Σ-Factorization method: A new development of molecular-orbital theories based on one-centre approximation of atomic and molecular densities

A new approach to one-centre approximation methods initiated by Mulliken and Ruedenberg in their earlier works has been developed in this paper. Despite the similarity of underlying ideas, the proposal to factorize thes-function product instead of the total density factorization along with a new technical background of the method provide more flexible and practical scheme since large orbital quantum numbers do present no longer the crucial point for extending the approach for compounds with heavy atoms. Both minimal and extended schemes are equally within the scope of the method. The technical links with the nuclear shell model formalism are discussed briefly.     

High-pt hadrons in the pionization region in QCD

We show that in QCD the production of high-p_t hadrons in the pionization region $\text{ln}\text{(}\text{p}{}_{\mathrm{<mtext>t</mtext>}}{}^2\text{μ}{}^2\text{) < [(}\text{8N}\text{D0.21 β}{}_2\text{)}\text{ln}\text{x}{}^{\mathrm{?1}}\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is not a rare process, but a usual “soft” one. Its inclusive cross section ? behaves as $\text{? =}\text{d}\text{σ}\text{d}\text{y}\text{d}\text{p}{}_{\mathrm{<mtext>t</mtext>}}{}^2\text{∝}\text{σ}{}_{\mathrm{<mtext>t</mtext>}}\text{p}{}_{\mathrm{t0}}{}^2$. At ISABELLE energies and p_t = 10 GeV we estimate this cross section to be at least an order larger than the value obtained by commonly used parametrizations.     

The matrix theory of electron spin multiplets for atoms and molecules

In this article a matrix method for the construction of spin multiplets (spinconfigurations) is suggested in order to solve the multielectron problem for atoms and mulecules by means of configuration interaction.A simple graphical way is given to enumerate configurations and to break their set into subsets of configurations related to the given projection of the total spin of a system S _z . It is found that all matrices in the theory of spin multiplets are convex and in cases of two, three, and four electrons are broken into blocks of an order no higher than 3.The model of the solution of the multielectron Schrödinger equation, in which the total spin of core electrons is zero, is considered. In this model the construction of linear combinations of configurations is reduced to the construction of those for but valence electrons.