Search

The Levinson theorem relates the difference of the phase shifts at the threshold and at infinity to the number of bound states. The theorem is modified in view of the fact that Castillejo–Dalitz–Dyson (CDD) poles and Jaffe–Low primitives corresponding to zeros of the $$D$$ function on the unitary cut are present in the scattering amplitude. It is shown that, in general, the difference of the phase shifts at the threshold and at infinity is determined by the number of bound states, the number of CDD poles, and the number of primitives. Some consequences of this theorem that concern the properties of the nucleon–nucleon interaction are discussed.

The problem of internal ionization in the beta decay of tritium due to the scattering of a β electron off a bound electron is discussed. The total probability of the process per a single decay event is calculated. The distributions over the momentum and the kinetic energy of a liberated electron are plotted. A correction to the β spectrum produced by internal ionization is determined. The identity of electrons is taken into account in all calculations. The results of calculations of the modified spectrum are of interest for the KATRIN experiment aimed at measuring the mass of an electron antineutrino. The high-luminosity source also makes it possible to search for keV-scale sterile neutrinos in the middle part of the β spectrum, where the internal ionization effect is significant.

The equation of state for neutron matter is derived in the framework of the Quark Compound Bag model, in which the nucleon–nucleon interaction is generated by the s-channel exchange of six-quark Jaffe–Low primitives.

The generalized Ward identity is derived for the vertex function of the weak vector current (VC) of nucleons within an effective theory with account of the isotopic symmetry breaking. The generalized Ward identity establishes a relationship between the form factor of the longitudinal weak VC component and the mass difference and the charge radii of an isotopic doublet on the mass shell. This relationship can be used to evaluate the form factors of both nucleons and nuclei with spin J = 1/2 and isospin I = 1/2. The reactions with large transferred momenta involving isotopic doublets, in which the mass splitting is maximized, offer the greatest promise for measuring the form factor. Numerical estimates of the form factor of the longitudinal weak VC component of a nucleon pair and eight nuclear isodoublets are presented.

The form factor f- of the longitudinal component of the weak vector current in pion β-decay is derived using the generalized Ward identity. The form factor is expressed through the pion mass difference and mean-square radii in the channels with angular momenta J = 1, 0 and isospins T = 1, 2.

We discuss oscillations of two neutral atoms which proceed with the violation of lepton number. One of the neutral atoms is stable, the other one represents a quasistationary state subjected to electromagnetic deexcitation. The system of neutral atoms exhibits oscillations similar to those of the system of neutral kaons and neutron-antineutron oscillations in the nuclear medium. The underlying mechanism is a transition of two protons and two bound electrons to two neutrons p + p + eb− + eb− ↔ n + n. A signature of the oscillations might be an electromagnetic deexcitation of the involved unstable nucleus and atomic shell with the electron holes. A resonant enhancement of the neutrinoless double electron capture takes place when the atomic masses tend to be degenerate. Qualitative estimates show that in searches for lepton number violation oscillations of atoms might be a possible alternative to the conventional mechanism of the neutrinoless double β decay process with emission of two electrons.