Glauber-theory analysis of nuclear reactions on 12C target with variational Monte Carlo wave functions

TL;DR

The paper addresses accurately describing high-energy nucleus-nucleus scattering using Glauber theory with realistic, ab initio-like wave functions. It implements a full Monte Carlo evaluation of the A-body phase-shift operator using variational Monte Carlo (VMC) wave functions for $^{4}$He, $^{6}$He, and $^{12}$C, and applies it to $p+^{12}$C, $^{4}$He+$^{12}$C, $^{6}$He+$^{12}$C, and $^{12}$C+$^{12}$C across a broad energy range. The results show good agreement with elastic differential and total reaction cross sections within the eikonal/adiabatic regimes, with Coulomb breakup contributions generally small; the cumulant expansion up to second order provides a reliable approximation in most cases, highlighting the importance of one- and two-body densities. The work demonstrates the viability and precision of ab initio Glauber calculations for light, spatially extended systems and informs the use of common approximations in reaction studies, with implications for interpreting data on unstable and halo nuclei.

Abstract

The application of Glauber theory has been playing an increasingly important role with the study of unstable or exotic nuclei. Its adaptation to medium and high-energy nucleus-nucleus collisions is severely limited because one has to evaluate the matrix elements of multiple-scattering operators. The extraction of physical observables has been done using 'approximate' Glauber theory whose validity is hard to evaluate. We perform a full calculation of the matrix elements using Monte Carlo integration and analyze the elastic differential cross sections and the total reaction cross sections for p+12C, 4,6He+12C, and 12C+12C collisions. We use the variational Monte Carlo wave functions for 4,6He and 12C obtained by using realistic two- and three-nucleon potentials. We demonstrate the performance of the Glauber-theory calculations by comparing with available experimental data. We further discuss the accuracy of the conventional approximate methods in the light of the cumulant expansion for Glauber's phase-shift function.

Figures (21)

• Figure 1: Wave numbers of $^{12}$C$+^{12}$C, $^{6,4}$He+$^{12}$C and $p+^{12}$C scatterings as a function of the incident energy per nucleon.
• Figure 2: Coulomb potentials between $^{12}$C$+^{12}$C, $^{6,4}$He+$^{12}$C and $p+^{12}$C as a function of the separation distance. Thin dashed curves are the corresponding point-Coulomb potentials, and arrows indicate the cut-off impact parameters, $b_C$.
• Figure 3: Impact parameter dependence of (a) $1-e^{i\chi(b)}$ and (b) $1-|e^{i\chi(b)}|^2$ for $p+^{12}$C scatterings at $E$ = 200, 300, 550, and 800 MeV.
• Figure 4: Same as Fig. \ref{['psf-p-CBU.fig']} but for $^{12}$C$+^{12}$C scatterings at incident energies of 100, 200, 550, and 800 MeV/nucleon.
• Figure 5: $p+^{12}{\rm C}$ elastic differential cross sections at (a) 240, 300, 425, 500, 650, 700, 800, 1000 MeV and (b) 40, 60, 80, 100, 120, 140, 160, 180, 200 MeV as a function of the momentum transfers $q$. For ease of viewing a factor of 10$^2 (10^{-2})$ is multiplied by the cross section at (a) 650 MeV or at (b) 120 MeV with the increase (decrease) of the incident energy. The results with CBU and CTC are also shown. The data are taken from Refs. Ieiri87 (40, 60, and 83 MeV), Strauch56 (96 MeV) Meyer83 (122 and 160 MeV) Taylor61Steinberg65Emmerson66 (142--145 MeV), Johansson61 (183 MeV), Meyer81 (200 MeV), Meyer88 (250 MeV), Meyer85Okamoto10 (300 MeV), Hoffmann90 (500 MeV), Azhgirey63 (660 MeV), Blanpied81 (800 MeV), Palevsky67Alkhazov72 (1000 MeV). Note that the eikonal approximation is fulfilled at $E\gtrsim 200$ MeV. See text for details.