Size and shape of the nuclear density distributions of20Ne and28Si from 104 MeV alpha particle scattering

Abstract

Measured differential cross sections for the scattering of 104 MeV ~ particles from 2~ and 28Si are analyzed on the basis of a deformed folding model. Rms-radii and values of the deformation parameters for the nuclear density distributions are extracted, and the effect of the size of the c~ particle is demonstrated. Previous discrepancies between (p, p') and (~, 0d) results are partly removed.It has been found that the real part U R (G) of the optical potential for the elastic a-nucleus scattering can be related to the nuclear density distribution p (r) by the equation [1,2,3] U,(r~) = S p(r) Vefr (r-G) d3 r.(1) An effective a-particle-bound nucleon interaction of a simple gaussian formis found to be quite satisfactory and was derived (as approximate result) [4,5] by folding the ~ particle form factor with a nucleon-nucleon interaction which fits the low energy data. According to Bernstein [3] the value of Vo = -37 MeV and the range p = 2.0 fm. The energy dependent constant 2R(E,) takes into account of deviations of the strength from the derived zero-energy a-nucleon scattering value Vo. The factor 2R may by determined empirically thus absorbing some uncertainties in the choice of Ve~. By fitting elastic a particle scattering to 4~ ,~R=0.815 was obtained at E, = 104 MeV [3]. This value proves to be a best value* throughout for the 104 MeV elastic a particle scattering [3,6]. Fortunately the scattering is rather insensitive to the detailed shape of the theoretically undefined imaginary potential [3]. Thus the imaginary potential Ux may be chosen proportional to the real part by introducing a further empirical * As pointed out in Ref.[5] Bernstein's value of V o is not correct. However, this is absorbed by the phenomenological value of JR"

Isoscalar transition rates from folding model analyses of (?, ??) scattering

“…This model has been extended to inelastic scattering by introducing deformed nuclear density distributions. As demonstrated in several cases [8][9][10] the size and shape parameters of the distributions found by the analysis of the experiments in this approach lead to an excellent agreement with electromagnetic moments and transition rates, and also with (p,p') results. For higher bombarding energies the folding model seems now well established, at least on an empirical basis so that by use of folding model results of flL and c,, the procedure for extracting IS transition rates can be improved.…”