Klein Tunnelling and the Klein Paradox

The Klein paradox is reassessed by considering the properties of a finite square well or barrier in the Dirac equation. It is shown that spontaneous positron emission occurs for a well if the potential is strong enough. The vacuum charge and lifetime of the well are estimated. If the well is wide enough, a seemingly constant current is emitted. These phenomena are transient whereas the tunnelling first calculated by Klein is time-independent. Klein tunnelling is a property of relativistic wave equations, not necessarily connected to particle emission. The Coulomb potential is investigated in this context: it is shown that a heavy nucleus of sufficiently large $Z$ will bind positrons. Correspondingly, it is expected that as $Z$ increases the Coulomb barrier will become increasingly transparent to positrons. This is an example of Klein tunnelling.Comment: 17 page

Polarisation observables in lepton antilepton to proton antiproton reactions including lepton mass

General expressions, including the lepton mass, for the spin averaged differential cross section for the annihilation reaction lepton antilepton to proton antiproton are given, as well as general formulae for the single and double spin asymmetries in the centre of mass frame. In particular we discuss the single spin asymmetry, normal to the scattering plane, which measures the relative phase difference between nucleon electromagnetic form factors $G_E$ and $G_M$. Recent experimental investigations of these form factors in the space and time like region are reviewed. It is thought that measurements of the phase of these form factors will provide fundamental information on the internal nucleon structure. The phases between $G_E$ and $G_M$ are accessible through polarisation observables measured in the antiproton proton to lepton antilepton reaction, or in its time reversed process.Comment: 14 pages, to be submitted to EPJ

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

Transmission resonances and supercritical states in a one dimensional cusp potential

We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for supercriticality.Comment: 10 pages. Revtex 4. To appear in Phys Rev.

A surprising method for polarising antiprotons

We propose a method for polarising antiprotons in a storage ring by means of a polarised positron beam moving parallel to the antiprotons. If the relative velocity is adjusted to $v/c \approx 0.002$ the cross section for spin-flip is as large as about $2 \cdot 10^{13}$ barn as shown by new QED-calculations of the triple spin-cross sections. Two possibilities for providing a positron source with sufficient flux density are presented. A polarised positron beam with a polarisation of 0.70 and a flux density of approximately $1.5 \cdot 10^{10}$/(mm$^2$ s) appears to be feasible by means of a radioactive $^{11}$C dc-source. A more involved proposal is the production of polarised positrons by pair production with circularly polarised photons. It yields a polarisation of 0.76 and requires the injection into a small storage ring. Such polariser sources can be used at low (100 MeV) as well as at high (1 GeV) energy storage rings providing a time of about one hour for polarisation build-up of about $10^{10}$ antiprotons to a polarisation of about 0.18. A comparison with other proposals show a gain in the figure-of-merit by a factor of about ten.Comment: 13 pages, 8 figures; v2: minor language and signification corrections v3: (14 pages, 12 figures) major error, nonapplicable polarisation transfer cross sections replaced by the mandatory spin-flip cross section

On the pion electroproduction amplitude

We analyze amplitudes for the pion electroproduction on proton derived from Lagrangians based on the local chiral SU(2) x SU(2) symmetries. We show that such amplitudes do contain information on the nucleon axial form factor F_A in both soft and hard pion regimes. This result invalidates recent Haberzettl's claim that the pion electroproduction at threshold cannot be used to extract any information regarding F_A.Comment: 14 pages, 6 figures, revised version, accepted for publication in Phys. Rev.

Pion electroproduction, PCAC, chiral Ward identities, and the axial form factor revisited

We re-investigate Adler's PCAC relation in the presence of an external electromagnetic field within the framework of QCD coupled to external fields. We discuss pion electroproduction within a tree-level approximation to chiral perturbation theory and explicitly verify a chiral Ward identity referred to as the Adler-Gilman relation. We critically examine soft-momentum techniques and point out how inadmissable approximations may lead to results incompatible with chiral symmetry. As a result we confirm that threshold pion electroproduction is indeed a tool to obtain information on the axial form factor of the nucleon.Comment: 33 pages, RevTex, 9 figure

Nucleon Charge and Magnetization Densities from Sachs Form Factors

Relativistic prescriptions relating Sachs form factors to nucleon charge and magnetization densities are used to fit recent data for both the proton and the neutron. The analysis uses expansions in complete radial bases to minimize model dependence and to estimate the uncertainties in radial densities due to limitation of the range of momentum transfer. We find that the charge distribution for the proton is significantly broad than its magnetization density and that the magnetization density is slightly broader for the neutron than the proton. The neutron charge form factor is consistent with the Galster parametrization over the available range of Q^2, but relativistic inversion produces a softer radial density. Discrete ambiguities in the inversion method are analyzed in detail. The method of Mitra and Kumari ensures compatibility with pQCD and is most useful for extrapolating form factors to large Q^2.Comment: To appear in Phys. Rev. C. Two new figures and accompanying text have been added and several discussions have been clarified with no significant changes to the conclusions. Now contains 47 pages including 21 figures and 2 table

Relativistic quantum effects of Dirac particles simulated by ultracold atoms

Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation of Dirac equation with tunable parameters by using ultracold neutral atoms trapped in optical lattices or subject to light-induced synthetic gauge fields. The effective theories for the quasiparticles become relativistic under certain conditions in these systems, making them ideal platforms for studying the exotic relativistic effects. We focus on the realization of one, two, and three dimensional Dirac equations as well as the detection of some relativistic effects, including particularly the well-known Zitterbewegung effect and Klein tunneling. The realization of quantum anomalous Hall effects is also briefly discussed.Comment: 22 pages, review article in Frontiers of Physics: Proceedings on Quantum Dynamics of Ultracold Atom

Induced pseudoscalar coupling of the proton weak interaction

The induced pseudoscalar coupling $g_p$ is the least well known of the weak coupling constants of the proton's charged--current interaction. Its size is dictated by chiral symmetry arguments, and its measurement represents an important test of quantum chromodynamics at low energies. During the past decade a large body of new data relevant to the coupling $g_p$ has been accumulated. This data includes measurements of radiative and non radiative muon capture on targets ranging from hydrogen and few--nucleon systems to complex nuclei. Herein the authors review the theoretical underpinnings of $g_p$, the experimental studies of $g_p$, and the procedures and uncertainties in extracting the coupling from data. Current puzzles are highlighted and future opportunities are discussed.Comment: 58 pages, Latex, Revtex4, prepared for Reviews of Modern Physic