p-wave phase shift and scattering length of $^6$Li

TL;DR

This paper calculates the p-wave phase shifts and scattering length of $^6$Li using Schrödinger equation solutions, analyzing semiclassical methods and employing the variable phase approach for validation.

Contribution

It introduces an approximate analytic solution for p-wave scattering and applies the variable phase method to accurately determine the scattering length of $^6$Li.

Findings

p-wave scattering length of $^6$Li is -45a_o

semiclassical solutions are not unique for p-waves

validated methods with Cs isotopes

Abstract

We have calculated the p-wave phase shifts and scattering length of $^6$Li. For this we solve the $p$ partial wave Schr\"odinger equation and analyze the validity of adopting the semiclassical solution to evaluate the constant factors in the solution. Unlike in the $s$ wave case, the semiclassical solution does not provide unique value of the constants. We suggest an approximate analytic solution, which provides reliable results in special cases. Further more, we also use the variable phase method to evaluate the phase shifts. The p-wave scattering lengths of $^{132}$Cs and $^{134}$Cs are calculated to validate the schemes followed. Based on our calculations, the value of the $p$ wave scattering length of $^6$Li is $-45a_o$.