Variation after projection calculations for high-spin states

TL;DR

This paper introduces a simplified variation after projection method for high-spin state calculations, reducing computational complexity while maintaining accuracy, and providing insights into nuclear state representations.

Contribution

It proposes a new simplified VAP scheme that uses only one projected state per spin, improving efficiency without sacrificing accuracy.

Findings

Simplified VAP still minimizes energy effectively.

Almost equivalent wave functions from different projected bases.

Challenges the traditional intrinsic state concept in nuclear models.

Abstract

In this paper, an improvement has been made on the variation after projection (VAP) method, which is crucial in the calculations of high-spin states. It turns out that, the form of the trial VAP wave function with spin $J$ can be simplified by adopting just one projected state rather than previously adopting all $(2J+1)$ angular momentum projected states for each selected reference state, $|\Phi\rangle$. The present calculations show that such simplification still minimizes the angular momentum projected energy up to a very good approximation. In this simplified VAP scheme, one can obtain almost equivalent VAP wave functions starting from different sets of the projected basis states. This clearly shows that a nuclear state can not be identified with a single intrinsic state, while in the traditional nuclear collective models, an intrinsic state is usually assigned to a well deformed rotational band.