The role of the effective range in strongly-interacting few-body systems

TL;DR

This paper explores how the finite effective range of interactions influences strongly interacting few-body systems, extending zero-range theories to include finite-range effects and deriving analytical expressions for bound states.

Contribution

It introduces an analytical expression for the two-body bound-state spectrum with finite-range effects and a trimer energy scaling function that explicitly includes the effective range.

Findings

Finite-range effects significantly impact the bound-state spectrum.

Derived an analytical formula for the Pöschl-Teller potential spectrum.

Presented a trimer energy scaling function incorporating effective range.

Abstract

Strongly interacting systems appear in several areas of physics and are characterized by attractive interactions that can almost, or just barely, loosely bind two particles. Although this definition is made at the two-body level, this gives rise to fascinating effects in larger systems, including the so-called Efimov physics. In this context, the zero-range theory aims to describe low-energy properties based only on the scattering length. However, for a broad range of physical applications, the finite range of the interactions plays an important role. In this work, I discuss some aspects of finite-range effects in strongly interacting systems. I present the zero-range and shapeless universalities in two-body systems with applications in atomic and nuclear physics. I derived an analytical expression for the $s$-wave bound-state spectrum of the modified P\"oschl-Teller potential for two particles in three dimensions, which is compared with the approximations to illustrate their usefulness. Concerning three identical bosons, I presented a trimer energy scaling function that explicitly includes the effective range. The implications for larger systems are briefly discussed.