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.     

Generalized hybrid derivative coupling model for finite nuclei

The generalized hybrid derivative coupling model has been applied to explore various ground state properties of different nuclei. In this work we have confined our calculation only to the model characterized by the hybridization parameter α = 1/4 which gives better results than the other models of the same class, as we have seen earlier, for nuclear matter calculations. The binding energy, single-particle energy spectra, density and charge radii of different doubly closed nuclei like ¹⁶O, ⁴⁰Ca, ⁴⁸Ca, ⁹⁰Zr, ¹³²Sn, ²⁰⁸Pb have been studied. The success of this model, in describing the doubly closed nuclei, motivates us to extend this calculation further in the case of open shell nuclei after incorporating the pairing interaction and using a BCS transformation. We have calculated the binding energy for such nuclei. We have also studied the isotopic shift for different Pb isotopes with respect to ²⁰⁸Pb. We have compared our results with the other standard theoretical results as well as with the experimental values. Received: 18 August 2000 / Accepted: 13 April 2001     

Whence the odd-even staggering in nuclear binding?

We explore the systematics of odd-even mass staggering with a view to identifying the physical mechanisms responsible. The BCS pairing and mean-field contributions have A - and number parity dependences which can help disentangle the different contributions. This motivates the two-term parametrization c ₁ + c ₂/A as a theoretically based alternative to the inverse-power form traditionally used to fit odd-even mass differences. Assuming that the A -dependence of the BCS pairing is weak, we find that mean-field contributions are dominant below mass number A ∼ 40 while BCS pairing dominates in heavier nuclei.     

Non-empirical pairing energy density functional

We perform systematic calculations of pairing gaps in semi-magic nuclei across the nuclear chart using the Energy Density Functional method and a non-empirical pairing functional derived, without further approximation, at lowest order in the two-nucleon vacuum interaction, including the Coulomb force. The correlated single-particle motion is accounted for by the SLy4 semi-empirical functional. Rather unexpectedly, both neutron and proton pairing gaps thus generated are systematically close to experimental data. Such a result further suggests that missing effects, i.e. higher partial waves of the NN interaction, the NNN interaction and the coupling to collective fluctuations, provide an overall contribution that is sub-leading as for generating pairing gaps in nuclei. We find that including the Coulomb interaction is essential as it reduces proton pairing gaps by up to 40%.     

Equation of state of superfluid neutron matter and the calculation of the 1S0 pairing gap

We present a quantum Monte Carlo study of the zero-temperature equation of state of neutron matter and the computation of the 1S0 pairing gap in the low-density regime with rho < 0.04 fm(-3). The system is described by a nonrelativistic nuclear Hamiltonian including both two- and three-nucleon interactions of the Argonne and Urbana type. This model interaction provides very accurate results in the calculation of the binding energy of light nuclei. A suppression of the gap with respect to the pure BCS theory is found, but sensibly weaker than in other works that attempt to include polarization effects in an approximate way.     

相对论平均场理论框架下对能的系统研究

在相对论平均场模型的框架内,沿原子核的稳定线,以每隔4个质子或中子提取样本的方法,计算了核谱图上数十个原子核的对能,特别是研究了氧同位素偶-偶核的对能随核子数的变化规律,发现在固定能隙Δ的条件下,对能的大小和核的壳结构有关,由此提出了一种检验闭壳效应的简便方法,进而发现中子数N=6不仅在轻核的丰中子区是一个新幻数,而且在丰质子区也是一个可能的新幻数. 关键词： 相对论平均场模型 对能 能隙 幻数     

GCM analysis of the collective properties of lead isotopes with exact projection on particle numbers

We present a microscopic analysis of the collective behaviour of the lead isotopes in the vicinity of ²⁰⁸Pb. In this study, we rely on a coherent approach based on the Generator Coordinate Method (GCM) including exact projection on N and Z numbers within a collective space generated by means of the constrained Hartree-Fock BCS method. With the same Hamiltonian used in HF + BCS calculations, we have performed a comprehensive study including monopole, quadrupole and octupole excitations as well as pairing vibrations. We find that, for the considered nuclei, the collective modes which modify the most the conclusions drawn from the mean-field theory are the octupole and pairing vibrations. Received: 31 May 2001 / Accepted: 23 August 2001     

Analytical relationship for the cranking inertia

The wave functions of a spheroidal harmonic oscillator without spin-orbit interaction are expressed in terms of associated Laguerre and Hermite polynomials. The pairing gap and Fermi energy are found by solving the BCS system of two equations. Analytical relationships for the matrix elements of inertia are obtained as a function of the main quantum numbers and potential derivative. They may be used to test complex computer codes developed in a realistic approach of the fission dynamics. Results given for the ²⁴⁰Pu nucleus are compared with a hydrodynamical model. The importance of taking into account the correction term due to the variation of the occupation number is stressed.     

Nuclear pairing from chiral pion-nucleon dynamics

We use a recently improved version of the chiral nucleon-nucleon potential at next-to-next-to-leading order to calculate the ¹S₀ pairing gap in isospin-symmetric nuclear matter. The pairing potential consists of the long-range one- and two-pion exchange terms and two short-distance NN-contact couplings. We find that the inclusion of the two-pion exchange at next-to-next-to-leading order reduces substantially the cutoff dependence of the ¹S₀ pairing gap determined by solving a regularised BCS equation. Our results are close to those obtained with the universal low-momentum nucleon-nucleon potential V_low-k or the phenomenological Gogny D1S force.     

Pairing and spectral statistics of low energy levels

The interplay of pairing with the different terms of the residual interaction is explored for the low-lying energy levels of semi-magic nuclei from the point of view of spectral statistics. The reduced degree of chaoticity present in this nuclei is shown to be directly related to the strength of the pairing interaction with respect to the total residual interaction. On the contrary, the pairing strength does not influence the spectral statistics near the ground state for nuclei with both neutrons and protons outside closed shells.     

Nilsson mean-field plus the extended pairing model description of rare earth nuclei

The Nilsson mean-field plus the extended pairing model for well-deformed nuclei is applied to some representative rare earth examples. The binding energies, some low-lying pair-excited states and even-odd mass differences of Er, Yb and Hf isotopes are calculated systematically within the proton frozen-pair excitation limit. A comparison with experimental data for these nuclei shows that the results of the extended pairing model are better than those for the standard pairing model with the BCS approximation and the nearest-orbit pairing model.     

Systematic study of properties of Hs nuclei

The ground-state properties of Hs nuclei are studied in the framework of the relativistic mean-field theory. We find that the more relatively stable isotopes are located on the proton abundant side of the isotopic chain. The last stable nucleus near the proton drip line is probably the ²⁵⁵Hs nucleus. The a \alpha -decay half-lives of Hs nuclei are predicted, and together with the evaluation of the spontaneous-fission half-lives it is shown that the nuclei, which are possibly stable against spontaneous fission are ^263-274Hs . This is in coincidence with the larger binding energies per nucleon. If ^271-274Hs can be synthesized and identified, only those nuclei from the upper Z = 118 isotopic chain, which are lighter than the nucleus ²⁹⁴118 , and those nuclei in the corresponding a \alpha -decay chain lead to Hs nuclei. The most stable unknown Hs nucleus is ²⁶⁸Hs . The density-dependent delta interaction pairing is used to improve the BCS pairing correction, which results in more reasonable single-particle energy level distributions and nucleon occupation probabilities. It is shown that the properties of nuclei in the superheavy region can be described with this interaction.     

Comparison between microscopic and phenomenological nuclear pairing calculations

The isospin and density dependent effective pairing interaction is revisited by fitting the neutron gaps from the microscopic calculations for the neutron matter and the symmetric nuclear matter.The neutron pairing gaps for 1S0 channel for asymmetric nuclear matter are obtained from the BCS gap equation with a realistic bare nucleon-nucleon interaction in the Skyrme mean field.It is shown that the neutron gaps obtained from the new effective pairing interaction for the asymmetric nuclear matter are much imp...     

The mass parameters for the average mean-field potential

Starting from a mean-field hamiltonian with pairing interaction, we use the generator coordinate method (GCM) and a generalized gaussian overlap approximation to derive a multidimensional collective hamiltonian for large-amplitude motion. Numerical calculations are performed for Nilsson and Woods-Saxon potentials with BCS pairing. The BCS wave function is taken as the generator function and the deformation parameters of the single-particle mean field are used as the generator coordinates. We find that the GCM mass parameters on the average are smaller than those of the cranking (+ BCS) model by a factor of $\text{～}\text{2}\text{3}$. In the present approach, the zero-point energy correction to the collective potential is shown to vanish identically.     

Relativistic many-body theory with radioactive ion beams: Surface pion condensation

We critically review the present relativistic mean-field theory from the viewpoint of missing pions. We introduce the interesting experimental data on pionic states taken at RCNP. These data seem to suggest the occurrence of pion condensation in the nuclear surface. Qualitative discussion is made on the consequence of surface pion condensation on Gamow-Teller transitions and spin response functions and others. The radioactive ion beams are the tools of studying the unstable nuclei, which have extended nuclear surfaces. We shall start with radioactive ion beams the nuclear surface science, which includes the surface pion condensation as the important ingredient in addition to spin-orbit splitting and surface pairing. Received: 1 May 2001 / Accepted: 4 December 2001     

Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field

We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method. In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF) theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained. This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei ¹⁶O and ²⁰⁸Pb, the deformed nucleus ²⁰Ne. Good agreement is obtained.