Benchmark calculation ofn-3H andp-3He

Abstract

The n-3 H and p-3 He elastic phase-shifts below the trinucleon disintegration thresholds are calculated by solving the 4-nucleon problem with three different realistic nucleon-nucleon interactions (the I-N3LO model by Entem and Machleidt, the Argonne v18 potential model, and a low-k model derived from the CD-Bonn potential). Three different methods -Alt, Grassberger and Sandhas, Hyperspherical Harmonics, and Faddeev-Yakubovsky -have been used and their respective results are compared. For both n-3 H and p-3 He we observe a rather good agreement between the three different theoretical methods. We also compare the theoretical predictions with the available experimental data, confirming the large underprediction of the p-3 He analyzing power.

Theory and application of explicitly correlated Gaussians

“…Because of the complexity of the NN interaction, only a few approaches (Nollett et al, 2007;Quaglioni and Navrátil, 2008;Suzuki, Horiuchi, and Arai, 2009;Viviani et al, 2011) have been applied to the ab initio study of nuclear scattering and reactions for A > 3 using realistic nuclear interactions. A common theme underpinning these approaches is to divide the configuration space into internal and external regions with the dynamical interactions confined to the internal region.…”

Ab initiocalculations of nuclear widths via an integral relation

“…For nuclei with A ≤ 4, methods using correlated hyperspherical harmonic bases or Faddeev and similar formulations have solved bound-state, scattering, and reaction problems quite successfully [7][8][9][10]. The ab initio methods that have been developed for A > 4 nuclei are suited mainly to treatment of bound states, but there has been significant progress on unbound states in recent years.…”

“…They match the data more closely and with less ambiguity than estimates based on spectroscopic factors. I consider the consequences of my results for identification of observed states in 8 B, 9 He, and 9 Li. I also examine failures of the method and conclude that they generally involve broad states and variational wave functions that are not strongly peaked in the interaction region.…”

Reactions in the four-nucleon system above breakup threshold

“…In the last decade accurate numerical calculations for low-energy nucleon-trinucleon elastic scattering have been performed using both coordinate-space and momentum-space rigorous approaches, namely, the hyperspherical harmonics (HH) expansion method [4,5], the Faddeev-Yakubovsky (FY) equations [1] for the wave function components [6], and the Alt, Grassberger and Sandhas (AGS) equations [3] for transition operators [7,8]. The reliability of all these methods was confirmed in a benchmark calculation [9] for neutron-3 H (n-3 H) and proton-3 He (p-3 He) elastic scattering observables.…”