Collisions for the quantum Coulomb Hamiltonian

We study the propagation of phase space singularities for the time dependent Schrödinger equation with potential having Coulomb-type singularities in space dimension equal tothree. We prove that the singularities (frequency set) of the solution are reflected by a Coulomb center exactly as in the classical problem, i.e. the frequency set follows theregularized trajectories of Classical Mechanics after a collision.     

Recurrence calculations of organic compound boiling temperatures from data on preceding homologues

A new approach to calculating the temperatures of boiling at atmospheric pressure (T _b) of organic compounds from arbitrary homologous series is suggested. The approach is based on the linear dependence of these values on T _b for the preceding homologues, T _b(n) = aT_b(n ? 1) + b. This dependence, revealed for the first time, was used to obtain a recurrence relation for calculating T _b of organic compounds within any series from the data on three simpler homologues of the same series. The mean a and b values can be used to estimate T _b of an arbitrary organic compound from T _b for one preceding homologue with an accuracy not inferior to that provided by the modern ACD software. Correlations of the general form P(n) = aP(n ? 1) + b are observed not only for the boiling points of organic compounds but also for their other properties P (refractive indexes, relative densities, and ionization energies). This opens up the possibility of creating unified algorithms for calculating various physicochemical constants of organic compounds instead of particular algorithms for every particular property known earlier.     

Intensities of inter-Stark transitions in activated crystals

A scheme of calculation of line strengths for indirect electric dipole transitions between Stark states of impurity ions in dielectric crystals is proposed. It is shown that knowledge of the three semiphenomenological Judd-Ofelt parameters of a crystalline system is sufficient for quantitative calculations. The formulas obtained were approved for YAG:Nd³⁺ crystals based on calculation of the spectroscopic characteristics of the lines of the inter-Stark transitions ⁴ F _3/2 → ⁴ I _9/2 and ⁴ F _3/2 → ⁴ I _11/2.     

Calculation of the dynamic temperature characteristics of a heated graphite tube used in electrothermal atomic absorption measurements

A method and computer program were developed for calculating the temperature of any part of a graphite furnace tube at any instant of time after onset of the heating cycle. Results for tubes of the Massman design show large differences in spatial temperature distributions during and at the end of the heating cycle when equilibrium is reached. When constant current is applied to contoured tubes, greater heating rates at the tube centres are obtained than with standard tubes.