We reconsider the derivation of the nucleon-nucleon parity-violating (PV) potential within a chiral effective field theory framework. We construct the potential up to next-to-next-to-leading order by including one-pion-exchange, two-pion-exchange, co
ntact, and 1/M (M being the nucleon mass) terms, and use dimensional regularization to renormalize the pion-loop corrections. A detailed analysis of the number of independent low-energy constants (LECs) entering the potential is carried out. We find that it depends on six LECs: the pion-nucleon PV coupling constant $h^1_pi$ and five parameters multiplying contact interactions. We investigate PV effects induced by this potential on several few-nucleon observables, including the $vec{p}$-$p$ longitudinal asymmetry, the neutron spin rotation in $vec{n}$-$p$ and $vec{n}$-$d$ scattering, and the longitudinal asymmetry in the $^3$He$(vec{n},p)^3$H charge-exchange reaction. An estimate for the range of values of the various LECs is provided by using available experimental data.
The Kohn variational principle and the hyperspherical harmonic technique are applied to study p-3He elastic scattering at low energies. Preliminary results obtained using several interaction models are reported. The calculations are compared to a rec
ent phase shift analysis performed at the Triangle University Nuclear Laboratory and to the available experimental data. Using a three-nucleon interaction derived from chiral perturbation theory at N2LO, we have found a noticeable reduction of the discrepancy observed for the A_y observable.
The hyperspherical harmonic basis is used to describe bound states in an $A$--body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this representation, th
e matrix elements between the basis elements are simple, and the potential energy is presented in a compact form, well suited for numerical implementation. The basis is neither symmetrized nor antisymmetrized, as required in the case of identical particles; however, after the diagonalization of the Hamiltonian matrix, the eigenvectors reflect the symmetries present in it, and the identification of the physical states is possible, as it will be shown in specific cases. We have in mind applications to atomic, molecular, and nuclear few-body systems in which symmetry breaking terms are present in the Hamiltonian; their inclusion is straightforward in the present method. As an example we solve the case of three and four particles interacting through a short-range central interaction and Coulomb potential.
The Kohn variational principle and the hyperspherical harmonics technique are applied to study n-3H elastic scattering at low energies. In this contribution the first results obtained using a non-local realistic interaction derived from the chiral pe
rturbation theory are reported. They are found to be in good agreement with those obtained solving the Faddeev-Yakubovsky equations. The calculated total and differential cross sections are compared with the available experimental data. The effect of including a three-nucleon interaction is also discussed.
The hyperspherical harmonic (HH) method has been widely applied in recent times to the study of the bound states, using the Rayleigh-Ritz variational principle, and of low-energy scattering processes, using the Kohn variational principle, of A=3 and
4 nuclear systems. When the wave function of the system is expanded over a sufficiently large set of HH basis functions, containing or not correlation factors, quite accurate results can be obtained for the observables of interest. In this paper, the main aspects of the method are discussed together with its application to the A=3 and 4 nuclear bound and zero-energy scattering states. Results for a variety of nucleon-nucleon (NN) and three-nucleon (3N) local or non-local interactions are reported. In particular, NN and 3N interactions derived in the framework of the chiral effective field theory and NN potentials from which the high momentum components have been removed, as recently presented in the literature, are considered for the first time within the context of the HH method. The purpose of this paper is two-fold. First, to present a complete description of the HH method for bound and scattering states, including also detailed formulas for the computation of the matrix elements of the NN and 3N interactions. Second, to report accurate results for bound and zero-energy scattering states obtained with the most commonly used interaction models. These results can be useful for comparison with those obtained by other techniques and are a significant test for different future approaches to such problems.
