Quantum Tunneling and Scattering of a Composite Object: Revisited and Reassessed

TL;DR

This paper investigates quantum tunneling and scattering of composite objects with internal degrees of freedom, providing exact solutions and analyzing how internal states influence reaction outcomes and tunneling probabilities.

Contribution

It develops new techniques for solving complex scattering problems involving composite particles with intrinsic degrees of freedom, including models with bound and continuum states.

Findings

Internal degrees of freedom significantly affect the S-matrix.

Virtual excitations can enhance or suppress tunneling.

Exact solutions for model Hamiltonians are presented.

Abstract

This work presents an extensive exploration of scattering and tunneling involving composite objects with intrinsic degrees of freedom. We aim at exact solutions to such scattering problems. Along this path we demonstrate solution to model Hamiltonians, and develop different techniques for addressing these complex reaction-physics problems, discuss their applicability, and investigate the relevant convergence issues. As examples, we study the scattering of a two-constituent deuteron-like systems either with an infinite set of intrinsic bound states or with a continuum of states that allows for breakup. We show that the internal degrees of freedom of the projectile and its virtual excitation in the course of reactions play an important role in shaping the S-matrix and related observables, giving rise to enhanced or reduced tunneling in various situations.