In-medium nucleon-nucleon cross sections with nonspherical Pauli blocking

We present a formalism to solve the Bethe-Goldstone scattering equation without the use of partial wave expansion which is alternative to the one we developed in a previous work. The present approach is more suitable for the calculation of in-medium nucleon-nucleon cross sections, which are the focal point of this paper. The impact of removing the spherical approximation on the angle and energy dependence of, particularly, in-medium proton-proton and proton-neutron differential cross sections is discussed along with its potential implication.

Figure 1

[(a) and (b)] $np$ elastic differential crosssection and [(c) and (d)] depolarization at a laboratory free-space energy of 50 MeV vs the c.m. scattering angle. The solid red curve shows the free-space prediction. The angle-averaged calculation is given by the dotted green curve whereas the dashed blue curve shows the prediction obtained with the exact Pauli operator in symmetric [left side, (a) and (c)] and asymmetric [right side, (b) and (d)] matter at a density equal to $k_{F_1}=k_{F_2}=1.4{\mathrm{fm}}^{-1}$ and $k_{F_1}=1.1{\mathrm{fm}}^{-1},k_{F_2}=1.4{\mathrm{fm}}^{-1}$ respectively.

Figure 2

Same as Fig. 1 but at 100 MeV.

Figure 3

Same as Fig. 1 but at 200 MeV.

Figure 4

Same as Fig. 1 but for $pp$ scattering.

Figure 5

Same as Fig. 4 but at 100 MeV.

Figure 6

Same as Fig. 4 but at 200 MeV.