Comment on: Diffusion through a slab

Mahan [J. Math. Phys. 36, 6758 (1995)] has calculated the transmission coefficient and angular distribution of particles which enter a thick slab at normal incidence and which diffuse in the slab with linear anisotropic, non-absorbing, scattering. Using orthogonality relations derived by McCormick & Kuscer [J. Math. Phys. 6, 1939 (1965); 7, 2036 (1966)] for the eigenfunctions of the problem, this calculation is generalised to a boundary condition with particle input at arbitrary angles. It is also shown how to use the orthogonality relations to relax in a simple way the restriction to a thick slab.Comment: 3 pages, LaTeX, uses RevTe

Energy correlation and asymmetry of secondary leptons in H→ttˉH\to t\bar t and H→W+W−H\to W^+W^-

We study the energy correlation of charged leptons produced in the decay of a heavy Higgs particle $H\to t\bar t\to bl^+\nu_l\bar bl^-\bar{\nu}_l$ and $H\to W^+W^-\to l^+\nu_ll^-\bar{\nu}_l.$ The possible influence of $CP$--violation in the $Ht\bar t$ and $HW^+W^-$ vertices on the energy spectrum of the secondary leptons is analyzed. The energy distribution of the charged leptons in the decay $H\to W^+W^-\to l^+\nu_ll^-\bar{\nu}_l$ is sensitive to the $CP$--parity of the Higgs particle and yields a simple criterion for distinguishing scalar Higgs from pseudoscalar Higgs.Comment: 12 pages, + 4 uuencoded figures. report PITHA 94/2

Numerical Studies of Cosmic Ray Injection and Acceleration

A numerical scheme that incorporates a thermal leakage injection model into a combined gas dynamics and cosmic ray (CR, hereafter) diffusion-convection code has been developed. The particle injection is followed numerically by filtering the diffusive flux of suprathermal particles across the shock to the upstream region according to a velocity-dependent transparency function that controls the fraction of leaking particles. We have studied CR injection and acceleration efficiencies during the evolution of CR modified planar shocks for a wide range of initial shock Mach numbers, $M_0$, assuming a Bohm-like diffusion coefficient. The injection process is very efficient when the subshock is strong, leading to fast and significant modification of the shock structure. As the CR pressure increases, the subshock weakens and the injection rate decreases accordingly, so that the subshock does not disappear. Although some fraction of the particles injected early in the evolution continue to be accelerated to ever higher energies, the postshock CR pressure reaches an approximate time-asymptotic value due to a balance between fresh injection/acceleration and advection/diffusion of the CR particles away from the shock. We conclude that the injection rates in strong parallel shocks are sufficient to lead to rapid nonlinear modifications to the shock structures and that self-consistent injection and time-dependent simulations are crucial to understanding the non-linear evolution of CR modified shocks.Comment: 28 pages, To appear in ApJ November 1, 2002 issu