Scattering of a weakly bound dimer from a hard wall in one dimension

TL;DR

This paper analyzes how a weakly bound one-dimensional dimer scatters off a hard wall, exploring phase shifts, reflection, and dissociation across various energies and mass ratios, using analytical and semiclassical methods.

Contribution

It provides new analytical and semiclassical insights into dimer-wall scattering, including dependence of scattering parameters on mass ratio and energy regimes.

Findings

Low-energy scattering results agree with previous studies.

Scattering length and effective range depend logarithmically on mass ratio for large ratios.

Dissociation probability inversely proportional to the square of incident momentum at high energies.

Abstract

We consider a dimer formed by two particles with an attractive contact interaction in one dimension, colliding with a hard wall. We compute the scattering phase shifts and the reflection coefficients for various collision energies and various mass ratios of the two particles. For low-energy collisions (with dimer kinetic energies much smaller than the binding energy) our results are consistent with those of D. Lee and M. Pine, The European Physical Journal A 47, 41 (2011). For mass ratios much greater than 1 we use the Born-Oppenheimer approximation to show that the scattering length and the effective range of the dimer-wall collision both depend logarithmically on the mass ratio. For collision energies much greater than the binding energy, the dissociation probability is inversely proportional to the square of the incident momentum of the dimer and we find the constant of proportionality analytically, and we use a semiclassical analysis to approximately derive the ``angular distribution" of the dissociated pair, where the ``angle" $\theta$ depends on the ratio of the velocities of the two outgoing unbound particles.