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A theoretical consideration of the direct capture process O¹⁶ (p,[gamma]) F⁷ at low energies Nash, George Francis

Abstract

The cross sections for the 0¹⁶ (p,ɤ) F¹⁷ transitions to the ground d-state and to an excited s-state of F¹⁷ have been measured in this laboratory and elsewhere, at different energies in the range from about 100 kev to 2.5 Mev incident proton energy. In this thesis an attempt is made to calculate these cross sections at several energies in the above range on the hypothesis of direct proton capture. Similar calculations have been made at the California Institute of Technology but have not been published. The standard formula for the cross section for an electric dipole transition from an incident p state to a final d-or s-state has been used. The matrix element appearing in this formula was split up into an angular part which can be evaluated exactly, and a radial integral which has to be calculated approximately. In the case of transitions to the excited s-state numerical calculations using tabulated wave-functions were made at center of mass proton energies of 150, 378 and 940 kev. The cross section at 150 kev was also calculated by the saddle point method using WKB approximations to the wave-functions, but this method was found to break down at energies above 200 kev due to difficulties with the WKB functions. Reasonably good agreement between the two methods was obtained at 150 kev. For transitions to the ground d-state the numerical method could not be used since tabulations of the required d-state wave-function are unavailable. Calculations were made only by the saddle point method at center of mass proton energies of 150, 378 and 500 kev. This method can not be used above 500 kev. The calculated ratio of [formula omitted] ≈ 9 at energies of 150 and 378 kev, and the absolute values of the cross sections agree reasonably well with the experimentally observed values. Some discrepancies are noted between these calculations and those carried out at the California Institute of Technology which are very briefly referred to in a preprint of an experimental paper, but a detailed comparison was not possible, as the details of those calculations are unavailable.

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