Successive variational method of the tensor-optimized antisymmetrized molecular dynamics for central interaction in finite nuclei

Tensor-optimized antisymmetrized molecular dynamics (TOAMD) is the basis of the successive variational method for the nuclear many-body problem. We apply TOAMD to finite nuclei described by the central interaction with strong short-range repulsion, and compare the results with those from the unitary correlation operator method (UCOM). In TOAMD, the pair-type correlation functions and their multiple products are operated to the antisymmetrized molecular dynamics (AMD) wave function. We show the results of TOAMD using the Malfliet-Tjon central potential containing the strong short-range repulsion. By adding the double products of the correlation functions in TOAMD, the binding energies are converged quickly to the exact values of the few-body calculations for $s$-shell nuclei. This indicates the high efficiency of TOAMD for treating the short-range repulsion in nuclei. We also employ the $s$-wave configurations of nuclei with the central part of UCOM, which reduces the short-range relative amplitudes of nucleon pair in nuclei to avoid the short-range repulsion. In UCOM, we further perform the superposition of the $s$-wave configurations with various size parameters, which provides a satisfactory solution of energies close to the exact and TOAMD values.

Figure 1

The functions $R_{+}\left(r\right)$ in ${}^3\mathrm{H}$ (solid) and ${}^4\mathrm{He}$ (dashed), respectively. The differences between $R_{+}\left(r\right)$ and the original distance $r$ are shown as the amount of shift of the wave function.

Figure 2

Energy surface of ${}^3\mathrm{H}$ as function of range parameter $\nu$ in TOAMD with single (dashed line) and double (solid line) correlation functions. Solid circles are the energy minimum points. Dotted line represents the exact energy in the few-body calculations [25].

Figure 3

Convergence of the energy of ${}^3\mathrm{H}$ with respect to the order of TOAMD. The range parameter $\nu$ is fixed as 0.11 ${\mathrm{fm}}^{-2}$, which is determined in the double TOAMD.

Figure 4

Energy surface of ${}^3\mathrm{H}$ as function of range parameter $\nu ={\left(2b^2\right)}^{-1}$ in UCOM (solid line) with the result of UCOM+GCM (short solid line).

Figure 5

Radius of ${}^3\mathrm{H}$ as function of range parameter $\nu$ in the double TOAMD (solid line) in comparison with UCOM (dashed line). Dotted line represents the value (1.67 fm) at the energy minimum in TOAMD.

Figure 6

Energy surface of ${}^4\mathrm{He}$ as function of range parameter $\nu$ in TOAMD with single (dashed line) and double (solid line) correlation functions. Solid circles are the energy minimum points. Dotted line represents the exact energy in the few-body calculations [25].

Figure 7

Convergence of the energy of ${}^4\mathrm{He}$ with respect to the order of TOAMD. The range parameter $\nu$ is fixed as 0.25 ${\mathrm{fm}}^{-2}$ which is determined in the double TOAMD.

Figure 8

Energy surface of ${}^4\mathrm{He}$ as function of range parameter $\nu ={\left(2b^2\right)}^{-1}$ in UCOM (solid line) and UCOM+GCM (short solid line).

Figure 9

Radius of ${}^4\mathrm{He}$ as function of range parameter $\nu$ in the double TOAMD (solid line) in comparison with UCOM (dashed line). Dotted line represents the value (1.40 fm) at the energy minimum state in TOAMD.