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The Particle Number Projected Generator Coordinate Method is formulated for the pairing Hamiltonian in a detailed way in the projection after variation and the variation after projection methods. The dependence of the wave functions on the generator coordinate is analyzed performing numerical applications for the most relevant collective coordinates. The calculations reproduce the exact solution in the weak, crossover and strong pairing regimes. The physical insight of the ansatz and its numerical simplicity make this theory an excellent tool to study pairing correlations in complex situations and/or involved Hamiltonians. [ABSTRACT FROM AUTHOR]

The fission barriers of the nuclei [SUP256]Fm and [SUP258]Fm are investigated in a fully microscopic way up to the scission point. The analysis is based on the constrained Hartree-Fock-Bogolyubov theory and Gogny's D1S force. The quadrupole, octupole, and hexadecapole moments, as well as the number of nucleons in the neck region, are used as constraints. Two fission paths, corresponding to bimodal fission, are found. The differerence between fission of [SUP256]Fm and [SUP258]Fm is explained. [ABSTRACT FROM AUTHOR]

The behavior of shell effects with temperature is studied within the framework of the finite-temperature Hartree-Fock-Bogoliubov theory with the Gogny force. Thermal shape fluctuations in the quadrupole degree of freedom are taken into account in the frame of the Landau theory. Numerical results for the superfluid-to-normal and deformed-to-spherical phase transitions are presented for the nucleus 164Er. We find that the critical temperature for the deformed-spherical shape transition is much lowered when the thermal shape fluctuations are considered. [ABSTRACT FROM AUTHOR]