Three-Body Bound State Calculations by Using Three-Dimensional Low Momentum Interaction $V_{low-k}$

TL;DR

This paper solves three-body bound state equations directly in three dimensions using a low momentum interaction without partial wave decomposition, analyzing the effects of cutoff momentum and numerical parameters on binding energy and wave functions.

Contribution

It introduces a 3D approach to three-body bound state calculations with $V_{low-k}$, avoiding partial wave expansion, and studies the impact of cutoff and numerical discretization.

Findings

Binding energy varies with cutoff momentum $\\Lambda$ from 1.0 to 7.0 fm$^{-1}$.

Properties of Faddeev components and wave functions are characterized.

Numerical stability depends on the number of grid points used.

Abstract

Three-dimensional (3D) Faddeev integral equations are solved for three-body (3B) bound state problem without using the partial wave (PW) form of low momentum two-body (2B) interaction $V_{low-k}$ which is constructed from spin independent Malfliet-Tjon V (MT-V) potential. The dependence of 3B binding energy on the cutoff momentum of $V_{low-k}$ is investigated for a wide range of $\Lambda$ from $1.0$ to $7.0\, fm^{-1}$. The properties of Faddeev components and 3B wave function are displayed and the effect of number of grid points for momentum and angle variables on the accuracy and the stability of numerical results is studied by calculation of the expectation value of total Hamiltonian.