Contact representation of short-range correlation in light nuclei studied by the high-momentum antisymmetrized molecular dynamics

The high-momentum antisymmetrized molecular dynamics (HMAMD) is a promising framework with significant analytical simplicity and efficiency inherited from its antisymmetrized molecular dynamics describing the high-momentum correlations in various nuclear states. With the aim of further improving the numerical efficiency for the description of nucleon-nucleon correlation, we introduce a formulation by including a Gaussian weighted basis of high-momentum pairs in the HMAMD wave function, with which very rapid convergence is obtained in numerical calculation. It is surprising that the very high-momentum components in the HMAMD basis are found to be almost equivalent to the contact representation of the nucleon-nucleon pairs with very small nucleon-nucleon distance. The explicit formulation for the contact term significantly improves the numerical efficiency of the HMAMD method, which shows the importance of the contact correlation in the formulation of light nuclei.

Figure 1

Energy curves for ${}^3\mathrm{H}$ of the AMD+discrete (red line) and AMD+discrete+Gaussian (blue line) calculations with respect to the successive addition of discrete HMAMD bases with the imaginary shift $D_z$. The dotted part of red line are the energies in AMD+discrete with $D_z>6$, which are not necessary in the AMD+discrete+Gaussian calculation. The first points of red and blue curves with $D_z=0$ correspond to the AMD and AMD+Gaussian results, respectively.

Figure 2

The total energy $E$ and the Hamiltonian components of ${}^3\mathrm{H}$ by adding Gaussian form basis (+Gau) and the discrete HMAMD basis (+Dis) successively to the AMD basis. The symbols $K$ and $V$ indicate the kinetic and central interaction energies, respectively. Dashed lines represent the corresponding results of AMD+discrete calculation in Ref. [15].

Figure 3

The figure with different values of parameter $\nu$ and the values of $\nu \times \beta$. The corresponding values for parameter $\beta$ are variationally optimized and presented as the blue dots. The red dotted line denotes the 0.5 value.