The projected functions of the coherent state model (CSM) describing the ground, gamma and beta bands are studied in the intrinsic frame of reference. Several symmetry relations for the intrinsic functions are obtained. Analytical expressions for the matrix elements of the collective operator flm+"cosm~ sin"~ are derived. Important selection rules are established for them. The probability distribution for the deformations fl and ~ are studied and compared to those corresponding to the solution of a microscopically determined Bohr-Mottelson Hamiltonian.

A microscopic calculation of Bohr's collective Hamiltonian is used to describe the collective motion in the 76Kr isotope. A single-particle basis calculated in a deformed Woods-Saxon potential leads to the potential energy surface obtained by the Strutinsky renormalization procedure, and to the inertial functions determined in the cranking model approximation. The collective Schr6dinger equation is solved numerically. The low-energy, even parity states in 76Kr are analyzed in the frame of this model. The theoretical results involve the potential energy and the inertial parameters as functions of intrinsic quadrupole deformations, the collective levels and wave functions including their transitions and electromagnetic moments. A good agreement between experiment and theory is obtained without adjusting specifically for this nucleus any parameter in the model. Some results regarding statical and dynamical characteristics of even-even 74'TS, S~ isotopes are also presented.

A new numerical method is applied to solving the equations of motion of the Friedberg-Lee soliton model for both ground and spherically symmetric excited states. General results have been obtained over a wide range of parameters. Critical coupling constants and particle numbers have been determined below which soliton solutions cease to exist. The static properties of the proton are considered to show that as currently formulated the model fails to fit all experimental data for any set of parameters.

A new model for coupling the motion of particles to that of a quadrupole collective core with rotations and fi and 7 vibrations is proposed. The Hamiltonian describing the core is obtained by quantising the classical Hamiltonian associated with the quadrupole degrees of freedom. The inertial parameters and the deformation energy surface are determined microscopically. The spherical shell model particles interacting among themselves by pairing are coupled to the core by a 22-pole (2=0, 2, 4) potential. The theory is applied to a95-19SHg. The predicted results agree very well the experimental data. A comparison of the present model to the other formalism is also given.

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