Neutron skins probed in proton knockout from neutron-rich nuclei

Abstract

Proton-induced quasifree knockout reactions provide a powerful probe of nuclear single-particle structure and reaction dynamics in both stable and neutron-rich nuclei. In this work we develop a unified theoretical framework for the calculation of inclusive (p,2p) and sequential (p,3p) reaction cross sections and fragment momentum distributions at intermediate and relativistic energies. The approach is based on a probabilistic extension of Glauber multiple-scattering theory combined with microscopic nuclear densities obtained from Hartree-Fock-Bogoliubov calculations using Skyrme energy-density functionals. We focus in particular on the sensitivity of total cross sections and longitudinal momentum dispersions to neutron-skin thickness along isotopic chains. Our results indicate that both (p,2p) and (p,3p) reactions exhibit a systematic decrease of cross section and momentum width with increasing neutron excess, reflecting enhanced attenuation and surface bias induced by neutron skins. The effect is significantly stronger for two-proton removal, suggesting that (p,3p) reactions may offer enhanced sensitivity to isovector nuclear structure. These findings establish proton-induced knockout reactions as complementary hadronic probes of neutron skins and the density dependence of the nuclear symmetry energy.

Figures (5)

• Figure 1: Schematic representation of a (p,3p) collision geometry considered in this work. The impact parameter ${\bf b}_1$, and ${\bf b}_1'$, correspond to the vector distance between the nuclear center and the velocity vector for the leading proton, and the proton knocked out from the nucleus, after the first collisions. A similar notation, with ${\bf b}_2$ and ${\bf b}_2'$, is used for the second collision.
• Figure 2: Experimental cross sections (filled symbols) PhysRevLett.125.012501 compared to our theoretical calculations (open diamonds) for (p,2p) and (p,3p) reactions as a function of the nuclear mass. The dashed lines are guides to the eye.
• Figure 3: Neutron skin $\Delta R_{np}$ for Sn isotopes calculated with HFB using 22 Skyrme interactions listed in the text. Each one of the lines corresponds to one of the interactions and they are guides to the eye.
• Figure 4: Calculated total cross sections for proton-induced one- and two-proton knockout reactions along the tin isotopic chain, shown as functions of neutron number $N$. The tin projectiles are assumed to have incident energy of 250 MeV/nucleon. The upper panel corresponds to the Sn(p,2p) reaction, while the lower panel shows results for the Sn(p,3p) reaction. In both cases, the calculations are performed using HFB ground-state densities obtained with 22 different Skyrme energy-density functionals.
• Figure 5: Longitudinal momentum dispersion $\Delta_{\|}$ of primary projectile-like fragments produced in (p,2p) (blue circles) and (p,3p) (orange squares) reactions on Sn isotopes at 250 MeV, calculated with the vectorized Monte Carlo abrasion model. The dashed horizontal lines show the corresponding Goldhaber model predictions with a fixed width parameter $p_0 = 90$ MeV/$c$. The Monte Carlo results exhibit a clear mass dependence, reflecting surface-dependence of proton removal and the reduction of the local Fermi momentum in neutron-rich nuclei, an effect absent in the Goldhaber approach.