Calculations of polarizabilities and hyperpolarizabilities for the Be$^+$ ion

TL;DR

This paper calculates the polarizabilities and hyperpolarizabilities of the Be$^+$ ion in different states using two independent methods, providing detailed data and comparisons with existing results.

Contribution

It introduces precise calculations of Be$^+$ ion polarizabilities and hyperpolarizabilities using variational and single-electron methods, and computes parameters for long-range interactions and Rydberg states.

Findings

Calculated polarizabilities and hyperpolarizabilities close to convergence.

Provided parameters for long-range interactions with H, He, and Li.

Compared results with existing literature for validation.

Abstract

The polarizabilities and hyperpolarizabilities of the Be$^+$ ion in the $2^2S$ state and the $2^2P$ state are determined. Calculations are performed using two independent methods: i) variationally determined wave functions using Hylleraas basis set expansions and ii) single electron calculations utilizing a frozen-core Hamiltonian. The first few parameters in the long-range interaction potential between a Be$^+$ ion and a H, He, or Li atom, and the leading parameters of the effective potential for the high-$L$ Rydberg states of beryllium were also computed. All the values reported are the results of calculations close to convergence. Comparisons are made with published results where available.