摘要: 对我们近几年发展的投影后变分（VAP）新方法做了比较全面的介绍。首先介绍了对JTA投影波函数的变分计算，指出自旋投影是获得很好壳模型近似的关键因素。基于这一结论，将VAP简化，并推广应用于所有晕态。即采用基于HF真空态的自旋投影波函数，通过变分，得到了与壳模型结果非常接近的VAP晕态能量及相应波函数。为进一步描述非晕态，依据柯西交错定理，可靠地对VAP低激发态能量之和进行最小化。如果这些能量值之和达到极小值，则与该极小对应的各态也就被确定下来。通过VAP计算，所得原子核非晕态能量与壳模型精确值非常接近。最近，在VAP计算中加入宇称投影，在psd模型空间中计算了¹²C的正负宇称晕态，同样得到了比较好的壳模型近似。值得指出的是，该方法具有普适性，可广泛应用于不同量子多体体系的低激发态研究中。


We present a comprehensive introduction in our newly developed Variation After Projection (VAP) calculations for the low-lying nuclear states. First, we discussed the VAP calculation with a fully JTA-projected wavefunction for the ground state in even-even nucleus. This leads to the conclusion that the spin projection plays a key role in obtaining a good shell model approximation. With this conclusion, we simplified the VAP with a time-odd Hartree-Fock mean field, on which only spin projection is required. Due to the time reversal symmetry breaking, this VAP now can be applied to the yrast states in all kinds of nuclei. It turns out that our VAP yrast energies as well as the corresponding VAP wavefunctions are very close the exact ones from the full shell model calculations. Such good approximation encourages us to extend the VAP calculations further to the non-yrast nuclear states. For this purpose, we proposed a new algorithm in our VAP based on the Cauchy's interlacing theorem. This theorem ensures that the sum of the calculated lowest projected energies with the same quantum numbers can be safely minimized. After minimization, all the calculated states can be determined simultaneously. Again, all the calculated VAP energies are very close to the exact shell model results. Recently, we have added the parity projection into the VAP, and the yrast states with both parity in ¹²C have been calculated in the psd model space. This time, we still have good shell model approximation for both parity states. Finally, we should point out that the present algorithm should be applicable to the low-lying states in different quantum many-body systems.