四川大学学报（自然科学版）2025，Vol.62Issue(6)：1432-1438,7.DOI:10.19907/j.0490-6756.250062
谐振子势束缚下两中子体系的能级:质心-相对坐标表象与单粒子基表象的比较
Energy levels of a two-neutron system confined by a harmonic oscillator trap:Comparison between the center-of-mass and relative coordinate representation and the single-particle basis representation
摘要
Abstract
In physics research,choosing an appropriate reference frame can significantly simplify the prob-lem.The center-of-mass and relative coordinate representation excels in two-or three-body systems:It sepa-rates the overall motion of the center of mass from the internal relative motion,thereby reducing redundant degrees of freedom and enabling a clearer focus on interparticle interactions.However,as the number of par-ticles increases,each additional particle requires the introduction of a new Jacobi coordinate system,which fundamentally alters the computational framework and sharply increases the complexity of theoretical deriva-tions and numerical calculation.In contrast,the single-particle basis offers greater flexibility:When a new particle is added to the system,one only needs to add the corresponding single-particle degrees of freedom without reconstructing the entire reference system.In this work,a two-particle system confined in a harmonic oscillator potential was adopted.The bound-state energy levels of this two-body system were calculated un-der two frameworks:The center-of-mass and relative coordinate representation and the single-particle basis representation.By employing the Moshinsky Brackets,we have successfully established the connection be-tween these two representations.By comparing the energy levels obtained under both representations,the re-liability of the method and the accuracy of the numerical calculations were validated.The comparison demon-strates that,with an appropriately truncated basis set,the energy levels calculated in both representations are highly consistent,which confirms the correctness of the numerical implementation.Furthermore,the single-particle basis framework established here exhibits strong extensibility:It can be straightforwardly generalized to three-,four-or even higher-particle systems,thus providing a robust technical approach for studies in few-body nuclear-physics.关键词
谐振子势/Moshinsky括号/单粒子基Key words
Harmonic oscillator potential/Moshinsky brackets/Single-particle basis分类
数理科学引用本文复制引用
贾婷婷,龙炳蔚..谐振子势束缚下两中子体系的能级:质心-相对坐标表象与单粒子基表象的比较[J].四川大学学报（自然科学版）,2025,62(6):1432-1438,7.基金项目
国家自然科学基金面上项目(12275185,12335002) （12275185,12335002）
