Radiative corrections to low energy neutrino reactions

We show that the radiative corrections to charged current (CC) nuclear reactions with an electron(positron) in the final state are described by a universal function. The consistency of our treatment of the radiative corrections with the procedure used to extract the value of the axial coupling constant $g_A$ is discussed. To illustrate we apply our results to (anti)neutrino deuterium disintegration and to $pp$ fusion in the sun. The limit of vanishing electron mass is considered, and a simple formula valid for E_{obs}\gsim 1 MeV is obtained. The size of the nuclear structure-dependent effects is also discussed. Finally, we consider CC transitions with an electron(positron) in the initial state and discuss some applications to electron capture reactions.Comment: 23 pages, 5 figure

Multipolar model of bremsstrahlung accompanying proton-decay of nuclei

Emission of bremsstrahlung photons accompanying proton decay of nuclei is studied. The new improved multipolar model describing such a process is presented. The angular formalism of calculations of the matrix elements is stated in details. The bremsstrahlung probabilities for the $^{157}{\rm Ta}$, $^{161}{\rm Re}$, $^{167}{\rm Ir}$ and $^{185}{\rm Bi}$ nuclei decaying from the $2s_{1/2}$ state, the $^{109}_{53}{\rm I}_{56}$ and $^{112}_{55}{\rm Cs}_{57}$ nuclei decaying from the $1d_{5/2}$ state, the $^{146}_{69}{\rm Tm}_{77}$ and $^{151}_{71}{\rm Lu}_{80}$ nuclei decaying from the $0h_{11/2}$ state are predicted. Such spectra have orders of values similar to the experimental data for the bremsstrahlung photons emitted during the $\alpha$-decay. This indicates on real possibility to study bremsstrahlung photons during proton decay experimentally and perform further measurements.Comment: 14 pages, 6 figure