Impact-Parameter Description of High-Energy Deuteron-Nucleus Collisions

TL;DR

This paper presents a theoretical impact-parameter framework for analyzing high-energy deuteron-nucleus collisions, deriving cross sections for various scattering and dissociation processes using diffraction approximation.

Contribution

It introduces new expressions for cross sections of deuteron breakup, absorption, and dissociation processes, employing a reduced two-particle density matrix and classical semi-quantitative insights.

Findings

Derived explicit cross sections for elastic scattering and dissociation.

Provided a semi-quantitative classical interpretation of diffraction dissociation.

Estimated the nuclear surface region where dissociation predominantly occurs.

Abstract

A theoretical analysis using an impact-parameter description of the collisions of deuterons with nuclei is carried out in the high-energy diffraction approximation. It is used to obtain the intensities and integrated cross sections for elastic scattering, for the emergence of the two incident nucleons from the collision whether they appear as an elastically scattered deuteron or as two unbound nucleons, and for the diffraction-induced dissociation of the deuteron into a free neutron and a free proton, as well as the total cross section. The cross section for collisions in which one or both of the nucleons is absorbed is derived in terms of the sum of the neutron-nucleus and proton-nucleus effective phase shifts. Expressions for the cross section for processes in which the proton (or neutron) is absorbed whether the neutron (or proton) is absorbed or not, and for the cross section for processes in which the neutron (or proton) is absorbed and the proton (or neutron) remains free are derived. A reduced form of a two-particle density matrix is introduced to directly derive expressions for the cross section for two-particle absorption in which both the proton and neutron are absorbed and for the cross section for stripping processes in which the proton (or neutron) is absorbed and the neutron (or proton) emerges as a free particle. The expression for the cross section for the breakup of the deuteron and the resulting emergence of one or two free nucleons is also derived. The mechanism by which the diffraction dissociation of the deuteron is induced is understood in an approximate semi-quantitative basis in classical terms (primarily the radial derivative of the radial impulse), allowing an estimate of where in the nuclear potential (beyond the "radius", near the "surface") the dissociation process tends to predominantly occur.