Supersymmetric isospectral formalism for the calculation of near-zero energy states: application to the very weakly bound ${^4}$He trimer excited state

TL;DR

This paper introduces a supersymmetric isospectral formalism to accurately compute near-zero energy states, demonstrated on the excited state of the 4He trimer, by transforming the potential into a more tractable form.

Contribution

The paper develops a new supersymmetric isospectral method to improve calculations of near-zero energy states in quantum systems.

Findings

Effective trapping of Efimov state in isospectral potential well

Enhanced accuracy in calculating the 4He trimer excited state

Generation of diverse isospectral potentials with adjustable features

Abstract

We propose a novel mathematical approach for the calculation of near-zero energy states by solving potentials which are isospectral with the original one. For any potential, families of strictly isospectral potentials (with very different shape) having desirable and adjustable features are generated by supersymmetric isospectral formalism. The near-zero energy Efimov state in the original potential is effectively trapped in the deep well of the isospectral family and facilitates more accurate calculation of the Efimov state. Application to the first excited state in 4He trimer is presented.