Leptodermous expansion of nuclear ground state energies and the anomaly in the nuclear curvature energy

The leptodermous expansion of the total ground state energy of a nucleus into volume, surface, curvature and gauss curvature contributions has been studied starting from a semi-classical energy density formalism of extended Thomas Fermi type. A numerical procedure was used to obtain the surface energy and curvature energy contributions from surface moments of energy density profilesH(r) for a sequence of nuclei withN=Z and neglecting the coulomb interaction for the three Skyrme forces. A transition to the liquid drop model type expansion in increasing powers ofA ^−1/3 is then made, taking into account the dependence of the central density and the surface structure on the mass of the nucleus. It is found that there is no inconsistency between the curvature contribution to the total energy in the leptodermous expansion and theA ^−1/3 term contribution in the liquid drop model expansion. It has been shown that the earlier apparent anomaly between the above two methods arises due to the use of semi-infinite approximation and the mass dependence of the central density and the surface structure of finite nuclei.     

Interaction potential between two 16O nuclei derived from the Skyrme interaction

The energy functional for the Skyrme density-dependent force is used to calculate the interaction potential between two ¹⁶O nuclei. A two-centre harmonic oscillator potential is employed to construct the density and kinetic energy density of the ground state of the combined system and of the separated nuclei. The antisymmetrization effects are investigated. The relative motion of the nuclei is taken approximately into account and the energy dependence of the potential derived from the Skyrme force is presented.     

Configuration interactions constrained by energy density functionals

A new method for constructing a Hamiltonian for configuration interaction calculations with constraints to energies of spherical configurations obtained with energy-density-functional (EDF) methods is presented. This results in a unified model that reproduced the EDF binding-energy in the limit of single-Slater determinants, but can also be used for obtaining energy spectra and correlation energies with renormalized nucleon–nucleon interactions. The three-body and/or density-dependent terms that are necessary for good nuclear saturation properties are contained in the EDF. Applications to binding-energies and spectra of nuclei in the region above ²⁰⁸Pb are given.     

Analysis of fission excitation functions and the determination of shell effects at the saddle point

A method is proposed to deduce the shell correction energy corresponding to the fission transition state shape of nuclei in the mass region around 200, from an analysis of the first chance fission values of the ratio of fission to neutron widths, (Γ _f /Γ _n )₁. The method is applied to the typical case of the fissioning nucleus²¹²Po, formed by alpha bombardment of²⁰⁸Pb. For the calculation of the neutron width, the level densities of the daughter nucleus after neutron emission were obtained from a numerical calculation starting from shell model single particle energy level scheme. It is shown that with the use of standard Fermi gas expression for the level densities of the fission transition state nucleus in the calculation of the fission width, an apparent energy dependence of the fission barrier height is required to fit the experimental data. This energy dependence, which arises from the excitation energy dependence of shell effects on level densities, can be used to deduce the shell correction energy at the fission transition state point. It is found that in the case of²¹²Po, the energy of the actual transition state point is higher than the energy of the liquid drop model (LDM) saddle point by (3 ± 1) MeV, implying significant positive shell correction energy at the fission transition state. Further, the liquid drop model value of level density parametera is found to be a few per cent smaller for the saddle point shape as compared to its spherical shape.     

Selfconsistent calculations of highly excited nuclei

Selfconsistent calculations of excitation energies and entropies of highly excited nuclei have been performed using the temperature-dependent constrained Hartree-Fock (HF)method with the Skyrme interaction. The selfconsistent variations of the level spectra as functions of the temperature (at a fixed deformation) are shown to be small and practically do not affect the results for the entropy versus excitationenergy. The disappearance of the shell fluctuations in the potential energy surface of a rare earth nucleus around T ～ 3 MeV is demonstrated.     

Prompt neutron emission spectra and multiplicities in the thermal neutron induced fission of235U

The emission spectra of prompt fission neutrons from mass and kinetic energy selected fission fragments have been measured in²³⁵U(n _th,f). Neutron energies were determined from the measurement of the neutron time of flight using a NE213 scintillation detector. The fragment energies were measured by a pair of surface barrier detectors in one set of measurements and by a back-to-back gridded ionization chamber in the second set of measurements. The data were analysed event by event to deduce neutron energy in the rest frame of the emitting fragment for the determination of neutron emission spectra and multiplicities as a function of the fragment mass and total kinetic energy. The results are compared with statistical model calculations using shell and excitation energy dependent level density formulations to deduce the level density parameters of the neutron rich fragment nuclei over a large range of fragment masses.     

Roles of tensor and isoscalar pairing interactions in β-decay calculations for possible r-process waiting point nuclei with N ~ 82 and 126

In this study, we adopt the self-consistent Hartree-Fock-Bogoliubov (HFB) theory with the proton-neutron quasi-particle random phase approximation (pnQRPA) based on the Skyrme force for calculation of the β^? decay half-lives for nuclei with N ~ 82 and 126 on possible r-process paths. In the calculations, the Skyrme interaction (e.g., SKO') is adopted, and the tensor interaction is added self-consistently in both HFB and QRPA calculations. We systematically study how the half-life is changed by varying the strength of the triplet-even (TE) and triplet-odd (TO) components as well as the IS pairing. We find that a variation in strength of the IS pairing of approximately 20% does not produce a substantial effect on β-decay rates with or without the tensor force, while a strength variation of the TO tensor force considerably affects the change in the β-decay half-lives for the very neutron rich N ~ 82 and 126 isotonic chains. In addition, with the inclusion of the tensor force, the GT decay becomes dominant for very neutron-rich nuclei.     

Low energy scattering data and phase shifts

We point out that at any given low energyσ _tot and a ratio of integrated scattering data likeF/B can, in principle, be used unambiguously to finds-andp-wave phase shifts. Thus efforts to obtain other low energy data like elastic dσ/dΩ andP/E are unnecessary. It is also indicated that the mere knowledge whetherF/B is greater than or less than unity enables us to draw important conclusions about the nature of the interaction in thep-state without performing detailed calculations. Thus a strong case is made out for obtaining much more preciseF/B data than are presently available. The discussion refers mainly to low energy ∧p scattering data.     

Potential of interaction between nuclei and nucleon-density distribution in nuclei

Nuclear-interaction potentials that are calculated by using Skyrme forces within the extended Thomas-Fermi approximation and Hartree-Fock-Bardeen-Cooper-Schrieffer theory are studied in detail. It is shown that the nuclear component of the potential simulating the interaction between nuclei grows with increasing number of neutrons in colliding isotopes and with increasing diffuseness parameter of the density distribution in interacting nuclei. An increase in the diffuseness parameter of the density distribution in interacting nuclei leads to a decrease in the height of the barrier between the nuclei and to an increase in the depth of the capture well and in the fusion cross section. It is shown that the diffuseness parameter calculated for the nuclear component of the potential at large distance between interacting nuclei by using Skyrme forces exceeds the diffuseness parameter of the nucleon-density distribution in these nuclei by a factor of about 1.5. Realistic values of the diffuseness parameter of nuclear interaction between medium-mass and heavy nuclei fall within the range a ≈ 0.75–0.90 fm.     

超重核密度的计算

用Skyrme Hartree Fock模型计算了超重核的密度分布,并讨论了其形状和同位旋相关性。 以292120核为例,计算表明形变对密度分布有相当大的影响。     

On the validity of pre-equilibrium model assumptions

The Hartree-Fock calculation is performed for nuclear matter using the Skyrme interaction. It is shown that a stable density wave periodic in only one direction exists at densities below about one-third of the normal nuclear density. The critical densityρ _c below which the energy of the density wave is lower than that of the Fermi gas is determined for Skyrme interactions SKI to SKVI. It is further shown that even at densities slightly higher thanρ _c the density wave still exists as ametastable state in the sense that its energy is a local minimum in the variation parameter space. The density wave solution suddenly disappears at a higher density, since there the local minimum changes to an inflection point.     

On the use of Skyrme forces in self-consistent RPA calculations

Self-consistent random-phase (RPA) calculations including the continuum are presented using Skyrme forces. The density-dependent interpretation of the interaction is favoured as it does not violate the spin stability. A possible density dependence of the momentum-dependent S- and P-interaction is taken into account, which allows one to vary the incompressibility K and the effective mass $\text{m}{}^1\text{/m}$ independently. It is shown by analytic relations that these two quantities are the only degrees of freedom left in the parameterization of this Skyrme force,if the ground-state properties shall be reproduced, except for a still open degree of freedom in the spin exchange parameterization. The Landau parameters are discussed as a function of these degrees of freedom in order to find the best possible particle-hole interaction. Continuum calculations of the 1^?, 2 ⁺ and 3^? states in ¹⁶O are presented and compared with-discretized continuum calculations. It is found that the existing Skyrme forces do not show enough attraction and in addition cause relatively large isospin impurities, in ¹⁶O as well as in ²⁰⁸Pb. The influence of large configuration spaces is discussed. A systematic search for an interaction with a stronger particle-hole interaction is presented which seems to favour interactions with a high effective mass, but a low compression modulus.     

Ground states of the hydrogen molecule and its molecular ion in the presence of a magnetic field using the variational Monte Carlo method

ABSTRACT

By using the variational Monte Carlo (VMC) method, we calculated the 1sσ_g-state energies, the dissociation energies, and the binding energies of the hydrogen molecule and its molecular ion in the presence of an aligned magnetic field regime between 0 and 10?a.u. The present calculations are based on using two types of compact and accurate trial wave functions, which are put forward for consideration in calculating energies in the absence of a magnetic field. The obtained results are compared with the most recent accurate values. We conclude that the applications of the VMC method can be successfully extended to cover the case of molecules under the effect of a magnetic field.     

Calculated oxygen 1s core-level photoemission spectra from cuprate superconductors

The observed O 1s X-ray photoemission spectra of the cuprate superconductors often exhibit a satellite at a higher binding energy to the main peak. The origin of this satellite is not fully understood. We have done model cluster calculations to investigate the origin of this satellite using the configuration interaction approach. The calculated spectra for the divalent and superconducting cuprates essentially exhibit a single peak. On distorting the cluster in-plane, the peak shifts to higher binding energies. This substantiates a deterioration of the surface leading to the observed satellite structure in the O 1s core-level photoemission spectra of the cuprate superconductors.     

T-REX

The potential barrier impeding the spontaneous emission of protons in the proton radioactive nuclei is calculated as the sum of nuclear, Coulomb and centrifugal contributions. The nuclear part of the proton-nucleus interaction potential is obtained in the energy density formalism using the Skyrme effective interaction that results into a simple algebraic expression. The half-lives of the proton emitters are calculated for the different Skyrme sets within the improved WKB framework. The results are found to be in reasonable agreement with the earlier results obtained for more complicated calculations involving finite-range interactions.     

Abnormal odd-even staggering behavior around 132Sn studied by density functional theory

In this work, we have performed Skyrme density functional theory (DFT) calculations of nuclei around ¹³²Sn to study whether the abnormal odd-even staggering (OES) behavior of binding energies around N = 82 can be reproduced. With the Skyrme forces SLy4 and SkM*, we tested the volume- and surface-type pairing forces and also the intermediate between these two pairing forces, in the Hartree-Fock-Bogoliubov (HFB) approximation with or without the Lipkin-Nogami (LN) approximation or particle number projection after the convergence of HFBLN (PLN). The Universal Nuclear Energy Density Function (UNEDF) parameter sets are also used. The trend of the neutron OES against the neutron number or proton number does not change significantly by tuning the density dependence of the pairing force. Moreover, for the pairing force that is favored more at the nuclear surface, a larger mass OES is obtained, and vice versa. It appears that the combination of volume and surface pairing can give better agreement with the data. In the studies of the OES, a larger ratio of surface to volume pairing might be favored. Additionally, in most cases, the OES given by the HFBLN approximation agrees more closely with the experimental data. We found that both the Skyrme and pairing forces can influence the OES behavior. The mass OES calculated by the UNEDF DFT is explicitly smaller than the experimental one. The UNEDF1 and UNEDF2 forces can reproduce the experimental trend of the abnormal OES around ¹³²Sn. The neutron OES of the tin isotopes given by the SkM* force agrees more closely with the experimental one than that given by the SLy4 force in most cases. Both SLy4 and SkM* DFT have difficulties in reproducing the abnormal OES around ¹³²Sn. Using the PLN method, the systematics of OES are improved for several combinations of Skyrme and pairing forces.     

Self-consistent theory of finite Fermi systems and Skyrme–Hartree–Fock method

Recent results obtained on the basis of the self-consistent theory of finite Fermi systems by employing the energy density functional proposed by Fayans and his coauthors are surveyed. These results are compared with the predictions of Skyrme–Hartree–Fock theory involving several popular versions of the Skyrme energy density functional. Spherical nuclei are predominantly considered. The charge radii of even and odd nuclei and features of low-lying 2⁺ excitations in semimagic nuclei are discussed briefly. The single-particle energies ofmagic nuclei are examined inmore detail with allowance for corrections to mean-field theory that are induced by particle coupling to low-lying collective surface excitations (phonons). The importance of taking into account, in this problem, nonpole (tadpole) diagrams, which are usually disregarded, is emphasized. The spectroscopic factors of magic and semimagic nuclei are also considered. In this problem, only the surface term stemming from the energy dependence induced in the mass operator by the exchange of surface phonons is usually taken into account. The volume contribution associated with the energy dependence initially present in the mass operator within the self-consistent theory of finite Fermi systems because of the exchange of high-lying particle–hole excitations is also included in the spectroscopic factor. The results of the first studies that employed the Fayans energy density functional for deformed nuclei are also presented.

     

Microscopic and proximity nucleus-nucleus potentials

The energy functional of the Skyrme interaction is employed to calculate the real part of the interaction potential between magic nuclei in the sudden approximation. The use of an approximation introduced by Kirzhnits and others for the kinetic energy density produces improvements over the previous results. The mass dependence of the potential is analysed and its consistency with the proximity potential is discussed.     

Statistical properties of deexcitation of fragments originating from the spontaneous fission of 252Cf

A method of parametrizing radiative strength functions for electric dipole transitions is used to calculate the spectra of photons emitted by fragments originating from the spontaneous fission of ²⁵²Cf nuclei. The LDPL-98 library of parameters, which contains data for 2000 nuclei, is composed for performing relevant calculations. It is shown that the use of this method leads to regular agreement with experimental data—that the structure and the energy dependence of the spectra are reproduced without varying parameters suggests a statistical character of fission-fragment deexcitation.