Equivalence between local Fermi gas and shell models in inclusive muon capture from nuclei

Abstract

Motivated by recent studies of inclusive neutrino nucleus processes and muon capture within a correlated local Fermi gas model (LFG), we discuss the relevance of nuclear finite size effects in these reactions at low energy, in particular for muon capture. To disentangle these effects from others coming from the reaction dynamics we employ here a simple uncorrelated shell model that embodies the typical finite size content of the problem. The integrated decay widths of muon atoms calculated with this shell model are then compared for several nuclei with those obtained within the uncorrelated LFG, using in both models exactly the same theoretical ingredients and parameters. We find that the two predictions are in quite good agreement, within 1--7%, when the shell model density and the correct energy balance is used as input in the LFG calculation. The present study indicates that, despite the low excitation energies involved in the reaction, integrated inclusive observables, like the total muon capture width, are quite independent of the fine details of the nuclear wave functions.

arXiv comment11 pages, 8 figures. Final version to be published in EPJA

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Cited by in corpus (7)

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• Progress and open questions in the physics of neutrino cross sections
• Inclusive Nucleon Emission Induced by Quasi--Elastic Neutrino--Nucleus Interactions
• In medium dispersion relation effects in nuclear inclusive reactions at intermediate and low energies
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• Muon capture on nuclei: random phase approximation evaluation versus data for 6 $\le$ Z $\le$ 94 nuclei
• Quasi-Elastic Neutrino-Nucleus Reactions