Calculation of hyperfine splitting in mesons using configuration interaction approach

The spin - spin mass splitting of light, heavy and mixed mesons are described within a good accuracy in the potential model with screened potential. We conclude that the long - distance part of the potential cannot be pure scalar and that a vector - scalar mixture is favoured. With the same parameters which gives correct average mass spectrum excellent spin - spin splittings of heavy quarkonia is obtained. The results are obtained by going beyond usually used perturbation method, namely using configuration interaction approach.Comment: 8 pages, LaTe

Energy dependence of cross section of photonuclear reactions on indium isotopes

Experimental isomeric yield ratios for the 113In({\gamma},n)112m,gIn reactions on the betatron B25/30 bremsstrahlung gamma beam of energy range 12-25 MeV are measured. Effective cross-sections of ({\gamma},n)-reactions with 112mIn and 114mIn isomers output are calculated. The Penfold-Leiss and Tikhonov methods are applied to solve the Volterra integral equation. The obtained experimental cross-sections are compared with theoretical calculations using the TALYS-1.6 code.Comment: 7 pages, 3 figures, 6 table

Spin Effects in Two Quark System and Mixed States

Based on the numeric solution of a system of coupled channels for vector mesons ($S$- and $D$-waves mixing) and for tensor mesons ($P$- and $F$-waves mixing) mass spectrum and wave functions of a family of vector mesons $q\bar{q}$ in triplet states are obtained. The calculations are performed using a well known Cornell potential with a mixed Lorentz-structure of the confinement term. The spin-dependent part of the potential is taken from the Breit-Fermi approach. The effect of singular terms of potential is considered in the framework of the perturbation theory and by a configuration interaction approach (CIA), modified for a system of coupled equations. It is shown that even a small contribution of the $D$-wave to be very important at the calculation of certain characteristics of the meson states.Comment: 12 pages, LaTe

Heuristic Models of Two-Fermion Relativistic Systems with Field-Type Interaction

We use the chain of simple heuristic expedients to obtain perturbative and exactly solvable relativistic spectra for a family of two-fermionic bound systems with Coulomb-like interaction. In the case of electromagnetic interaction the spectrum coincides up to the second order in a coupling constant with that following from the quantum electrodynamics. Discrepancy occurs only for S-states which is the well-known difficulty in the bound-state problem. The confinement interaction is considered too. PACS number(s): 03.65.Pm, 03.65.Ge, 12.39.PnComment: 16 pages, LaTeX 2.0

Сингулярний розв’язок рівняння Шредінгера для атома водню

Purpose. The authors of known for us textbooks on quantum mechanics pay attention only to the first regular solution of Schrödinger equation for the hydrogen atom. To exclude the second linearly independent solution from the general solution, different textbooks give various arguments such as invalid boundary condition in the coordinate origin, the appearance of Dirac delta function or divergence of the kinetic energy in the origin.Methods. Using the power series method, we obtained an exact analytic expression for the second independent solution of Schrödinger equation for the hydrogen atom.Results. The solution consists of a sum of two parts, one of which increases indefinitely over long distances, while the other is limited and contains a logarithmic term. This feature is peculiar to all values of the orbital angular momentums.Conclusions. On the example of the hydrogen atom, we demonstrated the mathematically correct algorithm of construction of the independent solutions for the power series method. In particular, this algorithm is important in the case of quantum systems with coupled channels which are described by two or more coupled Schrödinger equations.Методом разложения в степенной ряд, получено точное аналитическое выражение для второго независимого решения уравнения Шредингера для атома водорода. Решение состоит из суммы двух частей, одна из которых неограниченно возрастает на больших расстояниях, а вторая ограничена на бесконечности, хоть и содержит содержит логарифмический множитель. Такая структура решения характерна для всех величин орбитального момента. В известных нам учебным пособиям по квантовой механике приводится только выражение для первого регулярного решения. Для исключения второго линейно независимого решения в разных учебниках приводятся различные аргументы.Методом розкладу в степеневий ряд, отримано точний аналітичний вираз для другого незалежного розв’язку рівняння Шредінгера для атома водню. Розв’язок складається з двох доданків, один з яких необмежено зростає на великих відстанях, а другий на нескінченості прямує до нуля, хоч і містить логарифмічний множник. Така структура розв’язку характерна для всіх величин орбітального моменту. У відомих нам підручниках по квантовій механіці наводиться тільки вираз для першого регулярного розв’язку. Для усунення другого лінійно незалежного розв’язку в різних підручниках наводяться різні аргументи