The Hyperspherical Harmonics method: a tool for testing and improving nuclear interaction models

TL;DR

The paper reviews the Hyperspherical Harmonics method's formalism and recent results in solving quantum nuclear systems with up to four nucleons, highlighting its versatility in testing nuclear interaction models.

Contribution

It introduces the HH formalism for bound and scattering states and showcases recent advances and future prospects in nuclear physics applications.

Findings

Accurate solutions for A=3 and 4 nuclear systems.

Testing of two- and three-nucleon interactions.

Recent progress in scattering problem solutions.

Abstract

The Hyperspherical Harmonics (HH) method is one of the most accurate techniques to solve the quantum mechanical problem for nuclear systems with $A\le 4$. In particular, by applying the Rayleigh-Ritz or Kohn variational principle, both bound and scattering states can be addressed, using either local or non-local interactions. Thanks to this versatility, the method can be used to test the two- and three-nucleon components of the nuclear interaction. In the present review we introduce the formalism of the HH method, both for bound and scattering states. In particular, we describe the implementation of the method to study the $A=3$ and $4$ scattering problem. Second, we present a selected choice of results of the last decade, most representative of the latest achievements. Finally, we conclude with a discussion of what we believe will be the most significant developments within the HH method for the next five-to-ten years.