Two-body continuum states in non-integer geometry
- URL: http://arxiv.org/abs/2203.01133v1
- Date: Wed, 2 Mar 2022 14:26:06 GMT
- Title: Two-body continuum states in non-integer geometry
- Authors: Esben Rohan Christensen, Eduardo Garrido, Aksel Stenholm Jensen
- Abstract summary: Wave functions, phase shifts and corresponding elastic cross sections are investigated for two short-range interacting particles in an external field.
We derive analytic expressions for scattering lengths and phase shifts using a square-well potential.
We show that the phase shifts are the same in both methods.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Wave functions, phase shifts and corresponding elastic cross sections are
investigated for two short-range interacting particles in a deformed external
oscillator field. For this we use the equivalent $d$-method employing a
non-integer dimension $d$. Using a square-well potential, we derive analytic
expressions for scattering lengths and phase shifts. In particular, we consider
the dimension, $d_E$, for infinite scattering length, where the Efimov effect
occurs by addition of a third particle. We give explicitly the equivalent
continuum wave functions in $d$ and ordinary three dimensional (3D) space, and
show that the phase shifts are the same in both methods. Consequently the
$d$-method can be used to obtain low-energy two-body elastic cross sections in
an external field.
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