Finite particle-number description of symmetric nuclear matter with spin excitations of high-momentum pairs induced by the tensor force

We study symmetric nuclear matter using bare nucleon-nucleon ($NN$) interactions with the finite particle-number approach within finite cubic boxes. Due to the $NN$ correlations originating from the bare $NN$ interaction, two nucleons can be excited to the high-momentum region, leading to the increase of the kinetic energy in nuclear matter. We further consider the spin excitations in the nucleon pairs, where the spins of the two nucleons are changed, and this excitation is important for the tensor correlation. The unitary correlation operator method (UCOM) is used to treat the short-range correlation. The tail correction coming from the neighboring boxes is also included. We demonstrate the contributions of various excitations of nucleon pairs as well as the tail correction to the total energy at normal density. We also discuss the effects of UCOM and correlated nucleon pairs on the density dependence of the total energy. We calculate the equations of state of symmetric nuclear matter using two kinds of the Argonne potentials and the results agree with those from other many-body theories. The density dependences of the Hamiltonian components are also shown.

Figure 1

Sketch of momentum and spin/isospin exchange modes for 2p2h excitations.

Figure 2

Sketch of spin excitations for $pn$ pairs with opposite directions of spin.

Figure 3

Sketch of spin excitations for $pn$ pairs with parallel directions of spin.

Figure 4

Different excitation modes and channels for the two-particle state $(m,n)$ in 2p2h configurations.

Figure 5

Total number of 2p2h configurations, $N_{2\mathrm{p}2\mathrm{h}}$, varied with the maximum transfer mode $n_q^{\max }$ for symmetric nuclear matter with different excitation modes and involved boxes.

Figure 6

Convergence of the total energy per particle for symmetric nuclear matter with the maximum transfer mode $n_q^{\max }$ and the number of involved boxes $N_{\mathrm{b}}$ under ${\mathrm{AV6}}^{\prime }$ (left) and ${\mathrm{AV8}}^{\prime }$ (right) potentials.

Figure 7

Contributions of different excitation modes to the total energy per particle at the normal density $\rho =0.17{\mathrm{fm}}^{-3}$ in symmetric nuclear matter with ${\mathrm{AV6}}^{\prime }$ potential by taking the box numbers $N_{\mathrm{b}}=1$ (left) and $N_{\mathrm{b}}=8$ (right) as examples.

Figure 8

Contributions of different excitation modes to the total energy per particle at the normal density $\rho =0.17{\mathrm{fm}}^{-3}$ in symmetric nuclear matter with ${\mathrm{AV6}}^{\prime }$ potential by taking the box numbers $N_{\mathrm{b}}=1$ (left) and $N_{\mathrm{b}}=8$ (right) as examples.

Figure 9

Comparison of the density dependence of the total energy per particle in symmetric nuclear matter calculated with different wave functions under ${\mathrm{AV6}}^{\prime }$ (left) and ${\mathrm{AV8}}^{\prime }$ (right) potentials.

Figure 10

Equations of state of symmetric nuclear matter calculated under ${\mathrm{AV6}}^{\prime }$ (left) and ${\mathrm{AV8}}^{\prime }$ (right) potentials.

Figure 11

Energies of the Hamiltonian components for symmetric nuclear matter calculated under ${\mathrm{AV6}}^{\prime }$ (left) and ${\mathrm{AV8}}^{\prime }$ (right) potentials. $T$ is the total kinetic energy, $T_1$ is the summation of the one-body kinetic energy $t_i$, and $T_{\mathrm{UCOM}}=T-T_1$ is the two-body kinetic energy originating from the short-range correlation in UCOM. $V_{\mathrm{C}}$, $V_{\mathrm{TNS}}$, and $V_{\mathrm{LS}}$ are the central, tensor, and spin-orbit coupling parts of potential energy, respectively. The quantity $E_{\mathrm{b}}=E(N_{\mathrm{b}}=8)-E(N_{\mathrm{b}}=1)$ represents the contribution of the tail correction from the neighboring boxes.