Semirelativistic N-boson systems bound by attractive pair potentials

TL;DR

This paper derives bounds on the energy of N-boson systems with attractive pair potentials using semirelativistic equations, providing both lower and upper bounds with detailed analysis for exponential potentials.

Contribution

It introduces a novel method to bound the energy of semirelativistic N-boson systems, combining reduction techniques and trial functions for the first time.

Findings

Established a lower energy bound via reduction to a Klein-Gordon problem.

Provided an upper energy bound using Gaussian trial functions.

Presented detailed results for exponential pair potentials.

Abstract

We establish bounds on the energy of a system of N identical bosons bound by attractive pair potentials and obeying the semirelativistic Salpeter equation. The lower bound is provided by a `reduction', with the aid of Jacobi relative coordinates, to a suitably scaled one-body Klein-Gordon problem. Complementary upper energy bounds are provided by means of a Gaussian trial function. Detailed results are presented for the exponential pair potential V(r) = -v\exp(-r/a).