Total Level Density Research Articles

S-process stellar enhancement factors obtained within the statistical model with parity-dependent level densities

In stellar environments the medium modifications of the neutron capture cross-sections required for s-process nucleosynthesis simulations are accounted for by the stellar enhancement factors. We have calculated these enhancement factors using the statistical model for compound reactions. Improving previous calculations we take the parity distribution of states at all stages of the reaction into account by using parity-dependent level densities. The effect of this improvement on the stellar enhancement factors is small, although not negligible if one attempts to describe the stellar capture rates with an accuracy of order 10%. We observe, however, that the uncertainties introduced by the insufficient knowledge of the total level densities are noticeably larger.

Electronic structures of AlB2-type superconducting YbGa1+xSi1−x alloys probed by NMR and Seebeck coefficient

We report the electronic properties of the AlB2-type compounds YbGa1+xSi1−x (x=0, 0.15, and 0.3) studied by means of the nuclear magnetic resonance (NMR) and the Seebeck coefficient measurements. These materials are of current interest due to the presence of superconductivity with Yb element. From the analysis of G69a NMR spin-lattice relaxation rates, we deduce the Ga 4s partial Fermi level density of states Ns(EF) for these compounds. The result indicates a gradual increase in Ns(EF) with increasing x in YbGa1+xSi1−x. In addition, the evolution of the Seebeck coefficient feature can be understood well within the band-filling scenario. From the Seebeck coefficient analysis, we find that the variation in the total Fermi level density of states N(EF) is not consistent with the trend of superconducting temperature Tc which shows a gradual decrease with Ga content. These observations support the hypothesis that the electronic Fermi level density of states is not the key factor in determining the superconducting transition temperature of YbGa1+xSi1−x.

Long-term effects of high lipid and high energy diet on serum lipid, brain fatty acid composition, and memory and learning ability in mice

ObjectiveIt is well known that high lipid and high energy diet is harmful to health. But the different effects of high lipid diet composed of either saturated fatty acids or unsaturated fatty acids have not been distinguished. MethodEighteen pregnant C57BL/6j (22–25g) mice were randomly divided into three groups of six each and fed with chow or high lipid diet composed of either flaxseed oil (chow diet 84%, cholesterol 0.2%, flaxseed oil 15.8%) or lard fat (chow diet 84%, cholesterol 0.2%, lard fat 15.8%). After weaning, the offspring were fed the same diet as their mothers were fed during the experiment, and their spatial memory and learning ability were evaluated by Morris water maze when they were 8 weeks old. Next, the blood and tissues were sampled when they were 9 weeks old. Serum lipids were determined using kits, and brain fatty acids were measured using a gas chromatograph. ResultsCompared to chow diet (control), high flaxseed oil diet (HFO) increased high density lipoprotein cholesterol level (HDL-C) in the mothers but not in offspring; high lard fat diet (HLF) increased serum total cholesterol level (TC) and low density lipoprotein cholesterol level (LDL-C) both in mothers and offspring. Brain fatty acids profile was altered by HLF compared with chow diet. Polyunsaturated fatty acids and long-chain polyunsaturated fatty acids content were significantly lower in the HLF group than in the control group, but saturated fatty acids content were significantly higher in HLF group than those in control group. The changed fatty acids composition affected the spatial memory and learning ability of adult offspring. ConclusionsA long-term high lard diet increased offspring serum TC and LDL-C levels and affected the brain's fatty acid composition, and memory and learning ability. The polyunsaturated fatty acid content of the brain may be correlated with serum cholesterol levels.

RIPL – Reference Input Parameter Library for Calculation of Nuclear Reactions and Nuclear Data Evaluations

We describe the physics and data included in the Reference Input Parameter Library, which is devoted to input parameters needed in calculations of nuclear reactions and nuclear data evaluations. Advanced modelling codes require substantial numerical input, therefore the International Atomic Energy Agency (IAEA) has worked extensively since 1993 on a library of validated nuclear-model input parameters, referred to as the Reference Input Parameter Library (RIPL). A final RIPL coordinated research project (RIPL-3) was brought to a successful conclusion in December 2008, after 15 years of challenging work carried out through three consecutive IAEA projects. The RIPL-3 library was released in January 2009, and is available on the Web through (http://www-nds.iaea.org/RIPL-3/). This work and the resulting database are extremely important to theoreticians involved in the development and use of nuclear reaction modelling (ALICE, EMPIRE, GNASH, UNF, TALYS) both for theoretical research and nuclear data evaluations. The numerical data and computer codes included in RIPL-3 are arranged in seven segments: MASSES contains ground-state properties of nuclei for about 9000 nuclei, including three theoretical predictions of masses and the evaluated experimental masses of Audi et al. (2003). DISCRETE LEVELS contains 117 datasets (one for each element) with all known level schemes, electromagnetic andmore » {gamma}-ray decay probabilities available from ENSDF in October 2007. NEUTRON RESONANCES contains average resonance parameters prepared on the basis of the evaluations performed by Ignatyuk and Mughabghab. OPTICAL MODEL contains 495 sets of phenomenological optical model parameters defined in a wide energy range. When there are insufficient experimental data, the evaluator has to resort to either global parameterizations or microscopic approaches. Radial density distributions to be used as input for microscopic calculations are stored in the MASSES segment. LEVEL DENSITIES contains phenomenological parameterizations based on the modified Fermi gas and superfluid models and microscopic calculations which are based on a realistic microscopic single-particle level scheme. Partial level densities formulae are also recommended. All tabulated total level densities are consistent with both the recommended average neutron resonance parameters and discrete levels. GAMMA contains parameters that quantify giant resonances, experimental gamma-ray strength functions and methods for calculating gamma emission in statistical model codes. The experimental GDR parameters are represented by Lorentzian fits to the photo-absorption cross sections for 102 nuclides ranging from {sup 51}V to {sup 239}Pu. FISSION includes global prescriptions for fission barriers and nuclear level densities at fission saddle points based on microscopic HFB calculations constrained by experimental fission cross sections.« less

Isospin-projected nuclear level densities by the shell model Monte Carlo method

We have developed an efficient isospin projection method in the shell model Monte Carlo approach for isospin-conserving Hamiltonians. For isoscalar observables this method has the advantage of being exact sample by sample. It allows us to take into account the proper isospin dependence of the nuclear interaction, thus avoiding a sign problem that such an interaction introduces in unprojected calculations. We apply the method to calculate the isospin dependence of level densities in the complete $\mathit{pf}+{g}_{9/2}$ shell. We find that isospin-dependent corrections to the total level density are particularly important for $N~Z$ nuclei.

Exact Removal of the Center-of-Mass Spurious States from Level Densities

We give recursive formulae for the exact removal of the contribution of the center-of-mass spurious states from the fixed-spin and parity nuclear level density found in shell-model calculations, provided the total level density for restricted configurations is known. The method is valid for a large class of problems using a harmonic oscillator basis. Using our earlier methods based on statistical spectroscopy that utilize the centroids and widths for a restricted class of fixed-spin configurations, such as Nvariant Planck's over 2piomega excitations, one can calculate very accurately level densities free of spurious states. The approach is applicable to other fermion and boson systems trapped by an oscillator potential.

Plasma Total Homocysteine Level and Bone Mineral Density

Plasma total homocysteine (tHcy) has been associated with hip fracture but not directly with bone mineral density (BMD). We examined the association of hip BMD with levels of plasma tHcy, folate, and vitamin B12 and the methylenetetrahydrofolate reductase (MTHFR) 677C-->T and 1298A-->C polymorphisms. Bone mineral density was measured between 1997 and 2000 in 2268 men and 3070 women, aged 47 to 50 and 71 to 75 years, from the Hordaland Homocysteine Study cohort. Low BMD was defined as BMD in the lowest quintile for each sex and age group. Linear, logistic, and generalized additive regression models were used. Plasma levels of tHcy were inversely related to BMD among middle-aged and elderly women (P<.001) but not among men. The multiple adjusted odds ratio for low BMD among subjects with high (>or=15 micromol/L [>or=2.02 mg/L]) compared with low (<9 micromol/L [<1.22 mg/L]) tHcy level was 1.96 (95% confidence interval, 1.40-2.75) for women and was not significant for men. Additional adjustments for plasma folate level or intake of calcium and vitamin D did not substantially alter the results. Plasma folate level was associated with BMD in women only. We observed no association between BMD and vitamin B12 level or the MTHFR polymorphisms. Elevated tHcy and low folate levels were associated with reduced BMD in women but not in men. These findings suggest that tHcy may be a potential modifiable risk factor for osteoporosis in women.

Classical description of the level density and the relaxation behavior of multidimensional molecular curve‐crossing systems

AbstractBased on the mapping formulation of nonadiabatic dynamics (Phys. Rev. Lett. 1997, 78, 578), explicit classical expressions for the total level density N(E) of a vibronically coupled molecular system as well as quantum corrections to it are derived. The analytical results for N(E) reveal the relative importance of the various molecular parameters of a curve‐crossing system, such as the electronic bias, the reorganization energy, and the topology of the potential‐energy surfaces. To study the accuracy of the approximate description, numerical studies employing various spin‐boson models as well as a two‐state, three‐mode model of the ultrafast S2 → S1 electronic relaxation in pyrazine are presented. Comparing exact quantum and approximate classical data, the connection between the level density of a vibronically coupled molecular system and its nonadiabatic relaxation behavior is discussed in some detail.

Combinatorial nuclear level densities based on the Gogny nucleon-nucleon effective interaction

A combinatorial method to calculate total level densities from an arbitrary single-particle level scheme is presented. Parity, angular momentum, pairing correlations as well as collective enhancements are explicitly treated. This method is employed using single-particle level schemes obtained from Hartree-Fock-Bogoliubov calculations based on the Gogny effective interaction. Sixty five even-even nuclei with masses 26 ?A? 250 are considered. Rather good agreements are obtained when comparing our predictions with experimental data for energies of the order of the neutron binding energies and for low excitation energies where discrete levels are experimentally observed.

Flow of zero-point energy and exploration of phase space in classical simulations of quantum relaxation dynamics

Necessary conditions under which a classical description will give the correct quantum relaxation behavior are analyzed. Assuming a nonequilibrium preparation, it is shown that the long-time mean values of observables can be expressed in terms of the spectral density and state-specific level densities of the system. Any approximation that reproduces these quantities therefore yields the correct expectation values at long times. Apart from this rigorous condition, a weaker but more practical criterion is established, that is, to require that the total level density is well approximated in the energy range defined by the spectral density. Since the integral level density is directly proportional to the phase-space volume that is energetically accessible to the system, the latter condition means that an appropriate classical approximation should explore the same phase-space volume as the quantum description. In general, however, this is not the case. A well-known example is the unrestricted flow of zero-point energy in classical mechanics. To correct for this flaw of classical mechanics, quantum corrections are derived which result in a restriction of the classically accessible phase space. At the simplest level of the theory, these corrections are shown to correspond to the inclusion of only a fraction of the full zero-point energy into the classical calculation. Based on these considerations, a general strategy for the classical simulation of quantum relaxation dynamics is suggested. The method is (i) dynamically consistent in that it refers to the behavior of the ensemble rather than to the behavior of individual trajectories, (ii) systematic in that it provides (rigorous as well as minimal) criteria which can be checked in a practical calculation, and (iii) practical in that it retains the conceptional and computational simplicity of a standard quasiclassical calculation. Employing various model problems which allow for an analytical evaluation of the quantities of interest, the virtues and limitations of the approach are discussed.

Influence of pairing correlations on the excitation energy, angular momentum, and parity dependence of nuclear level densities

We have studied the effects of pairing correlations on the excitation energy ${(E}^{*})$ dependence of the total nuclear level density, parity-projected level density, and spin cutoff factor for two heavy systems ${}^{152}\mathrm{Sm}$ and ${}^{160}\mathrm{Yb},$ within a microscopic approach based on static path approximation to a grand canonical partition function. For both systems considered, we find that pairing has significant effects on the ${E}^{*}$ dependence of total level densities. At moderate excitation energies ${(E}^{*}\ensuremath{\sim}10 \mathrm{MeV})$ it supresses the total level density nearly by two orders of magnitude. By fitting the total level density to a Bethe-type formula with energy backshift $({\ensuremath{\Delta}}_{\mathrm{BS}}),$ we find that ${\ensuremath{\Delta}}_{\mathrm{BS}}\ensuremath{\approx}2.5 \mathrm{MeV}$ for the excitation energy beyond $15 \mathrm{MeV}.$ At lower excitation energies, however, ${\ensuremath{\Delta}}_{\mathrm{BS}}$ is strongly ${E}^{*}$ dependent. We find that the effects of pairing on the spin cutoff factor and the parity-projected level densities (or parity asymmetry) is somewhat less important. We also compare our results for the spin cutoff factor with the ones conventionally employed in statistical model codes.

Microscopic nuclear level densities from Fe to Ge by the shell model Monte Carlo method

We calculate microscopically total and parity-projected level densities for β-stable even-even nuclei between Fe and Ge, using the shell model Monte Carlo methods in the complete ( pf+0 g 9/2)-shell. A single-particle level density parameter a and backshift parameter Δ are extracted by fitting the calculated densities to a backshifted Bethe formula, and their systematics are studied across the region. Shell effects are observed in Δ for nuclei with Z=28 or N=28 and in the behavior of A/ a as a function of the number of neutrons. We find a significant parity dependence of the level densities for nuclei with A≲60, which diminishes as A increases.

Excitation energy and angular momentum dependence of nuclear level densities and spin cut-off factor in SPA and SPA + RPA approaches

We investigate the excitation energy ( E ∗ ) and angular momentum ( J) dependence of nuclear level density and spin cut-off factor (σ) within microscopic approaches based on SPA and its extension SPA + RPA representation of the grand partition function for quadrupole-quadrupole interaction model Hamiltonian. For 110Sn, we find that excitation energy dependence of the total level density obtained within these approaches is significantly different. On the other hand, these approaches yield similar behaviour for J-dependence of the level density at fixed values of E ∗ . Values of σ SPA + RPA at low E ∗ are found to be slightly smaller than σ SPA but they tend to become almost the same at higher E ∗ (> 30 MeV) . We also find that Bethe's formula for fixed- J level density based on the spin cut-off approximation can be used to compute ϱ(E ∗, J) near the yrast line provided one uses an appropriate value of the spin cut-off factor.

Total and Parity-Projected Level Densities of Iron-Region Nuclei in the Auxiliary Fields Monte Carlo Shell Model

We use the auxiliary-fields Monte Carlo method for the shell model in the complete $(pf+0g_{9/2})$-shell to calculate level densities. We introduce parity projection techniques which enable us to calculate the parity dependence of the level density. Results are presented for $^{56}$Fe, where the calculated total level density is found to be in remarkable agreement with the experimental level density. The parity-projected densities are well described by a backshifted Bethe formula, but with significant dependence of the single-particle level-density and backshift parameters on parity. We compare our exact results with those of the thermal Hartree-Fock approximation.

Generalized Bethe formula (GBF) and combinatorial calculations for the systematics of Pb nuclei

Total level densities and state densities up to 40 MeV of excitation energy are calculated combinatorially for the systematics of Pb nuclei using independent nucleons in the realistic single particle spectra. These combinatorial level densities are well fitted by GBF, both for doubly closed shell nucleus 208 Pb and away from the shell closure. The corresponding GBF parameters exhibit smooth behavior with the change of the neutron number N , having pronounced extrema at the double shell closure. The GBF fit to the combinatorial results is compared with the fit of standard Bethe formula (BF) and of the Ignatyuk formula.

Generalized Bethe formula for the total level density

It is pointed out that the generalized Bethe formula for the total level density encompasses the standard Bethe formula and the constant temperature formula as limiting cases. It is shown that the generalized Bethe formula provides an excellent fit to the results of combinatorial calculations in the region of doubly closed shell nucleus ${}^{208}\mathrm{Pb}$ where the standard Bethe formula fails. The new parameter $\ensuremath{\xi}$ associated with the generalized Bethe formula shows a systematic behavior with distance from double shell closure.

Exact nuclear level density formula for periodic spectra

AbstractThe total nuclear level density is obtained for periodic single particle spectra. First, we express the canonical partition function in terms of Jacobi theta functions for degenerated fermion systems. Secondly, we use a relation for the number of representations of an integer number as sums of smaller numbers to find an exact formula for the nuclear level density. The shell structure is incorporated in the result in a simple way. An asymptotic relation can be easily obtained from the exact result and shown to be the well known back‐shifted Bethe‐formula.

Level density and collective enhancement factor of a compound nucleus in non-adiabatic approach

In this paper a simple statistical formalism that takes into account the diabatic motion of a compound system to calculate total level density is given. The diabatic motion is introduced by coupling the adiabatic collective motion to an environment consisting of intrinsic degrees of freedom. The collective enhancement of level density is studied. It has anadiabatical coefficient that depends only on the excitation energy and adynamical one that depends on the excitation energy and the coupling between intrinsic and collective modes. Qualitatively, the coefficients of the vibrational enhancement factor forA=240 have been studied. The coupling is understood as the initial effect of the oscillatory motion of the mass asymmetry of fragments on the nucleonic motion. The damping effect of the vibrational motion is taken into account considering the collective motion of the fragments as a zero-sound wave propagating in the Fermiliquid. The intrinsic state in the framework of the Fermi Gas Model (FGM) is described. The Pashkevich’s parametrization is used to describe the binary decay of the compound nucleus.

Application of spectral averaging theory in large shell model spaces: Analysis of level density data of fp-shell nuclei

Abstract In the spectral averaging theory extended to large shell model spaces (i) using a significant unitary group decomposition under which a one-plus two-body nuclear hamiltonian H decomposes into an orthogonal effective one-body part h and an irreducible two-body part V(H → h+V), (ii) applying the Central Limit Theorems locally and (iii) decomposing the shell model space into distant non-interacting S-subspaces (for light nuclei S denotes hω excitation), the state densities IH(E) take convolution form, IH(E) = ∑SIh,S ⊗ ϱGV,S[E], where Ih is the renormalized non-interacting particle state density and ϱG is a normalized spreading Gaussian due to V. A similar convolution form is available for spin-cutoff densities that give spin-cutoff factors. For a first systematic analysis, using the extended spectral averaging theory, of experimental level density data in a given region of the periodic table, fp-shell nuclei are chosen as an example. Calculations, using surface delta interaction, are carried out by including configurations up to 2hω excitations and by employing eight spherical orbits (ds, fp, 1g 9 2 ) for the five nuclei 55Mn, 56Fe, 59Co, 60Co and 60Ni and by extending for obvious reasons to ten spherical orbits (ds, fp, 1g 9 2 , 2d 5 2 , 1g 7 2 ) for the three A > 60 nuclei 62Ni, 63Cu and 65Cu. In general, spectral averaging theory is seen to provide a good representation of the observed total level densities and spin-cutoff factors.

Spin-dependent level density in interacting boson-fermion-fermion model

The level density of the odd-odd nucleus 132Pr is investigated in the interacting boson-fermion-fermion model (IBFFM) which accounts for collectivity and complex interaction between quasiparticle and collective modes. The IBFFM total level density is fitted by a Gaussian and its tail is also fitted by Bethe formula and constant temperature Fermi gas model. The IBFFM spin-dependent level densities show high-spin reductions with respect to Bethe formula. This can be well accounted for by a modified spin-dependent level density formula.