四川大学学报（自然科学版）2026，Vol.63Issue(1)：121-126,6.DOI:10.19907/j.0490-6756.250072
基于微扰手征核力的质子-中子散射计算研究
n-p scattering calculation with perturbative chiral nuclear forces
摘要
Abstract
This study presents a systematic investigation of proton-neutron scattering observables using the perturbative chiral nuclear forces constructed based on the Minimal Modified Weinberg(MMW)power counting within the framework of chiral effective field theory(χEFT).The research focuses on calculating differential cross sections and spin-dependent observables through a comprehensive order-by-order analysis spanning from leading order(LO)to next-to-next-to-leading order(N2LO),providing crucial insights into the convergence pattern of the chiral expansion for nucleon-nucleon interactions.The theoretical framework encompasses both the pion exchange potential,which dominates the long-range interactions,and the short-range contact term,which becomes increasingly important at smaller nucleon spacings.A particularly impor-tant aspect of our research approach is the careful determination of the low-energy constants(LECs)associ-ated with the short-range nuclear force components.By simultaneously fitting the neutron-proton(n-p)scat-tering phase shifts of multiple partial waves and the binding energy of the deuteron,these low-energy con-stants are tightly constrained,ensuring consistency with established experimental data.In order to solve the UV divergence problem in the solution of the Lippmann-Schwinger equations,we introduce a Gaussian mod-erator function with a momentum truncation that varies between 600 and 2400 MeV.This extensive study of the variation of the truncation provides a reliable verification of renormalization group(RG)invariance,which is the key to reliable theoretical predictions.Our computational approach employs an innovative hybrid method that combines a partially nonperturbative solution for the major low partial waves(in particular,the 1 S0,3S1-3D1,and 3P0 channels)with a fully perturbative treatment of the higher partial waves(P-and D-waves).The N2LO results show significant improvements compared to lower order calculations,especially in characterizing the angular dependence of spin-independent and spin-dependent observables.In terms of dif-ferential cross sections,we observe systematic convergence with increasing chiral order,and the N2LO pre-dictions show excellent agreement with available experimental measurements.The spin-dependent observ-able poses a particular challenge to the theoretical description,where the LO results give a trend opposite to the experimental results,but it shows a clear improvement at N²LO with the introduction of perturbative cor-rections,giving a trend consistent with the experimental results.A key finding of this work is that the sensitiv-ity to changes in the momentum cutoff decreases as the order of the calculation increases.The extremely high cutoff independence shown in the N2LO calculations for Λ=600～2400 MeV validates the RG invariance of our nuclear force.This property is particularly important for subsequent applications in nuclear many-body calculations,where the use of smaller cutoffs can significantly reduce computational requirements without sac-rificing physical accuracy.The successful implementation of the MMW power counting scheme in this work provides important guidance for the future development of chiral nuclear forces.Our results provide a solid foundation for extending these interactions to higher orders(e.g.,N3LO)and applying them to nuclear struc-ture calculations in light and intermediate mass nuclei.The systematic order-by-order improvement observed in the two-nucleus regime suggests that there are promising prospects for achieving similar accuracies in more complex nuclear systems.关键词
手征有效场论/手征核力/质子-中子散射/自旋相关可观测量Key words
chiral effective field theory/chiral nuclear forces/n-p scattering/spin-dependent observables分类
数理科学引用本文复制引用
次仁曲措,李巧,彭锐,龙炳蔚..基于微扰手征核力的质子-中子散射计算研究[J].四川大学学报（自然科学版）,2026,63(1):121-126,6.基金项目
国家自然科学基金面上项目(12275185) （12275185）
国家自然科学基金专项项目(12347154) （12347154）
