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.
Highlights
The “standard” picture of a nucleus sees it as a system of A nucleons, protons or neutrons, interacting among themselves and eventually with external electroweak probes
We present selected results obtained with the Hyperspherical Harmonics (HH) method described above
The aim of this section is two-fold: first of all we wish to show the effectiveness of the HH method for few-nucleon systems; secondly, we want to emphasize that the HH method, as well as any ab initio method, is an essential tool for testing and eventually improving nuclear interaction models
Summary
The “standard” picture of a nucleus sees it as a system of A nucleons, protons or neutrons, interacting among themselves and eventually with external electroweak probes. The method has been applied to study the A ≤ 4 nuclear bound systems in references [23, 24] using local realistic interactions, and had been pushed to work up to A = 6 with central potential models [23]. Up to the year 2008, this had been developed and applied to study with great accuracy the A = 3, 4 bound states, with both local potentials, expressed in coordinate space, or non-local ones, given in momentum-space. The higher energy scattering states, still below the breakup threshold of the target nucleus, had been studied for both A = 3 and 4 systems only with local interactions, in a variety of contributions extensively mentioned in reference [19].
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