A Separable Pairing Force in Nuclear Matter

The method introduced by Duguet is adopted to derive a separable form of the pairing interaction in the ^1So channel from a bare or an effective nucleon-nucleon （NN） interaction in nuclear matter. With this approach the separable pairing interaction reproduces the pairing properties provided by its corresponding NN interaction. In this work, separable forms of pairing interactions in the ^1So channel for the bare NN interaction, Bonn potential and the Gogny effective interaction are obtained. It is found that the separable force of the Gogny effective interaction in the 1So channel has a clear link with the bare NN interaction. With such a simple separable form pairing properties provided by the Gogny force in nuclear matter can be reproduced.     

Finite-temperature density-dependent HF calculation of nuclear matter with gogny interaction

A finite-temperature density-dependent Hartree-Fock method is formulated starting from a variational principle for the thermodynamic potential. Based on this method, we have carried out a nuclear-matter calculation using the Gogny D1 finite-range effective interaction. The equation of state and several other thermal properties of nuclear matter so obtained are found to be rather similar to those given by the Skyrme SkM¹ interaction. The critical temperature and density for the liquid-gas phase transition of nuclear matter are found to be 15.1 MeV and 0.05 fm⁻³, respectively. The effect of the finite-temperature rearrangement potential is discussed     

Antiferromagnetism of nuclear matter in the model with effective Gogny interaction

The possibility of ferromagnetic (FM) and antiferromagnetic (AFM) phase transitions in symmetric nuclear matter is analyzed within the framework of a Fermi liquid theory with effective Gogny interaction. It is shown that, at some critical density, nuclear matter with the D1S effective force undergoes a phase transition to the AFM spin state (opposite directions of neutron and proton spins). The self-consistent equations of spin-polarized nuclear matter with the D1S force have no solutions corresponding to FM spin ordering (the same direction of neutron and proton spins) and, hence, the FM transition does not appear. The AFM spin polarization parameter is found for zero and finite temperature. It is shown that the AFM spin polarization parameter of partially polarized nuclear matter at low enough temperatures increases with temperature. The entropy of the AFM spin state for some temperature range is larger than the entropy of the normal state. Nevertheless, the free energy of the AFM spin state is always less than the free energy of the normal state, and the AFM spin-polarized state is preferable for all temperatures below the critical temperature. The text was submitted by the authors in English.     

Quadrupole collectivity of neutron-rich neon isotopes

The Angular Momentum Projected Generator Coordinate Method, with the quadrupole moment as collective coordinate and the Gogny force (D1S) as the effective interaction, is used to describe the properties of the ground state and low-lying excited states of the even-even neon isotopes ^20-34Ne, that is, from the stability valley up to the drip line. It is found that the ground state of the N = 20 nucleus ³⁰Ne is deformed but to a lesser extent than the N = 20 isotope of the magnesium. In the calculations, the isotope ³²Ne is at the drip line in good agreement with other theoretical predictions. On the other hand, rather good agreement with experimental data for many observables is obtained. Received: 19 Novemeber 2002 / Accepted: 24 January 2003 / Published online: 8 April 2003     

Giant resonances in exotic spherical nuclei within the RPA approach with the Gogny force

Theoretical results for giant resonances in the three doubly magic exotic nuclei ⁷⁸Ni, ¹⁰⁰Sn and ¹³²Sn are obtained from Hartree-Fock (HF) plus Random Phase Approximation (RPA) calculations using the D1S parameterization of the Gogny two-body effective interaction. Special attention is paid to full consistency between the HF field and the RPA particle-hole residual interaction. The results for the exotic nuclei, on average, appear similar to those of stable ones, especially for quadrupole and octupole states. More exotic systems have to be studied in order to confirm such a trend. The low energy of the monopole resonance in ⁷⁸Ni suggests that the compression modulus in this neutron-rich nucleus is lower than the one of stable ones.     

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.     

Large-scale mean-field calculations from proton to neutron drip lines using the D1S Gogny force

Large-scale axial mean-field calculations from proton to neutron drip lines have been performed within the Hartree-Fock-Bogoliubov method based on the D1S Gogny force. Nearly 7000 nuclides have been studied under the axial symmetric hypothesis and various properties are displayed on an Internet web site for every individual nucleus. Some global properties are presented such as the positions of the drip lines, the nuclide ground-state deformations and binding energies as well as regions where possible super- or hyper-deformation might be encountered.     

Infinite matter properties and zero-range limit of non-relativistic finite-range interactions

We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin–orbit terms from the spin–isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin–orbit of the M3Y interaction is not compatible with local gauge invariance. Finally, we show that the zero-range limit of both families of interactions coincides with the specific form of the zero-range Skyrme interaction extended to higher momentum orders and we emphasize from this analogy its benefits.     

Crossing of the πd<Subscript>5/2</Subscript> and πg<Subscript>7/2</Subscript> orbitals in the <Subscript>51</Subscript>Sb isotopes

Self-consistent calculations using the D1S Gogny force have been performed in order to study the mechanism involved in the crossing of the πd _5/2 and πg _7/2 orbitals in the Sb isotopes. This inversion is well predicted by the HFB + blocking calculations with spherical symmetry performed for the odd-A Sb isotopes. In addition, several HFB and HF calculations have been performed for even-even nuclei of the five neighbouring isotopic chains (Z = 46 to 54, from the proton dripline to N = 82). The results obtained for the binding energies of the two proton orbitals indicate that the radii of the systems play an important role in the crossing, even though some particular πν interactions also give a contribution. The spin-orbit interaction, which is known to be concentrated mainly at the nuclear surface, is proposed to be the main responsible of the crossing.     

Pairing properties of nuclear matter at finite temperature

The Gogny effective interaction is used to calculate the pairing properties of symmetric nuclear matter at various densities and temperatures. A pairing collapse is predicted at a critical temperature of half the gap parameter at temperature zero. The phase diagram which separates normal and superfluid phases is calculated.     

Ground-State Properties ,of C, O, and Ne Isotopes in Hartree——Fock-Bogoliubov Calculation with Gogny Interaction

Ground-state properties of C, O, and Ne isotopes are described in the framework of Hartree-Fock-Bogoliubov theory with density-dependent finite-range Gogny interaction D1S. We include all the contributions to the Hartree-Fock and pairing feld arising from Gogny and Coulomb interaction as well as the center of mass correction in the numerical calcu/ations. These ground-state properties of C, O, and Ne isotopes are compared with available experimental results, Hartree-Fock plus BCS, shell model and relativistic Hartree--Bogoliubov calculations. The agreement between experiments and our theoretical results is pretty well. The predicted drip-line is dependent strongly on the model and effective interaction due to their sensitivity to various theoretical details. The calculations predict no evidence for halo structure predicted for C,O, and Ne isotopes in a previous RHB study.     

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      

Ground-State Properties of C, O, and Ne Isotopes in Hartree-Fock-Bogoliubov Calculation with Gogny Interaction

Ground-state.properties of C, O, and Ne isotopes are described in the framework of Hartree-FockBogoliubov theory with density-dependent finite-range Gogny interaction D1S. We include all the contributions to the Hartree-Fock and pairing field arising from Gogny and Coulomb interaction as well as the center of mass correction in the numerical calculations. These ground-state properties of C, O, and Ne isotopes are compared with available experimental results, Hartree-Fock plus BCS, shell model and relativistic Hartree-Bogoliubov calculations. The agreement between experiments and our theoretical results is pretty well. The predicted drip-line is dependent strongly on the model and effective interaction due to their sensitivity to various theoretical details. The calculations predict no evidence for halo structure predicted for C, O, and Ne isotopes in a previous RHB study.     

190，192Pb原子核的超形变带的带外衰变（英文）

将基于组合方法的角动量投影的位能曲面群用于研究铅同位素原子核190,192Pb 的超形变转动带。位能曲面群计算中采用了Gogny D1S 以及Skyrme SkP SLy4 三种相互作用。如用Gogny D1S 相互作用,190Pb 原子核没有明显的超形变转动带,而192Pb 原子核有非常显著的超形变转动带。用W. K. B. 方法计算了192Pb 原子核的超形变带穿透宽度。该穿透宽度很大与用GW模型（Nucl. Phys. A 660 （1999）197）分析实验数据给出的结果相近。在Gogny D1S 相互作用情形下,就角动量投影对位能曲面群的影响作了讨论,发现角动量投影压低了分隔超形变转动带与正常形变转动带之间的位垒。还用Skyrme SkP 和SLy4 相互作用计算了角动量投影的位能曲面群,发现位垒明显高于Gogny D1S 相互作用给出的位垒。在Skyrme 相互作用情形下,192Pb 原子核的超形变带穿透宽度明显小于Gogny 相互作用给出的宽度,但是较SB方法（Phys. Rev. C,60 （1999） 051305） 分析实验数据得到的结果高出几个数量级。于是,对SB 方法提出了质疑,因为它给出了极其微小的传播宽度。The combined method is applied to calculate the angular momentum projected potential energy surfaces (AMPPES) of 190,192Pb. The Supper-deformed(SD) rotational bands of the two nuclei are studied with the AMPPES computed with the Gogny D1S and Skyrme SkP and SLy4 interactions. It is found that there is no pronounced SD band in 190Pb in the case of the Gogny interaction, which is consistent with the experimental observation. A well developed SD band with the Gogny interaction is found in 192Pb. The tunneling width of 192Pb is comparable to that given by the GW approach (Nucl. Phys. A 660 (1999)197) and orders of magnitude larger than that given by the SB approach (Phys. Rev. C 60 (1999) 051305). The influence of the angular momentum projection on the potential energy surfaces is examined in the case of the Gogny interaction for 190,192Pb. It is shown that the angular momentum projection suppresses the barrier separating the SD and ND rotational bands. Higher barriers of the AMPPESs for the two nuclei computed with the Skyrme SkP and SLy4 interactions are obtained compared with those given by the Gogny force. The tunneling width of 192Pb is also big for the Skyrme interactions. We put the SB approach into question which gives only an extremely small spreading width.     

Surface properties of nuclear pairing with the Gogny force in a simplified model

Surface properties of neutron-neutron (T=1) pairing in semi-infinite nuclear matter in a hard wall potential are investigated in BCS approximation using the Gogny force. Surface enhancement of the gap function, pairing tensor and correlation energy density is put into evidence.     

Determination of the stiffness of the nuclear symmetry energy from isospin diffusion

With an isospin- and momentum-dependent transport model, we find that the degree of isospin diffusion in heavy-ion collisions at intermediate energies is affected by both the stiffness of the nuclear symmetry energy and the momentum dependence of the nucleon potential. Using a momentum dependence derived from the Gogny effective interaction, recent experimental data from NSCL-MSU on isospin diffusion are shown to be consistent with a nuclear symmetry energy given by E(sym)(rho) approximately 31.6(rho/rho(0))(1.05) at subnormal densities. This leads to a significantly constrained value of about -550 MeV for the isospin-dependent part of the isobaric incompressibility of isospin asymmetric nuclear matter.     

RPA calculations with Gaussian expansion method

The Gaussian expansion method (GEM) is applied to calculations of the nuclear excitations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that is successful in the mean-field calculations. The RPA results obtained by the GEM are compared with those obtained by several other available methods in Ca isotopes, by using a density-dependent contact interaction along with the Woods–Saxon single-particle states. It is confirmed that energies, transition strengths and widths of their distribution are described by the GEM with good precision, for the 1⁻, 2⁺ and 3⁻ collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the E1 response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well. Properties of low-energy transitions in ⁶⁰Ca are investigated in some detail.     

Hartree-fock calculations of semi-infinite nuclear matter with complete forces (finite-range and spin-orbit term)

Complete Hartree-Fock calculations on semi-infinite nuclear matter have been performed for effective interactions that have finite range and also contain a spin-orbit component. With the Gogny force we extract the value a_sf = 20.1 MeV for the surface coefficient of the mass formula.     

Isoscalar and isovector nuclear matter properties and neutron skin thickness

Isoscalar and isovector nuclear matter properties are investigated in the Skyrme Hartree-Fock (SHF) and the relativistic mean field (RMF) models. The Skyrme parameters are related analytically to the isoscalar and the isovector nuclear matter properties of the Hamiltonian density. Linear correlations are found among the isovector nuclear matter properties of the Hamiltonian density in both the SHF and the RMF models. We also discovered that the correlations between the isovector properties and the incompressibility K show a singularity at the critical incompressibility K_c=306 MeV. It is shown that the neutron skin thickness gives crucial information about not only for the neutron EOS but also about the isovector nuclear matter properties and about the parameterization of Skyrme interaction. Charge exchange spin-dipole (SD) excitations are proposed to determine the neutron skin thickness model independently.