Power series expansion method in tensor-optimized antisymmetrized molecular dynamics beyond the Jastrow correlation method

We developed a new variational method for tensor-optimized antisymmetrized molecular dynamics (TOAMD) for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion are introduced and used in the power series form of the wave function, which is different from the Jastrow method. Here, nucleon pairs are correlated in multisteps with different forms, while they are correlated only once including all pairs in the Jastrow correlation method. Each correlation function in every term is independently optimized in the variation of total energy in TOAMD. For $s$-shell nuclei using the nucleon-nucleon interaction, the energies in TOAMD are better than those in the variational Monte Carlo method with the Jastrow correlation function. This means that the power series expansion using the correlation functions in TOAMD describes the nuclei better than the Jastrow correlation method.

Figure 1

Energy convergence of ${}^3\mathrm{H}$ using AV6 by adding each term of TOAMD successively with solid circles. Open circles denoted as “Fixed $F$” indicate the results obtained using the fixed correlation functions in TOAMD. Dashed line and short solid line represent the results of VMC and few-body (FB) calculations, respectively.

Figure 2

Hamiltonian components of ${}^3\mathrm{H}$ using AV6 in TOAMD with solid circles. The symbols K/2, C, and T indicate a half value of the kinetic energy, the central and tensor forces, respectively. Open circles indicate the results using the fixed correlation functions (Fixed $F$) in TOAMD. Dashed line and short solid line represent the half value of the kinetic energies in the calculations of VMC and few-body (FB) methods, respectively.

Figure 3

Energy convergence of ${}^4\mathrm{He}$ using AV6. Notations are the same as used in Fig. 1.

Figure 4

Hamiltonian components of ${}^4\mathrm{He}$ using AV6. Notations are the same as used in Fig. 2.