[en] Properties of density-dependent contact pairing interactions in nuclei are discussed. It is shown that the pairing interaction that is intermediate between surface and volume pairing forces gives the pairing gaps that are compatible with the experimental odd-even mass staggering. Results of the deformed Hartree-Fock-Bogoliubov calculations for this ''mixed'' pairing interaction, and using the transformed harmonic oscillator basis, are presented

[en] A general scheme of constructing boson expansions that was proposed in earlier work is applied to a number or examples. The Fukutome expansion is obtained by considering the spinor representation of the SO(2N+1) group. Its hermitian, Holstein-Primakofr-type version is also derived. The generalized Dyson expansions for even and odd fermion systems are given in terms of two spinor representations of the SO(2N) group. For fixed fermion number systems the relevant boson expansions are obtained by considering the fundamental representations of SU(N) while for fixed seniority those of Sp(N) are concerned. The collective boson expansions corresponding to the Ginocchio model, the interacting boson model of Arima and Iachello and the Elliot model are given for the symmetric representations of SO(8) and SU(1+1) and any representation of SU(3)

[en] The Hartree-Fock plus BCS method with the Skyrme interaction is used to analyse the equilibrium deformations of nuclei in the A≅100 region. It is shown that the theoretical results are consistent with the N_nN_p classification scheme. Relations between the nuclear deformation effects and the neutron-proton interaction are discussed

[en] We describe a method of solving the nuclear Skyrme-Hartree-Fock problem by using a deformed Cartesian harmonic oscillator basis. The complete list of expressions required to calculate local densities, total energy, and self-consistent fields is presented, and an implementation of the self-consistent symmetries is discussed. Formulas to calculate matrix elements in the Cartesian harmonic oscillator basis are derived for the nuclear and Coulomb interactions. (authors)

[en] We describe the code HFODD which solves the nuclear Skyrme-Hartree-Fock problem by using the deformed Cartesian harmonic oscillator basis. The user has a possibility of choosing among various symmetries of the nuclear HF problem for rotating or non-rotating nuclei; they vary from the non-axial parity-invariant nuclear shapes, through those also breaking the intrinsic parity, towards the least-restrictive case corresponding to only one symmetry plane. The code provides a solution for a complete superdeformed rotational band in an A∼150 nucleus within one CPU hour of the CRAY C-90 supercomputer or within two-three CPU hours of a fast workstation. (authors)

[en] A possible construction of the SU(6) algebra in the fermion Fock space has been discussed. It is argued that in order to find a microscopic justification of the Ineracting Boson Model one should construct the fermion-number-conserving shift operator F-circumflex_μ⁺, playing in the fermion SU(6) algebra a role analogous to the d_μ⁺s generator of the boson realization of SU(6) and that the boson operators itself need not to have a microscopic significance. It is shown however that such shift operator cannot be a single-particle operator. An example of a non-single-particle SU(6) shift operator is provided by the Ginocchio model but a closed algebraic form of it is difficult to unveil. 12 refs., 1 fig., 1 tab. (author)

No abstract available

[en] It is shown that the BCS state can be presented in a form of exponent of a single-particle operator acting on another BCS state. By using such a form, one can describe the quadrupole collective states as built of multiple single-particle coherent quadrupole excitations. In the fermion dynamical symmetry model (FDSM) one obtains a description entirely equivalent to the standard one, which uses the monopole and quadrupole particle pairs. In the single-j shell model the results are identical to those of the deformed BCS approach. (orig.)

[en] It is shown that the boson expansions hitherto known, as well as an infinite number of the new ones, can be derived in a unified way in terms of the functional representation technique. Each boson expansion (boson representation) is valid for the carrier space of an irreducible representation of a semisimple compact Lie subgroup of SO(2N+1) and can be presented as Dyson-type, Holstein-Primakoff-type or Garbaczewski (Marumori)-type expansion with the corresponding properties concerning finiteness, convergence and hermitian conjugation. The physical boson space can be determined for every expansion and the projection operator is explicitly found. The methods for solving the Schroedinger equation are discussed and the generator coordinate method is shown to be equivalent to the boson expansion approach. (orig.)

[en] The method for obtaining boson expansion by representing the fermion states as holomorphic functions of many complex variables is presented. Such functional representation is explicitly constructed for each space which is the carrier space of an irreducible representation of a semisimple compact Lie group. This is achieved by proving the unity resolution in terms of holomorphically parametrized Perelomov's generalized coherent states. The functional images of fermion states are polynomials of complex variables, while those of fermion operators are differential operators of finite order with polynomial coefficients. (orig.)