Matching universal behavior with potential models

TL;DR

This paper investigates few-boson systems near the unitary limit using potential models that match two-body scattering data, revealing universal behaviors and finite-range effects across different energy levels.

Contribution

It introduces a method to study few-boson systems near unitarity with potential models, deriving universal functions and analyzing finite-range effects on energy spectra.

Findings

Finite-range effects are absorbed in level functions for low-energy states.

Higher energy levels approach zero-range universal functions.

A zero-range equation for four-boson systems is proposed and solved.

Abstract

Two-, three-, and four-boson systems are studied close to the unitary limit using potential models constructed to reproduce the minimal information given by the two-body scattering length $a$ and the two-body binding energy or virtual state energy $E_2$. The particular path used to reach the unitary limit is given by varying the potential strength. In this way the energy spectrum in the three- and four-boson systems is computed. The lowest energy states show finite-range effects absorbed in the construction of level functions that can be used to study real systems. Higher energy levels are free from finite-range effects, therefore the corresponding level functions tend to the zero-range universal function. Using this property a zero-range equation for the four-boson system is proposed and the four-boson universal function is computed.