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A theoretical study of the reaction D(P,[gamma])He3 Rendell, David Hayward

Abstract

A theoretical study of the reaction D(pγ)He³ is made in an attempt to explain the experimental data for the reaction obtained by Fowler et al. (1949), Wilkinson (1952), Griffiths and Warren (1955) and Griffiths, Larson and Robertson (1961). The angular distribution of the emitted gamma radiation, measured with respect to the incident proton beam, is predominantly proportional to sin²θ. Measurements of the polarization of the radiation by Wilkinson (1952) indicate that the sin²θ component is electric dipole radiation. In addition there is a small, possibly isotropic, component. The proportion of the total yield coming from the smaller 'isotropic' component is 0.035 at a proton energy of 1 Mev, and this proportion increases with decreasing proton energy. The sin²θ component has been interpreted by Griffiths and Warren as coming from an electric dipole transition from an initial state of a P-wave proton (L = 1, L₂ =0) and ³S deuteron to the ²S ground state of He³. This interpretation is supported by the present calculations. They also suggest that the smaller 'isotropic* component could be either a magnetic dipole transition of S-wave protons to the ²S state of He³ or an electric dipole transition involving spin-orbit coupling. In this present work the cross-sections are examined for all possible channels which might conceivably contribute to the reaction. The channels considered are 1. electric dipole transitions for a. P-wave protons to the ²S state b. P-wave protons to the ⁴D state c. F-wave protons to the ⁴D state 2. electric quadrupole transitions for a. S-wave protons to the ⁴D state b. D-wave protons to the ²S state 3. the magnetic dipole transition for S-wave protons to the ²S state. Three-body wave functions are constructed, following Verde (1950) and Derrick and Blatt (1956), making use of the symmetry properties in spin space, isotypic spin space and in ordinary space. In addition to the states of total isotropic spin T = ½ considered by Derrick and Blatt the states of total isotopic spin T = 3/2 are included. The radiation matrix elements for the above channels are calculated and are expressed in terms of integrals over the three internal coordinates. These radial integrals are estimated by using very simple radial functions which are valid outside the range of the nuclear forces and which also disregard coulomb forces. The cross-sections depend on the unknown amplitudes and relative signs of the various possible symmetry states. Therefore the size, although not the angular dependance or the general energy dependance, of the cross-sections can be used only as an order-of-magnitude estimate. By comparison of the size, angular distribution and energy dependance of the calculated cross-sections with the experimental data it is shown conclusively that the sin²θ component of the radiation comes from the electric dipole transition of P-wave protons to the ²S state of He³. The smaller 'isotropic' component of the radiation comes from either (a) an electric dipole transition of P-wave protons to the ⁴D state, giving an angular distribution proportional to 1 – (1/7)cos²θ, or (b) a magnetic dipole transition of S-wave protons to the ²S state, giving an isotropic angular distribution. The observed energy dependence of the relative yield of the small component suggests the interpretation in terms of the magnetic dipole transition. The cross-sections of the other transitions examined are too small to explain the experimental results.

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