Photopion Production in the Fermi Gas Model
In order to understand some of the general properties of pion photoproduction from a nucleus, we have studied the photoproduction process from a Fermi gas. In this calculation, we used the non-relativistic pion photoproduction operator of Blomqvist and Laget1 which reproduces the γ + p → π+ n data through the 3-3 resonance region. One of the advantages of using this operator is that the momentum dependence of the struck nucleon is given explicitly. We studied the importance of the momentum dependent terms by calculating the Fermi gas cross section exactly and compared it with the results with these terms neglected, i.e., the frozen nucleon approximation. We found this to be a poor approximation leading to errors of about 25% in the resonance region. However, fixing the nucleon’ s momentum at the Fermi momentum and in the direction φp =π/2 (measured with respect to the plane formed by the photon and pion) the results only differed by up to 7%. Fixing the magnitude and direction of the struck nucleon’s momentum at some optimum value enables one to factor the pion production operator out of the nuclear overlap integral and greatly simplifies the calculation.
KeywordsResonance Region Factor Approximation Pion Production Momentum Dependence Fermi Momentum
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- 4.H. Ahrens.? Phys. Lett. 52B, (1974) and private communication from H. Gimm.Google Scholar