5 research outputs found
Nonrelativistic energy levels of helium atom
No full textThe nonrelativistic energy levels of a helium atom are calculated for S, P, D and F states. The calculations are based on the variational method of "exponential" expansion. The convergence of the calculated energy levels is studied as a function of the number of basis functions N. This allows us to claim that the obtained energy values (including the values for the states with a nonzero angular momentum) are accurate up to 28-35 significant digits. © 2019 Sissa Medialab Srl. All rights reserved
Leading-order relativistic corrections to the rovibrational spectrum of H2 + and HD+ molecular ions
No full textHigh-precision variational calculations of the operators for the relativistic corrections in the leading mα4 order are presented. The rovibrational states in the range of the total orbital angular momentum L=0-4 and vibrational quantum number v=0-10 for the H2+ and HD+ molecular ions are considered. We estimate that about 10 significant digits are obtained. This high precision is required for making theoretical predictions for transition frequencies at the level of 10-12 relative uncertainty. © 2019 American Physical Society
Nonrelativistic ionization energy levels of a helium atom
No full textThe nonrelativistic ionization energy levels of a helium atom are calculated for S, P, and D states. The calculations are based on the variational method of “exponential” expansion. Variational wave functions of bound states were obtained by solving the Schrodinger equation for the quantum three body problem with Coulomb interaction using a variational approach based on exponential expansion with the parameters of exponents being chosen in a pseudorandom way. The convergence of the calculated energy levels is studied as a function of the number of basis functions (N). This allows us to claim that the obtained energy values (including the values for the states with a nonzero angular momentum) are accurate to 20 significant digits
Formation of Turkic Group of Kalmaks and Sart-Kalmak Volost in Southern Trans-Urals of 18<sup>th</sup> Century
No full textThe formation of a tribal group of Kalmak in the Bashkir estate groups is considered. The author critically assesses the arguments given in the works of B. A. Aznabayev on the issue under consideration. Attention is paid to the problems of estate organization of society. The results of comparative analysis of archival materials and published sources relating to the formation and early history of the group of ayukinskie Kalmyks in the Southern Trans-Urals in 18th century are presented. The question of the role of the state in the creation of the Sart-Kalmak volost, as well as in creating conditions for the formation and preservation of the Kalmak tribal group is raised. Particular attention is paid to the definition of the social status of the yasak population as a class, whose duty was to pay yasak, and whose right (privilege) was the patrimonial right to land from which yasak was paid. The novelty of the study is seen in the fact that for the first time the archival documents concerning the decision on the land allotment to the groups of ayukin Kalmyks, serving Sarts and serving meshcheryaki were put into circulation in 1748, clearly showing the decisive role of the state in determining the social status and land rights of these groups of the population. The relevance of the study is determined by the relentless interest in ethnic history and rather contradictory interpretations of socio-cultural processes in the Southern Trans-Urals of the 18th century in the works of the opponent
