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The Hyperspherical Harmonics (HH) method is one of the most accurate techniques to solve the quantum mechanical problem for nuclear systems with a number of nucleons A ≤ 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 problems. 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 5–10 years.

The non-symmetrized hyperspherical harmonics method for a three-body system, composed by two particles having equal masses, but different from the mass of the third particle, is reviewed and applied to the 3H, 3He nuclei, and HΛ3 hyper-nucleus, seen respectively as nnp, ppn, and NNΛ three-body systems. The convergence of the method is first tested in order to estimate its accuracy. Then, the difference of binding energy between 3H and 3He due to the difference of the proton and the neutron masses is studied using several central spin-independent and spin-dependent potentials. Finally, the HΛ3 hypernucleus binding energy is calculated using different NN and ΛN potential models. The results have been compared with those present in the literature, finding a very nice agreement.