The Solar HepHep Process

The $Hep$ process is a weak-interaction reaction, $He3 + p \to He4 + e^+ + \nu_e$, which occurs in the sun. There is renewed interest in $Hep$ owing to current experimental efforts to extract from the observed solar neutrino spectrum information on non-standard physics in the neutrino sector. $Hep$ produces highest-energy solar neutrinos, although their flux is quite modest. This implies that the $Hep$ neutrios can at some level influence the solar neutrino spectrum near its upper end. Therefore, a precise interpretation of the observed solar neutrino spectrum requires an accurate estimate of the $Hep$ rate. This is an interesting but challenging task. We describe the difficulties involved and how the recent theoretical developments in nuclear physics have enabled us to largely overcome these difficulties. A historical survey of $Hep$ calculations is followed by an overview of the latest developments. We compare the results obtained in the conventional nuclear physics approach and those obtained in a newly developed effective field theory approach. We also discuss the current status of the experiments relevant to $Hep$.Comment: Published in Ann. Rev. Nuc. Part. Sci. vol. 54, 19 (2004). AR209 macros are include

Scaling of Coulomb pseudo-potential in s-wave narrow-band superconductors

The Coulomb pseudo-potential $\mu^*$ is extracted by fitting the numerically calculated transition temperature $T_c$ of the Eliashberg-Nambu equation which is extended to incorporate the narrow-band effects, that is, the vertex correction and the frequency dependence of the screened Coulomb interaction. It is shown that even for narrow-band superconductors, where the fermi energy $\epsilon_F$ is comparable with the phonon frequency $\omega_{ph}$, the Coulomb pseudo-potential is a pertinent parameter, and is still given by $\mu^* = \mu/[1+\mu \ln(\epsilon_F/\omega_{ph})]$, provided $\omega_{ph}$ is appropriately scaled.Comment: 5 pages, 3 figures, accepted for publication by Phys. Rev.