Calculation of asymptotic normalization coefficients in the complex-ranged Gaussian basis

A new technique towards finding asymptotic normalization coefficients in the complex-ranged Gaussian basis is presented. It is shown that a diagonalisation procedure for the total Hamiltonian matrix in the given basis results in approximation for a radial part of the bound state wave function from the origin up to the far asymptotic distances, which allows to extract ANCs rather accurately. The method is illustrated by calculations of single-particle ANCs for nuclei bound states in cases of non-local nucleon-nucleus interactions, in particular, phenomenological global potentials with the Perey-Buck’s non-locality.

Photodetachment of the Positronium Negative Ion with Excitation in the Positronium Atom

Lyman-α radiation ( 2 P → 1 S ) has been seen from astrophysical sources and the sun. The line shape of this transition has been measured recently in Ps atoms both inside and outside a porous silica target. In the photodetachment of Ps−, the residual Ps atom can be left in the 2P state instead of the 1S state giving rise to positronium Lyman radiation at 2432 A0. Photodetachment cross sections of Ps− have been calculated when the Ps atom is left in nP states, n being 2, 3, 4, 5, 6 and 7, using the asymptotic form of the bound-state wave function and a plane wave for the final state wave function, following the approach of Ohmura and Ohmura [Phys. Rev. 1960, 118, 154] in the photodetachment of H−.

Light WIMP Searches Involving Electron Scattering

In the present work we examine the possibility of detecting electrons in light dark matter searches. These detectors are considered to be the most appropriate for detecting dark matter particles with a mass in the MeV region. We analyze theoretically some key issues involved in such detection. More specifically we consider a particle model involving WIMPs interacting with fermions via Z-exchange. We find that for WIMPs with mass in the electron mass range the cross section for WIMP-atomic electron scattering is affected by the electron binding. For WIMPs more than 20 times heavier than the electron, the binding affects the kinematics very little. As a result, many electrons can be ejected with energy which increases linearly with the WIMP mass, but the cross section is somewhat reduced depending on the bound state wave function employed. On the other hand for lighter WIMPs, the effect of binding is dramatic. More specifically at most 10 electrons, namely, those with binding energy below 10 eV, become available even in the case of WIMPs with a mass as large as 20 times the electron mass. Even fewer electrons contribute if the WIMPs are lighter. The cross section is, however, substantially enhanced by the Fermi function corrections, which become more important at low energies of the outgoing electrons. Thus events of 0.5–2.5 per kg-y become possible.

RADIATIVE LEPTONIC DECAYS OF THE CHARGED B AND D MESONS INCLUDING LONG-DISTANCE CONTRIBUTION

In this work, we study the radiative leptonic decays of B-, D-and [Formula: see text], including both the short-distance and long-distance contributions. The short-distance contribution is calculated by using the relativistic quark model, where the bound state wave function we used is that obtained in the relativistic potential model. The long-distance contribution is estimated by using vector meson dominance model.

S-MATRIX AND WAVE FUNCTION METHODS FOR THE CALCULATION OF SMALL DECAY WIDTHS

Most of the decaying systems namely α-decay and proton radio activity have extremely narrow widths and hence are termed as quasi-bound states. There are three methods available for the computation of very narrow widths. First, the analytic S-matrix method which treats resonance as a pole in complex energy plane with its real part representing resonance energy and the imaginary part the half width. Another two methods namely (i) direct (D) method and (ii) distorted wave (DW) method are based on the property of the quasi-bound state wave function which is quite similar to a bound state wave function in the interior region and is matched with an outgoing spherical wave representing decaying behavior. We make a comparative study of these methods by applying them to the α-decay systems whose experimental results of Q-value and decay half-lives are known recently. It is observed that all the three methods give practically the same results for widths calculated at the same Q-value and explain the experimental results of Q-values and half-lives in several α-decaying nuclei quite well with a proper Coulomb nuclear interaction potential for the α+daughter nucleus system.

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.