Thomas-Fermi Calculations of Atoms and Matter in Magnetic Neutron Stars II: Finite Temperature Effects

We present numerical calculations of the equation of state for dense matter in high magnetic fields, using a temperature dependent Thomas-Fermi theory with a magnetic field that takes all Landau levels into account. Free energies for atoms and matter are also calculated as well as profiles of the electron density as a function of distance from the atomic nucleus for representative values of the magnetic field strength, total matter density, and temperature. The Landau shell structure, which is so prominent in cold dense matter in high magnetic fields, is still clearly present at finite temperature as long as it is less than approximately one tenth of the cyclotron energy. This structure is reflected in an oscillatory behaviour of the equation of state and other thermodynamic properties of dense matter and hence also in profiles of the density and pressure as functions of depth in the surface layers of magnetic neutron stars. These oscillations are completely smoothed out by thermal effects at temperatures of the order of the cyclotron energy or higher.Comment: 37 pages, 17 figures included, submitted to Ap

Quantum Drag Forces on a Sphere Moving Through a Rarefied Gas

As an application of quantum fluid mechanics, we consider the drag force exerted on a sphere by an ultra-dilute gas. Quantum mechanical diffraction scattering theory enters in that regime wherein the mean free path of a molecule in the gas is large compared with the sphere radius. The drag force is computed in a model specified by the ``sticking fraction'' of events in which a gaseous molecule is adsorbed by the spherical surface. Classical inelastic scattering theory is shown to be inadequate for physically reasonable sticking fraction values. The quantum mechanical scattering drag force is exhibited theoretically and compared with experimental data.Comment: 5 pages no figure

Integral Equations for Heat Kernel in Compound Media

By making use of the potentials of the heat conduction equation the integral equations are derived which determine the heat kernel for the Laplace operator $-a^2\Delta$ in the case of compound media. In each of the media the parameter $a^2$ acquires a certain constant value. At the interface of the media the conditions are imposed which demand the continuity of the `temperature' and the `heat flows'. The integration in the equations is spread out only over the interface of the media. As a result the dimension of the initial problem is reduced by 1. The perturbation series for the integral equations derived are nothing else as the multiple scattering expansions for the relevant heat kernels. Thus a rigorous derivation of these expansions is given. In the one dimensional case the integral equations at hand are solved explicitly (Abel equations) and the exact expressions for the regarding heat kernels are obtained for diverse matching conditions. Derivation of the asymptotic expansion of the integrated heat kernel for a compound media is considered by making use of the perturbation series for the integral equations obtained. The method proposed is also applicable to the configurations when the same medium is divided, by a smooth compact surface, into internal and external regions, or when only the region inside (or outside) this surface is considered with appropriate boundary conditions.Comment: 26 pages, no figures, no tables, REVTeX4; two items are added into the Reference List; a new section is added, a version that will be published in J. Math. Phy

Joule heating and the thermal evolution of old neutron stars

We consider Joule heating caused by dissipation of the magnetic field in the neutron star crust. This mechanism may be efficient in maintaining a relatively high surface temperature in very old neutron stars. Calculations of the thermal evolution show that, at the late evolutionary stage ($t \geq 10$ Myr), the luminosity of the neutron star is approximately equal to the energy released due to the field dissipation and is practically independent of the atmosphere models. At this stage, the surface temperature can be of the order of $3 \times 10^{4} - 10^{5}$K. Joule heating can maintain this high temperature during extremely long time ($\geq 100$ Myr), comparable with the decay time of the magnetic field.Comment: 13 pages (5 figures in the text). Accepted for publication in The Astrophysical Journa

PEN: a low energy test of lepton universality

Allowed charged $\pi$ meson decays are characterized by simple dynamics, few available decay channels, mainly into leptons, and extremely well controlled radiative and loop corrections. In that sense, pion decays represent a veritable triumph of the standard model (SM) of elementary particles and interactions. This relative theoretical simplicity makes charged pion decays a sensitive means for testing the underlying symmetries and the universality of weak fermion couplings, as well as for studying pion structure and chiral dynamics. Even after considerable recent improvements, experimental precision is lagging far behind that of the theoretical description for pion decays. We review the current state of experimental study of the pion electronic decay $\pi^+ \to e^+\nu_e(\gamma)$, or $\pi_{e2(\gamma)}$, where the $(\gamma)$ indicates inclusion and explicit treatment of radiative decay events. We briefly review the limits on non-SM processes arising from the present level of experimental precision in $\pi_{e2(\gamma)}$ decays. Focusing on the PEN experiment at the Paul Scherrer Institute (PSI), Switzerland, we examine the prospects for further improvement in the near term.Comment: 11 pages, 5 figures; paper presented at the XIII International Conference on Heavy Quarks and Leptons, 22-27 May 2016, Blacksburg, Virginia, US

PEN experiment: a precise measurement of the pi+ -> e+ nu decay branching fraction

A new measurement of $B_{\pi e2}$, the $\pi^+ \to e^+\nu(\gamma)$ decay branching ratio, is currently under way at the Paul Scherrer Institute. The present experimental result on $B_{\pi e2}$ constitutes the most accurate test of lepton universality available. The accuracy, however, still lags behind the theoretical precision by over an order of magnitude. Because of the large helicity suppression of the $\pi_{e2}$ decay, its branching ratio is susceptible to significant contributions from new physics, making this decay a particularly suitable subject of study.Comment: 4 pages, 3 figures, talk given at the Tenth Conference on the Intersections of Particle and Nuclear Physics (CIPANP 2009), La Jolla/San Diego, CA, 26-31 May 2009; to appear in Proceedings to be published by the American Institute of Physic