Algebraic methods in noolinear penurbation theory I Bogaevski. A. Povzner.p.em. ~ (Applied mathematical sciences)Translation of: Algebraicheski metody v nelineinoi tcori vozmusbchenii.Includes bibliographical references and inde~.

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Electronic structure of bcc Np, fcc Pu, Am, and Cm pure metals under pressure has been investigated employing the LDA+U method with spin-orbit coupling (LDA+U +SO). Magnetic state of the actinide ions was analyzed in both LS and jj coupling schemes to reveal the applicability of corresponding coupling bases. It was demonstrated that whereas Pu and Am are well described within the jj coupling scheme, Np and Cm can be described appropriately neither in {mσ}, nor in {jmj } basis, due to intermediate coupling scheme realizing in these metals that requires some finer treatment. The LDA+U +SO results for the considered transuranium metals reveal bands broadening and gradual 5f electron delocalization under pressure. 71.27.+a, Prominent structural transition from δ-to α-phase of plutonium gives substantial total volume contraction [1]. In americium and curium the similar transitions were also found under high pressure or increasing temperature [2,3]. These volume collapses are usually related to the drastic electron delocalization. In curium, additional magnetic stabilization of intermediate phases was also found [3,4].In many strongly correlated materials Coulomb and Hund interactions are dominant, whereas spin-orbit (SO) coupling is comparably smaller and usually can be treated within various perturbative techniques. In the case of 5f electronic shell of actinide metals all these three terms in Hamiltonian are of comparable strength. That results in a very sensitive (non)magnetic ground state, but also in coupling schemes varying from usual LS (Russel-Saunders) one. An intermediate or jj coupling schemes were found to be more appropriate for 5f electrons in transuranium metals [5,6,7,8].In actinide elements spin-orbit coupling is stronger than exchange Hund interaction, and hence the jj coupling scheme can be valid with a well defined total moment J, but in this case spin S and orbital L moments are not well defined. Then the basis of eigenfunctions of total moment operator {jm j } is the best choice, since the matrix of spin-orbit coupling operator and occupation matrix are diagonal in this basis. However the exchange interaction (spin-polarization) term in the Hamiltonian is not diagonal.In some 5f elements intermediate coupling scheme is realized, then the occupation matrix has nondiagonal elements in both {mσ} and {jm j } orbital bases. Therefore, both terms in the Hamiltonian: spin-orbit coupling and exchange interaction, should be taken in a general nondiagonal matrix form.Numerous band methods and approximations have been applied to describe magnetic and spectral properties of transuranium metals, see [5] for review. Nonmagnetic ground state of pure plutonium metal observed experimentally [9] was reproduced in the electronic structure calculations in the LDA+U +SO calculations [10] (local density approximation supplemented with the Hubbard U -correction and spin-orbit coupling). In these calculations the exchange interaction was found to be the reason of artificial antiferromagnetic ordering in various LSDA+U...

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