arXiv subjects

Zhan-Jiang Lian

Publications and source records attributed to Zhan-Jiang Lian.

4 recordsLinked to original sources

arXiv2026

Decomposition of angular momentum projected nuclear wave function

Angular momentum projection is a basic technique in constructing nuclear wave functions with good spins. Traditionally, a projected nuclear wave function is expressed in terms of the bases built by performing the angular momentum projection directly on reference states for the whole nuclear system. Alternatively, one can construct nuclear wave function with another kind of projected bases, called as the coupled projected bases, which are generated by first performing the angular momentum projections on the reference states for neutrons and protons, respectively, then coupling the neutron projected states with the proton ones via Clebsch-Gordon coefficients. In the present work, we derive a new identity, which provides a decomposition of the conventional angular momentum projected nuclear wave function in terms of the coupled projected bases. This decomposition offers direct insight into the underlying structure of nuclear states. To show this point, we present the decompositions of variation after projection shell model (VAPSM) wave functions for the ground states in some $sd$ shell nuclei. It is interesting to see that even for the ground states in even-even nuclei, the nucleons are not fully paired. Finally, we demonstrate that the VAPSM wave function can be further improved by adopting the coupled projected bases.

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arXiv2024

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

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.

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arXiv2023

Finding the best basis states for the variation after projection nuclear wave functions

The variation after projection (VAP) method is expected to be an efficient way of getting the optimized nuclear wave functions, so that they can be as close as possible to the exact shell model ones. However, we found there are two additional problems that may seriously affect the convergence of the VAP iteration. The first problem is, if a randomly selected projected basis state does not mix with a VAP wave function in the VAP calculation, then it is likely that this basis state will never mix with the VAP wave function even after the VAP iteration converges, which means such selected projected basis state is useless. The other problem is the poor orthonormality among the projected basis states that seriously affect the accuracy of the calculated VAP wave function. In the present work, solutions for these two problems are proposed and some examples are presented to test the validity. It turns out that, with the present solutions, the most important projected basis states can be reliably obtained and the fully optimized VAP wave functions can be accurately and efficiently calculated.

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arXiv2023

Mixing of one-particle-one-hole projected states with the variation after projection wave functions

In this paper, we study the mixing of one-particle-one-hole projected states with the variation after projection (VAP) wave functions in attempt to improve the approximation of this method. It turns out that when minimizing only the lowest (yrast) energy with given spin and parity, the one-particle-one-hole projected states can not be mixed into the converged VAP wave function, which is very similar to the situation of the Hartree-Fock method. However, if one minimizes the sum of several lowest energies with the same spin and parity, the one-particle-one-hole mixing can make some improvements to the VAP wave functions. We expect such one-particle-one-hole mixing may be useful in the calculations of the low-lying excited states in heavy nuclei with a large model space.

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