Two nucleon stripping and the 16O(3He, pγ)18F reaction

Coulomb Corrections to the Beta Decay ofO14

“…The value of R obtained for O 14 is about 1.3% larger, and that for C 14 , about 1.3% smaller, than the value obtained for N 14 *, the differences arising primarily from the different weights and values of the parameters a s and a p in Eq. (12), and only secondarily from the changes in the a's. The variation of the nuclear binding energies with VT is shown for potential I in Fig.…”

“…The wave functions to be used in the calculation of this integral will be of the independent-particle type, that is, linear combinations of Slater determinants of single-particle wave functions, restricted over-all to the required spin 7=0+ and isotopic spin T=l, and with parameters determined by minimization of the nuclear energy. The appropriate wave functions are readily constructed by starting with a Slater determinant for 16 nucleons in a (lsY(lp) 12 configuration. This can be regarded as an O 16 wave function with all closed shells and spherical symmetry, and corresponds to a /=0 + state.…”

“…For parameters of Table V, the sum of the T=0 and T=2 probabilities is 0.31%, in rough agreement with the value obtained by MacDonald in perturbation theory. 12 The higher order terms in the expansion of $' are negligible.…”

“…Since the spatial dependence of the potentials was given in terms of sums of Yukawa forms (the Coulomb potential is a degenerate case), a typical term would be of the form Ve-m V r d z k (Al) where r*y=r-r 3 . The corresponding direct and exchange integrals are denned as J(litni } ai; l 2 m 2 a 2 ) = / \u(liMiai) | 2 1u(l 2 m 2 a 2 ) \ 2 V(r 12 …”

“…The results for 8 differ somewhat, but are uniformly small. The most extensive calculations, those of Weidenmuller and Lovitch, 12 give 6<10X10~4 for a normal oscillator spacing of ^30 MeV, though corrections an order of magnitude larger can be obtained with particularly favorable assumptions about the spacing of the excited energy levels. In any case, it appears very unlikely that a correction as large as that required to eliminate the discrepancy between the values of 6> and Gp> 5=2X10~2, can be obtained without considering collective effects which are not readily describable within the context of the shell model.…”