abstract

The effective potential in the minimal flipped SU(5) \(\times \) U(1) model is calculated and the proton life-time in this model is discussed. Results are compared with those from the orthodox SU(5) GUT model.

abstract

A factorized subtraction formula for R-operation is discussed. The notion of T-diagrams as a special class of Feynman diagrams, is introduced. For T-diagrams the factorized renormalization formula is shown to be reducible to Zimmermann’s forest formula for R-operation.

abstract

It is shown that the One Pion Exchange (OPE) between the nucleon and the weak leptonic current accounts only for about 10\(\%\) of the total cross section of the peripheral single pion neutrino production off nucleons. This means that the pion coupling to the vector part of the weak leptonic current is very weak contrary to the expectations. A comparison is made with a recent CERN bubble chamber experiment.

abstract

The three-alpha structure of the ground (\(J^{\pi }\), \(T=0^+\), 0) and first excited (2\(^+\), 0) states of the C12 nucleus was investigated in the framework of the shell-model theory. The probability density for the space distribution of the three alphas was obtained by projecting three- -alpha states from the intermediate-coupling model wavefunctions of the C12 nucleus. The projection procedure was done with the use of three-alpha coefficients of fractional parentage of the translationally invariant shell model. The main result is that the triangular and linear configurations of the three alphas are present in the intermediate-coupling model wavefunctions of the analyzed states. The intermediate-coupling model privileges a linear oscillations in the ground state, while a triangular oscillations are more probable in the first excited state. The probability of the three-alpha clusterization of C12, predicted with the aid of intermediate-coupling model wavefunctions, is equal to 0.47 and 0.52 for the ground and first excited state, respectively.

abstract

A simple theory of the heavy-ion optical potential \(\cal {V}=\cal {V}_{\rm R}+ i\cal {V}_{\rm I}\) is applied to \(^{16}\)O and \(^{40}\)Ca nuclei. The colliding ions are described locally as two slabs of nuclear matter with the frozen density model for the local density and momentum distribution. \(\cal {V}_{\rm R}\) is defined as the energy difference between overlapping and separated nuclei. The energy density of the two slabs is derived from the properties of nuclear matter, and supplemented by inhomogeneity corrections. For \(\cal {V}_{\rm I}\) the frivolous model is applied. \(\cal {V}_{\rm R}\) agrees with, and \(\cal {V}_{\rm I}\) is smaller than results of “exact” \(\cal {K}\) matrix calculations.