Proton decay in a nucleus: Effects of the nuclear surface.

In this paper, a method to deal with proton decay in nuclear matter, previously published, ' is generalized in order to include effects arising from the nuclear surface. Although several theoretical estimates'~ indicate the (eventual) proton decay width in a nucleus to be rather similar to that of an isolated proton, things are different regarding the spectra of the emitted particles (both leptons and mesons). Hence, as experiments are planned5 for searching for proton decay mainly in complex nuclei ('sO, 5sFe), we consider it worthwhile to make a detailed study of nuclear effects on the corresponding decay properties. Our treatment is based upon the method of many-body Green's functions, which when applied to a spatially homogeneous system possesses several outstanding advantages. Thus, for instance, one can use rigorous analytic properties and sum up infinite sets of diagrams, which turns out to be quite relevant to dealing with the propagation of emitted pions in nuclear matter due to their strong interaction with nucleons. '2 However, once surface effects are accounted for, the spatial homegeneity is obviously missing and therefore the appropriate treatment becomes considerably more complicated. Fortunately enough, a great simplification is achieved provided one sticks to "first-order" surface effects. In other words, any quantity of interest, 8' (i.e., the total width, lepton spectrum, etc.), is expanded as