The 4He atomic nucleus is one of the best studied few-body systems, both experimentally and theoretically, as summarized in the recent A = 4 com­pilation [37]. Besides the many textbook examples of gross structure, there are subtle points yielding large effects that are only qualitatively understood. Except for [38] none of the existing calculations aims at a complete under­standing of the many features of 4He, which is not surprising in view of the number of different phenomena studied so far [37]. Here we are interested

in the 3He (n, p) reaction, which connects the two lowest fragmentations in energy.

To use the above described techniques, the potentials must also be given in terms of Gaussians. Here we use realistic nucleon-nucleon forces, suitably parametrized, the Bonn [40] and the Argonne AV18 potential [39] and even a three-nucleon interaction (TNI) Urbana IX [41]. The inclusion of the additional TN1 requires almost two orders of magnitude more computing power than the realistic NN-forces alone.

In the 4He system we use a model space with six two-fragment channels, namely the p-3H, the n-3He, the 2H-2H, the singlet deuteron and deuteron d -2H, the d — d, and the (nn)- (pp) channels. The last three are an ap­proximation to the three — and four-body breakup channels that cannot in practice be treated within the RGM. The 4He is taken as four clusters in the framework of the RGM to allow for the required internal orbital angular momenta of 3He, 3H or 2H.

For the scattering calculation we include S, P, and D wave contributions to the Jn = 0+, 1+, 2+, 0“, 1“, 2- channels. From the R-matrix analysis these channels are known to give essentially the experimental data. The full wave-functions for these channels contain over 200 different spin and orbital angular momentum configurations, hence, they are too complicated to be given in detail. For the deuteron we use a type similar to that given in [38]

yielding the binding energy of — 1.921 MeV, whereas for 3He and triton, we use an analogue to [42] for two model spaces, 29 and 35 dimensional, called small and large, respectively. For the triton AV18 yields -7.068 and -7.413 MeV binding energy, respectively, falling short of the experimental datum of -8.481 MeV. Adding the TNI improves the binding energies to -7.586 MeV and -8.241 MeV respectively, see table 1. The binding energy of the deuteron could be easily improved, but then the threshold energies deteriorate and thus yield worse results. All the Gaussian width parameters were obtained by a non-linear optimization using a genetic algorithm [43] for the combination of AV18 and Urbana IX. The model space described above (consisting of four to ten physical scattering channels for each Jf) is by no means sufficient to find reasonable results. So-called distortion or pseudo­inelastic channels [3] have to be added to improve the description of the wave function within the interaction region. Accordingly, the distortion channels have no asymptotic part. For practical purposes it is obvious to re-use some of the already calculated matrix elements as additional distortion channels. In that way we include all the positive parity states of the three-nucleon subsystems with Jf < 5/2+ in our calculation. However, it was recently pointed out by A. Fonseca [44] that states having a negative parity J3 in the
three-nucleon fragment increase the n-3H cross section noteably. Therefore we also added the appropriate distortion channels in a similar complexity as in the J+ case to our calculation, thereby roughly doubling the size of the model space.

In fig. 3 we compare the standard 3He(n, p) cross section as given in the ENDF/B-VI evaluation [36] with various calculations using the AV18 po­tential alone. The calculation using the smallest model space reproduces the data surprisingly well. (The kink in the calculated curves below 10 keV is due to a loss in precision of the energy.) Since the threshold energy is almost 70 keV too low, this result should not be overestimated. Especially as the calculated 0+ triton-proton phase shifts close to threshold and be­low demonstrate large differencies between themselves and to the R-matrix analysis, see fig. 4.

120

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60 30

0 0.2 0.4 0.6 0.8 MeV

Figure 4: Comparison of the 0+ triton-proton phase shifts from the R-matrix analysis (crosses) and calculations employing AV18 in the small model space (av18), adding neg­ative parity distortion channels (av18n), for the large model space (av18-l) and adding negative parity distortion channels (av18n-l).

The corresponding figure 5 including three-nucleon forces reveals a much better agreement, also for the threshold energies, see table 1. Unfortunately the 3He(n, p) cross sections including TNI are not yet available, due to the large amount of CPU time necessary.

Figure 5: As fig. 4, but R-matrix results (crosses) are compared to the full NN-calculation (av18), adding UIX (av18u) and adding V3 (av18uv).

Since the 3He(n, p) data at higher energy are usually deduced via detailed balance from the more easily accessible 3H(p, n) reaction we display in the following the results of a few calculations. In fig. 6 the results for the Bonn potential and a semi-realistic one, which will be used later on on the 6Li(n, t) reaction, are compared to data and the R-matrix analysis. At forward and backward angles large discrepancies between data and calculation are visible. In fig. 7 we change from using the Bonn potential to the Argonne AV18. Obviously the calculations reproduce the data much better. Again the cal­culation employing the smallest model space is by far the best, missing the data only close to the minimum around 90 degrees. Additional three-nucleon forces do not improve the situation. Considering the fact that the calcula­tions start ab initio from NN — and NNN-potentials the agreement between data, R-matrix analysis, and microscopic calculation is remarkably good. At the time being, any extension to heavier nuclei using the above forces fails due to lack of computing power.