Multiple Mechanisms in Proton-Induced Nucleon Removal at ∼100 MeV/Nucleon

Multiple Mechanisms in Proton-Induced Nucleon Removal at ∼100 MeV=Nucleon T. Pohl,1Y. L. Sun ,1,2,3,* A. Obertelli,1,2 J. Lee,3M. Gómez-Ramos,4K. Ogata,5,6 K. Yoshida,7B. S. Cai,8C. X. Yuan,8 B. A. Brown,9H. Baba,10 D. Beaumel,11 A. Corsi,2J. Gao,10,12 J. Gibelin,13 A. Gillibert,2K. I. Hahn,14,15 T. Isobe,10 D. Kim,14,15 Y. Kondo,16 T. Kobayashi,17 Y. Kubota,10,18 P. Li,3P. Liang,3H. N. Liu,1,2,19 J. Liu,3T. Lokotko,3 F. M. Marqu´es,13 Y. Matsuda,20,21 T. Motobayashi,10 T. Nakamura,16 N. A. Orr,13 H. Otsu,10 V. Panin,10,2 S. Y. Park,14,10 S. Sakaguchi,5M. Sasano,10 H. Sato,10 H. Sakurai,10,22 Y. Shimizu,10 A. I. Stefanescu,23,24,10 L. Stuhl,10,15 D. Suzuki,10 Y. Togano,16,10,25 D. Tudor,23,24,10 T. Uesaka,10 H. Wang,10 X. Xu,3Z. H. Yang,10 K. Yoneda,10 and J. Zenihiro10 1Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany 2IRFU, CEA, Universit´e Paris-Saclay, F-91191 Gif-sur-Yvette, France 3Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong 4Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain 5Department of Physics, Kyushu University, Fukuoka 812-8581, Japan 6Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki 567-0047, Japan 7Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan 8Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai, 519082 Guangdong, People’s Republic of China 9Department of Physics and Astronomy and the Facility for Rare Isotope Beams, Michigan State University, East Lansing, Michigan 48824-1321, USA 10RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan 11Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France 12State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, People’s Republic of China 13LPC Caen, ENSICAEN, Universit´e de Caen, CNRS/IN2P3, F-14050 Caen, France 14Department of Physics, Ewha Womans University, Seoul, South Korea 15Center for Exotic Nuclear Studies, Institute for Basic Science, Daejeon 34126, South Korea 16Department of Physics, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro, Tokyo 152-8551, Japan 17Department of Physics, Tohoku University, Sendai 980-8578, Japan 18Center for Nuclear Study, University of Tokyo, RIKEN campus, Wako, Saitama 351-0198, Japan 19Key Laboratory of Beam Technology and Material Modification of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, People’s Republic of China 20Cyclotron and Radioisotope Center, Tohoku University, Sendai 980-8578, Japan 21Department of Physics, Konan University, Kobe 658-8501, Japan 22Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan 23Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering, IFIN-HH, 077125 Bucureşti-Măgurele, Romania 24Doctoral School of Physics, University of Bucharest, 077125 Bucureşti-Măgurele, Romania 25Department of Physics, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 172-8501, Japan (Received 8 January 2023; revised 17 March 2023; accepted 29 March 2023; published 27 April 2023) We report on the first proton-induced single proton- and neutron-removal reactions from the neutrondeficient 14O nucleus with large Fermi-surface asymmetry Sn−Sp¼18.6MeV at ∼100 MeV=nucleon, a widely used energy regime for rare-isotope studies. The measured inclusive cross sections and parallel momentum distributions of the 13N and 13O residues are compared to the state-of-the-art reaction models, with nuclear structure inputs from many-body shell-model calculations. Our results provide the first quantitative contributions of multiple reaction mechanisms including the quasifree knockout, inelastic scattering, and nucleon transfer processes. It is shown that the inelastic scattering and nucleon transfer, usually neglected at such energy regime, contribute about 50% and 30% to the loosely bound proton and deeply bound neutron removal, respectively. These multiple reaction mechanisms should be considered in analyses of inclusive one-nucleon removal cross sections measured at intermediate energies for quantitative investigation of single-particle strengths and correlations in atomic nuclei. DOI: 10.1103/PhysRevLett.130.172501 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. PHYSICAL REVIEW LETTERS 130, 172501 (2023) 0031-9007=23=130(17)=172501(8) 172501-1 Published by the American Physical Society The concept of independent particle motion has played a fundamental role for the study of quantum many-body systems, such as metallic clusters, atoms, and nuclei [1]. For the nuclear many-body systems, a first-order description was realized via the independent particle model [2–4], in which nucleons move freely in an effective mean-field potential provided by all the other nucleons. Nucleonnucleon correlations should be added for a realistic description of nuclear properties. It was first revealed by ðe; e0pÞexperiments on stable nuclei that the nuclear single-particle strengths, quantified by the so-called spectroscopic factors, are reduced by (30–40)% relative to the independent particle model predictions [5,6]. The “quenching”of the single-particle strengths has been attributed to long-range [7,8] and short-range [9–12] correlations, whose investigations have significantly improved our understanding of the strongly correlated nuclear many-body system and led to new insights for dense nuclear matter such as neutron stars [13,14].One main focus of today’s nuclear physics is to extend the correlation studies toward the proton and neutron driplines [15,16]. One-nucleon removal reactions at intermediate energies near and above 100 MeV=nucleon have been a powerful tool to extract single-particle strengths of unstable nuclei [17]. The quenching of the single-particle strengths has been connected to the so-called reduction factor Rs[18], defined as the ratio of the experimental to the theoretical cross section that is usually computed using shell-model spectroscopic factors and a reaction model relying on the adiabatic (or sudden) and eikonal approximations [17]. The central assumptions are that the residue and removednucleon relative motion is considered as frozen and the trajectories follow straight lines before and after the collision. Systematic studies from light-ion-induced onenucleon removal reactions at ∼100 MeV=nucleon [19–21] and higher incident beam energies [22] revealed that Rshas a strong dependence on the Fermi-surface asymmetry quantified as ΔS¼Sn−Spor Sp−Snfor neutron or proton removal, respectively. However, results from transfer reactions [23–29] and proton-induced quasifree knockout ðp; pNÞreactions [30–34] did not confirm the strong ΔSdependence. The inconsistent dependence on ΔScalls for a deeper understanding of reaction mechanisms and correlations in nuclei [16]. Although the diffraction and stripping mechanisms have been well-established in the eikonal model down to ∼100 MeV=nucleon [35,36], multiple scattering, excitation, and decay of the one-nucleon removal residue, beyond the eikonal reaction model [37,38] or Pauli blocking [39,40], have been proposed as possible mechanisms that could reduce the deeply bound nucleon-removal cross sections. In particular, asymmetric parallel momentum distributions (PMDs) of the residue, characterized by a low-momentum tail [41–48] and a high-momentum cutoff [45], have been observed in several experiments, in contrast to the symmetric PMDs predicted by the lowest order eikonal model [49–51]. Aforementioned studies [19–22] have been conducted with light absorptive nuclear targets, 9Be or 12C, which introduce the complexity that the final state of the target is unknown. Here, we report on the first study of one-nucleon removal from a large Fermi-surface asymmetric nucleus 14O(ΔS¼18.6MeV) at ∼100 MeV=nucleon using a single-nucleon target, i.e., protons. 14O is an ideal nucleus to study the one-nucleon removal mechanisms at large proton-to-neutron asymmetry. The proton and neutron removal from it involves only the orbitals of π0p1=2and ν0p3=2, respectively, since both 13N(Jπ g:s:¼1=2−) and 13O (Jπ g:s:¼3=2−) do not exhibit bound excited states. Based on the measured PMDs and the state-of-the-art reaction models, we show that in addition to the quasifree knockout, the inelastic scattering, and nucleon transfer also make significant contributions to the loosely bound proton removal and deeply bound neutron removal, respectively. The experiment was performed at the Radioactive Isotope Beam Factory operated by the RIKEN Nishina Center and the Center for Nuclear Study, The University of Tokyo. A primary 18O beam at 230 MeV=nucleon with an intensity of 500 pnA bombarded on a 14-mm thick 9Be target. The 14O secondary beam was purified and identified using the time of flight (TOF) and the energy loss (ΔE) information by the BigRIPS fragment separator [52]. The typical 14O beam intensity and purity were 9×103particles per second and 78%, respectively. The 14O beam was tracked onto a 2.40(34)-mm thick solid hydrogen target [53] using two multiwire drift chambers. The beam energy at the target center was 94 MeV=nucleon with a narrow spread of 0.2MeV=nucleon (σ). The target density was determined to be 86 mg=cm3based on the monitored target-cell temperature. The target thickness and its uncertainty were extracted by measuring the momentum change of the unreacted 14O beam with and without the hydrogen target. The empty-target setting was also used to measure the background generated by nontarget beamline materials, which were subtracted in the cross section and PMD analyses. The reaction residues were measured by the SAMURAI spectrometer [54], with a magnetic field set at 1.49 Tesla with filled target and 1.51 Tesla with empty target. Positions and angles of the particles were measured by two multiwire drift chambers located before and after the dipole magnet. A 10-mm thick plastic scintillator array hodoscope located downstream of the spectrometer was used to measure the ΔEand to determine the TOF together with a 0.2-mm thick plastic scintillator before the target. The magnetic rigidity Bρand the flight length from the target to hodoscope were deduced from multidimensionalfit functions using measured positions and angles as inputs. PHYSICAL REVIEW LETTERS 130, 172501 (2023) 172501-2 The functions, obtained through Geant4 [55] simulations and multidimensional fit package of ROOT [56], reproduce the simulated Bρand flight length with relative deviations below 0.02%. As shown in Fig. 1,13O and 13N can be unambiguously identified using the ΔE-Bρ-TOF and ΔE-velocity method. In Fig. 1(a), the deduced atomic number Zeff for 13O (A=Q ¼1.625) and 14O(A=Q ¼1.75) both show tails extending to smaller Zeff region. The Zeff tail of 14Ois caused by unreacted 14O projectiles interacting in the hodoscope, while the Zeff tail of 13O has a strong component steaming from the low-energy 13O stopped in the hodoscope. As demonstrated in Figs. 1(b) and 1(c), most 13O stopped in the hodoscope and had ΔEproportional to velocity, while most 13N punched through the hodoscope and had ΔEantiproportional to velocity. The resulting experimental cross sections are listed in Table I. Momentum acceptances, 94(1)% for 13O and 96(1)% for 13N, determined from Geant4 simulations and 7(1)% reaction loss in the beamline materials have been taken into account. In addition, a 5(1)% loss was considered to account for 13Oor13N events outside of the gates in Figs. 1(b) and 1(c), based on simulations with the Li`ege Intranuclear Cascade model [57], which is a wellestablished model for the description of spallation reactions. The cross section errors for 13O and 13N contain statistical uncertainties (0.6% and 1.3%), particle selections (0.9% and 2.3%), and systematic uncertainties (14.2% and 14.7%) mainly resulting from the target-thickness uncertainty. The experimental PMDs of 13O and 13N are shown in Fig. 2. An asymmetric PMD with a low-momentum tail and a high-momentum sharp edge is observed in the deeply bound neutron removal channel, while the PMD from the loosely bound proton removal is close to symmetric. The experimental cross sections and PMDs were compared to predictions combining structure and reaction inputs. Spectroscopic factors for the removed nucleons were obtained from shell-model calculations. See Supplemental Material (SM) [58] for details. For the ðp; pNÞknockout process, we adopted the DWIA (Distorted-Wave Impulse Approximation) [74–78] and the QTC (Quantum Transfer-to-the-Continuum) [32,79] 1.6 1.7 1.8 1.9 2 2.1 Q/A 4 5 6 7 8 9 Z eff 1 10 10 10 10 10 (a) CUT 1 CUT 2 100 105 110 115 120 125 130 [mm/ns]v 0 10 20 30 40 50 [arb. unit]E 1 10 10 (b) O 13 C 10 w/ CUT 1 100 105 110 115 120 125 130 [mm/ns]v 0 10 20 30 40 50 [arb. unit]E 1 10 10 (c) w/ CUT 2 O 15 N 13 C 11 FIG. 1. Particle identification of projectilelike residues. Particle’s velocity (ν) is deduced from TOF. Combining Bρand velocity allows to determine particle’s mass-to-charge ratio A=Q. Zeff is the deduced effective atomic number with ΔEand velocity using the Bethe-Bloch formula. The energy deposit of a charged particle in a material is related to its velocity, charge, and mass, as shown in the ΔE-νspectra with (w/) the A=Q selections from 1.59 to 1.66 (b) and from 1.81 to 1.93 (c). Black contours in (b) and (c) select 13O and 13N, respectively. TABLE I. Experimental (σexp) and theoretical (σth) cross sections for one-nucleon removal from 14Oat 94 MeV=nucleon. SF represents the spectroscopic factor from shell-model calculations (see SM [58]). The reduction factors Rs¼σexp=σth are also given. Residue Jπσexp (mb) SF Theory σsp (mb) σth (mb) Rs 13Ng:s:1=2−10.7(16) 1.58 DWIA 5.2 8.8 1.22(18) Inelastic …9 Sum 17.8 0.60(9) QTC 7.0 11.9 0.90(13) Inelastic …9 Sum 20.9 0.51(8) 13Og:s:3=2−16.7(24) 3.42 DWIA 6.3 23.2 0.72(10) Transfer 3 11 Sum 34.2 0.49(7) QTC 10.2 37.6 0.44(6) w=o transfer QTC 13.5 49.7 0.34(5) PHYSICAL REVIEW LETTERS 130, 172501 (2023) 172501-3 models (see SM [58]). Both models assume a single scattering between the removed nucleon and the target proton, using the transition amplitude to calculate the cross sections. The key disparity lies in how they handle the three-body final state: DWIA factorizes it as the product of the p-residue and N-residue states, while QTC expands it in terms of p-Nstates, including deuteron ground state for neutron removal [78]. The DWIA and QTC reaction models have been developed and benchmarked for ðp; pNÞ reactions at beam energies higher than 200 MeV=nucleon [32,78].Above200 MeV=nucleon, both models reproduce well the shape of the experimental momentum distributions [32,80–82], and the calculated single-particle cross sections (σsp) are consistent with each other within 20% [83]. The obtained σsp for 14Oðp; 2pÞ13N and 14Oðp; pnÞ13O reactions are listed in Table I. In addition, we also considered the ðp; p0Þinelastic excitation of 14O to its low-lying excited states located above Spand below ∼S2p, which decay to the ground state of 13N via one-proton emission. Giant-resonance excitations were not considered. A total inelastic cross section of 9 mb was obtained (see SM [58]). As shown in Figs. 2(a) and 2(b), the sum of the ðp; 2pÞand ðp; p0ÞPMDs is close to symmetric and reproduces well the PMD of 13N. The good agreement confirms the predicted strong inelasticscattering component in the loosely bound proton removal, which has fractional contributions of 51% with the DWIA and of 43% with the QTC. The inelastic-scattering component was also observed in the one-nucleon removal with a9Be target using the invariant-mass technique [48,59]. Percentage contributions of 17% and 21% from the inelastic scattering were extracted for the one-proton removal from 9C and 13Oat∼65 MeV/nucleon [48].If the inelastic-scattering component is ignored, the present one-proton removal Rswill be around unity, coinciding with the loosely bound nucleon-removal Rsfrom eikonal model based analysis [19–21,35]. Performing additional coincidence measurements with the recoil and decayed protons to obtain the angular distribution and the 14O excitation energy would further characterize the inelastic components. The low-lying excited states considered here have multiparticle-multihole configurations. It was shown recently that inelastic scattering with large momentum transfer has the advantage of populating multiparticlemultihole states [84]. Descriptions of such states are beyond the ðp; pNÞand the eikonal models, which assume beforehand that the projectile is a single-particle state plus an inert core [17]. For the deeply bound neutron removal, the ðp; dÞ transfer is considered in the QTC formalism but not in the DWIA. To study the ðp; dÞtransfer effect, we performed the QTC calculation with the outgoing channel coupled only to the deuteron ground state, that is equivalent to the so-called DWBA (Distorted-Wave Born Approximation) calculation. The obtained σsp for the transfer reaction is 3 mb with an uncertainty of about 1 mb (see SM [58]). The QTC σsp without the ðp; dÞ transfer is still larger than the DWIA result. Other effects, such as low-energy neutron-core absorption, contribute to this difference. As shown in Fig. 2(c), the PMD of 13O is well reproduced by combining the contributions from the DWIA and the DWBA, in which the latter corresponding to ðp; dÞtransfer contributes to ∼30%. Our data supports the interpretation of Ref. [76] that the low-momentum tail is caused by the attractive potential between the outgoing nucleons and 13O. Meanwhile, the ðp; dÞtransfer reaction creates a sharp high-momentum edge, as observed in the data, due to the two-body kinematics of the transfer reaction. The sharp edge is found in a kinematic region 0 20 40 60 DWIA Inelastic Sum O (-1p) 14 (a) O 14 Unreacted QTC Inelastic Sum (b) O (-1p) 14 5000 5200 5400 5600 5800 ]c [MeV/ ¨¨ P 0 20 40 60 DWIA Transfer Sum O (-1n) 14 (c) 5 000 5200 5400 5600 5800 ]c [MeV/ ¨¨ P QTC w/o Transfer Transfer O (-1n) 14 (d) )]cb / (MeV/P [ ¨¨ P/dVd)]cb / (MeV/P [ ¨¨ P/dVd FIG. 2. Parallel momentum distributions of 13N and 13O. The black-filled markers show the experimental data. The orange bands represent the uncertainties from the background subtractions. The gray empty bins indicate the other systematic uncertainties. Panels (a)–(c) compare the data to DWIA and QTC calculations (blue dotted lines), with additional contributions from inelastic excitation for 13N and ðp; dÞtransfer for 13O (red dashed lines). Panel (d) displays the QTC calculation as a black solid line, while the calculation without (w=o) ðp; dÞtransfer is represented by a blue dotted line. The blue solid line in (a) shows the distribution of the unreacted 14O beam (shifted by −200 MeV=c) to demonstrate the experimental response, which introduces a shift and broadening of the momentum due to energy losses and detector resolutions. Theoretical distributions have been convoluted with the experimental response and their integrals have been normalized to the experimental cross sections, without any momentum shift to match the data. Note that the sharp ðp; dÞtransfer peak is smoothed out by the experimental response. See SM [58] for theoretical distributions before experimental response convolution. PHYSICAL REVIEW LETTERS 130, 172501 (2023) 172501-4 inaccessible to ðp; pnÞknockout and is thus a proof of the significant transfer contribution. Note that the sharp edge here has a different origin with that observed in Ref. [45], which is due to a threshold effect when the incident energy per particle is comparable to the nucleon separation energy. Additional characterization of the transfer contribution would be to measure the angular distribution of cross sections in coincidence with the deuteron. See for example Ref. [85]. Since QTC formalism treats ðp; dÞtransfer consistently with ðp; pnÞ, it reproduces better the sharp high-momentum side than DWIA, as shown in Fig. 2(d). However, QTC does not reproduce the low-momentum tail as well as DWIA. The reason might be due to the different treatment of the final state interaction in QTC, especially that the nucleon-residue interaction at low relative energy is not explicitly treated in QTC formalism. It is the first time the PMD measured near 100 MeV=nucleon shows a distinctive contribution from the ðp; dÞtransfer reaction, usually neglected at such beam energies [16]. One-nucleon pickup cross sections have been measured around 60 MeV=nucleon with heavy-ion beams on 12Cor9Be target [86–89]. Here, the extracted oneneutron transfer cross section is higher due to the momentum matching of the well-bound neutron. The product of the momentum transfer qand the radius of 14O nucleus Ris around (1–2) ℏat forward angles, which fits the momentum matching condition [26,90]. Further calculations at 300 MeV=nucleon show the qR product increases to (3–5) ℏand the ðp; dÞtransfer cross section decreases to about 0.2 mb, negligible compared to the quasifree knockout cross sections [31,51]. The transfer contribution should thus be assessed for one-nucleon removal reactions at intermediate energies, especially at energies below 100 MeV=nucleon. We infer that the one-nucleon removal with a nuclear target may also contain non-negligible transfer contributions, where the removed nucleon combines with the target nucleus forming bound or resonance states, depending on the energy and angular momentum matching. Rsas a function of ΔSis shown in Fig. 3. Most light-ion- induced nucleon removal Rslie within a band with a slope of −1.6×10−2MeV−1and a half width of 0.1 [19–21],as shown by the shaded gray region. Contrastingly, analyses of low-energy one-nucleon transfer [25,27,28,91] and highenergy quasifree scattering data [30–32,34] give slope absolute values of ð10−3–10−5ÞMeV−1. By considering the two datasets of the present work, we obtain a slope of −3.0ð5Þð5Þ×10−3MeV−1when the DWIA together with the inelastic and transfer calculations are considered, and of −4.6ð4Þð7Þ×10−3MeV−1when the QTC and the inelastic scattering are considered. Both slopes are negative and their absolute values are almost zero, indicating Rshave a weak ΔSdependence. For comparison, we also extract the Rsif the inelastic scattering and nucleon transfer are neglected in cross-section calculations. The resulting Rsslopes in the absolute values are 3–5 times larger and look compatible with the strong ΔSdependence indicated by the light-ion- induced nucleon removal. In summary, we have reported on the first study of the one-nucleon removal reactions from a large Fermi-surface asymmetric nucleus 14O(ΔS¼18.6MeV) using a proton target at ∼100 MeV=nucleon, a widely used energy regime for rare-isotope studies. The measured cross sections and PMDs were compared to the state-of-the-art reaction models, including quasifree knockout, inelastic scattering, and nucleon transfer calculations. In the loosely bound proton removal channel, the ðp; p0Þinelastic scattering and the ðp; 2pÞquasifree knockout are found of almost equal contributions, advocating for an explicit treatment of the inelastic scattering for quantitative interpretation of loosely bound nucleon-removal cross sections. A highly asymmetric PMD was observed in the deeply bound neutron-removal channel, which was reproduced by combining the ðp; pnÞknockout component from DWIA calculations and the ðp; dÞtransfer component from DWBA calculations. We observed a distinctive contribution of ∼30% in the high-momentum part of the residue PMD from the deeply bound nucleon stripping ðp; dÞ transfer reaction, usually not considered at such beam energies. The reduction factors extracted from the present two new datasets show a weak ΔSdependence, which is at tension with the eikonal analysis of light-ion-induced knockout reactions. The extracted dependence becomes markedly steeper if the inelastic scattering and nucleon transfer contributions are ignored, suggesting that these processes should be considered in analyses of inclusive one-nucleon removal cross sections measured at intermediate energies for quantitative investigation of single-particle strengths and correlations in atomic nuclei. 20 10 01020 [MeV]S 0 0.2 0.4 0.6 0.8 1 1.2 1.4 th / exp = s R DWIA w/ Inelastic & Transfer QTC w/ Inelastic w/o Inelastic & Transfer FIG. 3. Rsas a function of ΔSfrom the present work (blue dots and black squares) compared to the trend extracted from Be or C induced nucleon-removal cross sections analyzed with the eikonal model [19–21] (gray shaded region). The square brackets indicate the total systematic uncertainties. Red solid and black dashed lines are shown to guide the eyes. PHYSICAL REVIEW LETTERS 130, 172501 (2023) 172501-5 We are grateful to the RIKEN Nishina Center accelerator staff for providing the stable and high-intensity 18O beam and to the BigRIPS team for the smooth operation of the secondary beam. This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)–Projektnummer 279384907–SFB 1245. Y. L. S. and A. O. acknowledge the support from the Alexander von Humboldt foundation. Y. L. S. acknowledges the support of Marie Skłodowska-Curie Individual Fellowship (H2020-MSCA-IF-2015-705023) from the European Union and the support from the Helmholtz International Center for FAIR. K. O. acknowledges the support by Grant-in-Aid for Scientific Research JP21H00125. M. G. R. acknowledges financial support by MCIN/AEI/10.13039/501100011033 under I þDþi project No. PID2020–114687 GB-I00, by the Consejería de Economía, Conocimiento, Empresas y Universidad, Junta de Andalucía (Spain) and “ERDF-A Way of Making Europe”under PAIDI 2020 project No. P20_01247, and by the European Social Fund and Junta de Andalucía (PAIDI 2020) under grant no. DOC-01006. C. X. Y. acknowledges Guangdong Major Project of Basic and Applied Basic Research (2021B0301030006). J. L. acknowledges the support from Research Grants Council (RGC) of Hong Kong (GRF-17303717). T. N. acknowledges the JSPS Kakenhi Grants No. JP16H02179, JP18H05404. Y. T. acknowledges the JSPS Grant-in-Aid for Scientific Research Grants No. JP21H01114. H. N. L. acknowledges the Fundamental Research Funds for the Central Universities of China. This work was supported by the Institute for Basic Science (IBS-R031-D1). B. A. B. was supported by NSF Grant No. PHY-2110365. Y. 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