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.

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.

Systematic study of global optical model potentials in(d,p)transfer reactions

In the T-matrix form of the transfer reaction,the optical model potentials(OMPs)are used to compute the scattering wave function and transition operator.For most cases,the elastic scattering cross sections,normally used to generate the OMPs,are not directly given in the same experiment.Then,the global OMPs,which fit the experimental data over a broad mass and energy range,are widely used in the theoretical calculations.Different sets of global OMPs with different parameter sets can reproduce the scattering cross section equally well within the uncertainty.Here,we apply different global OMPs to calculate the(differential)cross sections of(d,p)transfer reactions on the target nuclei^(12)C,^(48)Ca,^(124)Sn,and^(208)Pb at different energies.The results demonstrate that the effects of deuteron and nucleon global OMPs on transfer(differential)cross sections vary with energy and target mass.Furthermore,the influences of the spin-orbit coupling term of deuteron and nucleon global OMPs on the transfer cross sections are not negligible.

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.

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.

The Nucleon-Actinide Global Optical Model Potential Below 300 MeV

A set of new global phenomenological optical model potential parameters has been obtained in the mass range of target nuclei 220≤A≤260 with incident energies below 300 MeV, by simultaneously fitting the experimental data of 232Th and 23Su, and these potential parameters are analyzed and used to calculate the reaction cross sections, energy spectra and double differ- ential cross sections for p＋232Th reaction. Comparison of calculated results using these potential parameters with available experimental data shows that the present form of global optical model potential could reproduce experimental data for both the neutron and the proton.

Helium-3 global optical model potential with energies below 250 MeV

A new set of global phenomenological optical model potential parameters has been obtained for helium-3 projectile, by simultaneously fitting the experimental data of helium-3 total reaction cross sections and elastic scattering angular distributions in the mass range of target nuclei 20〈〈A〈209 at incident energies below 250 MeV. A comparison has been made between the extracted helium-3 global optical model potential parameters and the existing ones. The calculated results of total reaction cross sections and elastic scattering angular distributions are also agreement. compared with experimental data with their satisfactory

Test of the notch technique for determining the radial sensitivity of the optical model potential

Detailed investigations on the notch technique are performed on ideal data generated by the optical model potential parameters extracted from the 16O＋208spb system at the laboratory energy of 129.5 MeV, to study the sensitivities of this technique to the model parameters as well as the experimental data. It is found that for the perturbation parameters, a sufficiently large reduced fraction and an appropriate small perturbation width are necessary to determine the accurate radial sensitivity; while for the potential parameters, almost no dependence was observed. For the experimental measurements, the number of data points has little influence for heavy target systems, and the relative inner information of the nuclear potential can be derived when the measurement is extended to a lower cross section.

Global optical model potential describing 12C-nucleus elastic scattering

We construct a new global optical model potential to describe the elastic scattering of 12C.The experimental data of elastic-scattering angular distributions and total reaction cross sections for targets from 24Mg to 209Bi are considered below 200 MeV within the framework of the optical model.The results calculated using the derived global optical potential are then compared with the existing experimental data.The reliability of the global optical potential is further tested by predicting the elastic scattering data out of the mass and energy ranges,within which the global potential parameters are determined,and reasonable results are also obtained.

Total Cross Sections for Electron Scattering on Polyatomic Molecules （CH4, CO2,NO2, and N2O） at 10～3000 eV

A new modified formulation of the Additivity Rule (AR) was proposed to calculate the total electron scattering cross sections for CH4, CO2, NO2, and N2O, considering the overlapping between atoms in molecules and the not fully transparency of the molecules. The present calculation covers the range of impact energy from 10 to 3000 eV. The results are compared with experimental data and other theories where available. The atoms are presented by spherical complex optical potential, which is composed of static, exchange, polarization, and absorption terms.

Applicability of 9Be global optical potential to description of 8,10,11B elastic scattering

We achieved a set of 9Be global phenomenological optical model potentials by fitting a large experimental dataset of the elastic scattering observable for target mass numbers from 24 to 209.The obtained 9Be global optical model potential was applied to predict elastic-scattering angular distributions and total reaction cross-sections of 8,10,11B projectiles.The predictions are made by performing a detailed analysis comparing with the available experimental data.Furthermore,these elastic scattering observables are also predicted for some lighter targets outside of the given mass number range,and reasonable results are obtained.Possible physical explanations for the observed differences are also discussed.

Causality principle and nuclear dispersion anomaly in the elastic scattering for α+^(12)C system

The optical model analysis of the alpha particle elastic scattering on a carbon target was performed on the basis of the dispersion relation between the real and imaginary parts of the calculated volume integrals. A nuclear dispersion anomaly in an α＋12C system was observed and interpreted clearly.

New measurements and reanalysis of^14N elastic scattering on^10B target

The angular distributions of elastic scattering of^14N ions on^10B targets have been measured at incident beam energies of 21.0 and 24.5 MeV.Angular distributions at higher energies 38–94.0 MeV(previously measured)were also included in the analysis.All data were analyzed within the framework of the optical model and the distorted waves Born approximation method.The observed rise in cross sections at large angles was interpreted as a possible contribution of theα-cluster exchange mechanism.Spectroscopic amplitudes SA2 and SA4 for the configuration^14N→^10B+αwere extracted.Their average values are 0.58±0.10 and 0.81±0.12 for SA2 and SA4,respectively,suggesting that the exchange mechanism is a major component of the elastic scattering for this system.The energy dependence of the depths for the real and imaginary potentials was found.

Description of elastic scattering induced by the unstable nuclei^(9,10,11,13,14)C

The elastic-scattering angular distributions and total reaction cross sections of ^(9,10,11,13,14)C projectiles were predicted using the obtained ^(12)C and ^(9)Be global optical model potentials,respectively.The predictions were analyzed in detail by comparison with the available experimental data.The results indicate that the ^(12)C and ^(9)Be global optical model potentials provide a satisfactory description of the elastic scattering data for the reactions induced by the ^(9,10,11,13)C.For the neutron-rich carbon isotope ^(14)C,the elastic scattering can be well described by changing the real part radius parameter of the ^(12)C global optical model potential.Possible physical explanations for the observed differences are further discussed.