Deformation properties of lead isotopes

The deformation properties of a long lead isotopic chain up to the neutron drip line are analyzed on the basis of the energy density functional (EDF) in the FaNDF⁰ Fayans form. The question of whether the ground state of neutron-deficient lead isotopes can have a stable deformation is studied in detail. The prediction of this deformation is contained in the results obtained on the basis of the HFB-17 and HFB-27 Skyrme EDF versions and reported on Internet. The present analysis reveals that this is at odds with experimental data on charge radii and magnetic moments of odd lead isotopes. The Fayans EDF version predicts a spherical ground state for all light lead isotopes, but some of them (for example, ¹⁸⁰Pb and ¹⁸⁴Pb) prove to be very soft—that is, close to the point of a phase transition to a deformed state. Also, the results obtained in our present study are compared with the predictions of some other Skyrme EDF versions, including SKM*, SLy4, SLy6, and UNE1. By and large, their predictions are closer to the results arising upon the application of the Fayans functional. For example, the SLy4 functional predicts, in just the same way as the FaNDF⁰ functional, a spherical shape for all nuclei of this region. The remaining three Skyrme EDF versions lead to a deformation of some light lead isotopes, but their number is substantially smaller than that in the case of the HFB-17 and HFB-27 functionals. Moreover, the respective deformation energy is substantially lower, which gives grounds to hope for the restoration of a spherical shape upon going beyond the mean-field approximation, which we use here. Also, the deformation properties of neutron-rich lead isotopes are studied up to the neutron drip line. Here, the results obtained with the FaNDF⁰ functional are compared with the predictions of the HFB-17, HFB-27, SKM*, and SLy4 Skyrme EDF versions. All of the EDF versions considered here predict the existence of a region where neutron-rich lead isotopes undergo deformations, but the size of this region is substantially different for the different functionals being considered. Once again, it is maximal for the HFB-17 and HFB-27 functionals, is substantially narrower for the FaNDF⁰ functional, and is still narrower for the SKM* and SLy4 functionals. The two-neutron drip line proved to be A_drip²ⁿ = 266 for all of the EDF versions considered here, with the exception of SKM*, for which it is shifted to A_drip²ⁿ(SKM*) = 272.     

Properties of the quasiparticle excitations in 207Pb and 209Pb from an extrapolation of the optical-model potential

A previously developed dispersion relation approach is used to calculate the shell-model potential in the case of neutrons in ²⁰⁸Pb, in the energy domain (-50 MeV, 0). This potential contains a dispersive contribution besides a Hartree-Fock type component, and thereby includes correlation and polarization effects. The shell-model and the Hartree-Fock type potentials are assumed to have Woods-Saxon shapes with diffuseness a_v = 0.70 fm; the energy dependence of their depths and radii is calculated. The energy dependence of the shell-model potential is characterized by the effective mass, whose dependence upon radial distance and neutron energy is determined. The effective mass is a sensitive function of energy, in contrast to its Hartree-Fock type component which is nearly independent of energy. Attention is drawn to the fact that the effective mass in nuclear matter cannot be straightforwardly identified with the effective mass at the nuclear centre. The effective mass presents a sharp peak at the nuclear surface near the Fermi energy and a dip at the surface for energies 10 to 20 MeV away from the Fermi energy. The spectroscopic factors of single-particle excitations in ²⁰⁷Pb and ²⁰⁹Pb are calculated from the difference between the effective mass and its Hartree-Fock type component. The predicted values of the valence single-particle wave functions at large radial distances are in fair agreement with experimental values deduced from analyses of sub-Coulomb pickup reactions. It is shown that the dispersive contribution increases the level density parameter by about 25%, in agreement with previous microscopic or semi-phenomenological models; the calculated level density parameter is in good agreement with the empirical value.     

Effect of tensor force on dissipation dynamics in time-dependent Hartree-Fock theory

The role of tensor force on the collision dynamics of ¹⁶O+¹⁶O is investigated in the framework of a fully three-dimensional time-dependent Hartree-Fock theory. The calculations are performed with modern Skyrme energy functional plus tensor terms. Particular attention is given on the analysis of dissipation dynamics in heavy-ion collisions. The energy dissipation is found to decrease as an initial bombarding energy increases in deep-inelastic collisions for all the Skyrme parameter sets studied here because of the competition between the collective motion and the single-particle degrees of freedom. We reveal that the tensor forces may either enhance or reduce the energy dissipation depending on the different parameter sets. The fusion cross section without tensor force overestimates the experimental value by about 25%, while the calculation with tensor force T11 has good agreement with experimental cross section.     

Systematically too low values of the cranking model collective inertia parameters

Deformed Nilsson and Woods-Saxon potentials were employed for generating single particle states used henceforth for calculating the inertia tensor (cranking model and monopole pairing) and the collective energy surfaces (Strutinsky method). The deformation was parametrized in terms of quadrupole and hexadecapole degrees of freedom. The classical energy expression obtained from the inertia tensor and energy surfaces was quantized and the resulting stationary Schrödinger equation was solved using the approximate method. The secondI ^π=0 ₂ ⁺ collective level energies were calculated for the Rare Earth and Actinide nuclei and the results compared with the experimental data. The vibrational level energies agree with the experimental ones much better for spherical nuclei for both single particle potentials; the discrepancies for deformed nuclei overestimate the experimental results by roughly a factor of two. It is argued that coupling of the axially symmetric quadrupole degrees of freedom to non-axial and hexadecapole ones does not affect the conclusions about systematically too low mass parameter values. The alternative explanation of the systematic deviations from the 0 ₂ ⁺ level energies could be a systematically too high stiffness of the energy surfaces obtained with the Strutinsky method.     

Hyperdeformation and clusterization in the actinide region

The ²³³U(d,pf)²³⁴U, and the ²³⁵U(d,pf)²³⁶U reactions have been studied with high energy resolution. The observed fission resonances were described as members of rotational bands with rotational parameters characteristic of hyperdeformed nuclear shapes. Information on the K values of the bands and for the J values of the band members has been obtained from fission fragment angular distribution measurements. The level density of the most strongly excited states has been compared to the prediction of the back-shifted Fermi-gas formula and the energy of the ground state in the third minimum has been estimated for ²³⁴U. The fission fragment mass distribution of the hyperdeformed states in ²³⁶U has also been measured. The width of the mass distribution, coincident with the hyperdeformed bands, is significantly smaller than the ones obtained in coincidence with background regions below and above the resonances, which suggests a pear-shaped di-nuclear configuration of ²³⁶U in the third well of the potential barrier.     

LiNH2 的晶格动力学、介电性质和热力学性质第一性原理研究

采用基于密度泛函理论的平面波赝势方法,在局域密度近似下采用线性响应的密度泛函微扰理论计算了LiNH₂的晶格动力学、介电性质和热力学性质,得到了布里渊区高对称方向上的声子色散曲线和相应的声子态密度,分析了 LiNH₂的红外和拉曼活性声子频率,同时给出它的介电张量和玻恩有效电荷张量. 研究表明,LiNH₂存在小的各向异性,计算所得结果与实验值和其他理论值符合较好.最后,利用得到的声子态密度进一步预测了LiNH₂的热力学性质 关键词： 密度泛函理论 晶格动力学 热力学性质 第一性原理计算     

Exchange interaction in GdGa from first-principles

The electronic structure and magnetic properties for GdGa have been studied from a first-principles density functional calculation. The energy band structure has been calculated in a local spin density approximation (LSDA), plus Hubbard U approach (LSDA+U). For Gd atoms, seven spin up 4f bands are fully occupied and situated at the bottom of Ga 4s states, while the spin down 4f hole levels are completely unoccupied and well above the Fermi level (E_f). The p- and d-like states dominate at E_f. The calculated magnetic moment is 7.37μ_B per formula unit (f.u.) and is not sensitive to the change of the unit cell volume. The effective exchange parameters, J₀, decrease from 2.6 to 0.9 mRy with increasing lattice volume from 35.7 to 55.3 Å³/f.u., resulting in a pressure induced enhancement of the Curie temperature (T_C). With the experimental lattice constants, the calculated mean field T_C is 187 K, in good agreement with the experimental value (T_C^exp.=183 K).     

Fission barriers and other characteristics of nuclei from the uranium region

Fission barriers in nuclei belonging to the uranium region and their other characteristics are calculated on the basis of the FaNDF⁰ energy density functional. In particular, the neutron-separation energies S _n and S _2n, the proton-separation energies S _p, and the beta-transition energiesQ _β are calculated for uranium, neptunium, and plutonium isotopes. In addition, the deformation energies and parameters of these nuclei are presented along with their radii. A comparison with the predictions of the Skyrme–Hartree–Fock method implemented with several versions of the Skyrme energy density functionals is performed. The role of the octupole deformation β ₃ is studied for the ²³⁸U nucleus. It is shown that this deformation does not have any significant effect on the first-barrier height B ⁽¹⁾ _f or ground-state properties. At the same time, the second-barrier height B(2) f decreases by a factor of about two upon taking into account β ₃. A phase transition at A ~ 260 is found for the three isotopic chains being considered: this point is a bifurcation point at which B ⁽¹⁾ _f (A) forks into two curves. Of these, the curve B ⁽²⁾ _f (A) splits from it, prolonging the former curve for B ⁽¹⁾ _f (A) almost continuously, whereas the curve for B ⁽¹⁾ _f (A) itself goes down sharply.     

Analysis of209Bi and238U photofission cross section in the quasi-deuteron region of photonuclear absorption

An analysis of the photofission reactions in the quasi-deuteron energy range of photonuclear absorption (30–140 MeV) has been performed for²⁰⁹Bi and²³⁸U nuclei. Experimental cross section data available in the literature have been compared with calculated values obtained from a model in which the incoming photon is assumed to be absorbed by a neutron-proton pair (Levinger's quasi-deuteron photoabsorption), followed by a mechanism of evaporation-fission competition for the excited residual nuclei. The model has been shown to reproduce the main experimental features of²⁰⁹Bi and²³⁸U photofission cross section, although unexplained differences still remain in the case of²³⁸U-fission by 30– 50 MeV incident photons.     

Debye frequency tensor and anisotropy of the Mössbauer effect in tellurium and antimony single crystals

We suggest a semiphenomenological expression for the recoilless fraction in the Mössbauer effect in noncubic, and in particular, uniaxial crystals based on the idea of the Debye frequency tensor. Convenient formulae are derived expressing the principal values of the Debye tensor in terms of the elastic stiffness constants and density with the aid of integrals over an irreducible part of the solid angle. Tetragonal and trigonal system are both considered. The principal values of the Debye frequency tensor for tellurium and antimony single crystals belonging to the trigonal system are found by numerical integration through these formulae. The recoilless fractions for the isotopes ¹²⁵Te and ¹²¹Sb are found in the direction of the principal crystallographic axis and in the directions normal to it over the temperature range 0–320°K. The calculated values of the recoil-free fractions at 0°K and their ratio at liquid nitrogen temperature agree with the available experimental data.     

Spontaneous symmetry breaking vacuum energy in cosmology

The gravitational effect of spontaneous symmetry breaking vacuum energy density is investigated by subtracting the flat space-time contribution from the energy in the curved space-time. We find that the remaining effective energy-momentum tensor is too small to cause the acceleration of the universe, although it satisfies the characteristics of dark energy. However, it could provide a promising explanation to the puzzle of why the gravitational effect produced by the huge symmetry breaking vacuum energy in the electroweak theory has not been observed, as it has a sufficiently small value (smaller than the observed cosmic energy density by a factor of 1032).     

Effect of tensor correlations on Gamow–Teller states in Zr and Pb

The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree–Fock plus Random Phase Approximation (HF + RPA) model. The Gamow–Teller (GT) strength function of ⁹⁰Zr and ²⁰⁸Pb are calculated with and without the tensor terms. The main peaks are moved downwards by about 2 MeV when including the tensor contribution. About 10% of the non-energy weighted sum rule is shifted to the excitation energy region above 30 MeV by the RPA tensor correlations. The contribution of the tensor terms to the energy weighted sum rule is given analytically, and compared to the outcome of RPA.     

Influence of the weakly interacting light U boson on the properties of massive protoneutron stars

Considering the octet baryons in relativistic mean field theory and selecting entropy per baryon S=l,we calculate and discuss the influence of U bosons on the equation of state,mass-radius,moment of inertia and gravitational redshift of massive protoneutron stars(PNSs).The effective coupling constant gu of U bosons and nucleons is selected from 0 to 70 GeV~(-2).The results indicate that U bosons will stiffen the equation of state(EOS).The influence of U bosons on the pressure is more obvious at low density than high density,while the influence of U bosons on the energy density is more obvious at high density than low density.The U bosons play a significant role in increasing the maximum mass and radius of PNS.When the value of gu changes from 0 to 70 GeV~(-2),the maximum mass of a massive PNS increases from 2.11M_⊙ to 2.58M_⊙,and the radius of a PNS corresponding to PSR J0348+0432 increases from 13.71 km to 24.35 km.The U bosons will increase the moment of inertia and decrease the gravitational redshift of a PNS.For the PNS of the massive PSR J0348+0432,the radius and moment of inertia vary directly with gu,and the gravitational redshift varies approximately inversely with gu.     

Deuteron form factors and the tensor force

Results of a non-relativistic calculation of deuteron form factors are presented for separable potentials with and without tensor force. The tensor term in triplet state is added in such a way as to keep the values of deuteron binding energy,a _t andr _0t unaltered, so that the difference in the form factors can be regarded as the effect of tensor force only. The calculation has been performed for two different shapes of separable potentials and for three differentD-state probabilities to study their comparative effect.     

Search for the emission of π<Superscript>0</Superscript> mesons from the neutron-induced fission of <Superscript>235</Superscript>U nuclei

A nuclear-reactor experiment on the search for the emission of neutral pions from the neutron-induced fission of ²³⁵U nuclei has been carried out. To this end, an experimental setup for searching for the emission of π⁰ mesons with high sensitivity to this process has been designed and produced. This setup consisted of two Cherenkov total-absorption spectrometers for the detection and measurements of the energy of two gamma-ray photons from π ⁰-meson decay. The spectrometers were placed at the exits of two coaxial horizontal experimental channels. To protect the detectors from low-energy β and γ rays and neutron fluxes, 3.5-m-long water filters were situated in the channels. To reject the cosmic background, large-area scintillation counters operating in the anticoincidence mode were placed over each spectrometer. The energy and time resolution of the spectrometers, as well as the efficiency of detecting charged particles by scintillation counters, were tested on the secondary electron beam of the Tomsk electron synchrotron Sirius. Runs of measurements of the effect on the operating reactor (duration of 805 h) were alternated with runs of measurements of background on the stopped reactor (duration of 403 h). Statistical processing of the experimental results yields an upper limit of ≤5.3×10 ^?12 with a 90% confidence level for the probability of the emission of neutral pions from the neutron-induced fission of ²³⁵U nuclei. This result and results of other works carried out with sources of spontaneously fissioning ²⁵²Cf nuclei show that the probabilities of the emission of π⁰ mesons from spontaneous fission and fission induced by fission-spectrum neutrons are equal to each other.     

Shell structure fingerprints of tensor interaction

We address the consequences of strong tensor terms in the local energy density functional, resulting from fits to the f _5/2 -f _7/2 splittings in ⁴⁰Ca , ⁴⁸Ca , and ⁵⁶Ni . In this study, we focus on the tensor contribution to the nuclear binding energy. In particular, we show that it exhibits an interesting topological feature closely resembling that of the shell correction. We demonstrate that in the extreme single-particle scenario at spherical shape, the tensor contribution shows tensorial magic numbers equal to N(Z) = 14 , 32, 56, and 90, and that this structure is smeared out due to configuration mixing caused by pairing correlations and migration of proton/neutron sub-shells with neutron/proton shell filling. Based on a specific Skyrme-type functional SLy4_T, we show that the proton tensorial magic numbers shift with increasing neutron excess to Z = 14 , 28, and 50.     

Accurate 13-C and 15-N molecular crystal chemical shielding tensors from fragment-based electronic structure theory

Standard nuclear magnetic resonance (NMR) spectroscopy experiments measure isotropic chemical shifts, but measuring the chemical shielding anisotropy (CSA) tensor can provide additional insights into solid state chemical structures. Interpreting the principal components of these tensors is facilitated by first-principles chemical shielding tensor predictions. Here, the ability to predict molecular crystal CSA tensor components for ¹³C and ¹⁵N nuclei with fragment-based electronic structure techniques is explored. Similar to what has been found previously for isotropic chemical shifts, the benchmarking demonstrates that fragment-based techniques can accurately reproduce CSA tensor components. The use of hybrid density functionals like PBE0 or B3LYP provide higher accuracy than generalized gradient approximation functionals like PBE. Unlike for planewave density functional techniques, hybrid density functionals can be employed routinely with modest computational cost in fragment approaches. Finally, good consistency between the regression parameters used to map either isotropic shieldings or CSA tensor components is demonstrated, providing further evidence for the quality of the models and highlighting that models trained for isotropic shifts can also be applied to CSA tensor components.     

Low-energy parameters of neutron-neutron interaction in the effective-range approximation

The effect of the mass difference between the charged and neutral pions on the low-energy parameters of nucleon-nucleon interaction in the ¹ S ₀ state is studied in the effective-range approximation. On the basis of experimental values of the singlet parameters of neutron-proton scattering and the experimental value of the virtual-state energy for the neutron-neutron systemin the ¹ S ₀ state, the following values were obtained for the neutron-neutron scattering length and effective range: a _nn = ?16.59(117) fm and r _nn = 2.83(11) fm. The calculated values agree well with present-day experimental results.     

Exact four-body calculation of the 4ΛHe-4ΛH binding energy difference

The coupled, two-variable integral equations that determine the ⁴_ΛHe and ⁴_ΛH bound states, when the NN and ΛN interactions are represented by separable potentials, are derived from the Schrödinger equation. The integral equations are solved numerically for simple s-wave potentials and for tensor potentials in the truncated t-matrix approximation without resort to separable expansion of the kernels. The Λ-separation energy difference ΔB_Λ resulting from the genuine four-body model is shown to be approximately twice as large as that coming from an “effective two-body” model calculation, when identical central potentials are used. The four-body model estimate of ΔB_Λ made with tensor forces is consistent with the experimental value, indicating that charge symmetry breaking implied by the low energy Λ N scattering parameters is compatible with that suggested by the known binding energy difference in the A = 4 hypernuclear isodoublet.     

Electronic structure and spectra of CuO

We report the electronic structure of monoclinic CuO as obtained from first principles calculations utilizing density functional theory plus effective Coulomb interaction (DFT + U) method. In contrast to standard DFT calculations taking into account electronic correlations in DFT + U gave antiferromagnetic insulator with energy gap and magnetic moment values in good agreement with experimental data. The electronic states around the Fermi level are formed by partially filled Cu 3d _x²?y² orbitals with significant admixture of O 2p states. Theoretical spectra are calculated using DFT + U electronic structure method and their comparison with experimental photoemission and optical spectra show very good agreement.