Analytical expressions of non-relativistic static polarizabilities for hydrogen-like ions

TL;DR

This paper derives analytical formulas for static multipole polarizabilities of hydrogen-like ions, providing benchmarks and applying them to blackbody radiation shifts across temperatures.

Contribution

It introduces new analytical expressions for polarizabilities of hydrogen-like ions using wave functions and Green functions, aiding future theoretical work.

Findings

Analytical formulas for polarizabilities derived

Results applied to blackbody radiation shifts

Serves as benchmark for other methods

Abstract

In this work, analytical formulas for the static multipole polarizabilities of hydrogen-like ions are derived by using the analytical wave functions and the reduced Green function and by applying a numerical fitting procedure. Our results are then applied to the studies of blackbody radiation shifts to atomic energy levels at different temperatures. Our analytical results can be served as a benchmark for other theoretical methods.