DIVISION OF NUCLEAR STRUCTURE THEORY
Head: Prof. Jacek Dobaczewski
Academic teachers: Prof. Witold Nazarewicz1, Prof. Stanisław G. Rohoziński, Prof. Wojciech Satuła, Dr hab. Tomasz Werner
Postgraduate students: Mgr Przemysław Olbratowski, Mgr Honorata Zduńczuk
Graduate students: Michał Rafalski
In 2002 and 2003, members of the Division have published 30 papers in refereed periodicals (see the list below), and have presented 28 invited talks and 16 contributions at international conferences. During this period of time the following main research projects have been realized:
In Ref. , rotational bands were found in Co using the Si(S,3p) reaction at 130 MeV. The bands, extending the mass 60 region of large deformation down to , are signature partner sequences. Their quadrupole moments are similar to those of bands in the neighboring nuclei. The features of the new bands were described by Skyrme Hartree-Fock calculations favoring a configuration assignment with one neutron and one proton excited in the respective 1g intruder orbital. An attempt to describe the magnetic () properties of the signature partner structure was also presented.
First fully self-consistent Skyrme-Hartree-Fock calculations have been performed  for a nucleus rotating about an axis that is not a principal axis of the density distribution (Tilted-Axis Cranking). It was shown that an exited rotational band in Gd has the character of a shears band, in which the angular momentum is generated mainly from the gradual alignment of a few valence nucleons. However, the important role of the collective rotation was also pointed out. In addition, paper  discusses the symmetries of the mean field and differences between the self-consistent and phenomenological implementations of the Tilted-Axis Cranking method.
In Ref. , nearly degenerate partner bands observed in odd-odd nuclei were interpreted as a manifestation of chirality in the intrinsic reference frame. A phenomenological approach, based on a core-particle-hole coupling model, has been developed to address the experimental observables. This laboratory-frame model, in which chiral symmetry has been restored, includes a triaxial core, a particle and hole single-particle Hamiltonians, and quadrupole-quadrupole interactions. The optimal model parameters were investigated. The results of the calculations indicated the existence of states with the same spin, parity, and similar excitation energy forming partner bands that were nearly degenerate over a range of spins. These calculated partner bands were consistent with the chiral band interpretation and were in agreement with experimental observations in this region. The model has been applied to excited states in La.
In Ref. , the superdeformed bands in Cu, Cu, Zn, and Zn were analyzed within the frameworks of the Skyrme-Hartree-Fock as well as Strutinsky-Woods-Saxon total routhian surface methods with and without the =1 pairing correlations between like particles. It was shown that a consistent description within these standard approaches cannot be achieved. A =0 neutron-proton pairing configuration mixing of signature-separated bands in Zn was suggested as a possible solution to the problem.
Paper  contains systematic experimental and theoretical study of superdeformed (SD) bands in Sr, Y, and Zr. Two types of mean-field models, such as Strutinsky-type calculations with pairing and unpaired self-consistent Skyrme-Hartree-Fock approach, were used to analyze the data. For both models, experimental data appear to place rather stringent conditions on configuration assignment, leading to a consistent understanding of the underlying configurations. Both models provide a satisfactory quantitative description of moments of inertia and quadrupole moments in these bands.
Ref.  presents results of differential lifetime measurements, free from common systematic errors, for more than 30 rotational bands in over 15 different nuclei in the A135 mass region. The extracted single-particle effective quadrupole moments are compared to theoretical values obtained within self-consistent Skyrme-Hartree-Fock as well as within relativistic-Hartree mean-field models. Detailed comparison convincingly demonstrates a validity of the additivity of single-particle quadrupole moments in this mass region. Similar additivity scheme was previously firmly established [Satua et al. Phys. Rev. Lett. 77 (1996) 5182] to hold in super-deformed bands in the A150 mass region.
In Ref. , the latest experimental data on the high-spin states in Eu were analysed. One new magnetic band was identified, and the known level schemes of other two were extended. The level energies and reduced transition probabilities were compared with the phenomenological Tilted-Axis Cranking calculations. A satisfactory agreement was obtained, which allowed for the assignment of proper single-particle configurations to the observed bands.
In Ref. , we investigated the effects of the spin-isospin channel of the Skyrme energy functional on predictions for Gamow-Teller distributions and superdeformed rotational bands. We used the generalized Skyrme interaction SkO' to describe even-even ground states and then analyzed the effects of time-odd spin-isospin couplings, first term by term and then together via linear regression. Some terms affect the strength and energy of the Gamow-Teller resonance in finite nuclei without altering the Landau parameter that to leading order determines spin-isospin properties of nuclear matter. Though the existing data are not sufficient to uniquely determine all the spin-isospin couplings, we were able to fit them locally. Altering these coupling constants does not change the quality with which the Skyrme functional describes rotational bands.
In Refs.  and , the quadrupole collective excitations of even-even transactinide nuclei, U, Pu, Cm, Cf, Fm i No, were described in the framework of the microscopic Bohr Hamiltonian modified by including the coupling between the quadrupole degrees of freedom and collective pairing vibrations. The excitation energies of the states of the ground-state, and bands as well as the reduced transition probabilities were calculated. A reasonable agreement of the results with experimental data available so far was obtained with no adjustable parameters. The mean values of the and deformations in the ground states and in the - and -vibrational states were calculated and analysed. Superdeformed states localized in the econd minimumóf the collective potential energy surface for No were also studied.
In certain neutron-rich Te isotopes, a decrease in the energy of the first excited 2 state is accompanied by a decrease in the E2 strength to that state from the ground state, contradicting simple systematics and general intuition about quadrupole collectivity. In Ref. , we used a separable quadrupole-plus-pairing Hamiltonian and the quasiparticle random phase approximation to calculate energies, B(E2,02) strengths, and g factors for the lowest 2 states near Sn. We trace the anomalous behavior in the Te isotopes to a reduced neutron pairing above the =82 magic gap.
In Ref. , we calculated the low-lying B(E2,02) distribution of strength in Ni and other nickel isotopes using several theoretical approaches. We find that in Ni the calculated B(E2) transition to the first 2 state exhausts only a fraction of the low-lying B(E2) strength, while the remainder of the low-lying strength is mainly collected in the group of states lying above 4MeV. This fragmentation is sensitive to the size of the =40 gap. We argue that the small experimental B(E2) value to the first 2 state is not strong evidence for the double-magic character of Ni.
In Ref. , we performed shell model Monte Carlo calculations for proton-rich Kr, Sr, and Zr isotopes in the mass range of =72-84. We employed a complete 1p0f-0g1d2s configuration space and an effective quadrupole-plus-pairing residual interaction. Our calculation reproduced the large B(E2) values observed in these nuclei. We related these values to the gain in correlation energy obtained by moving nucleons across the =40 subshell closure into g orbitals.
According to standard textbooks, the nuclear symmetry energy is devided into parts originating from the kinetic energy and interaction. In Ref.  we argued that this traditional view requires modifications and we proposed an alternative scenario. Starting from the idea of isospin cranking model we ascribed the physical origin of the kinetic term to the granularity of fermionic levels of an arbitrary, in principle, fermionic quantal system. In nuclear physics, such a scenario connects the symmetry energy directly to the isoscalar mean-potential. The reliability of this concept was verified using fully self-consistent Skyrme-Hartree-Fock calculations.
Using relations between wave functions obtained in the framework of the relativistic mean field theory, in Ref.  we investigated the effects of pseudospin and spin symmetry breaking on the single nucleon wave functions in spherical nuclei. In our analysis, we applied both relativistic and non-relativistic self-consistent models, as well as the harmonic oscillator model. In the pseudospin symmetry limit, radial wave functions of the upper components of pseudospin doublets satisfy certain differential relations. We demonstrated that these relations are not only approximately valid for the relativistic mean field eigenfunctions but also for the non-relativistic Hartree-Fock and harmonic oscillator eigenfunctions. Generally, we expect them to be approximately valid for eigenfunctions of any non-relativistic phenomenological nuclear potential that fits the spin-orbit splittings of nuclei. Likewise in the spin symmetry limit, the radial amplitudes of the upper components of the Dirac eigenfunctions of spin doublets were predicted to be equal, and this is approximately valid for both non-relativistic and relativistic mean-field models. Also the spatial amplitudes of the lower components of the Dirac eigenfunctions of spin doublets satisfy differential relations in spin symmetry limit, and these relations are approximately valid in the relativistic mean field model.
In Ref. , we performed large-scale Hartree-Fock-Bogolyubov calculations using finite range Gogny force D1S, in order to extract theoretical mass dependence of the nuclear pair gap, . The theoretical values of the gap were compared to the experimental data extracted according to the method given in our previous paper [Satua et al. Phys. Rev. Lett. 81 (1998) 3599]. This method is supposed to remove, or minimize, the contamination due to the mean-level-spacing contribution, which may otherwise be present in the experimentally deduced gap. Good overall agreement was found between theory and experiment, without discrepancies in light nuclei, confirming that mass-dependence of the nuclear pairing gap is indeed weaker than the commonly accepted one, vis. 12/MeV.
In paper , the theory of the superheavy elements was reviewed with the main focus on nuclear structure aspects. Structure of odd- superheavy elements was investigated using a variety of self-consistent approaches. Microscopic shell corrections, extracted from the Skyrme-Hartree-Fock and relativistic mean-field calculations, elucidated the question of the centre-of-shell-stability in the superheavy region. Finally, the existence of exotic configurations, having gross non-uniformities of nucleonic density, expected to occur in nuclei with very large atomic numbers, was addressed.
The discovery of new superheavy nuclei has brought much excitement to the atomic and nuclear physics communities. Hopes of finding regions of long-lived superheavy nuclei, predicted in the early 1960s, have reemerged. The superheavy elements mark the limit of nuclear mass and charge; they inhabit the upper right corner of the nuclear landscape, but the borderlines of their territory are unknown. The stability of the superheavy elements has been a longstanding fundamental question in nuclear science. How can they survive the huge electrostatic repulsion? What are their properties? How large is the region of superheavy elements? We do not know yet all the answers to these questions. In short article  we presented the current status of research in this field.
Recent mass measurements show a substantial weakening of the binding energy difference in the neutron-deficient Pb isotopes. As is often attributed to the size of the proton magic gap, it might be speculated that the reduction in is related to a weakening of the spherical =82 shell. In Ref.  we demonstrated that the observed trend is described quantitatively by self-consistent mean-field models in terms of deformed ground states of Hg and Po isotopes.
In papers  and , a new 7 ms isomer in the drip line nucleus Dy was selected from the products of the Fe (315 MeV)Mo reaction by a recoil mass spectrometer and studied with recoil-delayed - coincidences. Five cascading -transitions were interpreted as the decay of an =8 -isomer via the ground-state band. The probability of proton emission from Ho to the =0 ground state and to the =2 excited state in Dy was discussed.
Work  presents the first continuum shell-model study of weakly bound neutron-rich nuclei involving multiconfiguration mixing. For the single-particle basis, the complex-energy Berggren ensemble representing the bound single-particle states, narrow resonances, and the non-resonant continuum background is taken. Our shell-model Hamiltonian consists of a one-body finite potential and a zero-range residual two-body interaction. The systems with two valence neutrons are considered. The Gamow shell model, which is a straightforward extension of the traditional shell model, is shown to be an excellent tool for the microscopic description of weakly bound systems. It is demonstrated that the residual interaction coupling to the particle continuum is important; in some cases, it can give rise to the binding of a nucleus.
In Ref. , we presented the study of weakly bound, neutron-rich nuclei using the nuclear shell model employing the complex Berggren ensemble representing the bound single-particle states, unbound Gamow states, and the non-resonant continuum. In the proposed Gamow Shell Model, the Hamiltonian consists of a one-body finite depth (Woods-Saxon) potential and a residual two-body interaction. We discussed the basic ingredients of the Gamow Shell Model. The formalism wass illustrated by calculations involving several valence neutrons outside the double-magic core: He and O.
In Ref. , nuclear binding energies and two-neutron separation energies were analysed starting from the liquid-drop model and the nuclear shell model in order to describe the global trends of the above observables. We subsequently concentrated on the Interacting Boson Model (IBM) and discussed a new method in order to provide a consistent description of both, ground-state and excited-state properties. We addressed the artefacts that appear when crossing mid-shell using the IBM formulation and performed detailed numerical calculations for nuclei situated in the 50–82 shell. We also concentrateed on local deviations from the above global trends in binding energy and two-neutron separation energies that appear in the neutron-deficient Pb region. We addressed possible effects on the binding energy, caused by mixing of low-lying 0 intruder states into the ground state, using configuration mixing in the IBM framework. We also studied ground-state properties using a macroscopic–microscopic model. Detailed comparisons with recent experimental data in the Pb region were amply discussed.
In years to come, we shall see substantial progress in our understanding of nuclear structure - a rich and many-faceted field. An important element in this task will be to extend the study of nuclei into new domains. The journey to ``the limitsóf isospin, angular momentum, and mass and charge is a quest for new and unexpected phenomena which await us in uncharted territories. What is extremely important from a theoretical point of view is that the new data are also expected to bring qualitatively new information about the effective nucleon-nucleon interaction and hence about the fundamental properties of the nucleonic many-body system. In Ref.  we discussed some of the challenges and opportunities for nuclear structure research with radioactive nuclear beams.
In Ref. , the volume and surface effects in the nuclear local energy density and the volume and surface components of the pairing interaction were discussed in the context of the mean-field, Hartree-Fock-Bogoliubov description of atomic nuclei. Predictions of properties of exotic nuclei close to the particle drip lines were presented.
Nuclear life in neutron-rich and proton-rich Terra Incognita is different from that around the stability line; the promised access to completely new combinations of proton and neutron numbers offers prospects for new structural phenomena. The main objective of Ref.  was to discuss some of the theoretical challenges and opportunities for nuclear structure research with new Electro-Magnetic Isotope Separators.
In Ref. , an improved prescription for choosing a transformed harmonic oscillator (THO) basis for use in configuration-space Hartree-Fock-Bogoliubov (HFB) calculations was presented. The new HFB+THO framework that follows accurately reproduces the results of coordinate-space HFB calculations for spherical nuclei, including those that are weakly bound. Furthermore, it is fully automated, facilitating its use in systematic investigations of large sets of nuclei throughout the periodic table. As a first application, we have carried out calculations using the Skyrme Force SLy4 and volume pairing, with exact particle number projection following application of the Lipkin-Nogami prescription. Calculations were performed for all even-even nuclei from the proton drip line to the neutron drip line having proton numbers and neutron numbers . We focused on nuclei near the neutron drip line and found that there exist numerous particle-bound even-even nuclei (i.e., nuclei with negative Fermi energies) that have at the same time negative two-neutron separation energies. This phenomenon, which was earlier noted for light nuclei, is attributed to bound shape isomers beyond the drip line.
In Ref. , we used the Skyrme-Hartree-Fock method, allowing all symmetries to be broken, to calculate the time-reversal-violating nuclear Schiff moment (which induces atomic electric dipole moments) in the octupole-deformed nucleus Ra. Our calculation included several effects neglected in earlier work, including self consistency and polarization of the core by the last nucleon. We found that the Schiff moment, while large compared to those of reflection-symmetric nuclei, is generally a few times smaller than the recent estimates.
In Ref. , K-shell and L-shell ionization potentials for the superheavy elements with =112, 114, 116, and 118 are predicted to an accuracy of a few 10eV using Dirac-Hartree-Fock theory and taking into account quantum electrodynamic and nuclear size effects. The data obtained are for any number of electrons and can be used in future theoretical and experimental studies of these elements involving K-electron conversion spectroscopy. As a by-product of our work, we performed systematic calculations of K (1s) and L (2s) ionization potentials for the neutral atoms from hydrogen to lawrencium and obtained excellent agreement with experiment. The major cause of the 5-10eV deviation from experiment seems to come from solid-state effects present in the experimental data.