Photoproduction of Neutral Pions in Complex Nuclei

Citation

Engelbrecht, Christian Albertus (1962) Photoproduction of Neutral Pions in Complex Nuclei. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/W82V-D913. https://resolver.caltech.edu/CaltechTHESIS:08192011-115123033

Abstract

The photoproduction of neutral pions from complex nuclei is expressed in terms of the photoproduction from single nucleons by means of the direct interaction model and the impulse approximation. A summation over all final states of the nucleus is performed by means of a closure approximation.

Within the framework of the independent particle model of the nucleus, the nuclear matrix elements are evaluated exactly for closed shell nuclei, the final results being expressed in terms of the nucleon density and the two-particle correlation functions in the nuclear ground state. For quantitative purposes the correlation functions are calculated both in the ease of a Fermi gas and for harmonic oscillator wave functions.

The differential cross section is decomposed into an elastic part, which leaves the nucleus in its ground state, and an inelastic part. The elastic cross section has a coherent peak close to the forward direction. The inelastic part is suppressed at small angles because of the contribution from the correlation functions, which is a manifestation of the exclusion principle.

The interactions of the produced pion with the nucleus are included by means of the optical model. Numerical integrations are performed using an approximate wave function for the pion.

Neutral pions can also be produced by the interaction with the electrostatic field of the nucleus. This process is related to the lifetime of the pion for decay into two photons.

When compared with the available experimental results, the theoretically predicted cross sections seem to be too low. Possible reasons for this discrepancy are discussed.

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