Spectroscopic factors of resonance states with the Gamow shell model

We provide an investigation of the spectroscopic factor of resonance states in A=5-8 nuclei,utilizing the Gamow shell model(GSM).Within the GSM,the configuration mixing is taken into account exactly with the shell model framework,and the continuum coupling is addressed via the complex-energy Berggren ensemble,which treats bound,resonance,and non-resonant continuum single-particle states on an equal footing.As a result,both the configuration mixing and continuum coupling are meticulously considered in the GSM.We first calculate the low-lying states of helium isotopes and isotones with the GSM,and the results are compared with that of ab initio no-core shell model(NCSM)calculations.The results indicate that GSM can reproduce the low-lying resonance states more accurately than the NCSM.Following this,we delve into the spectroscopic factors of the resonance states as computed through both GSM and NCSM,concurrently conducting systematic calculations of overlap functions pertinent to these resonance states.Finally,the calculated overlap function and spectroscopic factor of6He(01+)■νp3/2→^(7)He(3/2_(1)-)with GSM are compared with the results from ab initio NCSM,variational Monte Carlo,and Green’s function Monte Carlo calculations,as well as available experimental data.The results assert that wave function asymptotes can only be reproduced in GSM,where resonance and continuum coupling are precisely addressed.

New determination of the^7Be ground state spectroscopic factor and the^6Li(p,γ)^7Be astrophysical S(E)factors

The ＇lithium problem, in Big Bang nucleosynthesis（BBN） has recently focused on reactions involving ^7 Be.The ^6 Li（p,γ）^7 Be reaction can provide us not only with information about ^6 Li destruction but also with information about ^7 Be production. In the present work, the proton spectroscopic factor in ^7 Be is extracted to be 0.70 ± 0.17 from the angular distribution of ^7 Be（d, ^3 He）^6 Li at Ec.m. = 6.7 MeV. This value is then used to compute the direct component of the astrophysical ^6 Li（p,γ）^7 Beg.s. S（E） factors and determine the resonance parameters from the total S（E） factors.

Isovector pairing and particle-number fluctuation effects on the spectroscopic factors of one-proton stripping and one-neutron pick-up reactions in proton-rich nuclei

Expressions of the spectroscopic factors（SFs） corresponding to one-particle transfer reactions have been established using a schematic definition.These expressions have been derived by taking into account the isovector neutron-proton（np） pairing correlations and a particle-number projection in the framework of the generalized SharpBCS（SBCS） method.Recently proposed expressions of the projected wave-functions of odd-mass nuclei have been used for this purpose.The formalism has first been tested using the single-particle energies of the schematic picketfence model.It is shown that the np pairing and particle-number fluctuation effects are far from negligible and they depend on the pairing gap parameter values.Their behavior is not the same when the parent nuclei are even-even or odd.Predictions dealing with the SFs corresponding to one-proton stripping and one-neutron pick-up reactions in proton-rich nuclei have then been established within the framework of the realistic Woods-Saxon model.It is shown that the np pairing effect as well as the particle-number projection effect are important and thus have to be included in future calculations of the SF corresponding to these kinds of reactions.

Influence of isovector pairing and particle-number projection effects on spectroscopic factors for one-pair like-particle transfer reactions in proton-rich even-even nuclei

Isovector neutron-proton（np） pairing and particle-number fluctuation effects on the spectroscopic factors（SF） corresponding to one-pair like-particle transfer reactions in proton-rich even-even nuclei are studied. With this aim, expressions of the SF corresponding to two-neutron stripping and two-proton pick-up reactions, which take into account the isovector np pairing effect, are established within the generalized BCS approach, using a schematic definition proposed by Chasman. Expressions of the same SF which strictly conserve the particle number are also established within the Sharp-BCS（SBCS） discrete projection method. In both cases, it is shown that these expressions generalize those obtained when only the pairing between like particles is considered. First, the formalism is tested within the Richardson schematic model. Second, it is applied to study even-even proton-rich nuclei using the single-particle energies of a Woods-Saxon mean-field. In both cases, it is shown that the np pairing effect and the particle-number projection effect on the SF values are important, particularly in N =Z nuclei, and must then be taken into account.

Application of a microscopic optical potential of chiral effective field theory in (p, d) transfer reactions

The microscopic global nucleon–nucleus optical model potential(OMP)proposed by Whitehead,Lim,and Holt,the WLH potential(Whitehead et al.,Phys Rev Lett 127:182502,2021),which was constructed in the framework of many-body per-turbation theory with state-of-the-art nuclear interactions from chiral effective field theory(EFT),was tested with(p,d)transfer reactions calculated using adiabatic wave approximation.The target nuclei included both stable and unstable nuclei,and the incident energies reached 200 MeV.The results were compared with experimental data and predictions using the phenomenological global optical potential of Koning and Delaroche,the KD02 potential.Overall,we found that the micro-scopic WLH potential described the(p,d)reaction angular distributions similarly to the phenomenological KD02 potential;however,the former was slightly better than the latter for radioactive targets.On average,the obtained spectroscopic factors(SFs)using both microscopic and phenomenological potentials were similar when the incident energies were below approxi-mately 120 MeV.However,their difference tended to increase at higher incident energies,which was particularly apparent for the doubly magic target nucleus 40Ca.

Determination of the Astrophysical S(E) Factors or Rates for Radiative Capture Reaction with One Nucleon Transfer Reaction

The radiative capture reaction plays an important role in nuclear astrophysics. We have indirectly measured the astrophysical S（E） factors for some proton capture reactions and reaction rates for several neutron capture reactions with one nucleon transfer reactions at HI-13 tandem accelerator in recent years. Some of them are compiled into IAEA EXFOR database and JINA REACLIB project, and used in the network calculations of Big Bang nucleosynthesis and type-I X-ray bursts.

Theoretical uncertainties of(d,^(3)He)and(^(3)He,d)reactions owing to the uncertainties of optical model potentials

The theoretical uncertainties of single proton transfer cross sections of the(^(3)He,d)and(d,^(3)He)reactions,owing to the uncertainties of the entrance-and exit-channel optical model potentials,are examined with the^(30)Si(^(3)He,d)^(31)P,^(13)B(d,^(3)He)^(12)Be,and^(34)S(^(3)He,d)^(35)Cl reactions at incident energies of 25,46,and 25 MeV,respectively,within the framework of the distorted wave Born approximation.The differential cross sections at the first peaks in the angular distributions of these reactions are found to have uncertainties of approximately 5%,owing to the uncertainties in the optical model potentials from 20,000 calculations of randomly sampled parameters.This amount of uncertainty is found to be nearly independent of the angular momentum transfer and the target masses within the studied range of incident energies.Uncertainties in the single proton spectroscopic factors obtained by matching the theoretical and experimental cross sections at different scattering angles are also discussed.

Determination of the Astrophysically Relevant ~6Li(n,γ)~7Li Cross Sections from the ~7Li(~6Li,~7Li)~6Li Elastic-Transfer Reaction

Angular distributions for the 7^Li（6^Li, 7^Li）6^Li elastic-transfer reaction have been measured with the Q3D magnetic spectrograph at the HI-13 tandem accelerator of Beijing, China. The neutron spectroscopic factors of 7^Li are derived by comparing the calculated differential cross sections, which are obtained through the distorted-wave Born approximation （DWBA） calculation, to the experimental data. And these spectroscopic factors are then used to deduce the direct capture cross sections in 6^Li（n, γ）TLi at energies of astrophysical relevance.

Computing Transfer Amplitude between BCS-Pair Condensates

I propose a new algorithm that uses recursive relations to compute spectroscopic factor, pair transfer amplitude and cluster transfer amplitude. I demonstrate the algorithm that it can be calculated very quickly and stored within small computer memory consumption. In BCS case, the particle number is always conserved and the time-consuming projection is avoided. I drive analytical expressions for the pair transfer amplitude and the cluster transfer amplitude expressed by asymmetry many-pair density matrix. This algorithm practically could be used in all of the nuclear double beta decay fields, the heavy cluster emission fields and the single-nucleon transfer of the odd-mass isotopes.

Theoretical study of spin-forbidden cooling transitions of indium hydride using ab initio methods

The feasibility of spin-forbidden cooling of the In H molecule is investigated based on ab initio quantum chemistry calculations. The potential energy curves for the X^1Σ0^＋^＋, a^3Π0-, a^3Π0^＋, a^3Π1, a-3Π2, A-1Π1, 1-3Σ^0^-＋, and 1-3Σ1-＋states of In H are obtained based on multi-reference configuration interaction plus the Davidson corrections method. The calculated spectroscopic constants are in good agreement with the available experimental data. In addition, the influences of the active space and spin–orbit coupling effects on the potential energy curves and spectroscopic constants are also studied. For Re of a^3Π0^-, a^3Π0^＋, a^3Π1, and a-3Π2 states, the error from large active space is small. The potential energy curve of the A-1Π1state is not smooth for small active space. The spin–orbit coupling effects have great influences on the potential well depth and equilibrium internuclear distance of the A-1Π state. The Franck–Condon factors and radiative lifetimes are obtained on the basis of the transition dipole moments of the a^3Π0^＋）→ X^1Σ0^＋^＋, a-3Π1 → X-1Σ0^＋-＋, and A-1Π1 → X-1Σ0^＋^＋ transitions. Our calculation indicates that the a^3Π1（ ν＇= 0） → X-1Σ0^＋^＋（ν = 0） transition provides a highly diagonally distributed Franck–Condon factor and a short radiative lifetime for the a3Π1 state, which can ensure rapid and efficient laser cooling of In H.The proposed laser drives a-3Π1 → X-1Σ0^＋^＋ transitions by using three wavelengths.

Cosmic implications of the 12C(n, γ)13C reaction: a nuclear astrophysical perspective

We conducted a comprehensive study of the neutron capture cross section of 12C within the relevant astrophysical energy range.Through rigorous R-matrix analysis,we determined the Maxwellian-averaged cross section to be 11.98±0.25μb at kT=30 keV.This result is approximately four times higher than the thermal neutron capture cross section estimated in earlier studies assuming the 1/v law.The implications of our findings extend to the region of inhomogeneous Big-Bang models in nuclear astrophysics,where understanding the behaviour of neutron capture cross sections plays a crucial role in elucidating the intricate processes that shaped the early universe.

Systematic investigation of nucleon optical model potentials in(p,d)transfer reactions

The consistent three-body model reaction methodology(TBMRM)proposed by J.Lee et al.[Phys.Rev.C 69,064313(2004);Phys.Rev.C 73,044608(2006);Phys.Rev.C 75,064320(2007)],which includes adopting the simple zero-range adiabatic wave approximation,constraining the single-particle potentials using modern Hartree-Fock calculations,and using global nucleon optical model potential(OMP)geometries,are widely applied in systematic studies of transfer reactions.In this study,we investigate the influence of different nucleon OMPs in extracting spectroscopic factors(SFs)from(p,d)reactions.Our study covers 32 sets of angular distribution data of(p,d)reactions on four targets and a large range of incident energies(20-200 MeV/nucleon).This study uses two semi-microscopic nucleon OMPs,i.e.,Jeukenne,Lejeune,and Mahaux(JLM)[Phys.Rev.C 16,80(1977);Phys.Rev.C 58,1118(1998)]and CTOM[Phys.Rev.C 94,034606(2016)],and a pure microscopic nucleon potential,i.e.,WLH[Phys.Rev.Lett.127,182502(2021)].The results are compared with those using the phenomenological global optical potential KD02[Nucl.Phys.A 713,231(2003)].We find that the incident energy dependence of spectroscopic factors extracted from(p,d)reactions is evidently suppressed when microscopic OMPs are employed for ^(12)C,^(28)Si,and 40Ca.In addition,spectroscopic factors extracted using the systematic microscopic optical potential CTOM based on the Dirac-Brueckner-Hartree-Fock theory are more in line with the results obtained from(e,e′p)measurements,except for 16O and ^(40)Ca at high energies(>100 MeV),necessitating an exact treatment of double-magic nuclei.The results obtained by using the pure microscopic optical potential,WLH,based on the EFT theory show the same trend as those of CTOM but are generally higher.The JLM potential,which relies on simplified nuclear matter calculations with old-fashioned bare interactions,produces results that are very similar to those of the phenomenological potential KD02.Our results indicate that modern microscopic OMPs are reliable tools for probing the nuclear structure using transfer reactions across a wide energy range.

What kind of optical model potentials should be used for deuteron stripping reactions?

This paper presents the results of a study that compares CTOM, a microscopic optical model potential(OMP), which is an optical model co-created by the China Nuclear Data Center & Tuebingen University, to CH89, which is a typical phenomenological OMP.The respective OMPs were tested by applying them to the modelling of nucleon elastic scattering and(d,p) transfer reactions involving14C,36S, and58Ni targets at both low and relatively high energies. The results demonstrated that although both potentials successfully accounted for the angular distributions of both the elastic scattering and transfer cross sections, the absolute values of the transfer cross sections calculated using CTOM were approximately 25% larger than those calculated using CH89. This increased transfer cross sections allowed CTOM to produce single particle strength reduction factors for the three reactions that were consistent with those extracted from(e,e′p) reactions as well as with more recent(p,2p) and(p,pn) reactions. Notch tests suggested that nucleon elastic scattering and transfer reactions are sensitive to different regions of the OMP;accordingly,phenomenological OMPs, which are constrained only by elastic scattering cross sections, may not be sufficient for nucleon transfer reactions. Therefore, we suggest that microscopic OMPs, which reflect more theoretical considerations, should be preferred over phenomenological ones in calculations of direct nuclear reactions.

Quenching of single-particle strengths of carbon isotopes 9-12,14-20C with knockout reactions for incident energies 43–2100 MeV/nucleon

To study the quenching of single-particle strengths of carbon isotopes,a systematic analysis is performed for ^(9-12,14-20) C,with single neutron knockout reactions on Be/C targets,within an energy range from approximately 43 to 2100 MeV/nucleon,using the Glauber model.Incident energies do not show any obvious effect on the resulting values across this wide energy range.The extracted quenching factors are found to be strongly dependent on the proton-neutron asymmetry,which is consistent with the recent analysis of knockout reactions but is inconsistent with the systematics of transfer and quasi-free knockout reactions.

Configuration of the valence neutrons of ^(17)B

The reaction cross section of 17B on 12C target at （43.7±2.4） MeV/u has been measured at the Radioactive Ion Beam Line in Lanzhou （RIBLL）. The root-mean-square matter radius （Rrms） was deduced to be （2.92±0.10） fro, while the Rrras of the core and the valence neutron distribution are 2.28 fm and 5.98 fm respectively. Assuming a ＂core plus 2n11 structure in 17B, the mixed configuration of （2s1/2） and （1d5/2） of the valence neutrons is studied and the s-wave spectroscopic factor is found to be （80±21）%.

Calculation of astrophysical reaction rate of ^(82)Ge(n,γ)^(83)Ge

The neutron capture reaction on a neutron-rich near closed-shell nucleus 82Ge may play an important role in the r-process following the fallout from nuclear statistical equilibrium in core-collapse supernovae. By carrying out a DWBA analysis for the experimental angular distribution of 82Ge(d, p)83Ge reaction we obtain the single particle spectroscopic factors, S2,5/2 and S0,1/2 for the ground and first excited states of 83Ge=82Gen, respectively. And then these spectroscopic factors are used to calculate the direct capture cross sections for the 82Ge(n, γ)83Ge reaction at energies of astrophysical interest. The optical potential for neutron scattering on unstable nucleus 82Ge is not known experimentally. We employed a real folding potential which was calculated by using the proper 82Ge density distribution and an effective nucleon-nucleon force DDM3Y. The neutron capture reactions on neutron-rich closed-shell nuclei are expected to be dominated by the direct capture to bound states. We will show that the direct capture rates on these nuclei are sensitive to the structure of the low-lying states.

A formula for half-life of proton radioactivity

We present a formula for proton radioactivity half-lives of spherical proton emitters with the inclusion of the spectroscopic factor. The coefficients in the formula are calibrated with the available experimental data. As an input to calculate the half-life, the spectroscopic factor that characterizes the important information on nuclear structure should be obtained with a nuclear many-body approach. This formula is found to work quite well, and in better agreement with experimental measurements than other theoretical models. Therefore, it can be used as a powerful tool in the investigation of proton emission, in particular for experimentalists.