Electric monopole transitions from low energy excitations in nuclei

Electric monopole (E0) properties are studied across the entire nuclear mass surface. Besides an introductory discussion of various model results (shell model, geometric vibrational and rotational models, algebraic models), we point out that many of the largest E0 transition strengths, ϱ²(E0), are associated with shape mixing. We discuss in detail the manifestation of E0 transitions and present extensive data for single-closed shell nuclei, vibrational nuclei, well-deformed nuclei, nuclei that exhibit sudden ground-state changes, and nuclei that exhibit shape coexistence and intruder states. We also pay attention to light nuclei, odd-A nuclei, and illustrate a suggested relation between ϱ²(E0) and isotopic shifts.     

Systematic study of decay properties of heaviest elements

Decay properties and stability of heaviest nuclei with Z ?? 132 are studied within the macro-microscopical approach for nuclear ground-state masses. We use phenomenological relations for the half-lives with respect to ??-decay, ??-decay and spontaneous fission. Our calculations demonstrate that the ??-stable isotopes ²⁹¹Cn and ²⁹³Cn with a half-life of about 100 years are the longest-living superheavy nuclei located on the first island of stability. We found the second island of stability of superheavy nuclei in the region of Z ?? 124 and N ?? 198. It is separated from the ??continent?? by the ??gulf?? of short-living nuclei with half-lives shorted than 1 ??s.     

On the stability of the transeinsteinium elements

We calculate ground-state properties of nuclei in the Z≧100 region. The most stable superheavy elements are predicted for lower neutron number than in previous investigations, namely ₁₁₀ ²⁸⁸ X and ₁₁₀ ²⁹⁰ X, both with a calculated half-life of around 200 days. A new feature is a local minimum in the ground-state shell correction at Z=110 andN=162. Elements in this region are therefore expected to show increased stability relative to some earlier expectations.     

Statistical spectroscopy for nuclei in the fp shell

Nuclei in the fp shell have been studied using the spectral averaging method. This was attempted with a view to provide a rather simple alternative to detailed microscopic calculations. We have considered a decomposition of the overall spectroscopic space (m particles in the fp shell) in terms of a spherical j-orbit, isospin, configuration-isospin and SU(4) isospin subspaces. Centroid energies and widths of these subspaces are evaluated and used to determine binding energies, low-energy spectra and fractional occupancy of j-orbits. We have also examined the extent of Wigner SU(4) symmetry mixing for nuclei in this shell. The ratio of binding energies of isobars suggested by Franzini and Radicati to test the validity of SU(4) symmetry is also evaluated from the calculated binding energies. Comparisons are made with microscopic calculations like the shell model and Hartree-Fock where available. We find that the distribution method is able to determine ground-state energies and spectra of nuclei very well despite the fact that the vector spaces are quite large. The SU(4) symmetry in the ground-state region of these nuclei is strongly mixed largely due to the single particle spin-orbit coupling.     

Nuclear mass formula with a Yukawa-plus-exponential macroscopic model and a folded-Yukawa single-particle potential

We use a Yukawa-plus-exponential macroscopic model and a folded-Yukawa single-particle potential to systematically calculate the ground-state masses of 4023 nuclei ranging from ¹⁶O to {279}112. The method is also used to calculate the fission-barrier heights of 28 nuclei ranging from ¹⁰⁹Cd to ²⁵²Cf. We introduce several previously neglected physical effects, including a smaller nuclear radius constant, a proton form factor, an exact diffuseness correction, an A⁰ term, a chargeasymmetry term, and microscopic zero-point energies. The nuclear radius constant is determined from elastic electron scattering and microscopic calculations of nuclear density distributions, the range of the Yukawa-plus-exponential folding function is determined from heavy-ion elastic scattering, the surface-energy constant and surface-asymmetry constant are determined from the fission-barrier heights of the 28 nuclei that are considered, and the remaining constants are determined from the ground-state masses of 1323 nuclei ranging from ¹⁶O to ²⁵⁹No for which experimental values are known with experimental errors less than 1 MeV. For the final formula, the root-mean-square error in the ground-state masses is 0.835 MeV and the root-mean-square error in the fission-barrier heights is 1.331 MeV. Some of the remaining discrepancies in the groundstate masses can be understood in terms of instabilities with respect to ε₃ and ε₆ deformations.     

Light nuclei near neutron and proton drip lines in relativistic mean-field theory

We have made a detailed study of the ground-state properties of nuclei in the light-mass region with atomic numbers Z = 10–22 in the framework of the relativistic mean-field (RMF) theory. The nonlinear σω model with scalar self-interaction has been employed. The RMF calculations have been performed in an axially deformed configuration using the force NL-SH. We have considered nuclei about the stability line as well as those close to proton and neutron drip lines. It is shown that the RMF results provide good agreement with the available empirical data. The RMF predictions also show reasonably good agreement with those of the mass models. It is observed that nuclei in this mass region are found to possess strong deformations and exhibit shape changes all along the isotopic chains. The phenomenon of shape coexistence is found to persist near the stability line as well as near the drip lines. It is shown that the magic number N = 28 is quenched strongly, thus enabling the corresponding nuclei to assume strong deformations. Nuclei near the neutron and proton drip lines in this region are also shown to be strongly deformed.     

On the deexcitation of phonon excitations in nonspherical even-even nuclei by <Emphasis Type="Italic">M</Emphasis>1 transitions

The reasons for the violation of sign invariability for the parameter of mixture of M1 and E2 multipoles in the deexcitation of levels of the β-and γ-rotational bands to levels of the ground-state rotational band are considered for N = 90–114 nonspherical even-even nuclei.     

Nuclear structure with the dinuclear model

The dinuclear system concept is applied to the explanation of the structure of nuclei. The appearance of a low-lying band with negative parity states near the ground-state band in actinides and other nuclei is described by oscillations of the dinuclear system in the mass-asymmetry coordinate. The results for the parity splitting and electric multipole moments in alternating parity bands of these nuclei are in agreement with experimental data. The ground-state band and the superdeformed band of ⁶⁰Zn are interpreted as being caused by α-particle and Be clusterizations, respectively. Hyperdeformed nuclei are assumed as dinuclear systems which could directly be built up in heavy-ion collisions. Signatures of hyperdeformed states in such reactions could be γ transitions between these states and their decay into the nuclei forming the hyperdeformed nucleus.     

Rotational bands from shell-model Hamiltonians

Shell-model Hamiltonians with eigenstates forming rotational bands are considered. Such states have eigenvalues proportional to J(J+ 1) and can be projected from a Slater determinant of deformed orbitals. The latter are linear combinations of single-nucleon wave functions of j-orbits in a major shell. Conditions on matrix elements and single-nucleon energies are obtained in terms of the deformation parameters. An actual effective interaction is constructed yielding exact ground-state rotational bands for ²⁰Ne and ²⁴Mg which gives reasonable agreement with energies of other sd shell nuclei. Unlike the case of SU(3) symmetry, spin-orbit interaction and different single-nucleon energies can be accommodated and the procedure is not confined to oscillator major shells. Other welcome departures of our effective interaction from the SU(3) picture are the absence of rotational spectra in oxygen isotopes and that the ²⁴Mg ground-state band is projected from a Nilsson-type deformed state with axial symmetry.     

Excited collective states of heavy even-even nuclei

Quadrupole-type collective excitations of even-even nuclei are analyzed. In this analysis, transverse γ vibrations of the nuclear surface are taken into account effectively, while longitudinal beta vibrations remain free. A potential energy of the exponential form is used for free surface longitudinal beta vibrations. The behavior of the energy levels of excited states in the ground-state, β, and γ bands of heavy nuclei is studied, and the predictive potential of the model used is demonstrated for transfermium nuclei.     

Hartree-Fock and Hartree-Bogolyubov calculations inp shell nuclei

Hartree-Fock (HF) and Hartree-Fock-Bogolyubov (HFB) calculations have been performed for the 1p shell nuclei. Nuclear deformations are assumed to be at most axially symmetric. The HFB transformation is restricted to allow forp-p andn-n pairing only.Volkov's force, a soft-core, two-body interaction of semi-realistic nature, is used which does not produce any single-particle spin-orbit splittings. Coulomb force and the usual correction for centre-of-mass motion are taken into account. The calculations are carried out in a single-particle basis including all states up to principle oscillator quantum numberN=3 (in some cases,N=4). Binding energies, rms radii, density distributions, and quadrupole moments are calculated and found to be in reasonable agreement with experiment. Large Hartree-Fock energy gaps are obtained. They prevent the pairing correlations considered from becoming effective in an HFB approach and from changing the HF ground-state properties appreciably. In non-selfconjugate nuclei, the Pauli principle, rather than the Coulomb interaction, yields large differences between the charge and mass distributions. A theorem on selfconsistent symmetries is proved. The coefficients of the HFB transformation turn out to be real, if time-reversal and angular momentum projection flip are selfconsistent symmetries.     

Study of the Gamow-Teller resonance in 90Nb and 208Bi

An approach is proposed for studying the spreading properties of the Gamow-Teller resonance (GTR) in heavy nuclei including the coupling to 2p2h configurations and the ground-state correlations beyond RPA. The GTR is generated by a proton p-neutron h (πp-νh) phonon within the renormalized RPA. The second-order configuration mixing beyond RPA is realized by constructing two-phonon configurations, in which one of two intermediate phonon states is a πp-νh phonon. The numerical calculations are performed in the parent nuclei ⁹⁰Zr and ²⁰⁸Pb making use of M3Y nucleon-nucleon interaction and the single-particle wave functions obtained in the standard harmonic oscillator potential. The single-particle energies around the Fermi surface are substituted with the empirical values or those given by a Woods-Saxon potential. The results obtained provide a reasonable account for recent experimental findings on the GTR in these nuclei. The extension of the present approach to highly excited (hot) nuclei is also provided. The GTR is found to be stable against temperatures up to T = 6 MeV.     

Thermostatic properties of symmetric nuclear matter

The thermostatic properties of symmetric nuclear matter are calculated by extension of a recent Thomas-Fermi approach to ground-state nuclei by Myers and Swiatecki [1]. We have computed the free energy per nucleon f(T, n) in Landau's quasiparticle approximation and have derived from it the relevant thermostatic properties. In view of its application to finite excited nuclei, the degenerate limit of nuclear matter is discussed in particular. As an interesting result we find at higher temperatures van-der-Waals-like isotherms in the p-n plane. Below the critical temperature T_c = 17.3 MeV two phases of nuclear matter, liquid and vapour, are defined by these. Comparing these results with the reduced phase transition data of ³He, ⁴He, and “inert gases,” we find that nuclear matter is similar to the He-isotopes, but differs considerably from the inert gases.     

Influence of the nuclear Meissner - effect on the ground - state rotational bands of deformed nuclei

The possible regions of singularities in ground-state bands of deformed nuclei such as those observed in ¹⁶⁰Dy and ¹⁶²Er isotopes are predicted on the basis of the nuclear Meissner effect. The singularities can occur at Z=66,68 or N=90,112(110) in rare-earth nuclei and 92?Z96 or 138?N?144 in the actinides.     

Some problems in the generalized theory of finite Fermi systems

A realistic version of the generalization of the theory of finite Fermi systems to the case where some complex configurations involving phonons are explicitly taken into account is proposed. Secular equations describing the fragmentation of simple states in odd and even-even nuclei over complex configurations that belong to, respectively, the quasiparticle ? phonon + quasiparticle ? phonon ? phonon and the two quasiparticles ? phonon type and which are presently of greatest interest are derived on the basis of general relations for nuclei that involve pairing (nonmagic nuclei). These equations take into account effects associated with ground-state correlations due to complex configurations and with the additional quasiparticle-phonon mechanism of Cooper pairing in nuclei. The effects in question were disregarded previously, but they are of interest since they can be observed in present-day experiments.     

The nilsson-potential parameters for neutrons at A≃-100 and new deformation values for103Mo and105Mo

The half-lives of the first excited levels in odd-neutron nuclei¹⁰³Mo and¹⁰⁵Mo have been measured. From these data, values of the deformation parameter of?=0.31±0.05 and 0.29±0.06 for¹⁰³Mo and¹⁰⁵Mo, respectively, have been deduced assuming prolate spheroidal shapes. The present results in combination with previously determined properties of the ground-state bands of these nuclei are used to determineμ, the magnitude of the coefficient of the 1² term, in the Nilsson Hamiltonian, for the new region of deformation atA～-100.     

An investigation of the scaled modified oscillator potential

In the second volume of their book Nuclear structure, Bohr and Mottelson propose that in the modified oscillator potential the spin-orbit term and the l² term should be scaled according to the deformation of the potential. This scaling has been studied in detail, and some of its more general consequences are discussed. The single-particle parameters κ and μ have been fitted for nuclei in the rare earth region, for lead and for actinides. The scaled potential has been used for a detailed investigation of the nuclei in the actinide region, including calculations of potential energy surfaces, fission barriers and ground-state masses. Both symmetric and reflection asymmetric deformations have been considered and the results thus obtained with the scaled potential have been compared to those obtained with the modified oscillator potential and the folded-Yukawa potential.     

On magnetic dipole form factors in deformed nuclei

Properties of magnetic dipole form factors for deformed nuclei are discussed in terms of the angular momentum projected Hartree-Fock-Bogoljubov approximation and the neutron-proton interacting boson model. It is pointed out that there exists a relation between the M1 form factor for the excitation of the orbital K^π=1⁺ band, the M1 form factor for the ground-state band, and the collective M1 form factor in odd-A nuclei.