Toward the Application of Three-Dimensional Approach to Few-body Atomic Bound States

TL;DR

This paper develops a three-dimensional numerical approach for analyzing few-body atomic bound states, focusing on the transition amplitude's angular and momentum dependence using realistic interatomic potentials.

Contribution

It introduces a non partial wave numerical method for few-body atomic systems and studies the transition amplitude's behavior at negative energies.

Findings

Transition amplitude shows characteristic angular behavior near 4He dimer pole.

The method is demonstrated with realistic interatomic potentials.

Angular and momentum dependence are effectively characterized.

Abstract

The first step toward the application of an effective non partial wave (PW) numerical approach to few-body atomic bound states has been taken. The two-body transition amplitude which appears in the kernel of three-dimensional Faddeev-Yakubovsky integral equations is calculated as function of two-body Jacobi momentum vectors, i.e. as a function of the magnitude of initial and final momentum vectors and the angle between them. For numerical calculation the realistic interatomic interactions HFDHE2, HFD-B, LM2M2 and TTY are used. The angular and momentum dependence of the fully off-shell transition amplitude is studied at negative energies. It has been numerically shown that, similar to the nuclear case, the transition amplitude exhibits a characteristic angular behavior in the vicinity of 4He dimer pole.