Calculation of microscopic nuclear level densities based on covariant density functional theory

In this study,a microscopic method for calculating the nuclear level density(NLD)based on the covariant density functional theory(CDFT)is developed.The particle-hole state density is calculated by a combinatorial method using single-particle level schemes obtained from the CDFT,and the level densities are then obtained by considering collective effects such as vibration and rotation.Our results are compared with those of other NLD models,including phenomenological,microstatisti-cal and nonrelativistic Hartree–Fock–Bogoliubov combinatorial models.This comparison suggests that the general trends among these models are essentially the same,except for some deviations among the different NLD models.In addition,the NLDs obtained using the CDFT combinatorial method with normalization are compared with experimental data,including the observed cumulative number of levels at low excitation energies and the measured NLDs.The CDFT combinatorial method yields results that are in reasonable agreement with the existing experimental data.

A Cautionary Note on the Application of GIS in Spatial Optimization Modeling

Spatial optimization as part of spatial modeling has been facilitated significantly by integration with GIS techniques. However, for certain research topics, applying standard GIS techniques may create problems which require attention. This paper serves as a cautionary note to demonstrate two problems associated with applying GIS in spatial optimization, using a capacitated p-median facility location optimization problem as an example. The first problem involves errors in interpolating spatial variations of travel costs from using kriging, a common set of techniques for raster files. The second problem is inaccuracy in routing performed on a graph directly created from polyline shapefiles, a common vector file type. While revealing these problems, the paper also suggests remedies. Specifically, interpolation errors can be eliminated by using agent-based spatial modeling while the inaccuracy in routing can be improved through altering the graph topology by splitting the long edges of the shapefile. These issues suggest the need for caution in applying GIS in spatial optimization study.

Model Selection in Estimation of Covariance Functions for Growth of Angora Goats

Covariance functions have been proposed as an alternative to model longitudinal data in animal breeding because of their various merits in comparison to the classical analytical methods.In practical estimation,different models and polynomial orders fitted can influence the estimates of covariance functions and thus genetic parameters.The objective of this study was to select model for estimation of covariance functions for body weights of Angora goats at 7 time points.Covariance functions were estimated by fitting 6 random regression models with birth year,birth month,sex,age of dam,birth type,and relative birth date as fixed effects.Random effects involved were direct and maternal additive genetic,and animal and maternal permanent environmental effects with different orders of fit.Selection of model and orders of fit were carried out by likelihood ratio test and 4 types of information criteria.The results showed that model with 6 orders of polynomial fit for direct additive genetic and animal permanent environmental effects and 4 and 5 orders for maternal genetic and permanent environmental effects,respectively,were preferable for estimation of covariance functions.Models with and without maternal effects influenced the estimates of covariance functions greatly.Maternal permanent environmental effect does not explain the variation of all permanent environments,well suggesting different sources of permanent environmental effects also has large influence on covariance function estimates.

Tilted Axis Rotation of ^(57)Mn in Covariant Density Functional Theory

The self-consistent tilted axis cranking covariant density functional theory based on the point-coupling interaction is applied to investigate the tilted axis rotation in ^57 Mn. The observed data for band C are reproduced well with the assigned configuration eonfig 1. The shears mechanism for magnetic rotation is examined by investigating microscopically the orientation of angular momentum and the corresponding contributions. It is found that config 1 and config 3 correspond to a rotation of high-K character. Config 2 corresponds to a rotation of magnetic character. However, due to the presence of electromagnetic transition B（M1） and B（E2）, collective rotation plays an essential role in the competition with magnetic rotation.

Level density of odd-A nuclei at saddle point

Based on the covariant density functional theory,by employing the core–quasiparticle coupling(CQC)model,the nuclear level density of odd-A nuclei at the saddle point is achieved.The total level density is calculated via the convolution of the intrinsic level density and the collective level density.The intrinsic level densities are obtained in the finite-temperature covariant density functional theory,which takes into account the nuclear deformation and pairing self-consistently.For saddle points on the free energy surface in the(β_(2),γ)plane,the entropy and the associated intrinsic level density are compared with those of the global minima.By introducing a quasiparticle to the two neighboring even–even core nuclei,whose properties are determined by the five-dimensional collective Hamiltonian model,the collective levels of the odd-A nuclei are obtained via the CQC model.The total level densities of the^(234-240)U agree well with the available experimental data and Hilaire’s result.Furthermore,the ratio of the total level densities at the saddle points to those at the global minima and the ratio of the total level densities to the intrinsic level densities are discussed separately.

Dynamic Spatio-Temporal Modeling in Disease Mapping

Spatio-temporal models are valuable tools for disease mapping and understanding the geographical distribution of diseases and temporal dynamics. Spatio-temporal models have been proven empirically to be very complex and this complexity has led many to oversimply and model the spatial and temporal dependencies independently. Unlike common practice, this study formulated a new spatio-temporal model in a Bayesian hierarchical framework that accounts for spatial and temporal dependencies jointly. The spatial and temporal dependencies were dynamically modelled via the matern exponential covariance function. The temporal aspect was captured by the parameters of the exponential with a first-order autoregressive structure. Inferences about the parameters were obtained via Markov Chain Monte Carlo (MCMC) techniques and the spatio-temporal maps were obtained by mapping stable posterior means from the specific location and time from the best model that includes the significant risk factors. The model formulated was fitted to both simulation data and Kenya meningitis incidence data from 2013 to 2019 along with two covariates;Gross County Product (GCP) and average rainfall. The study found that both average rainfall and GCP had a significant positive association with meningitis occurrence. Also, regarding geographical distribution, the spatio-temporal maps showed that meningitis is not evenly distributed across the country as some counties reported a high number of cases compared with other counties.

Variation in growth potential between hybrid clones of Eucalyptus trees in eastern South Africa

Growth of commercial forestry is highly dependent on the availability of fast-growing planting materials. Consequently, the efficient utilization of fastgrowing plantations can greatly impact productivity. The objectives of this study were to evaluate variations in the growth potential of two clones and to estimate the average stem radial growth advantage of a fast-growing clone using data obtained from Sappi landholdings in eastern South Africa and a mixed modelling approach that permits the incorporation of covariance structure into the statistical model. During the first 2 years of growth, the stem radius of nine trees each of two clones was measured using dendrometer attached to the tree. A second-degree fractional polynomial model was chosen to show the functional relationship between stem radius and tree age. Growth of the two hybrid clones differed significantly. The Eucalyptus grandis×Eucalyptus urophylla clone grew faster than the E. grandis×camaldulensis clone, indicating better genetic potential for rapid growth and yield. This study can be considered as starting point to further compare the potential for rapid growth of several hybrid clones using the longitudinal data modelling approach.

The 4-D integrated geodesy and strain analysis

Research of the practical 4-D integrated geodesy(IG) and strain analysis is presented in this paper.The practical model and basic observation equation are established by using IG and dynamic adjustment.Furthermore,the observation equations about gravity vector,zenith distance,azimuth angle,difference are derived and determination of local gravity field covariance solved.The 3-D strain formular is derived and the strain parameters calculated from it.The improvement of the OPERA software of Landan and Hem etc,FRG has been done to get a new software in Fortran Language which implements in MASSCOMP computer.Using the software,the integrated adjustment of two term observation data of triangle chain, triangle net,gravity,level,astronomic observation and strain analysis are established.The result is satisfactory.

Three-dimensional potential energy surface for fission of^(236)U within covariant density functional theory

We calculate the three-dimensional potential energy surface(PES)for the fission of the compound nucleus^(236)U using covariant density functional theory with constraints on the axial quadrupole and octupole deformations(β_(2),β_(3))coexistence of the elongated and compact fission modes is predicted for comes shallow across a large range of quadrupole and octupole deformations for small scission line in the(β_(2),β_(3))plane extends to a shallow band,leading to fluctuations of several to ten MeV in the estimated total kinetic energies and of several to approximately ten nucleons in the fragment masses.

Evolution of N=20,28,50 shell closures in the 20≤Z≤30 region in deformed relativistic Hartree-Bogoliubov theory in continuum

Magicity,or shell closure,plays an important role in our understanding of complex nuclear phenomena.In this work,we employ one of the state-of-the-art density functional theories,the deformed relativistic Hartree-Bogoliubov theory in continuum(DRHBc)with the density functional PC-PK1,to investigate the evolution of the N=20,28,50 shell closures in the 20≤Z≤30 region.We show how these three conventional shell closures evolve from the proton drip line to the neutron drip line by studying the charge radii,two-neutron separation energies,two-neutron gaps,quadrupole deformations,and single-particle levels.In particular,we find that in the 21≤Z≤27 region,the N=50 shell closure disappears or becomes quenched,mainly due to the deformation effects.Similarly,both experimental data and theoretical predictions indicate that the N=28 shell closure disappears in the Mn isotopic chain,mainly due to the deformation effects.The DRHBc theory predicts the existence of the N=20 shell closure in the Ca,Sc,and Ti isotopic chains,but the existing data for the Ti isotopes suggest the contrary,and therefore further research is needed.

α-cluster structure of ^(12)C and ^(16)O in the covariant density functional theory with a shell-model-like approach

The α-cluster structures for 12^C and 16^O are investigated in the framework of the covariant density functional theory, where the pairing correlation is treated with a particle number conserving shell-model-like approach. The ground states of 12^C and 160 have been calculated and the density distributions demonstrate an equilateral triangle 3α clustering for 12^C and a regular tetrahedron 4α clustering for 16^O The existence of linear nα chain structure of both 12^C and 16^O is revealed at high quadrupole deformation.

Exact treatment of pairing correlations in Yb isotopes with covariant density functional theory

The effects of pairing correlation in Yb isotopes are investigated by covariant density functional theory with pairing correlations and blocking effects treated exactly by a shell model like approach （SLAP）. Experimental one- and two-neutron separation energies are reproduced quite well. The traditional BCS calculations always give larger pairing energies than those given by SLAP calculations, particularly for the nuclei near the proton and neutron drip lines. This may be caused because many of the single particle orbits above the Fermi surface are involved in the BCS calculations, but many of them are excluded in the SLAP calculations.

Magnetic moments of odd-A aluminum isotopes in covariant density functional theory

The ground-state properties,especially the magnetic moments,of odd-A aluminum isotopes have been studied and well reproduced in covariant density functional theory after considering the rotational coupling.The present calculations support the rotational structure in the ground state of odd-A aluminum isotopes,i.e.the ground state 5/2^+is built on the intrinsic state 5/2[202].In addition,the contribution from the time-odd fields is also discussed.

Center-of-mass correction and rotational correction in covariant density functional theory

Center-of-mass（c.m.） correction and rotational correction in even-even Ge isotopes are systematically investigated within the triaxially deformed relativistic Hartree-Bogoliubov model using the PC-PK1 force. The shell effect and deformation effect on the microscopic c.m. correction and rotational correction are discussed, and the importance of both corrections on reproducing the binding energy is demonstrated.

Nuclear chart in covariant density functional theory with dynamic correlations: From oxygen to tin

Nuclear masses of even-even nuclei with the proton number 8≤Z≤50(O to Sn isotopes)from the proton drip line to neutron drip line are investigated using the triaxial relativistic Hartree-Bogoliubov theory with the relativistic density functional PC-PK1.Further,the dynamical correlation energies(DCEs)associated with the rotational motion and quadrupole-shaped vibrational motion are taken into account by the five-dimensional collective Hamiltonian(5DCH)method.The root-mean-square deviation with respect to the experimental masses reduces from 2.50 to 1.59 MeV after the consideration of DCEs.The inclusion of DCEs has little influence on the position of drip lines,and the predicted numbers of bound even-even nuclei between proton and neutron drip lines from O to Sn isotopes are 569 and 564 with and without DCEs,respectively.

Nonparametric Estimation of Extreme Conditional Quantiles with Functional Covariate

Estimation of the extreme conditional quantiles with functional covariate is an important problem in quantile regression. The existing methods, however, are only applicable for heavy-tailed distributions with a positive conditional tail index. In this paper, we propose a new framework for estimating the extreme conditional quantiles with functional covariate that combines the nonparametric modeling techniques and extreme value theory systematically. Our proposed method is widely applicable, no matter whether the conditional distribution of a response variable Y given a vector of functional covariates X is short, light or heavy-tailed. It thus enriches the existing literature.

The interplay of single-particle and collective motions in the low-lying states of ^(21)_(A)Ne with quadrupole-octupole correlations

The beyond mean-field approach for low-lying hypernuclear states is extended by mixing the configurations associated with both single-particle and quadrupole-octupole collective excitations within the generator coordinate method based on a covariant den-sity functional theory.The method is demonstrated in the application to the low-lying states of 21ΛNe,where the configurations with theΛhyperon occupying the first(Λ_(s))and second(Λ_(p))lowest-energy states are considered.The results indicate that the positive-parity states are dominated by theα+^(12)C+α+Λ_(s) structure.In contrast,the low-lying negative-parity states are domi-nated by a strong admixture ofα+16O+Λ_(s) structure andα+12C+α+Λ_(p) structure due to the inclusion of octupole correlations.As a result,the low-lying negative-parity states become much lower than what is expected from the previous studies without the mixing,and the electric multipole transition strengths are significantly quenched.

Low-lying state investigations of odd-A Mn isotopes around N=28

Based on the systematic studies for low-lying states of the odd-A^(49-57)Mn isotopes,the groundstates inversion and the rotational properties of a ground-state-based sequence are revealed and discussed.The energy levels of low-lying states and electromagnetic moments in odd-A^(49-57)Mn isotopes have been well reproduced in shell-model calculations,and the above phenomena could be understood with obviously different occupation numbers in proton orbitals such asπf_(7/2)andπp_(3/2),which changes similarly with the obtained quadrupole deformation in covariant density functional theory(CDFT).After considering the coupling of collective rotation and intrinsic single-particle motion,the available experimental magnetic moments in53Mn and adjacent nuclei can be well explained with CDFT.The present calculations suggest that the 5/2^(-)and 7/2^(-)states in53Mn are formed byπ5/2^(-)[312]andπ7/2^(-)[303]respectively.Together with the behavior of levels,this provides proofs for the level sequences of low-lying states in53Mn distinct from the K^(π)=5/2^(-)rotational band in^(49)Cr and other odd-A Mn isotopes.

Triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis

A triaxially deformed relativistic Hartree–Bogoliubov theory in the Woods–Saxon basis is developed with the aim of treating the triaxial deformation,pairing correlations and continuum in a unified way.In order to consider the triaxial deformation,the deformed potentials are expanded in terms of spherical harmonic functions in the coordinate space.In order to take the pairing correlations into account and treat the continuum properly,by using the Dirac Woods–Saxon basis,which has correct asymptotic behavior,the relativistic Hartree–Bogoliubov equation with triaxial deformation is solved.The formalism of triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is presented.Taking an axially deformed nucleus24Ne and a triaxially deformed nucleus76Ge as examples,the numerical checks are performed.A weakly bound nucleus112Ge is taken as an example to carry out the necessary converge checks for the numerical parameters.In addition,the ground-state properties of even–even germanium isotopes are investigated.The evolutions of two-neutron separation energy,deformation,root-mean-square radii and density distribution with mass number are analyzed.The comparison between the calculations from the relativistic Hartree–Bogoliubov theory based on harmonic-oscillator basis and the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is performed.It is found that the neutron drip line is extended from114Ge to118Ge in the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis.

Local variations of charge radii for nuclei with even Z from 84 to 120

Pronounced changes of nuclear charge radii provide a stringent benchmark on the theoretical models and play a vital role in recognizing various nuclear phenomena.In this work,the systematic evolutions of nuclear charge radii along even Z=84-120 isotopic chains are first investigated by the recently developed new ansatz under the covariant density functional.The calculated results show that the shell closure effects of nuclear charge radii appear remarkably at the neutron numbers N=126 and 184.Interestingly,the arch-like shapes of charge radii between these two strong neutron-closed shells are naturally observed.Across the N=184 shell closure,the abrupt increase in charge radii is still evidently emerged.In addition,the rapid raise of nuclear charge radii from the neutron numbers N=138 to N=144 is disclosed clearly in superheavy regions due to the enhanced shape deformation.