Sven Gösta Nilsson

On the nuclear structure and stability of heavy and superheavy elements

Abstract Nuclear potential energy surfaces as a function of deformations are calculated on the basis of a modified oscillator model. In particular, quadrupole ( P 2 ) and hexadecapole ( P 4 ) deformations are considered. The average behavior of the surface is normalized to that of a liquid drop through the employment of a generalized Strutinsky prescription. In this way a synthesis of the single-particle model and the liquid-drop model is obtained. Lowest minima in the potential energy surfaces give the ground state masses and distortions. These results compare extremely well with experimental data. Spontaneous fission half-lives are also obtained. The inertial parameters associated with fission barrier penetration are derived empirically as well as by a microscopic model. Shape (fission) isomeric states are also found. Their N and Z dependence in the present model are discussed and results tabulated. The calculations are extended to the predicted superheavy region around Z = 114 and N = 184. The total overall stability with respect to alpha and beta decay, and spontaneous fission is found to be most favorable in the vicinity of Z = 110 and N = 184. Detailed diagrams and tables are exhibited.

Nuclear shell structure at very high angular momentum

Abstract A cranked modified-oscillator model (with triaxial shape coordinates ϵ and γ) is used to study the nuclear potential-energy surface (based on a Strutinsky type of shell correction method) for very high angular momenta (30 ≦ I ≦ 100). For this region of spin, pair correlation is assumed to have collapsed. The influence of rapid rotation on the shell structure has been studied in the light and heavy rare-earth region as well as the Te-Ba region. Preliminary studies have also been made in the regions of superheavy and light nuclei. The possible occurrence of yrast traps is discussed.

On the spontaneous fission of nuclei with Z near 114 and N near 184

Abstract Theoretical calculations of the potential energy surface as a function of quadrupole and hexadecapole distortion parameters are reported for super-heavy nuclei with Z near 114 and N near 184. Estimates of spontaneous fission half-lives indicate a sizable island of relative stability in the vicinity of these closed-shell nucleon numbers.

Collective gyromagnetic ratios of deformed nuclei

Abstract The effective gyromagnetic ratios of the ground-state rotational band in deformed nuclei have been calculated on the basis of the cranking model formula. The latter has been evaluated in terms of deformed shell-model wave functions with inclusion of pair correlations. Comparison with experimental data both as to doubly even and odd-mass nuclei shows in general very good agreement within a range determined by the present experimental inaccuracy and the uncertainty in the specification of the nuclear-model parameters.

STABILITY OF SUPERHEAVY NUCLEI AND THEIR POSSIBLE OCCURRENCE IN NATURE.

Abstract Alpha and spontaneous fission half-lives were estimated theoretically in the region of beta-stable nuclei with Z ≈ 114, N ≈ 184. The possible existence of an island of stability is strongly supported. A preliminary search for surviving superheavy elements in nature gave negative results.

A coupling scheme relevant to high angular momenta and intermediate nuclear deformations

Abstract Based on the particle-plus-rotor model, it is shown that a new coupling scheme should occur in nuclei under certain conditions. In this coupling scheme, j is quantized along the direction of I rather than along the symmetry axis. Simple approximate wave functions for this scheme have been developed and compared with the exact solutions of the particle-plus-rotor model.

The giant E1 resonance for deformed nuclei

Abstract The random-phase approximation has been applied in particular to treat the giant E1 resonance of the deformed nucleus Mg 24 . Two well separated peaks are predicted on the basis of reasonable force parameters. The backward-going graphs are found not to affect significantly the positions of the 1 − states or the relative distribution of the oscillator strength. On the other hand the Thomas-Kuhn-Reiche sum is diminished for the case of a Ferrell-Visscher force by a magnitude of up to 30% by the inclusion of ground state correlations. The violation of the TKR sum rule encountered in the shell-model calculations is thus reduced considerably.

Shape isomeric states in heavy nuclei

Abstract The trend for the occurrence of secondary minima (shape isomers) in the potential-energy surface is discussed for an extended region of heavy nuclei. The calculations reported are based on a modified oscillator potential, and a renormalization of the average behaviour of the total energy to that of the liquid-drop model is performed. The regions treated are the actinide region, the rare-earth region along the stability line, and a region of neutron deficient isotopes of elements in the Pb region.

Microscopic calculations of the inertial mass parameter for fissioning nuclei

Abstract Inertia mass parameter B in a fissioning nucleus is calculated. The method of calculation is based on the assumption of adiabatic collective motion in the fission degree of freedom. Resulting values for B are 4 to 11 times larger than those obtained from the liquid-drop model estimates. It turns out that the inertial parameter increases almost linearly with nuclear deformation. It also appears to be a sensitive function of the pairing force strength. Rough estimates of the coupling between quadrupole and hexadecapole modes seem to indicate that it may modify considerably the obtained results. The calculations are extended to the predicted superheavy region connected with Z ≈ 114.

The nuclear energy gap and fluctuations in particle number in pairing wave functions

Abstract The effect of fluctuations in particle number for ensemble mean values calculated on the basis of BCS wave functions is investigated, in particular with reference to so-called “blocked” wave functions. Two simple models, the “degenerate” model and the “homogeneous” model, are studied in some detail. It is found that calculated energy changes ascribed to blocking are often largely spurious and due to a decrease in the width of the particle number distribution over the nuclear ensemble for the blocked broken-pair states relative to the ground state. A method to correct for the effect mentioned is suggested.