Weak pion production

The matrix element for the interaction W+N→π+N is studied, where W is a virtual intermediate boson for the weak interactions (or just the weak current). Weak pion production—production of a pion by high-energy neutrino collisions with nucleons—is governed by this matrix element. The main case of interest is in the energy region where the pion-nucleon 3-3 resonance is dominant. Formulas are derived for solving the problem in this region

The Strong Levinson Theorem for the Dirac Equation

We consider the Dirac equation in one space dimension in the presence of a symmetric potential well. We connect the scattering phase shifts at E=+m and E=-m to the number of states that have left the positive energy continuum or joined the negative energy continuum respectively as the potential is turned on from zero.Comment: Submitted to Physical Review Letter

Intermediate boson production in pion-proton collisions

The current-current hypothesis has been applied in recent years to the study of the weak interactions. The conserved vector current(1) hypothesis and the pionic character of the divergence of the axial vector current(2) have evolved in its wake. So has the idea of a boson field which mediates all weak interactions.(3) This note deals only with the vector part of the current, leaving for another time similar calculations with the axial vector part; and examines the possibility of producing the boson W, in pion-nucleon collisions, in case of W having relatively low mass.(4

Positron Tunnelling through the Coulomb Barrier of Superheavy Nuclei

We study beams of medium-energy electrons and positrons which obey the Dirac equation and scatter from nuclei with $Z > 100.$ At small distances the potential is modelled to be that of a charged sphere. A large peak is found in the probability of positron penetration to the origin for $Z \approx 184.$ This may be understood as an example of Klein tunnelling through the Coulomb barrier: it is the analogue of the Klein Paradox for the Coulomb potential.Comment: 3 figures, to be published in Physics Letters

The hydrino and other unlikely states

We discuss the tightly bound (hydrino) solution of the Klein-Gordon equation for the Coulomb potential in 3 dimensions. We show that a similarly tightly bound state occurs for the Dirac equation in 2 dimensions. These states are unphysical since they disappear if the nuclear charge distribution is taken to have an arbitrarily small but non-zero radius.Comment: Submitted to Physics Letters

Low Momentum Scattering in the Dirac Equation

It is shown that the amplitude for reflection of a Dirac particle with arbitrarily low momentum incident on a potential of finite range is -1 and hence the transmission coefficient T=0 in general. If however the potential supports a half-bound state at k=0 this result does not hold. In the case of an asymmetric potential the transmission coefficient T will be non-zero whilst for a symmetric potential T=1.Comment: 12 pages; revised to include additional references; to be published in J Phys

Relativistic two-body system in (1+1)-dimensions

The relativistic two-body system in (1+1)-dimensional quantum electrodynamics is studied. It is proved that the eigenvalue problem for the two-body Hamiltonian without the self-interaction terms reduces to the problem of solving an one-dimensional stationary Schr\"odinger type equation with an energy-dependent effective potential which includes the delta-functional and inverted oscillator parts. The conditions determining the metastable energy spectrum are derived, and the energies and widths of the metastable levels are estimated in the limit of large particle masses. The effects of the self-interaction are discussed.Comment: LATEX file, 21 pp., 4 figure