Deformation properties of osmium,platinum, mercury isotopes from self-consistent calculations: Influence of the pairing treatment

The deformation properties of several isotopes of the elements Os, Pt and Hg have been computed by means of Hartree-Fock plus BCS calculations. The Hartree-Fock potential has been derived from the Skyrme interaction SIII. Two approximations have been used for the treatment of pairing correlations: the constant (versus deformation) gap method and the constant (versus deformation) pairing matrix element method. A good agreement with experimental data is obtained for ground state deformation properties except for the exact location of the prolate-oblate transition as a function of the neutron number. For one nucleus ¹⁸⁴Hg, the pairing matrix elements have been calculated from the Gogny interaction D1, in order to study their single-particle state — and deformation — dependence. From these results, the validity of the two approximations used for pairing correlations is discussed.     

Relativistic Hartree-Bogoliubov description of deformed light nuclei

The Relativistic Hartree-Bogoliubov model is applied in the analysis of ground-state properties of Be, B, C, N, F, Ne and Na isotopes. The model uses the NL3 effective interaction in the mean-field Lagrangian, and describes pairing correlations by the pairing part of the finite-range Gogny interaction D1S. Neutron separation energies, quadrupole deformations, nuclear matter radii, and differences in radii of proton and neutron distributions are compared with recent experimental data.Received: 27 August 2003, Revised: 12 March 2004, Published online: 19 October 2004PACS:   21.60.Jz Hartree-Fock and random-phase approximations - 21.10.Gv Mass and neutron distributions - 27.20. + n - 27.30. + t      

Pairing in exotic and in stable nuclei

The exchange of low-lying collective vibrations between pairs of nucleons moving in time reversal states close to the Fermi energy provides a conspicuous contribution to the nuclear pairing interaction, which accounts for 30-50% of the pairing gap in the case of nuclei along the stability valley, and to essentially all of the pairing correlations of the most loosely bound nucleons in the case of halo nuclei.Received: 30 October 2002, Published online: 23 March 2004PACS: 21.30.Fe Forces in hadronic systems and effective interactions - 21.60.Jz Hartree-Fock and random-phase approximations     

Comment on “Energies of the ground state and first excited 0<Superscript> + </Superscript> state in an exactly solvable pairing model” by N. Dinh Dang

We comment on a recent application of the RPA method and its extensions to the case of the two-level pairing model by N. Dinh Dang (Eur. Phys. J. A 16, 181 (2003)).Received: 16 July 2003, Published online: 17 February 2004PACS: 21.60.Jz Hartree-Fock and random-phase approximations - 21.60.-n Nuclear-structure models and methods     

Many-body effects in nuclear structure

We calculate, for the first time, the state-dependent pairing gap of a finite nucleus (¹²⁰Sn) diagonalizing the bare nucleon-nucleon potential (Argonne v ₁₄) in a Hartree-Fock basis (with effective k-mass ), within the framework of the generalized Bogoliubov-Valatin approximation including scattering states up to 800 MeV above the Fermi energy to achieve convergence. The resulting gap accounts for about half of the experimental gap. The combined effect of the bare nucleon-nucleon potential and of the induced pairing interaction arising from the exchange of low-lying surface vibrations between nucleons moving in time-reversal states close to the Fermi energy accounts for the experimental gap.Received: 3 November 2003, Published online: 6 July 2004PACS: 21.30.Fe Forces in hadronic systems and effective interactions - 21.60.Jz Hartree-Fock and random-phase approximations - 21.60.-n Nuclear structure models and methods - 27.60. + j      

Quasi spin pairing and the structure of the Lipkin Model

By introducing the concepts of quasi-spin pairing and quasi-spin seniority, the Lipkin model is extended to a variable number of particles. The properties of quasi-spin pairing are seen to be quite similar to those of ordinary pairing. The quasi-spin seniority allows one to obtain a simple classification of excited multiplets. A “pairing plus monopole” model is studied in connection with the Hartree-Fock theory.     

Effects of pairing correlation on neutron drop

In this work, the effects of the pairing correlation on the properties of neutron drops N=6-50 trapped in a harmonic oscillator potential with ω = 10 Me V are investigated by comparing the results given by the Skyrme Hartree-Fock and Hartree-FockBogoliubov theories with the density-dependent delta interaction(DDDI) pairing force. The results showed that the pairing correlation slightly made the neutron drops more bound, and increased the central neutron density, the spin-orbit and pseudo spin-orbit splittings. Thus, the pairing correlation must be accounted for to improve the Skyrme functional compared with the ab initio calculations. Furthermore, although the single-particle energy gaps with or without pairing were similar, the shell closures varied due to pair scattering. Here, the shell closures in neutron drops using the Sk M* parameter set and DDDI pairing force were found at N=8, 16, and 32.     

Critical temperature for shape transitions in excited nuclei

The behavior of shell effects with temperature is studied within the framework of the finite-temperature Hartree-Fock-Bogoliubov theory with the Gogny force. Thermal shape fluctuations in the quadrupole degree of freedom are taken into account in the frame of the Landau theory. Numerical results for the superfluid-to-normal and deformed-to-spherical phase transitions are presented for the nucleus ¹⁶⁴Er. We find that the critical temperature for the deformed-spherical shape transition is much lowered when the thermal shape fluctuations are considered.Received: 31 October 2002, Published online: 17 February 2004PACS: 21.60.Jz Hartree-Fock and random-phase approximations - 21.10.Ky Electromagnetic moments - 21.10.Ma Level density     

Deexcitation Modes in Spallation Nuclear Reactions

Spallation nuclear reactions in the range of 0.2 to 1.2 GeV are studied using the CRISP code. A new approach for the deexcitation stage of the compound nucleus was introduced. For the calculations of the level densities, this approach is based on the Back-shifted Fermi gas model (BSFG), which takes into account pairing effects and shell corrections, whereas the calculation of the fission barriers were performed by means of the Extended Thomas-Fermi plus Strutinsky Integral (ETFSI) method, which is a high-speed approximation to the Hartree-Fock method with pairing correlations treated as in the usual BCS plus blocking approach. This procedure is more appropriate to calculate level densities for exotic nuclei. Satisfactory results were obtained and compared with experimental data obtained in the GSI experiments. As another important result, we highlight some directions for the development of a qualitatively superior version of the CRISP code with the implementation of more realistic and suitable physical models to be applied in stable and exotic nuclei that participate in the process. This new version of the code includes several substantial changes in the decay of the hot compound nucleus which allow satisfactory agreement with the experimental data and a reduction of the adjustment parameters.     

Lifetimes of metastable levels in Ar II

We report on a calculation of five lifetimes of metastable levels in Ar II, obtained with a relativistic Hartree-Fock method in which most of the intravalence correlation is represented within a configuration interaction scheme while core-valence correlation is described by a core-polarization model potential with a core-penetration corrective term. The quality of the calculation has been assessed through an experimental determination of the radiative lifetime of the metastable 3d ⁴F_9/2 level. The experiment was performed with a laser probing technique on a stored ion beam at the CRYRING of Stockholm.Received: 16 January 2004, Published online: 30 March 2004PACS: 31.10. + z Theory of electronic structure, electronic transitions, and chemical binding - 32.70.Cs Oscillator strengths, lifetimes, transition moments     

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.     

Structure calculations in18O nucleus

A multishell Hartree-Fock calculation for¹⁸O nucleus has been done with the Tabakin and Hamada-Johnston interactions followed by pairing correlations and angular momentum projection. TheB(E2) transition rates have been reproduced with an effective charge of 1.5e for protons and 0.5e for neutrons, but the fit to energy levels is poor. An approximate alternative formalism has then been developed which casts the eighteen-particle problem into a two-valence nucleon problem. The two valence nucleons interact through the RPA-type oscillation modes of the core. Calculations with the two interactions mentioned above have reproduced roughly the uncorrelated projected Hartree-Fock spectrum. Lastly, the excited band spectra of¹⁸O have been examined in the TDA approach followed by band mixing.     

Proton- and neutron-induced fission on uranium carbide target

In the frame of the R&D program for the SPES project of the Legnaro Laboratories, the production yields of Rb, In and Cs isotopes have bean measured at the synchrocyclotron of the Petersburg Nuclear Physics Institute (PNPI) of Gatchina (Russia). Production yields for direct proton fission and neutron-induced fission on a high-density UC₂ powder target are compared. The overall efficiencies as a function of the target temperature have been measured.Received: 3 July 2003, Revised: 2 October 2003, Published online: 27 January 2004PACS: 24.75. + i General properties of fission - 25.85.Ec Neutron-induced fission     

Large amplitude collective motion in nuclei and metallic clusters — Applicability of adiabatic theory for a pairing model

A model Hamiltonian describing a two-level system with a crossing plus a pairing force is investigated using the technique of large-amplitude collective motion. The collective path, which is determined by the decoupling conditions, is found to be almost identical to the one in the Born-Oppenheimer approximation for the case of a strong pairing force. For the weak pairing case, the obtained path describes a diabatic dynamics of the system. Presented by T. Nakatsukasa at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997. This work is supported by EPSRC (UK).     

Monte Carlo methods for yrast spectroscopy

We discuss the details of the recently proposed Monte Carlo method to evaluate the exact energies of yrast levels. Energy levels are evaluated up to J = 18 with small statistical errors using the Metropolis method for the case of ¹⁶⁶Er using the pairing plus quadrupole model within one major shell. We also discuss the evaluation of the probabilities of the Hartree-Fock-Bogoliubov wave functions in the corresponding yrast eigenstates and they are found to be large. The model displays a too strong backbending behaviour not seen experimentally.Received: 29 September 2003, Published online: 24 August 2004PACS: 21.60.-n Nuclear-structure models and methods - 02.70.Ss Quantum Monte Carlo methods - 21.60.Ka Monte Carlo models - 21.10.Re Collective levels     

Fission barriers of preactinide nuclei from electrofission experiments

Absolute electrofission cross sections for ^182,184,186W, ^natPt, and ²⁰⁹Bi have been measured using solid-state track detectors and parallel-plate avalanche counters for the detection of the fission fragments. The measured cross sections — together with others known from literature — have been analyzed within an extended statistical model to deduce fission barriers and compared with theoretical calculations. From the derived barrier height for platinum, it is concluded that the pairing strength G most likely does not change with deformation (G = const). All experimental fission barriers agree very well with theoretical predictions for G = const.