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Inelastic nucleon-nucleus scattering from a microscopic point of view

Matteo Vorabbi, Michael Gennari, Paolo Finelli, Carlotta Giusti, Petr Navrátil

Abstract

We apply to the nucleon-nucleus inelastic process a fully coherent microscopic multiple scattering approach. Our study addresses the complexities inherent in characterizing inelastic scattering events, offering a comprehensive theoretical model grounded in the reaction theory. The approach is based on the distorted-wave approximation and requires the knowledge of three potentials, which give the initial and final distorted wave functions and the transition potential. All of them are derived just like the microscopic optical potential for elastic nucleon-nucleus scattering we derived in previous papers of ours within the framework of the Watson multiple scattering theory and adopting the impulse approximation. The potentials are obtained by folding nonlocal ab initio nuclear densities from the No-Core Shell Model (NCSM) with a nucleon-nucleon $t$ matrix computed with a chiral interaction consistent with the one used in the calculation of the density. The only difference in the formal expressions of the three potentials resides in the nuclear density, where we use the ground and excited state densities of the target and the transition density. By extending methods traditionally applied to elastic scattering, we incorporate the effects of inelastic transitions enabling an accurate description of the experimental differential cross section. The predictive power of our numerical results is benchmarked against empirical data of inelastic proton scattering off $^{12}$C, for the transition to the $2^+$ state at 4.44 MeV, in a range of projectile energies of 65-300 MeV. The generally good description of the experimental cross sections as functions of the scattering angle gives clear evidence of the reliability and robustness of a model that does not contain any free adjustable parameters.

Inelastic nucleon-nucleus scattering from a microscopic point of view

Abstract

We apply to the nucleon-nucleus inelastic process a fully coherent microscopic multiple scattering approach. Our study addresses the complexities inherent in characterizing inelastic scattering events, offering a comprehensive theoretical model grounded in the reaction theory. The approach is based on the distorted-wave approximation and requires the knowledge of three potentials, which give the initial and final distorted wave functions and the transition potential. All of them are derived just like the microscopic optical potential for elastic nucleon-nucleus scattering we derived in previous papers of ours within the framework of the Watson multiple scattering theory and adopting the impulse approximation. The potentials are obtained by folding nonlocal ab initio nuclear densities from the No-Core Shell Model (NCSM) with a nucleon-nucleon matrix computed with a chiral interaction consistent with the one used in the calculation of the density. The only difference in the formal expressions of the three potentials resides in the nuclear density, where we use the ground and excited state densities of the target and the transition density. By extending methods traditionally applied to elastic scattering, we incorporate the effects of inelastic transitions enabling an accurate description of the experimental differential cross section. The predictive power of our numerical results is benchmarked against empirical data of inelastic proton scattering off C, for the transition to the state at 4.44 MeV, in a range of projectile energies of 65-300 MeV. The generally good description of the experimental cross sections as functions of the scattering angle gives clear evidence of the reliability and robustness of a model that does not contain any free adjustable parameters.

Paper Structure

This paper contains 10 sections, 67 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Distorted-wave formalism
  3. Algorithm
  4. Distorted wave impulse approximation
  5. Derivation of the potentials
  6. Nucleon-nucleon interaction
  7. Target description
  8. Results
  9. Conclusions
  10. Computational framework

Figures (2)

  • Figure 1: Differential cross sections as functions of the scattering angle for inelastic proton scattering off $^{12}$C leading to the $2^+$ state at 4.44 MeV for different projectile energies: 65, 120 ($\times 10^{-3}$), 135 MeV ($\times 10^{-6}$). The experimental data are taken from Refs. Pignanelli:1986zzPhysRevC.31.1616PhysRevC.24.1834BAUHOFF1983180. The red lines show the results of our microscopic model. The results of other available theoretical models are also shown for a comparison: DWBA calculations with the AMD+GCM densities PhysRevC.100.064616 (dashed blue line), $g$-folding model with NCSM densities Kim:2007cg (dashed yellow line), and phenomenological coupled-channel calculation with the $3\alpha$-RGM densities and $DD3MY$ interaction PhysRevC.92.024609 (dashed green line).
  • Figure 2: Same as in Fig. \ref{['fig1']} but for the projectile energies of 185, 200($\times 10^{-3}$), 250 ($\times 10^{-6}$), and 300 MeV ($\times 10^{-9}$). The experimental data are taken from Refs. Ingemarsson:1979ebPhysRevC.26.1800PhysRevC.37.544Okamoto:2010zzb.