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Two-body calculations from the direct radiative reactions D(p,⋎)He³(⋎,p) and O¹⁶(p,⋎)F¹⁷ Donnelly, Thomas William


The direct radiative capture reactions D(p,⋎)He³ and O¹⁶(p,⋎)F¹⁷, both of which are of interest in astrophysical processes, have been studied theoretically using a simple two-body direct radiative capture model in order to estimate the cross sections at low energies. In addition, the time inverse of the first reaction, namely the photodisintegration of He³, has been studied for high excitation energies in He³ by applying the reciprocity relations to the direct capture theory. The calculations involve taking matrix elements of the particle-radiation interaction Hamiltonian between bound and continuum states and using first-order perturbation theory to obtain the cross sections. Bound state wave functions are generated in simple potentials involving square-well and Saxon-Woods forms with appropriate Coulomb barriers and with one free parameter which is adjusted to fit the binding energy. The potential parameters for the continuum state wave functions are adjusted to fit available scattering data. For the reaction O¹⁶(p,⋎)F¹⁷ the cross sections for transitions to both the ground and first excited states are in good agreement with the somewhat limited experimental data from 150 KeV to 2.5 MeV and the astrophysical S-factors are shown to be energy dependent even at energies below 100 KeV. The photodisintegration cross section for the reaction He³(⋎,p)D is well fitted in the neighbourhood of the peak at around 11 MeV as well as at lower energies. The D(p,⋎)He³ direct capture cross sections in the energy range around 1 MeV are shown to be sensitive to admixtures of ²S-state of mixed symmetry and of ⁴D-state in the ground state of He³, which is predominantly Symmetric ²S. The same model including the ²S-state of mixed symmetry leads to a capture cross section for thermal neutrons by deuterons in good agreement with the experimental value.

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