Division of Nuclear Structure Theory
Prof. Jacek Dobaczewski, head
Prof. Witold Nazarewicz
Prof. Stanisaw G. Rohozinski
Dr. Wojciech Satua
Prof. Zdzisaw Szymanski
Dr. Tomasz Werner
In Ref.  neutron and proton radii of all even-even nuclei of the periodic table were analyzed in terms of the Skyrme-Hartree-Fock-Bogolyubov method. In particular, behavior of the radii when approaching the proton and neutron drip lines as well as its correlation with the shell structure of exotic nuclei was discussed. It was shown that the possible disappearance of magic shell gaps in neutron drip-line systems, predicted by theory, may lead to pronounced neutron-skin effects while virtually no such effect can be seen on the proton-rich side. The results obtained are of significant importance for the description of exotic nuclei, the properties of which play a crucial role in astrophysical processes.
Paper  was devoted to a detailed analysis of proton drip-line nuclei around doubly magic Ni. These nuclei can already be accessed experimentally, and their properties, in particular their stability and half-lives against one- and two-proton emissions, can provide a sensitive test of various models used for their description. Calculations presented in this work were performed in the framework of the self-consistent mean-field theories (Hartree-Fock, Hartree-Fock-Bogolyubov, and relativistic mean field). Separation energies, deformations, single-particle structure, proton average potentials, and diproton decay half-lives were investigated. It was shown that half-lives depend crucially on nuclear masses (binding energy) but not on the detailed radial form of the mean field.
Applications of the Hartree-Fock-Bogolyubov theory in spatial coordinates to very neutron rich nuclei were presented in Ref. . This theory properly describes pairing coupling of bound states with the particle continuum and guarantees correct asymptotic properties of nuclear wave functions even for very weakly bound systems. Properties of canonical single particle wave functions as well as spectral amplitudes of quasiparticle states were discussed. In view of a rapidly growing efforts to reach experimentally very neutron rich nuclei, two novel features of such systems have been suggested. First, changes of nuclear shell structure due to an increased surface diffuseness were pointed out, and second, the possibility of spatially extended pairing fields was discussed. These effects may constitute fingerprints of modified structural properties of systems with large neutron excess.
Masses, deformations, radii, two-neutron separation energies, and single-particle properties of Si, S, Ar, and Ca isotopes were investigated in Ref.  in the framework of the self-consistent mean-field theories (Hartree-Fock and relativistic mean field). In particular, the role of the N=28 magic gap in the neutron-rich isotopes, and differences between proton and neutron deformations were discussed. Calculations showed strong deformation effects for N28 isotones due to the 1 core breaking. For isotopes close to the neutron drip line the results suggest the possibility of large isovector-deformation effects. Microscopic structure of nuclei studied in this work is of particular interest for astrophysics, as they play an important role in the nucleosynthesis of the heavy Ca-Ti-Cr isotopes.
In paper , using the cranking Skyrme-Hartree-Fock model, we performed systematic analysis of intrinsic relative charge quadrupole moments, , in superdeformed (SD) bands around doubly-magic SD core of 152Dy. The most striking observation was that can be written with a surprisingly high accuracy as a sum of independent single-particle and/or single-hole contributions. Verification of this very simple extreme shell-model relation stimulated a lot of experimental activity. This is so because the 's are rather robust fingerprints of intrinsic configurations and, therefore, when measured, they allow for a stringent empirical verification of theoretical models. A very good agreement between experiment and our theoretical calculations suggests that the SD bands around 152Dy are excellent examples of an almost unperturbed single-particle motion.
Description of odd nuclei in terms of algebraic models based on group theory was presented in Ref. . It was shown that algebraic structures constructed from bifermion operators can be enriched by adding single fermion operators and considering superalgebras. This leads to sets of simple solvable models for collective states in odd nuclei. Such models can be effectively bosonised by considering boson-fermion systems composed of many bosons and one ideal fermion which commutes with bosons. The construction ensures the Pauli exclusion principle exactly, while physical exchange correlations between the odd fermion and the core are cast in a form of particular interaction terms. Our study constitutes the only existing attempt where an exact bosonisation methods can be used for odd nuclei.
In Ref. , within the single-j shell model, we analyzed the influence of hexadecapole interactions on the structure of rotational bands. Results of an exact shell-model diagonalization of the quadrupole-plus-hexadecapole Hamiltonian were discussed in terms of the intrinsic deformations extracted by means of the self-consistent Hartree-Fock method. The purpose of the study was twofold. First, we tested the conjecture that the hexadecapole degree of freedom might be responsible for the effect of staggering of moments of inertia (as a function of angular momentum) in rotational bands. Our results suggest that such a staggering effect cannot be explained by the coupling between the rotation and the hexadecapole vibration. Second, we investigated the evolution of the hexadecapole shapes with rotational frequency. We showed that the self-consistent results strongly prefer one particular parametrization of the hexadecapole tensor.
Papers  and  describe methods of solving self-consistent equations for the Skyrme interaction by employing the Cartesian deformed harmonic oscillator basis. An expansion of single-particle wave functions on such a basis allows for a very rapid, effective and robust algorithm to find the self-consistent solutions. We were able to built a numerical code which can find self-consistent states without the time-reversal symmetry imposed, and with only one symmetry plane. This allows for systematic studies of rapidly rotating, nonaxially deformed, and at the same time octupolly deformed nuclei. Methods based on the Green function expansion have been used, which gives the possibility to rapidly calculate the Coulomb fields for arbitrarily deformed shapes. Numerical codes have been put in the public domain and are intensely used by different groups, especially for studying rotational bands in superdeformed nuclei.
In nuclei with a considerable excess of neutrons (or protons) the valence particles occupy different shell-model orbits and pairing correlations between like particles dominate. In NZ nuclei, however, an enhancement of neutron-proton (np) correlations is expected. In paper  we extended traditional seniority pairing model by incorporating directly schematic np pairing correlations. Generic properties of the isovector (T=1) and isoscalar (T=0) collective pairing phases were discussed within the mean-field Bogolyubov theory as well as in the framework of the number-projected theory. For the first time, a conjecture has been made that the T=0 np pairing may offer possible explanation of the so called Wigner singularity of nuclear masses at the N=Z line.
In paper  we developed a method which allows to extract the Wigner energy directly from the experimental data. Furthermore, we found independent empirical arguments that it is mostly due to the T=0 part of the nuclear interaction. Using the nuclear shell model, we analyzed the Wigner singularity in terms of the np pairs of a given angular momentum and isospin. It was shown that it cannot be solely explained in terms of simple building blocks like deuteron-like J=1, T=0 pairs, at least not in the light nuclei. An advent of radioactive ion beams opens nowadays a unique opportunity to explore heavy NZ nuclei with many valence particles where collective np pairing phenomena are most likely to appear bringing hopes for final clues to resolve this fascinating issue.
A parametrization of arbitrary non-axial octupole and hexadecapole nuclear surfaces was proposed  in terms of deformation parameters covariant under changes of names and directions of the coordinate axes (O transformations) defined externally, for instance, by the quadrupole deformation. The parametrization conserves the O symmetry of the coordinate system and thus does not single out any of the 48 equivalent frames. For multipolarities higher than four a similar unified parametrization of non-axial nuclear shapes (still having three mutually perpendicular symmetry planes, i.e., conserving the D symmetry) was applied. For such shapes natural coordinate axes are just the intersections of the symmetry planes. Moreover, it was shown that the deformation parameters of arbitrary multipolarity describing the D-symmetric shapes can always be treated as functions of the quadrupole deformation parameters. This gives a possibility to pass from the axial-symmetric to the D-symmetric nuclear shapes of higher multipolarities even without enlarging the deformation space. The octupole and hexadecapole deformations (and also deformations of higher multipolarities) give a significant contribution to the total energy of heavy nuclei and play an essential role for their ground-state properties, super and hyperdeformations and, especially, spontaneous-fission properties. Therefore, the obtained results constitute an important advance over methods used up to now where mainly axial-symmetric shapes of higher multipolarities have been considered.
A general formula for the double angular correlation between polarized gamma quanta emitted from an oriented nucleus was found and analyzed . It was shown that a measurement of the linear polarization for one or both correlated quanta, in addition to the observation of their directions, can give a new information about spins and parities of nuclear excited states and, consequently, lead to the unique assignment of them. Such a result is very important and timely in the present-day "in-beam" nuclear gamma spectroscopy. On the one hand, the unique spin and parity assignments are crucial for the nuclear structure investigations. On the other hand, the modern multidetector gamma-ray spectrometers containing new generation segmented detectors (e.g., CLOVER), which are sensitive to the polarization, give the possibility to measure not only directional, but also polarizational correlations. In consequence, the present research became a ground breaking step for modern spectroscopic analyses.
Distributions of fractional changes in the dynamical moments of inertia of pairs of bands in superdeformed nuclei were studied . These distributions indicate that: (i) there is an excess of pairs of bands with very similar moments of inertia, (ii) there exists a large excess of identical bands in superdeformed nuclei compared to normally deformed nuclei at low spins, and (iii) the intrinsic structure of superdeformed bands is clearly reflected in their moments of inertia. This unexpected result suggests that the single-particle motion in a well deformed rotating potential is very diabatic. That is, superdeformed bands are very well characterized by single-particle quantum numbers of an intrinsic one-body potential. Surprisingly, it is at very large deformations and high angular momenta where the very best examples of the extreme shell model (i.e., an almost undisturbed single-particle motion) are found.
Deformation properties of weakly bound nuclei were discussed in the deformed single-particle model . It has been demonstrated that in the limit of a very small binding energy the valence particles in specific orbitals, characterized by a very small projection of single-particle angular momentum onto the symmetry axis of a nucleus, can give rise to the halo structure which is completely decoupled from the rest of the system. The quadrupole deformation of the resulting halo is completely determined by the intrinsic structure of a weakly bound orbital, irrespective of the shape of the core. This work points out that for very diffused and spatially extended systems the geometric interpretation of nuclear shape and its deformations is lost.
Paper  contains systematic calculations of half-lives and spectroscopic properties of spherical ground-state proton-emitters. Various theoretical approaches to proton emission from spherical nuclei have been investigated. Proton half-lives of observed heavy proton emitters have been well reproduced by spherical calculations with the spectroscopic factors calculated in the independent quasiparticle approximation. The quantitative agreement with experimental data obtained in our study requires that the parameters of the proton-nucleus potential be chosen carefully. It also suggests that deformed proton emitters will provide invaluable spectroscopic information on the angular momentum decomposition of single-proton orbitals in deformed nuclei.
Papers published in refereed periodicals in 1996 and 1997