Constrained relativistic mean-field approach with fixed configurations

A diabatic (configuration-fixed) constrained approach to calculate the potential energy surface (PES) of the nucleus is developed in the relativistic mean-field model. As an example, the potential energy surfaces of ²⁰⁸Pb obtained from both adiabatic and diabatic constrained approaches are investigated and compared. It is shown that the diabatic constrained approach enables one to decompose the segmented PES obtained in usual adiabatic approaches into separate parts uniquely characterized by different configurations, to follow the evolution of single-particle orbits till the very deformed region, and to obtain several well-defined deformed excited states which can hardly be expected from the adiabatic PESs.     

Quantum Monte Carlo calculation for the neutron-rich Ca isotopes

We computed ground-state energies of calcium isotopes from ⁴²Ca to ⁴⁸Ca by means of the Auxiliary Field Diffusion Monte Carlo (AFDMC) method. Calculations were performed by replacing the ⁴⁰Ca core with a mean-field self-consistent potential computed using the Skyrme interaction. The energy of the external neutrons is calculated by projecting the ground state from a wave function built with the single-particle orbitals computed in the self-consistent external potential. The shells considered were the 1F _7/2 and the 1F _5/2 . The Hamiltonian employed is semi-realistic and includes tensor, spin-orbit and three-body forces. While absolute binding energies are too deep if compared with experimental data, the differences between the energies for nearly all isotopes are in very good agreement with the experimental data.     

Magic gaps and intruder levels in triaxially superdeformed nuclei

Nuclear shell model calculations based on a modified harmonic-oscillator potential result in amazingly stable triaxial nuclear shapes. Major gaps in the single-particle energy spectra at proton number 71 and neutron number 94 combine constructively at low and intermediate rotational frequencies. At high frequencies, gaps at proton number 72 and neutron number 97 combine in an equally favourable way. The sizes of the gaps may be as large as 35% of the values for the gaps at the classical magic numbers 50 and 82 at spherical shape. The dependence on the positions of the intruder levels in forming the gaps is discussed. Experimentally observed rotational bands in lutetium (Z = 71) and hafnium (Z = 72) appear in isotopes and frequency ranges, which are consistent with the gaps in the theoretical single-particle energy spectra.     

Parity Violating Electron Scattering in the Relativistic Eikonal Approximation

The parity violating electron scattering is investigated in the relativistic Eikonal approximation. The parity violating asymmetry parameters for many isotopes are calculated. In calculations the proton and neutron densities are obtained from the relativistic mean-field theory. We take Ni isotopes as examples to analyse the behaviour of the parity violating asymmetry parameters. The results show that the parity violating asymmetry parameter is sensitive to the difference between the proton and neutron densities. The amplitude of the parity violating asymmetry parameter increases with the distance between the minima of proton and neutron form factors. Our results are useful for future parity violating electron scattering experiments. By comparing our results with experimental data one can test the validity of the relativistic mean-field theory in calculating the neutron densities of nuclei.     

Covalently bound molecular structures in the α + 16O system

Using the concept of covalent molecular orbitals for neutrons and the known properties of the local α + ¹⁶O potential the formation of asymmetric molecular structures in neon isotopes is discussed. Experimental evidence for parity doublets in ²¹Ne is reviewed and a corresponding band structure for the states in ²¹Ne at moderate excitation energy of E _x = 0-8 MeV is proposed. The structure of some bands can be interpreted as consisting of an instrinsic asymmetric ( ⁴He + ¹⁶O) structure bound by a covalent neutron in σ and π orbitals. An extension of the observed structures to symmetric molecular structures in isotopes of Mg and heavier nuclei is suggested. In particular shape isomers in isotopes of magnesium, namely (He)₂O molecules, can be predicted and an extended Ikeda diagram is proposed. Received: 11 July 2001 / Accepted: 22 August 2001     

Neutron halos in hypernuclei

Properties of single- Λ and double- Λ hypernuclei for even-N Ca isotopes ranging from the proton dripline to the neutron dripline are studied using the relativistic continuum Hartree-Bogoliubov theory with a zero-range pairing interaction. Compared with ordinary nuclei, the addition of one or two Λ-hyperons lowers the Fermi level. The predicted neutron dripline nuclei are, respectively, ⁷⁵ _ΛCa and ⁷⁶ _2ΛCa, as the additional attractive force provided by the Λ-N interaction shifts nuclei from outside to inside the dripline. Therefore, the last bound hypernuclei have two more neutrons than the corresponding ordinary nuclei. Based on the analysis of two-neutron separation energies, neutron single-particle energy levels, the contribution of continuum and nucleon density distribution, giant halo phenomena due to the pairing correlation, and the contribution from the continuum are suggested to exist in Ca hypernuclei similar to those that appear in ordinary Ca isotopes. Received: 21 October 2002 / Accepted: 11 January 2003 / Published online: 8 April 2003     

Coulomb and nuclear excitation effects on 16O scattering from samarium isotopes

Elastic scattering of ¹⁶O on ^{148, 150, 152}Sm isotopes and inelastic scattering leading to the first 2⁺ state for the three isotopes and the 4⁺ state for ¹⁵²Sm have been measured at several energies in the vicinity of the Coulomb barrier. The whole set of data was reproduced at forward angles with an effective potential taking into account Coulomb excitation and in the full angular range by CCBA calculations including separate nuclear and Coulomb deformations.     

Relativistic wave functions for single-proton resonant states

With the relativistic boundary condition, single-proton resonant states in spherical nuclei are studied by an analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean-field (RMF) theory. In this scheme, we investigate the wave functions for l≠ 0 proton resonant states close to the continuum threshold in the stable nuclide ¹²⁰Sn for the first time. Some hints for pseudospin symmetry in the resonant states of nuclei are mentioned as well.     

Evolution of the N = 20 and N = 28 shell closures in neutron-rich nuclei

The isospin dependence of shell closure phenomena is studied for light neutron-rich nuclei within a microscopic self-consistent approach using the Gogny force. Introducing configuration mixing, ³²Mg is found to be dynamically deformed, although the N = 20 spherical shell closure persists at the mean-field level for all N = 20 isotones. In contrast, the N = 28 spherical shell closure is found to disappear for N - Z≥ 10 whereas deformed shell closures are preserved and lead to shape coexistence in ⁴⁴ S. Configuration mixing shows that the ground state of this nucleus is triaxially deformed. The first 2⁺ excitation energy E_x = 1.46 MeV and the reduced transition probability B(E2;0⁺ _gs→ 2⁺ ₁)= 420 e ² fm ⁴ obtained with our approach are in good agreement with experimental data. Received: 26 July 2000 / Accepted: 30 August 2000     

Low-lying magnetic dipole strength distribution in the γ-soft even-even 130-136Ba

In this study the scissors mode 1⁺ states are systematically investigated within the rotational invariant Quasiparticle Random Phase Approximation (QRPA) for ^130-136Ba isotopes. We consider the 1⁺ vibrations generated by the isovector spin-spin interactions and the isoscalar and isovector quadrupole-type separable forces restoring the broken symmetry by a deformed mean field according to A.A. Kuliev et al. (Int. J. Mod. Phys. E 9, 249 (2000)). It has been shown that the restoration of the broken rotational symmetry of the Hamiltonian essentially decreases the B(M1) value of the low-lying 1⁺ states and increases the collectivization of the scissors mode excitations in the spectroscopic energy region. The agreement between the calculated mean excitation energies as well as the summed B(M1) value of the scissors mode excitations and the available experimental data of ¹³⁴Ba and ¹³⁶Ba is rather good. A destructive interference between the orbit and spin part of the M1 strength has been found for barium isotopes near the shell closer. For all the nuclei under investigation, the low-lying M1 transitions have ΔK = 1 character as it is the case for the well-deformed nuclei.     

The two-proton shell gap in Sn isotopes

We present an analysis of two-proton shell gaps in Sn isotopes. As theoretical tool we use self-consistent mean-field models, namely the relativistic mean-field model and the Skyrme-Hartree-Fock approach, both with two different pairing forces, a delta interaction (DI) model and a density-dependent delta interaction (DDDI). We investigate the influence of nuclear deformation as well as collective correlations and find that both effects contribute significantly. Moreover, we find a further significant dependence on the pairing force used. The inclusion of deformation plus correlation effects and the use of DDDI pairing provides agreement with the data.     

A muonic X-ray study of the charge distribution of 144, 148, 150, 152, 154Sm

We report the measurement of the energies of the 4f → 3d, 3d → 2p and 2p → Is muonic atomic transitions in separated isotopes of ^{144, 148, 150, 152, 154}Sm, and that of the 2s → 2p transitions of ¹⁵²Sm as well. Using these transition energies as well as the hyperfine splittings of the 2p levels, we have interpreted our data in terms of a deformed Fermi distribution for the charge density and obtained good fits. A model independent analysis of the isotope shifts in terms of generalized R_h moments has been made and is in good agreement with electronic X-ray and optical isotope shifts. The static quadrupole moments and the isomer shifts of the first excited state of ^{152, 154}Sm have been determined from the 2p hyperfine structure.     

Stability of Strutinsky Shell Correction Energy in Relativistic Mean Field Theory

The single-particle spectrum obtained from the relativistic mean field （RMF） theory is used to extract the shell correction energy with the Strutinsky method. Considering the delicate balance between the plateau condition in the Strutinsky smoothing procedure and the convergence for the total binding energy, the proper space sizes used in solving the RMF equations are investigated in detail by taking ^208 Pb as an example. With the proper space sizes, almost the same shell correction energies are obtained by solving the RMF equations either on basis space or in coordinate space.     

Interaction of the single-particle and collective degrees of freedom in non-magic nuclei: The role of phonon tadpole terms

A method of consistent treatment of phonon contributions to the self-energy and gap terms in non-magic nuclei is developed in so-called g ² approximation, where g is the creation amplitude of a low-lying phonon. The method simultaneously takes into account both usual non-local and local phonon tadpole terms. Relations that allow the tadpoles to be calculated without introduction of new parameters are derived. As an application of the method, the effect of the phonon tadpoles on the single-particle strength distribution, single-particle energies and gap values is considered. Hypothesis of the surface nature of pairing correlations is discussed in the light of the tadpole effect.     

Laser-atomic-beam spectroscopy in Sm: Isotope shifts and changes in mean-square nuclear charge radii

A systematic investigation of the isotope shifts of all natural Samarium isotopes was performed in 15 lines of the Sm I spectrum using the laser-atomic-beam technique. The observed lines correspond to transitions between the ground configuration 4f ⁶6s ² and the upper configurations 4f ⁶6s6p and 4f ⁵5d6s ². In one line a contribution of hyperfine-structure second-order effects to the isotope shift of the odd isotopes could be demonstrated. The measured isotope shifts have been separated in all lines into field shift and mass shift contributions assuming the specific mass shift to be zero in pures ²-sp transitions. From the field shift of the pures ²-sp transitions the changes in mean-square nuclear charge radii, δ<r ²>, have been evaluated for all natural Sm isotopes (in fm²): [144, 148] 0.517(27); [148, 150] 0.303(16); [150, 152] 0.423(22); [152, 154] 0.230(12); [147, 148] 0.152(8); [148, 149] 0.092(5). There is good consistency with recent muonic x-ray measurements of the changes in the Barrett nuclear charge radii,δR _k , of the even Sm isotopes.     

Pseudospin symmetry in the Dirac phenomenology

In the phenomenological relativistic framework of the Dirac equation for spherical nuclei, we use different kinds of single-particle central potentials ( Σ_S + Σ₀ to investigate certain aspects of the spin and pseudospin (PS) symmetries. Neither the splitting of PS doublets (PSDs) nor the similarity of the radial parts of the small components (F/r of the corresponding Dirac spinors have been found related with the magnitude of Σ_S + Σ₀ , in the sense predicted by several authors in the last decade. This conclusion is shown to be valid, in particular, for a potential of Coulomb type. We give a simple explanation for the strong correlation established in the relativistic calculations between the similarity of the radial parts of the big (small) components of the Dirac spinors of two spin (pseudospin) partners and the number of their nodes. The direct effects of the so-called PS symmetry-breaking term (and its singularity point) on the F functions of the PSDs are also analysed.     

Dispersive optical potential from an analysis of neutron single-particle energies in the Ti, Cr, and Fe isotopes featuring 20 to 50 neutrons

Neutron single-particle energies in unstable Ti, Cr, and Fe isotopes containing 20 to 26 neutrons were evaluated on the basis of experimental proton energies in the mirror-symmetric nuclei. The neutron single-particle energies in the 20 ? N ? 50 Ti, Cr, and Fe isotopes were calculated on the basis of the mean-field model with a dispersive optical potential, and the results were compared with available experimental data and with the results of estimations and calculations based on the relativistic mean-field model and on the multiparticle shell model with the GXPF1 interaction.