Direct T-Matrix Approach to Determination of the Electric Polarizabilities of Quantum Bound Systems

TL;DR

This paper introduces a novel T-matrix formalism for calculating electric polarizabilities of quantum bound systems, avoiding spectral expansion, and demonstrates its application to hydrogen atom polarizabilities.

Contribution

A new formalism using the T-matrix approach for directly calculating polarizabilities of quantum bound systems without spectral expansion.

Findings

Successfully applied to hydrogen atom polarizabilities

Derived formulas for two-body bound complexes with central potentials

Enabled direct calculation of multipole polarizabilities

Abstract

A new general formalism for determining the electric multipole polarizabilities of quantum (atomic and nuclear) bound systems based on the use of the transition matrix in momentum space has been developed. As distinct from the conventional approach with the application of the spectral expansion of the total Green's function, our approach does not require preliminary determination of the entire unperturbated spectrum; instead, it makes possible to calculate the polarizability of a few-body bound complex directly based on solving integral equations for the wave function of the ground bound state and the transition matrix at negative energy, both of them being real functions of momenta. A formula for the multipole polarizabilities of a two-body bound complex formed by a central interaction potential has been derived and studied. To test, the developed $T$-matrix formalism has been applied to the calculation of the dipole, quadrupole and octupole polarizabilities of the hydrogen atom.