Removal of $K$-mixing in angular momentum projected nuclear wave functions

Abstract

Angular momentum projection plays a key role in studying quantum many-body systems with rotational invariance such as atomic nuclei. At a given spin $J$, one can generate $2J+1$ angular momentum projected states labeled with $-J\leq K \leq J$ from a deformed Slater determinant. Usually, a nuclear wave function with $K$-mixing can be expressed as a superposition of all these $2J+1$ projected states, where the coefficients can be obtained by solving the generalized eigenvalue equation. In this Letter, we report a new fundamental feature that the frequently discussed $K$-mixing in the angular momentum projected nuclear wave function can be safely removed. Strikingly, we found that such nuclear wave function with $K$-mixing can always be equivalently replaced by a single projected state with any given $K$. Consequently, such nuclear wave function can be significantly simplified, especially for high-spin states. This also indicates that the $K$-mixing in the angular momentum projected nuclear wave functions, adopted by many present-day nuclear models, does not carry any physical meaning, and is essentially different from that $K$-mixing caused by the Coriolis force in the cranked shell model.