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Decay-spectroscopy study of the 67mFe isomer has been performed at GANIL. This isomer is found to have an energy of 387 keV and a half-life of 75(21) μs. An intermediate excited state is introduced at 367 keV. The results are interpreted in terms of various nuclear models, and a deformed shape is inferred for 67Fe.

A thorough examination of the level structure of 223Ra provides evidence that leads to an extensive re-evaluation of spin assignments and hence band structure. Altogether six bands corresponding to three parity-coupled pairs are identified and the interpretation of the data suggests that this N=135 nucleus may possess an octupole deformation. The band structure is interpreted within the framework of calculations using the Strutinski shell-correction method with a single-particle level scheme obtained with a Woods-Saxon mean field. The minimisation procedure for the total energy is achieved in a multideformation space including higher-order multipolarity deformations up to lambda =7. The importance of higher-order multipolarity deformation parameters is underlined.

Using the space rotation and translation invariance of the nuclear Hamiltonian the residual interactions for rotating nucleus are constructed. The connection between the Goldstone modes of motion (spurious states) and the symmetries of equations of motion in Random Phase Approximation for the states near the yrast line is found.

The general form of nuclear Hamiltonian equation of motion is derived within the Random Phase Approximation (RPA). The connection between the Goldstone modes of motion (spurious states) and the equations of motion is shown. The general method of extraction of spurious states from the solution of the RPA equations of motion is proposed.

The fast rotating erbium nuclei in the vicinity ofN=82 are investigated in the framework of the Strutinsky shell-correction method using the Woods-Saxon potential including non-axial hexadecapole deformations. The equilibrium deformation and moment of inertia are calculated for different spin values. The influence of nuclear temperature on the shell-effects is also discussed.

Our results confirm the fact that the CHFB + RPA model, originally introduced for high-spin states, can be successfully used in a low-spin region for the description of states near the yrast line. To get a better agreement with experimental data, one has to go beyond the scope of the RPA and to involve into the Hamiltonian also the terms of higher order in the boson expansion which lead to the mixing of states with different signature. This mixing is expected to play a role especially in the low-spin region. The inclusion of the residual interactions completely restoring the rotational symmetry of the total Hamiltonian (see [34]) into our model can also improve the results.

Calculations have been carried out of the fission barriers of excited nuclei for elements with Z = 102−108. The effect of nuclear heating is taken into account according to conventional quantum-statistical formulae. A realistic Woods-Saxon potential is employed to calculate single particle states. The- degree of deviation of the fissioning nucleus shape from axial symmetry and changes in the depth of the intermediate minimum are discussed.

Using the space translation invariance of the nuclear Hamiltonian the residual interaction for the rotating nucleus is constructed. The nuclear Hamiltonian thus obtained is used to describe negative-parity states near the yrast line within the random-phase approximation (RPA). The connection between the Goldstone modes of motion (spurious states) and the symmetries of equations of motion for the negative-parity states near the yrast line is found.

The height and structure of fission barriers for odd-mass nuclei and odd nuclei with 100 ⩽ Z ⩽ 111 are calculated by the Strutinsky method and using a realistic Woods-Saxon potential. Non-axial variations of the nuclear shape are taken into account. The influence of the blocking effect and of taking into account the conservation of spin and parity on the height of the barriers is considered. As in the adjacent even-even nuclei, in heavy isotopes of the heavy elements (Z = 107–111, N = 160–165) the occurrence of a shape isomer is possible. In the nuclei considered the fission barrier heights do not show a tendency of decreasing with increasing mass number.

High-spin states up to I${=31}^{\mathrm{\ensuremath{-}}}$ have been studied in the $^{218}\mathrm{Ra}$ nucleus and the staggering sequence of levels of positive and negative parity persists up to highest level. This observation supports the idea that in some nuclei the high-spin excitations may primarily be dominated by deformations which do not conserve the intrinsic parity (such as octupole, \ensuremath{\lambda}=3, and higher odd-\ensuremath{\lambda} multipolarities) rather than by the ``usual'' quadrupole (\ensuremath{\lambda}=2) and possibly higher even-\ensuremath{\lambda} multipolarities.

The alignment of the intrinsic angular momentum of a rotating nucleus into the rotational axis is studied in terms of a simple quasi-adiabatic approach. In the framework of this approach using the “quasi-particle + phonon” model with Harris non-adiabatic corrections it is possible to describe the rotational bands up to relatively high spins. In the case of235U it is demonstrated that this simple approach enables the qualitative description of the process of alignment of the intrinsic angular momentum with respect to the rotational axis.