Variation after projection with multi-shells and its preliminary calculation in the <italic>psd</italic> model space
Abstract
<p indent="0mm">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 <italic>psd</italic> model space. The low-lying states in <sup>12</sup>C 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.</p>
