Caen Normandie, CNRS/IN2P3, F-14050 Caen Cedex, France Department of Physics, Tohoku University, Aramaki Aza-Aoba 6-3, Aoba, Sendai, Miyagi 980-8578, Japan Department of Applied Physics, University of Miyazaki, Gakuen-Kibanadai-Nishi 1-1, Miyazaki 889-2192, Japan Center for Exotic Nuclear Studies, Institute for Basic Science, Daejeon 34126, Republic of Korea Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, Japan Department of Physics, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro, Tokyo 152-8551, Japan Institute for Nuclear Research, Hungarian Academy of Sciences (MTA Atomki), P.O. Box 51, H-4001 Debrecen, Hungary Department of Physics, Kyoto University, Kitashirakawa, Sakyo, Kyoto 606-8502, Japan Department of Physics, Kyushu University, Nishi, Fukuoka 819-0395, Japan Physik Department, Technische Universit¨at M¨unchen, D-85748 Garching, Germany Department of Physics, Rikkyo University, 3-34-1, Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan Cluster for Pioneering Research, RIKEN, Hirosawa 2-1, Wako, Saitama 351-0198, Japan
A kinematically complete quasi-free ( p, pn ) experiment in inverse kinematics was performed tostudy the structure of the Borromean nucleus B, which had long been considered to have neutronhalo. By analyzing the momentum distributions and exclusive cross sections, we obtained thespectroscopic factors for 1 s / and 0 d / orbitals, and a surprisingly small percentage of 9(2)% wasdetermined for 1 s / . Our finding of such a small 1 s / component and the halo features reportedin prior experiments can be explained by the deformed relativistic Hartree-Bogoliubov theory incontinuum, revealing a definite but not dominant neutron halo in B. The present work gives thesmallest s - or p -orbital component among known nuclei exhibiting halo features, and implies thatthe dominant occupation of s or p orbitals is not a prerequisite for the occurrence of neutron halo. Along an isotopic chain, with increasing neutron num-ber the nuclei gradually lose binding as the dripline (thelimit of nuclear existence) is approached [1, 2]. Whenoccupying the s or p orbital, the least bound neutronsof near-dripline nuclei can tunnel far out into the “clas-sically forbidden” region, and a novel phenomenon—the neutron halo—occurs [3–10]. It is a prime example of theemergent simplicity in nuclear many-body systems on topof the complexity of interactions among the constituentnucleons [11–14].In the context of halo, of particular interest are nu-clei with a 2 n -halo structure, which generally exhibit a a r X i v : . [ nu c l - e x ] F e b Borromean character without any bound binary subsys-tems [4–9]. Recently, 2 n -halo structure was reported in C and F from the large matter radius [15–17] and in B from the enhanced electric dipole strength measure-ments [18]. It has been of great interest to search fornew 2 n -halo systems [8] and new halo features such asthe core-halo shape decoupling [19–21] and the Efimovstate [22, 23]. Meanwhile, it is also important to havecomprehensive investigation of the structure of a varietyof nuclei with both well- and less-developed halos, par-ticularly using transfer or knockout reactions, to reach adetailed understanding of 2 n halo [6–9]. Such measure-ments have so far only been made for light systems witha well-developed 2 n halo, He [24–26], Li [27–34], Be[34–38]. In all these cases, the valence neutrons domi-nantly occupy p and s orbitals. This naturally raises thequestion whether the dominant occupation of s or p or-bitals is universal for 2 n -halo nuclei and should thus be acriterion to identify 2 n -halo systems [6, 7]. On the otherhand, recent theoretical calculations show that a slight s -wave tail should be sufficient for the occurrence of 2 n halo in very weakly bound neutron-rich systems [39].In this Letter, we report the observation of a sur-prisingly small s -orbital component in the Borromeannucleus B, which has long been considered as a 2 n -halo system [8]. Halo features in B have already beenreported—the large matter radius [40, 41], the narrowmomentum distribution of B [42], and the thick neu-tron surface [43], but the s -orbital percentage has hith-erto not been directly measured. Using a B+ n + n B being an inert and spherical core,a large s -orbital percentage was deduced from the mat-ter radius and the B momentum distribution—36(19)%[41], 69(20)% [42], 50(10)% [44], 53(21)% [45]. However,Estrad´e et al. found its neutron skin thickness did not fitin with such a 3-body picture bearing out a dominant s -orbital component [43]. The large s -orbital percentage inthe neighboring isotopes— B (64% ∼ B( ∼ B [49], and B ( ∼ s -orbital percentage in B an intriguing question.In the present work, we have achieved the first directmeasurement of the s -orbital percentage in B using thequasi-free ( p, pn ) reaction in inverse kinematics. Thisstudy concerns a kinematically complete measurement,which was made possible by combining the high-intensitybeams provided by the Radioactive Isotope Beam Fac-tory of RIKEN Nishina Center and the state-of-the-artdetector instruments including the vertex-tracking liquidhydrogen target MINOS [50], in-beam γ -ray spectrome-ter DALI2 [51], and the SAMURAI spectrometer [52–54]. Experiment.—
Secondary B beams ( ∼ × pps , ∼
277 MeV/nucleon) were produced from the fragmenta-tion of Ca at 345 MeV/nucleon and prepared using theBigRIPS fragment separator [55, 56]. They were thentracked onto the 150 mm-thick MINOS target [50] us-ing two multi-wire drift chambers. At the target region, we placed a γ -ray detector array constructed with 68NaI crystals of DALI2 [51], a recoil-proton spectrometercomposted of a multi-wire drift chamber and a plasticscintillator array, and the recoil-neutron detector arrayWINDS [57]. The charged fragments and decay neutronswere detected by SAMURAI [52, 53] and NEBULA [54].The relative energy E rel of the unbound nucleus B wasreconstructed from the momenta of B and the decayneutron, with a resolution (FWHM) of ∼ √ E rel (inMeV). When B is in an excited state, the energy of B ( E d ) with respect to the B( g.s. ) + n threshold canbe obtained as the sum of E rel and the excitation energyof B. Population of excited B fragments was reportedin a prior breakup experiment of B [58]. Details of thesetup can be found in [32, 33, 38].
Quasi-free ( p, pn ) .— We first confirmed the quasi-free( p, pn ) process by checking the kinematical correlationbetween recoil protons and recoil neutrons [38, 59, 60].The correlation between the polar angles, θ p and θ n ,agrees nicely with the kinematical simulation (Fig. 1(a)).The kinematically complete measurement allows usto reconstruct the momentum of the recoil neutronfrom momentum conservation without detecting it, whichlargely enhances the statistics. The corresponding angu-lar correlation is presented in Fig. 1(b). The correlationlocus gets broadened relative to panel (a), but followswell the expected correlation pattern of quasi-free ( p, pn ). Gamma-coincidence.—
The Doppler-shift-corrected γ -ray spectrum in coincidence with B ( E rel ≤ γ rays, 1327 keV and1407 keV from B excited states [58, 61, 62], and a two-exponential background ( χ /ndf =1.4). For each γ ray,the response function was obtained from Geant4 simula-tions considering the realistic setup and the resolution ofeach crystal. The inset shows the γ -gated E rel spectrumafter correcting for the γ efficiency ( ∼ ∼ E rel spectrum (see below). B statesfrom γ -coincident analysis [63] are presented in Table I. E rel spectrum of B.—For B with N =12, theknocked-out neutron should mainly come from 1 s / and0 d / orbitals. The small contribution from p -wave or-bitals was confirmed by checking the angular correlation[28]. Ignoring higher-lying 0 d / is justified by the theo-retical calculations we employed (see below).We first checked the E rel spectrum gated by the mo-mentum ( P ) of the knocked-out neutron to disentanglestates populated by 1 s / and 0 d / knockout. The E rel spectra gated by 0 MeV/ c ≤ P ≤
60 MeV/ c (selectivefor 1 s / ) and 60 MeV/ c ≤ P ≤
160 MeV/ c (selective for0 d / ) are shown in Fig. 2(a), together with the inclusiveone for comparison. All the spectra are normalized ac-cording to the peak at ∼
0, since it is 3 − associated purelywith 0 d / (see below). Its d -wave character has also been ( c ) ( a ) ( b ) FIG. 1. Angular correlation between recoil protons and neu-trons for events with recoil neutrons detected by WINDS(a) and reconstructed from momentum conservation (b).The black line indicates the kinematical simulation assumingquasi-free ( p, pn ) off B. (c) Doppler-corrected γ -ray spec-trum, fitted using two γ rays (1327 keV and 1407 keV) and atwo-exponential background. The inset presents the γ -gated E rel spectrum, together with the inclusive one for comparison. established in [64]. To enhance the visibility, in Fig. 2(b)we presented the ratio of the P -gated spectrum to the in-clusive one. Obviously, the prominent peak at ∼ d / knockout. Meanwhile,the red histogram in Fig. 2(b) clearly shows two 1 s / -associated states, one at ∼ ∼ E rel spectrum was fitted using four reso-nances, after taking into account the experimental ac-ceptance and resolutions. The states at ∼ ∼ d -wave Breit-Wigner lineshapes and the other two with s -wave line shapes [65].Since the intrinsic width of the ∼ ∼
20 keV wasestimated. The results are presented in Fig. 2(c) and Ta-ble I. Errors of the resonance parameters include bothstatistical and systematic errors, the latter being dom-inated by the effect of the fitting range. The 0.046(3)-MeV state agrees with prior reports [49, 64, 66], but theresonant energy is refined; meanwhile, the inset of Fig.1(c) clearly shows that it is associated with B( g.s. ).The 2.38(8)-MeV state observed in the γ -coincident anal-ysis also agrees well with the reported state at 2.40(7)MeV [66]. Results and Discussions.—
In Fig. 3, we compare thelevel scheme of B to theoretical calculations: ( i ) Shellmodel (SM) calculation with YSOX interactions, consid- ( c ) FIG. 2. (a) B E rel spectra gated by 0 MeV/ c ≤ P ≤ c (red) and 60 MeV/ c ≤ P ≤
160 MeV/ c (blue) incomparison to the inclusive one (black). (b) Ratios of themomentum-gated spectrum to the inclusive one. The greydashed line, with a constant value of 1, stands for the scenariothat the entire spectrum is associated with knockout of 0 d / neutrons. (c) The fitting with a sum of four resonances. Theinset is a zoom-in view of the 0-1 MeV region. ering the reduction of sd -shell n - n interactions by a factorof 0.75 [67–71]. ( ii ) Valence-space in-medium similarityrenormalization group (VS-IMSRG) calculation [72] us-ing the optimized chiral effective field theory interactionat next-to-next-to-leading order [73] in Hartree-Fock ba-sis with 15 major harmonic-oscillator shells ( (cid:126) ω = 24MeV). ( iii ) Antisymmetrized molecular dynamics plusgenerator coordinate method (AMD) calculation usingthe Gogny D1S interaction [43, 74]. ( iv ) Gamow shellmodel (GSM) calculation with a He core [75–77]. Allpartial waves up to l = 3 were included for the valenceneutrons, while p / and p / basis states were includedfor the well-bound valence protons. For the two-bodyforce we adopted the Minnesota force [78], and the one-body force was modeled with a Woods-Saxon potentialwith the potential parameters adjusted to reproduce theseparation energies and low-lying states of B and B.Given that the spin-parity ( J π ) of B( g.s ) is 3 / − , J π of the two 1 s / -associated states (0.183 MeV, 2.8MeV) should be either 1 − or 2 − , while the other twonon-1 s / states should be more likely 3 − or 4 − . Ten-tative assignments of J π can thus be made, as shown inFig. 3. Though predicted as the ground state by SM,AMD, and VS-IMSRG, 0 − should be safely excluded forthe 0.046 MeV state, because of the small spectroscopicfactors ( < TABLE I. Summary of B states and experimental spectroscopic factors ( S exp ). The experimental ( σ exp ) and theoreticalsingle-particle cross sections ( σ th ) are the integrated value over the detector coverage. S exp is defined as S exp = σ exp /σ th . E x ( B) [MeV] E rel [MeV] Γ r [MeV] E d [MeV] a J π n orbital σ exp [mb] σ th [mb] S exp < − d / − d / s / − d / − / 2 − d / s / − ) 0 d / b (3 − / 4 − ) 0 d / < − / 4 − ) 0 d / s / spectroscopic factor percentage 9(2) % a E d = E rel + E x ( B). b Taken as the weighted average of the results of the two decay channels.
FIG. 3. Observed B states compared to Gamow shellmodel (GSM), valence-space in-medium similarity renormal-ization group (VS-IMSRG), antisymmetrized molecular dy-namics (AMD), and shell model (SM) calculations. The 1 n -separation energies are shown in the parentheses (in MeV). In order to analyze the momentum distribution of theknocked-out neutron and extract the 0 d / and 1 s / spectroscopic factors in B, we carried out the distorted-wave impulse approximation (DWIA) calculation [79].This model has recently been applied in several ( p, pn )and ( p, p ) experiments [32, 33, 80–86]. The single-particle wave function and the nuclear density were ob-tained using the Bohr-Mottelson potential [87]. The op-tical potentials for the distorted waves in the initial andfinal channels were constructed with the microscopic fold-ing 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 sepa-rately for all reaction channels listed in Table I, takinginto account E d of B.Figure 4 shows the transverse momentum ( P x ) distri-butions, together with DWIA calculated curves for 1 s / and 0 d / knockout after folding in the experimental res-olution (FWHM) of 45 MeV/ c . For the 0.046-MeV state(0 MeV ≤ E rel ≤ . ≤ E rel ≤ . d / component, in line with the above J π assignment of 3 − and 4 − .For the 0.183-MeV state (0.25 MeV ≤ E rel ≤ . ≤ E rel ≤ . χ fitting using acombination of 1 s / and 0 d / . A 1 s / fraction of14(4)% and 28(3)% was obtained, respectively. The er-rors include both the statistical and systematic errors,the latter being dominated by DWIA and the E rel gatefor the data. For the 2.8-MeV state, the same 1 s / frac-tion is obtained when gating on the left (29(2)%) or righthalf (28(2)%) of the E rel peak in the analysis, providingfurther evidence that it is a singlet rather than a doublet.For γ -coincident B states, the P x distributions are allin agreement with knockout of 0 d / neutrons from B[63]. This naturally leads to a J π of 3 − or 4 − , as shownin Fig. 3. The contribution of the B+2 n channel isvery small ( ∼ P x distribution is consistent with 0 d / knockout.We then deduced the exclusive cross sections ( σ exp ),as tabulated in Table I. For the 0.183-MeV and 2.8-MeV states, the 1 s / fraction determined above has beenused. The experimental spectroscopic factor ( S exp ) is ob-tained by dividing σ exp with the theoretical cross sectionfor a unit spectroscopic factor ( σ th ) from DWIA. Both σ exp and σ th are the integrated cross sections over the de-tector coverage (35 ◦ < θ p < ◦ ). We have incorporatedthe experimental conditions into DWIA to facilitate thedirect comparison of σ exp and σ th [63]. The errors quotedare the combined statistical and systematic errors. Forthe 0.046-MeV and 1.08-MeV states, the systematic errorof σ exp is dominated by the correction of detector efficien-cies (9%). For the 0.183-MeV and 2.8-MeV states, theuncertainty of the 1 s / fraction has also been consid-ered. For S exp , the uncertainty on σ th (within 10%) hasfurther been included, estimated by varying the potential - - - Y i e l d [ a . u .] (a) - - [MeV/c] x P - - Y i e l d [ a . u .] (c) - - - (b) - - [MeV/c] x P - - (d) neutron neutron Fitting
FIG. 4. Transverse momentum ( P x ) distributions for different B states. The vertical error bars stand for the statisticalerror, while the horizontal for the bin size. In (a) and (b),DWIA calculated curves for knockout of 1 s / (red-dashed)and 0 d / (black-dotted) neutrons are normalized to the peakof the experimental spectrum; in (c) and (d), the blue-solidcurves represent the fitting with a combination of 1 s / (red-dashed) and 0 d / (black-dotted). All DWIA curves havebeen convoluted with the experimental resolution. parameters and E d of B in the DWIA calculation.The total spectroscopic factors for 1 s / ( S s = 0.24(4))and 0 d / ( S d = 2.53(21)) are obtained by summing upthe S exp for 1 s / and 0 d / respectively in Table I, anda 1 s / spectroscopic factor percentage of 9(2)% is thusdeduced from the ratio of S s and S s + S d . As shown inFig. 3, some B states are not observed in the currentquasi-free ( p, pn ) experiment, indicating that these statesshould have very small spectroscopic factors in B; theireffect on S s and the 1 s / spectroscopic factor percentageis negligible compared to the errors quoted above. Notethat the 1.08-MeV state could be a doublet of two closelylocated states, given its relatively large width. But suchpossibility will not affect our conclusion—a small 1 s / component in B, since the P x distribution in Fig. 4(b)clearly shows it is populated (almost) purely by 0 d / knockout. Following the conventional picture for “2 n -halo nuclei” [6], one may expect a B+2 n structure for B [41, 42, 44, 45], and the 1 s / spectroscopic fac-tor percentage of 9(2)% thus leads to a percentage ofonly 9(2)% for the halo-relevant (1 s / ) configuration.As discussed by Estrad´e et al. [43], B may be bet-ter described in a B+4 n model, and our result wouldthen lead to a percentage of ∼
18% for the halo-relevant(1 s / ) (0 d / ) configuration, which is also small.However, prior experiments indeed consistently pointto the formation of halo in B [40–44], which seems tosuggest a predominant s orbital component ( ∼ n -halo nuclei”—an inert core plus two spatially decou-pled valence neutrons [6]. To understand this seemingdiscrepancy, we compared our result to theoretical pre- dictions obtained by summing up the 1 s / and 0 d / spectroscopic factors of states shown in Fig. 3. The1 s / 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 tothe one-body Hamiltonian of 1 s / . This may suggestsignificant impact of deformation or other many-body ef-fects, which can not be sufficiently considered within theshell-model framework. A small 1 s / percentage of 5%is provided by AMD, which is based on the nucleonicdegrees of freedom and also predicts a large prolate de-formation in B ( β = 0.4). But the 1 s / percentage issignificantly underestimated by AMD, mainly due to theuse of Gaussian wave functions [91].We then resort to the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) [19, 20, 92–95], which self-consistently considers weak binding, de-formation, and pairing-induced continuum coupling. Weused the effective interaction PK1 [96] and a density-dependent zero-range pairing force [20]. The neutron andmatter radius [43], deformation [62, 97], and S n [98] of B are well reproduced [63]. DRHBc provides a small1 s / orbital percentage of 14% for the valence neutrons,close to the experimental result of 9(2)%. Meanwhile, theneutron density distribution shows a slight but definitelow-density tail extending into large radial distances [63],indicating a weak halo component in B. Hence, the neu-tron halo exists in B as reported in prior experiments[40–44], but not as the dominant structure component.
Summary.—
We have measured the 0 d / and 1 s / spectroscopic factors in B using the quasi-free ( p, pn )reaction in inverse kinematics. A small spectroscopic fac-tor percentage of 9(2)% was determined for the 1 s / orbital. Our result thus reveals a surprisingly small s -orbital component in B whether it is described in a sim-ple B+2 n model or more properly in a B+4 n model.Our finding of such a small 1 s / component and the halofeatures in B reported in prior experiments [40–44] canbe well explained by DRHBc, revealing a definite but notdominant halo component in B. The present work givesthe smallest s - or p -orbital component among known nu-clei exhibiting halo features, and implies that the dom-inant occupation of s or p orbitals is not a prerequisitefor the occurrence of neutron halo. In weakly boundneutron-rich nuclei, as long as s or p orbitals around theFermi surface are occupied by the least bound neutronswith an appreciable strength, the halo naturally occursand coexists with other non-halo configurations [4, 6–9].The halo component, whether or not dominant, resultsin a distinctive diffused surface, and thus manifests itselfin reactions sensitive to the surface properties [6–9].We would like to thank the RIBF accelerator staff forthe primary beam delivery and the BigRIPS team fortheir 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 supportfrom the Foreign Postdoctoral Researcher program ofRIKEN. This work has been supported by the EuropeanResearch Council through the ERC Grant No. MINOS-25856; the JSPS KAKENHI Grants No. JP16K05352,No. JP18H05404, and No. JP16H02179; the NationalNatural Science Foundation of China under Grants No.11525524, No. 11835001, No. 11921006, No. 11975282,No. 11435014, No. 11775316, and No. 11961141004; theStrategic Priority Research Program of Chinese Academyof Sciences, Grant No. XDB34000000; the Institute forBasic Science (IBS-R031-D1). The computation of thiswork was partly supported by the HPC Cluster of ITP-CAS and the Supercomputing Center, CNIC of CAS. ∗ [email protected] † Present address: Institut f¨ur Kernphysik, TechnischeUniversit¨at Darmstadt, D-64289 Darmstadt, Germany ‡ Present address: LPC Caen, ENSICAEN, Universit´e deCaen Normandie, CNRS/IN2P3, F-14050 Caen Cedex,France § Present address: Department of Physics, University ofYork, Heslington, York YO10 5DD, United Kingdom[1] T. Otsuka, A. Gade, O. Sorlin, T. Suzuki, and Y. Utsuno,Rev. Mod. Phys. , 015002 (2020).[2] C. Forssen, G. Hagen, M. Hjorth-Jensen, W. Nazarewicz,and J. Rotureau, Phys. Scr. T152 , 014022 (2013).[3] I. Tanihata, H. Hamagaki, O. Hashimoto, Y. Shida, N.Yoshikawa, K. Sugimoto, O. Yamakawa, T. Kobayashi,and N. Takahashi, Phys. Rev. Lett. , 2676 (1985).[4] P. G. Hansen and B. Jonson, Europhys. Lett. , 409(1987).[5] P. G. Hansen and A. S. Jensen, Ann. Rev. Nucl. Part.Sci. , 591(1995).[6] A. S. Jensen, K. Riisager, D. V. Fedorov, and E. Garrido,Rev. Mod. Phys. , 215(2004).[7] T. Frederico, A. Delfino, L. Tomio, and M. T. Yamashita,Prog. Part. Nucl. Phys. , 939 (2012).[8] I. Tanihata, H. Savajols, and R. Kanungo, Prog. Part.Nucl. Phys. , 215 (2013).[9] K. Riisager, Phys. Scr. T152 , 014001 (2013).[10] J. Meng, H. Toki, S. G. Zhou, S. Q. Zhang, W. Long,and L. S. Geng, Prog. Part. Nucl. Phys. , 470 (2006).[11] P. W. Anderson, Science , 393 (1972).[12] G. Hagen, M. Hjorth-Jensen, G. R. Jansen, and T. Pa-penbrock, Phys. Scr. , 063006 (2016).[13] M. Freer, H. Horiuchi, Y. Kanada-En’yo, D. Lee, andUlf-G. Meißner, Rev. Mod. Phys. , 035004 (2018).[14] R. F. G. Ruiz and A. R. Vernon, Eur. Phys. J. A , 136(2020).[15] K. Tanaka, T. Yamaguchi, T. Suzuki, T. Ohtsubo, M.Fukuda, D. Nishimura, M. Takechi, K. Ogata, A. Ozawa,T. Izumikawa et al. , Phys. Rev. Lett. , 062701 (2010).[16] Y. Togano, T. Nakamura, Y. Kondo, J. A. Tostevin, A.T. Saito, J. Gibelin, N. A. Orr, N.L. Achouri, T. Au-mann, H. Baba et al. , Phys. Lett. B , 412 (2016).[17] S. Bagchi, R. Kanungo, Y. K. Tanaka, H. Geissel, P.Doornenbal, W. Horiuchi, G. Hagen, T. Suzuki, N. Tsun-oda, D. S. Ahn et al. , Phys. Rev. Lett. , 222504(2020). [18] K. J. Cook, T. Nakamura, Y. Kondo, K. Hagino, K.Ogata, A. T. Saito, N. L. Achouri, T. Aumann, H. Baba,F. Delaunay et al. , Phys. Rev. Lett. , 212503 (2020).[19] S.-G. Zhou, J. Meng, P. Ring, and E.-G. Zhao, Phys.Rev. C , 011301(R) (2010);[20] X.-X. Sun, J. Zhao, and S.-G. Zhou, Phys. Lett. B ,530 (2018).[21] J. C. Pei, Y. N. Zhang, and F. R. Xu, Phys. Rev. C ,051302(R)(2013).[22] H.-W. Hammer, and L. Platter, Annu. Rev. Nucl. Part.Sci. , 207(2010).[23] G. Hagen, P. Hagen, H.-W. Hammer, and L. Platter,Phys. Rev. Lett. , 132501 (2013).[24] T. Aumann, D. Aleksandrov, L. Axelsson, T. Baumann,M. J. G. Borge, L. V. Chulkov, J. Cub, W. Dostal, B.Eberlein, T.W. Elze, H. Emling et al. , Phys. Rev. C ,1252 (1999).[25] J. Wang, A. Galonsky, J. J. Kruse, E. Tryggestad, R.H. White-Stevens, P. D. Zecher, Y. Iwata, K. Ieki, A.Horv´ath, F. De´ak et al. , Phys. Rev. C , 034306 (2002).[26] K. Markenroth, M. Meister, B. Eberlein, D. Aleksandrov,T. Aumann, L. Axelsson, T. Baumann, M.J.G. Borge,L.V. Chulkov, W. Dostal et al. , Nucl. Phys. A , 462(2001).[27] M. Zinser, E Humbert, T. Nilsson, W. Schwab, H. Simon,T. Aumann, M.J.G. Borge, L.V. Chulkov, J. Cub, Th. W.Elze et al. , Nucl. Phys. A , 151 (1997).[28] H. Simon, D. Aleksandrov, T. Aumann, L. Axelsson, T.Baumann, M. J. G. Borge, L. V. Chulkov, R. Collatz, J.Cub, W. Dostal et al. , Phys. Rev. Lett. , 496 (1999).[29] T. Nakamura, A. M. Vinodkumar, T. Sugimoto, N. Aoi,H. Baba, D. Bazin, N. Fukuda, T. Gomi, H. Hasegawa,N. Imai et al. , Phys. Rev. Lett. , 252502 (2006).[30] I. Tanihata, M. Alcorta, D. Bandyopadhyay, R. Bieri, L.Buchmann, B. Davids, N. Galinski, D. Howell, W. Mills,S. Mythili et al. , Phys. Rev. Lett. , 192502 (2008).[31] A. Sanetullaev, et al. , Phys. Lett. B , 481 (2016).[32] Y. Kubota, PhD thesis, University of Tokyo, 2017.[33] Y. Kubota, A. Corsi, G. Authelet, H. Baba, C. Caesar,D. Calvet, A. Delbart, M. Dozono, J. Feng, F. Flavigny et al. , Phys. Rev. Lett. , 252501 (2020).[34] Y. Aksyutina, T. Aumann, K. Boretzky, M. J. G. Borge,C. Caesar, A. Chatillon, L. V. Chulkov, D. CortinaGil,U. D. Pramanik, H. Emling et al. , Phys. Lett. B ,1309 (2013).[35] M. Labiche, N. A. Orr, F. M. Marqu´es, J. C. Ang´elique,L. Axelsson, B. Benoit, U. C. Bergmann, M. J. G. Borge,W. N. Catford, S. P. G. Chappell et al. , Phys. Rev. Lett. , 600 (2001).[36] Y. Kondo, T. Nakamura, Y. Satou, T. Matsumoto, N.Aoi, N. Endo, N. Fukuda, T. Gomi, Y. Hashimoto, M.Ishihara et al. , Phys. Lett. B , 245 (2010).[37] Y. Aksyutina, T. Aumann, K. Boretzky, M. J. G. Borge,C. Caesar, A. Chatillon, L. V. Chulkov, D. Cortina-Gil,U. Datta Pramanik, H. Emling et al. , Phys. Rev. C ,064316 (2013).[38] A. Corsi, Y. Kubota, J.Casal, M. G´omez-Ramos, A.M. Moro, G. Authelet, H.Baba, C.Caesar, D.Calvet,A.Delbart et al. , Phys. Lett. B , 134843 (2019).[39] D. Hove,E. Garrido, P. Sarriguren, D. V. Fedorov, H. O.U. Fynbo, A. S. Jensen, and N. T. Zinner, Phys. Rev.Lett. , 052502 (2018).[40] A. Ozawa, T. Suzuki, I. Tanihata, Nucl. Phys. A , 32(2001). [41] T. Suzuki, T. Suzuki, R. Kanungo, O. Bochkarev, L.Chulkov, D. Cortina, M. Fukuda, H. Geissel, M. Hell-strom, M. Ivanov, R. Janik et al. , Nucl. Phys. A ,313 (1999).[42] T. Suzuki, Y. Ogawa, M. Chiba, M. Fukuda, N. Iwasa,T. Izumikawa, R. Kanungo, Y. Kawamura, A. Ozawa, T.Suda et al. , Phys. Rev. Lett. , 012501 (2002).[43] A. Estrad´e, R. Kanungo, W. Horiuchi, F. Ameil, J.Atkinson, Y. Ayyad, D. Cortina-Gil, I. Dillmann, A. Ev-dokimov, F. Farinon et al. , Phys. Rev. Lett. , 132501(2014).[44] Y. Yamaguchi, C. Wu,T. Suzuki, A. Ozawa, D. Q. Fang,M. Fukuda, N. Iwasa, T. Izumikawa, H. Jeppesen, R.Kanungo et al. , Phys. Rev. C , 054320 (2004).[45] H. T. Fortune and R. Sherr, Eur. Phys. J. A , 103(2012).[46] V. Guimar˜aes, J. J. Kolata, D. Bazin, B. Blank, B. A.Brown, T. Glasmacher, P. G. Hansen, R. W. Ibbotson,D. Karnes, V. Maddalena et al. , Phys. Rev. C , 064609(2000).[47] E. Sauvan, F. Carstoiu, N. A. Orr, J. S. Winfield, M.Freer, J. C. Ang´elique, W. N. Catford, N. M. Clarke, M.MacCormick, N. Curtis et al. , Phys. Rev. C , 044603(2004).[48] S. Bedoor, A. H. Wuosmaa, J. C. Lighthall, M. Alcorta,B. B. Back, P. F. Bertone, B. A. Brown, C. M. Deibel,C. R. Hoffman, S. T. Marley et al. , Phys. Rev. C ,011304(R) (2013).[49] A. Spyrou, T. Baumann, D. Bazin, G. Blanchon, A.Bonaccorso, E. Breitbach, J. Brown, G. Christian, A.Deline, P. A. DeYoung et al. , Phys. Lett. B , 129(2010).[50] A. Obertelli, A. Delbart, S. Anvar, L. Audirac, G. Au-thelet, H. Baba, B. Bruyneel, D. Calvet, F. Chˆateau, A.Corsi et al. Eur. Phys. J. A , 8 (2014).[51] S. Takeuchi, T. Motobayashi, Y. Togano, M. Matsushita,N. Aoi, K. Demichi, H. Hasegawa, and H. Murakami,Nucl. Instrum. Methods Phys. Res., Sect. A , 596(2014).[52] T. Kobayashi, N. Chiga, T. Isobe, Y. Kondo, T. Kubo,K. Kusaka, T. Motobayashi, T. Nakamura, J. Ohnishi, H.Okuno et al. , Nucl. Instrum. Methods Phys. Res., Sect.B , 294 (2013).[53] Y. Shimizu, H. Otsu, T. Kobayashi, T. Kubo, T. Moto-bayashi, H. Sato, and K. Yoneda, Nucl. Instrum. Meth-ods Phys. Res. Sect. B 317, 739 (2013).[54] Y. Kondo, T. Tomai, and T. Nakamura, Nucl. Instrum.Methods Phys. Res., Sect. B , 173 (2020).[55] T. Kubo, Nucl. Instrum. Methods Phys. Res., Sect. B , 97 (2003).[56] T. Kubo, D. Kameda, H. Suzuki, N. Fukuda, H. Takeda,Y. Yanagisawa, M. Ohtake, K. Kusaka, K. Yoshida, N.Inabe et al. , Prog. Theor. Exp. Phys. , 03C003(2012).[57] J. Yasuda, M. Sasano, R. G. T. Zegers, H. Baba, W.Chao, M. Dozono, N. Fukuda, N. Inabe, T. Isobe, G.Jhang et al. , Nucl. Instrum. Methods Phys. Res., Sect. B , 393 (2016).[58] R. Kanungo, Z. Elekes, H. Baba, Z. Dombr´adi, Z. F¨ul¨op,J. Gibelin, ´A. Horv´ath, Y. Ichikawa, E. Ideguchi, N.Iwasa et al. , Phys. Lett. B , 206 (2005).[59] L. Atar, S. Paschalis, C. Barbieri, C. A. Bertulani, P.D´ıaz Fern´andez, M. Holl, M. A. Najafi, V. Panin, H. Alvarez-Pol, T. Aumann et al. , Phys. Rev. Lett. ,052501 (2018).[60] V. Panin, J. T. Taylor, S. Paschalis, F. Wamers, Y.Aksyutina, H. Alvarez-Pol, T. Aumann, C. A. Bertulani,K. Boretzky, C.Caesar, et al. , Phys. Lett. B , 204(2016).[61] M. Stanoiu, M. Belleguic, Zs. Dombr´adi, D. Sohler, F.Azaiez1, B. A. Brown, M. J. Lopez-Jimenez, M. G. Saint-Laurent, O. Sorlin, Yu.-E. Penionzhkevich et al. , Eur.Phys. J. A , 5 (2004).[62] Y. Kondo, T. Nakamura, N. Aoi, H. Baba, D. Bazin, N.Fukuda, T. Gomi, H. Hasegawa, N. Imai, M. Ishihara etal. , Phys. Rev. C , 044611 (2005).[63] See the Supplemental Material for more details of the γ -coincident analysis, the distorted-wave impulse approxi-mation (DWIA) calculation, and the deformed relativis-tic Hartree-Bogoliubov theory in continuum (DRHBc)calculation.[64] J.-L. Lecouey, N. A. Orr, F. M. Marqu´es, N. L. Achouri,J. -C. Ang´elique, B. A. Brown, F. Carstoiu, W. N. Cat-ford, N. M. Clarkee, M. Freer et al. , Phys. Lett. B ,6 (2009).[65] A. M. Lane and R. G. Thomas, Rev. Mod. Phys. , 257(1958).[66] R. Kalpakchieva, H.G. Bohlen, W. von Oertzen, B.Gebauer, M. von Lucke-Petsch, T.N. Massey, A.N. Os-trowski, Th. Stolla, M. Wilpert, and Th. Wilpert, Eur.Phys. J. A , 451 (2000).[67] C. X. Yuan, T Suzuki, T. Otsuka, F. R. Xu, and N.Tsunoda, Phys. Rev. C , 064324 (2012).[68] C. X. Yuan, C. Qi, and F. R. Xu, Nucl. Phys. A , 25(2012).[69] M. Stanoiu, D. Sohler, O. Sorlin, F. Azaiez, Zs.Dombr´adi, B. A. Brown, M. Belleguic, C. Borcea, C.Bourgeois, Z. Dlouhy et al. , Phys. Rev. C , 034315(2008).[70] D. Sohler, M. Stanoiu, Zs. Dombr´adi, F. Azaiez, B.A. Brown, M. G. Saint-Laurent, O. Sorlin, Yu.-E. Pe-nionzhkevich, N. L. Achouri, J. C. Ang´elique et al. , Phys.Rev. C , 044303 (2008).[71] H. Ueno, K. Asahi, H. Izumi, K. Nagata, H. Ogawa, A.Yoshimi, H. Sato, M. Adachi, Y. Hori, and K. Mochinaga et al. , Phys. Rev. C , 2142 (1996).[72] S. R. Stroberg, A. Calci, H. Hergert, J. D. Holt, S.K.Bogner, R. Roth, and A. Schwenk, Phys. Rev. Lett. ,032502 (2017).[73] A. Ekstr¨om, G. Baardsen, C. Forss´en, G. Hagen,M. Hjorth-Jensen, G. R. Jansen, R. Machleidt, W.Nazarewicz, T. Papenbrock, J. Sarich, and S. M. Wild,Phys. Rev. Lett. , 192502 (2013).[74] M. Kimura, Phys. Rev. C , 044319 (2004).[75] N. Michel, W. Nazarewicz, M. Ploszajczak, and T.Vertse, J. Phys. G: Nucl. Part. Phys. , 013101 (2009).[76] N. Michel, W. Nazarewicz, M. Ploszajczak, and K. Ben-naceur, Phys. Rev. Lett. , 042502 (2002).[77] N. Michel, J. G. Li, F. R. Xu, and W. Zuo, Phys. Rev.C , 031301(R) (2020).[78] D. Thompson, M. Lemere, and Y. Tang, Nucl. Phys. A , 53 (1977).[79] T. Wakasa, K. Ogata, and T. Noro, Prog. Part. Nucl.Phys. , 32 (2017).[80] R. Taniuchi, C. Santamaria, P. Doornenbal, A. Obertelli,K. Yoneda, G. Authelet, H. Baba, D. Calvet, F. Chˆateau,A. Corsi et al. , Nature , 53 (2019). [81] S. D. Chen, J. Lee, P. Doornenbal, A. Obertelli, C. Bar-bieri, Y. Chazono, P. Navr´atil, K. Ogata, T. Otsuka, F.Raimondi et al. , Phys. Rev. Lett. , 142501 (2019).[82] M. L. Cort´es, W. Rodriguez, P. Doornenbal, A. Obertelli,J. D. Holt, S. M. Lenzi, J. Men’endez, F. Nowacki, K.Ogata, A. Poves et al. , Phys. Lett. B , 135071 (2019).[83] Z. Elekes, ´A. Kripk´o, D. Sohler, K. Sieja, K. Ogata, K.Yoshida, P. Doornenbal, A. Obertelli, G. Authelet, H.Baba et al. , Phys. Rev. C , 014312 (2019).[84] Y. L. Sun, A.Obertelli, P. Doornenbal, C. Barbieri, Y.Chazono, T. Duguet, H. N. Liu, P. Navr’atil, F. Nowacki,K. Ogata et al. , Phys. Lett. B , 135215 (2020).[85] T. Lokotko, S. Leblond, J. Lee, P. Doornenbal, A.Obertelli, A. Poves, F. Nowacki, K. Ogata, K. Yoshida,G. Authelet et al. , Phys. Rev. C , 034314 (2020).[86] T. L. Tang, T. Uesaka, S. Kawase, D. Beaumel, M. Do-zono, T. Fujii, N. Fukuda, T. Fukunaga, A. Galindo-Uribarri, S. H. Hwang et al. , Phys. Rev. Lett. ,212502 (2020).[87] A. Bohr and B. Mottelson, Nuclear Structure (Ben-jamin,New York, 1969), Vol. I.[88] M. Toyokawa, K. Minomo, and M. Yahiro, Phys. Rev. C , 054602 (2013). [89] K. Amos, P. Dortmans, H. von Geramb, S. Karataglidis,and J. Raynal, Adv. Nucl. Phys. , 275 (2000).[90] M. A. Franey and W. G. Love, Phys. Rev. C , 488(1985).[91] M. Kimura, T. Suhara, and Y. Kanada-En’yo, Eur. Phys.J. A , 373 (2016).[92] L. Li, J. Meng, P. Ring, E.-G. Zhao, and S.-G. Zhou,Chin. Phys. Lett. , 042101 (2012).[93] L. Li, J. Meng, P. Ring, E.-G. Zhao, and S.-G. Zhou,Phys. Rev. C , 024312 (2012).[94] J. Meng and S.-G. Zhou, J. Phys. G: Nucl. Part. Phys. , 093101 (2015).[95] X.-X. Sun, J. Zhao, and S.-G. Zhou, Nucl. Phys. A ,122011 (2020).[96] W. Long, J. Meng, N. Van Giai, and S.-G. Zhou, Phys.Rev. C , 034319 (2004).[97] Zs. Dombr´adi, Z. Elekes, R. Kanungo, H. Baba, Z. F¨ul¨op,J. Gibelin, ´A. Horv´ath, E. Ideguchi, Y. Ichikawa, N.Iwasa et al. , Phys. Lett. B , 81(2005).[98] M. Wang, G. Audi, F. G. Kondev, W.J. Huang, S. Naimiand X. Xu, Chin. Phys. C41