Successive variational approach with the tensor-optimized antisymmetrized molecular dynamics for the 5He nucleus

Takayuki Myo,Hisashi Horiuchi,Mengjiao Lyu,Hiroshi Toki

doi:10.1093/ptep/ptab002

Abstract

Abstract We study $^5$He variationally as the first $p$-shell nucleus in the tensor-optimized antisymmetrized molecular dynamics (TOAMD) using the bare nucleon–nucleon interaction without any renormalization. In TOAMD, the central and tensor correlation operators promote the AMD’s Gaussian wave function to a sophisticated many-body state including the short-range and tensor correlations with high-momentum nucleon pairs. We develop a successive approach by applying these operators successively with up to double correlation operators to get converging results. We obtain satisfactory results for $^5$He, not only for the ground state but also for the excited state, and discuss explicitly the correlated Hamiltonian components in each state. We also show the importance of the independent optimization of the correlation functions in the variation of the total energy beyond the condition assuming common correlation forms used in the Jastrow approach.

Highlights

The bare nucleon–nucleon (NN ) interaction has a strong short-range repulsion and a strong tensor force [1,2]
We have introduced the tensor-optimized antisymmetrized molecular dynamics (TOAMD) [5,6,7,8,9,10,11,12,13,14,15], which is an analytical variational approach directly treating the correlations induced by nuclear force
3.3. 5He with the generator coordinate method (GCM) We extend TOAMD by superposing the TOAMD basis states having different AMD wave functions according to Eq (13) and investigate this effect on 5He

Summary

Introduction

The bare nucleon–nucleon (NN ) interaction has a strong short-range repulsion and a strong tensor force [1,2]. We employ the AV6 potential [29,30,31] as vij consisting of central and tensor terms without LS and Coulomb terms We directly use this Hamiltonian in TOAMD without any renormalization, which enables us to investigate the explicit roles of the short-range and tensor correlations in nuclei on any observables such as the nucleon momentum distribution [15]. In TOAMD, we adopt all of the resulting many-body operators in the cluster expansion of the correlated operators and calculate their many-body matrix elements using the AMD wave function. This treatment is important to keep TOAMD as a variational framework. The amplitudes {Cα,k } are determined in the minimization of the total energy EGCM as an eigenvalue problem in the same form as Eq (12)

Results

Findings

Summary