Effective contact pairing forces from realistic calculations in infinite homogeneous nuclear matter

Nonempirical effective contact pairing forces to be used in self-consistent mean-field calculations are presented. These pairing forces, constructed so as to reproduce exactly any given microscopic pairing gaps in infinite homogeneous nuclear matter for any isospin asymmetry, are given in analytical form. As a by-product, this work provides an analytical solution of the BCS gap equations which could be applied to describe various many-body systems.

Figure 1

Neutron pairing strength $v^{\pi n}[{\rho }_n,{\rho }_p]$, as defined by Eq. (3), vs nucleon number density $\rho$ in symmetric nuclear matter using the effective interaction underlying the nuclear mass model HFB-17 [12, 13]. The symbols are the results of numerically integrating Eq. (4). The dashed and solid lines were obtained using Eqs. (9) (12), respectively.

Figure 2

Same as Fig. 1 but for pure neutron matter.

Figure 3

Neutron pairing strength $v^{\pi n}[{\rho }_n,{\rho }_p]$, as defined by Eq. (3), vs nucleon number density $\rho$ in symmetric nuclear matter (SNM) and pure neutron matter (NeuM) using the effective interaction underlying the nuclear mass model HFB-17 [12, 13]. The symbols are the results of numerically integrating Eq. (4) and the solid line was obtained from Eq. (12).

Figure 4

Relative error between the neutron pairing strength $v^{\pi n}[{\rho }_n,{\rho }_p]$ calculated numerically and that obtained from the weak-coupling approximation vs nucleon number density $\rho$. The different curves correspond to different values of the pairing cutoff ${\varepsilon }_{\Lambda }$ indicated in the plot. Calculations were carried out in symmetric nuclear matter using the effective interaction underlying the nuclear mass model HFB-17 [12, 13].

Figure 5

Same as Fig. 4 but in neutron matter.