多主壳投影后变分方法及其在psd壳的初步计算

Variation after projection with multi-shells and its preliminary calculation in the psd model space

在已有的投影后变分(Variation After Projection,VAP)方法的基础上,进一步考虑宇称投影,VAP计算可将模型空间扩展至多个主大壳.然而,在多主壳的壳模型计算中,质心问题需要额外处理.由于现实壳模型哈密顿量不具有平移不变性,多主壳模型空间的波函数会有质心部分的混杂,需要把质心部分从波函数中分离出来,以便得到纯净的内部波函数.这里,VAP计算也需要处理相同的质心问题.采用与标准壳模型完全一致的办法,实现了VAP波函数质心部分的有效分离.作为新方法的初步应用,我们在psd模型空间中计算了12C的正负宇称低激发态.结果表明,无论晕态还是非晕态,VAP方法仅采用几个HF真空态,就已能给出非常好的壳模型近似结果.至此,本文发展的VAP新方法,可以计算壳模型中所有类型的低激发态.

We improved our recently developed variation after projection(VAP)method by considering the parity projection.This makes it possible that the model space of VAP can be extended to multi-shells.However,in the shell model calculations within the multi-shell model space,the center of mass problem should be properly treated.Because the realistic shell model Hamiltonian does not have translational invariance,the wavefunction in the multi-shell model space may be mixed with the center of mass part.Thus,one should separate such center of mass part from the shell model wavefunction to obtain a pure internal part.Similarly,such center of mass problem exists in the VAP calculation.In this study,we used the same technique as that used in the shell model calculation and successfully separated the center of mass part from the VAP wavefunction.As a very preliminary application,we performed the VAP calculations in the psd model space.The low-lying states in 12C with both parities were calculated.Our results showed that,with only a few HF vacuum states,the VAP energies,including yrast and non-yrast ones,were very close to the shell model energies.Therefore,the present VAP is capable of calculating all types of low-lying nuclear states,as calculated by the standard shell model.