Description of Four- and Five-Nucleon Systems by Solving Faddeev-Yakubovsky Equations in Configuration Space

Abstract

The Faddeev-Yakubovsky equations constitute a rigorous formulation of the quantum mechanical N-body problem in the framework of non-relativistic dynamics. They allow the exact solutions of the Schrödinger equation for bound and scattering states to be obtained. In this review, we will present the general formalism as well as the numerical tools we use to solve Faddeev-Yakubovsky equations in configuration space. We will consider in detail the description of the four-and five-nucleon systems based on modern realistic nuclear Hamiltonians. Recent achievements in this domain will be summarized. Some of the still controversial issues related with the nuclear Hamiltonians as well as the numerical methods traditionally employed to solve few-nucleon problems will be highlighted.

Parity- and Time-Reversal-Violating Nuclear Forces

“…From the theoretical point of view, recently there has been a rapid progress in solving accurately the A = 5 nuclear problem. In particular, the solution of A = 5 Faddeev-Yakubovsky equations [235,236] has allowed a first study of the n-4 He spin rotation [237]. Also accurate applications using the so called "No-Core-Shell-Model with Continuum" technique have been reported [238,239].…”

Resonances of $A=4$ $T=1$ isospin triplet states within the \textit{ab initio} no-core Gamow shell model

“…In theoretical studies, a relatively small number of nucleons allows theories to probe the underlying dynamics directly with enough accuracy and, therefore, to verify nuclear models as well as interactions [23]. As commented in [24], 3N systems remain relatively simple due to the absence of resonance structures in the continuum, while 4N systems present several resonance states and therefore provide better laboratories for the underlying theoretical tests. The isospin symmetry in A = 4 T = 1 multiplet states is expected to be broken, which is due in particular to the Coulomb force [1,10,25].…”

“…However, the resonance is much difficult to be described due to the complex-energy characteristics, and continuum channels must be considered. Indeed, the nuclear complexity really starts at A = 4 [9,24], and A = 4 nuclei are of special interest [26]. The scatterings of the 4N systems have been well studied by the Faddeev-Yakubovsky (FY) [24,[27][28][29][30][31][32][33][34], Alt-Grassberger-Sandhas (AGS) [35][36][37][38][39][40] and hyperspherical harmonics (HH) calculations [40][41][42][43].…”

“…Indeed, the nuclear complexity really starts at A = 4 [9,24], and A = 4 nuclei are of special interest [26]. The scatterings of the 4N systems have been well studied by the Faddeev-Yakubovsky (FY) [24,[27][28][29][30][31][32][33][34], Alt-Grassberger-Sandhas (AGS) [35][36][37][38][39][40] and hyperspherical harmonics (HH) calculations [40][41][42][43]. However, the theoretical calculations of the energies and decay widths of the A = 4 resonance systems are still missing.…”

Light nuclei with semilocal momentum-space regularized chiral interactions up to third order

“…Remarkable progress has been achieved in recent years in both lines of research, see Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13] for a selection of review articles on these topics. At least for not-too-heavy nuclei, the accuracy of theoretical predictions is, in most cases, limited by the uncertainties of the nuclear interactions.…”