Microscopic calculation of the 4He system

Abstract

We report on a consistent, microscopic calculation of the bound and scattering states in the 4 He system employing a realistic nucleon-nucleon potential in the framework of the resonating group model (RGM). We present for comparison with these microscopic RGM calculations the results from a charge-independent, Coulomb-corrected R-matrix analysis of all types of data for reactions in the A = 4 system. Comparisons are made between the phase shifts, and with a selection of measurements from each reaction, as well as between the resonance spectra obtained from both calculations. In general, the comparisons are favorable, but distinct differences are observed between the RGM calculations and some of the polarisation data. The partial-wave decomposition of the experimental data produced by the Rmatrix analysis shows that these differences can be attributed to just a few S-matrix elements, for which inadequate tensor-force strength in the N − N interaction used appears to be responsible.

Proton-He3elastic scattering at low energies

“…The same increases in computational power, however, have opened the possibility for accurate calculations of the 4N observables using realistic models for nucleon-nucleon (N N ) and three-nucleon (3N ) forces. These calculations have been performed mainly by means of the Faddeev-Yakubovsky (FY) approach [6,7,8] and the Kohn variational principle [9,10,11,12,13]. In spite of this progress, some disagreements still exist between theoretical groups, as for example, in the calculation of the n-3 H total cross section in the peak region (around E c.m.…”

Three-Nucleon Force in the 4He Scattering System

“…This is given by the R-matrix analysis as described in [2] in detail. The lowest channel, triton-proton contains the intriguing first exited state of 4 He, a 0 + -resonance, sometimes considered a breathing mode, which is clearly seen in the 0 + phase shift, see fig.…”

“…This must be compared to −6.92MeV known from Faddeev calculations [18]. For the deuteron we use the structure given in [2], yielding a binding energy of -1.921 MeV, which could be easily improved. But then the relative threshold energies deteriorate, see table 1.…”

“…Besides the many textbook examples of gross structure, there are subtle points yielding large effects that are only qualitatively understood. Except for [2] none of the existing calculations aims at a complete understanding of the many features of 4 He, which is not surprising in view of the number of different phenomena studied so far [1]. With the recent compilation [1] and the comprehensive R-matrix analysis [3] of a large amount of scattering data below E x = 30 MeV, a new, microscopic calculation for the 4 He system in this energy range using modern realistic two-and three-nucleon forces is most desirable.…”

“…Furthermore very many operators can contribute to a TNI and the lack of stringent conditions in the three-nucleon system on the structure of the TNI makes its application to other systems desirable. In [2] it was shown that although a realistic N N force can generally reproduce the 4 He system, there remain differences, most notably in the analyzing powers. Since the intensely studied 4 He system [1] is unfortunately very difficult to describe due to the many resonances and the 4 He bound state, the much simpler systems p− 3 He and n− 3 H where data exist in the energy range of interest were investigated in [8].…”