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.

Uncertainties of nuclear level density estimated using Bayesian neural networks

Nuclear level density(NLD)is a critical parameter for understanding nuclear reactions and the structure of atomic nuclei;however,accurate estimation of NLD is challenging owing to limitations inherent in both experimental measurements and theoretical models.This paper presents a sophisticated approach using Bayesian neural networks(BNNs)to analyze NLD across a wide range of models.It uniquely incorporates the assessment of model uncertainties.The application of BNNs demonstrates remarkable success in accurately predicting NLD values when compared to recent experimental data,confirming the effectiveness of our methodology.The reliability and predictive power of the BNN approach not only validates its current application but also encourages its integration into future analyses of nuclear reaction cross sections.

Buckling Optimization of Curved Grid Stiffeners through the Level Set Based Density Method

Stiffened structures have great potential for improvingmechanical performance,and the study of their stability is of great interest.In this paper,the optimization of the critical buckling load factor for curved grid stiffeners is solved by using the level set based density method,where the shape and cross section(including thickness and width)of the stiffeners can be optimized simultaneously.The grid stiffeners are a combination ofmany single stiffenerswhich are projected by the corresponding level set functions.The thickness and width of each stiffener are designed to be independent variables in the projection applied to each level set function.Besides,the path of each single stiffener is described by the zero iso-contour of the level set function.All the single stiffeners are combined together by using the p-norm method to obtain the stiffener grid.The proposed method is validated by several numerical examples to optimize the critical buckling load factor.

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.

Cascade-exciton model analysis of level density parameter dependence in proton induced fission cross sections of some sub-actinide nuclei

Fission cross sections strongly depend on the ratio of the level density parameter in fission to neutron emission, af/an . In this work, a cascade-exciton model implemented in the code CEM95 has been used to observe this effect for proton induced fission cross sections of tungsten, lead and bismuth. The method was employed using different level density parameter ratios for each fission cross section calculation. The calculated fission cross sections are compared with the available experimental data in the literature. It has been observed that a change of the ratio of the level density parameter, af/an , is necessary with the incident energy of the proton, to best estimate the fission cross sections in CEM95.

Mass dependence of pion-induced fission cross sections on the level density parameter

Fission probabilities and fission cross sections strongly depend on the mass number of the target and energy of the projectile. In this research work, a cascade-exciton model （using CEM95 computer code） has been implemented to observe the dependence of pion-induced fission cross sections and fission probabilities on the target mass and ratio of the level density parameter in fission to neutron emission. The analysis has been performed for both the positive and negative pions as the projectile at 80, 100 and 150 MeV energies. The computed cross sections satisfactorily reproduced the experimental findings when compared with the available experimental data in the literature. We observed a smooth dependence at 150 MeV, and a sharper dependence at 80 and 100 MeV pion energy, in the fissility region above 29.44.

Relationship of serum GDF11 levels with bone mineral density and bone turnover markers in postmenopausal Chinese women

Growth differentiation factor 11 （GDF11） is an important circulating factor that regulates aging. However, the role of GDF11 in bone metabolism remains unclear. The present study was undertaken to investigate the relationship between serum GDF11 level, bone mass, and bone turnover markers in postmenopausal Chinese women. Serum GDF11 level, bone turnover biochemical markers, and bone mineral density （BMD） were determined in 169 postmenopausal Chinese women （47-78 years old）. GDF11 serum levels increased with aging. There were negative correlations between GDF11 and BMD at the various skeletal sites. After adjusting for age and body mass index （BMI）, the correlations remained statistically significant. In the multiple linear stepwise regression analysis, age or years since menopause, BMI, GDF11, and estradiol were independent predictors of BMD. A significant negative correlation between GDF11 and bone alkaline phosphatase （BAP） was identified and remained significant after adjusting for age and BMI. No significant correlation was noted between cross-linked N-telopeptides of type I collagen （NTX） and GDF11. In conclusion, GDF11 is an independent negative predictor of BMD and correlates with a biomarker of bone formation, BAP, in postmenopausal Chinese women. GDF11 potentially exerts a negative effect on bone mass by regulating bone formation.

Relationship between the low density lipoprotein receptor gene polymorphism and serum lipid levels in the Guangxi Bai Ku Yao population

Objectives Bai Ku Yao(White-trousers Yaos)is a special branch of Yao minority in China.They are now living in both Lihu and Baxu villages,Nandan County, Guangxi,China.The population size is about 30,000.The special customs and culture of Bai Ku Yao,including their special clothing,intra-ethnic marriages and alcohol intake are still completely conserved to the present day.In previous epidemiologic studies,we found that the serum lipid levels and the prevalence of hyperlipidaemia were lower in Bai Ku Yao than in Han Chinese from the same region.This ethnic difference in serum lipid profiles is still not well known.We hypothesized that there may be significant differences in some genetic polymorphismsssociation of low density lipoprotein receptor (LDL-R) genepolymorphism and several environmental factors with serum lipid levels in the Guangxi Bai Ku Yao and Han populations.Methods A total of 1024 subjects of Bai Ku Yao and 792 participants of Han Chinese were stud- ied by a stratified randomized cluster sampling.Epidemiological survey was carried out using internationally standardized methods.Information on demographics,socioeconomic status, and lifestyle factors was collected with standardized questionnaires. The height,weight,waist circumference,blood pressure, and serum total cholesterol(TC),triglyceride(TG), high-density lipoprotein cholesterol(HDL-C),low-density lipoprotein cholesterol(LDL-C),apolipoprotein(Apo) A1, and ApoB were measured.Body massindex(BMI,kg/m2) was calculated.Genotyping of the LDL-RAvaⅡwas performed by polymerse chain reaction and restriction fragment length polymorphism combined with gel electrophoresis,and then confirmed by direct sequencing.Results(l)The height,weight,serum TC,HDL-C,LDL-C,ApoAl levels and the ratio of ApoAl to ApoB were lower in Bai Ku Yao than in Han Chinese(P【0.01 for all),whereas the percentage of subjects who consumed alcohol or smoked cigarettes was higher in Bai Ku Yao than in Han Chinese(P【0.01 for each).(2) The frequency of A+ allele in Bai Ku Yao was 34.5%,and the frequencies of A-A-,A-A+ and A+A + genotypes were 42.6%,45.9%and 11.5%;respectively. The frequency of A+ allele in Han Chinese was 19.3%(P【0.001),and the frequencies of A-A-,A-A + and A+A+ genotypes were 64.9%,31.6%and 3.5%(P【0.001);respectively. The frequencies of A-A-,A-A+ and A+A+ genotypes in Bai Ku Yao were significant difference between males and females,between normal TC and high TC subgroup, and between normal LDL-C and high LDL-C subgroup (P【0.05 for all),whereas the frequencies of A- and A+ ? alleles in Han Chinese were significant difference between males and females(P【0.05).(3) Serum LDL-C levels in Bai Ku Yao were significant difference among the A-A-, A-A+ and A+A+ genotypes(P【0.05),the A+ carriers had higher serum LDL-C levels.Serum HDL-C levels in Han Chiese were significant difference among the A-A-,A-A + and A+A+ genotypes(P【0.01),the A+ carriers had higher serum HDL-C levels.(4) After adjusting other factors,the prevalence of LDL-C abnormality was still higher in Han Chiese than in Bai Ku Yao.The prevalence of TC abnormality in Han Chinese was almost twice high as in Bai Ku Yao. The age and diet were common risk factor for TC abnormality. No effect of AvaⅡgenotype or alcohol consumption on the TC abnormality was found,but the combination of geno-type and alcohol consumption can increase the prevalence of TC abnormality[Exp(B) =(1.154)].Age was negatively cor- related with TG level.Conclusions Serum TC and LDL-C levels were lower in Bai Ku Yao than in Han Chinese.There were significant differences in the AvaⅡallele and genotype frequencies between the he A+ carriers in Bai Ku Yao had higher serum LDL-C levels,whereas the A+ carriers in Han had higher serum HDL-C levels.Interactions between alcohol consumption or cigarette smoking and the LDL-R AvaⅡgenotype were also observed.The differences in the serum lipid profiles between the two ethnic groups might partly result from different genotypic frequency of LDL-R AvaⅡpolymorphism or differentgene-enviromental interactions.Bai Ku Yao and Han population,the frequency of A + allele was higher in Bai Ku Yao than in Han.T between the two ethnic groups.Therefore,the aim of the present study was to detect the

Statistical Treatment of Low-Energy Nuclear Level Schemes

The level density parameter and the back shift energy E1 are determined for nuclei with A-values across the whole periodic table from fits to complete level schemes at low excitation energy near the neutron binding energies. We find that the energy back shift EI shows complicated behavior and depends on the type of the nucleus, even-even, odd mass, and odd-odd. The spin cut-off factor has also been investigated for nuclei mentioned above. The results are compared with the previous results and different experimental data on level densities.

Microscopic Study of Nuclear Level Densities and Thermal Properties in^56,57 Fe

We calculate level densities for ^56,57 Fe nuclei using BCS hamiltonian with inclusion of pairing interaction. The results of calculations show that the step structure observed experimentally has been supported by microscopic theory, Also the S-shaped energy and entropy as function of temperature have been obtained in theoretical calculations. Structures in the curves are interpreted as fingerprints of breaking Cooper pairs and quenching of pairing correlations.

Static Frame Model Validation with Small Samples Solution Using Improved Kernel Density Estimation and Confidence Level Method

An improved method using kernel density estimation （KDE） and confidence level is presented for model validation with small samples. Decision making is a challenging problem because of input uncertainty and only small samples can be used due to the high costs of experimental measurements. However, model validation provides more confidence for decision makers when improving prediction accuracy at the same time. The confidence level method is introduced and the optimum sample variance is determined using a new method in kernel density estimation to increase the credibility of model validation. As a numerical example, the static frame model validation challenge problem presented by Sandia National Laboratories has been chosen. The optimum bandwidth is selected in kernel density estimation in order to build the probability model based on the calibration data. The model assessment is achieved using validation and accreditation experimental data respectively based on the probability model. Finally, the target structure prediction is performed using validated model, which are consistent with the results obtained by other researchers. The results demonstrate that the method using the improved confidence level and kernel density estimation is an effective approach to solve the model validation problem with small samples.

Re-analysis of temperature dependent neutron capture rates and stellarβ-decay rates of^(95-98)Mo

The neutron capture rates and temperature dependent stellar beta decay rates of Mo isotopes are investigated within the framework of the statistical code TALYS v1.96 and the proton neutron quasi particle random phase approximation(pn-QRPA)model.The Maxwellian average cross-section(MACS)and neutron capture rates for the^(95-98)Mo(n,γ)^(96-99)Mo radiative capture process are analyzed within the framework of the statistical code TALYS v1.96 based on the phenomenological nuclear level density model and gamma strength functions.The present model-based computations for the MACS are comparable to the existing measured data.The sensitivity of stellar weak interaction rates to various densities and temperatures is investigated within the framework of the pn-QRPA model.Particular attention is paid to the impact of thermally filled excited states in the decaying nuclei(^(95-98)Mo)on electron emission and positron capture rates.Furthermore,we compare the neutron capture rates and stellar beta decay rates.It is found that neutron capture rates are higher than stellar beta decay rates at both lower and higher temperatures.

Investigation of 58Ni(n, p)58Co reaction cross-section with covariance analysis

The excitation function of the 58Ni(n,p)58Co reaction was measured using the well-established neutron activation technique andγ-ray spectroscopy.Neutrons in the energy range of 1.7 to 2.7 MeV were generated using the 7Li(p,n)reaction.The neutron flux was measured using the standard 115In(n,n’)115mIn monitor reaction.The results of the neutron spectrum averaged cross-section of 58Ni(n,p)58Co reactions were compared with existing cross-section data available in the EXFOR data library as well as with various evaluated data libraries such as ENDF/B-VIII.0,JEFF-3.3,JENDL-4.0,and CENDL-3.2.Theoretical calculations were performed using the nuclear reaction code TALYS.Various nuclear level density(NLD)models were tested,and their results were compared with the present findings.Realistic NLDs were also obtained through the spectral distribution method(SDM).The cross-section results,along with the absolute errors,were obtained by investigating the uncertainty propagation and using the covariance technique.Corrections forγ-ray true coincidence summing,low-energy background neutrons,andγ-ray self attenuation were performed.The experimental cross-section obtained in the present study is consistent with previously published experimental data,evaluated libraries,and theoretical calculations carried out using the TALYS code.

Isomeric pair 95m,g Nb in the photonuclear reactions on natMo at the bremsstrahlung end-point energy of 38–93 MeV

The ^(nat)Mo(γ,xnp)^(95m,g)Nb photonuclear reaction was studied using the electron beam from the NSC KIPT linear accelerator LUE-40.The experiment was performed using the activation and off-line γ-ray spectrometric technique.The experimental isomeric yield ratio(IR) was determined for the reaction products ^(95m,g)Nb at the bremsstrahlung end-point energy E_(γmax) range of 38-93 MeV.The obtained values of IR are in satisfactory agreement with the results of other studies and extend the range of previously known data.The theoretical values of the yields Y_(m,g)(E_(γmax)) and the IR for the isomeric pair ^(95m,g)Nb from the ^(nat)Mo(γ,xnp) reaction were calculated using the partial cross-sections σ(E) from the TALYS1.95 code for six different level density models.For the investigated range of E_(γmax),the theoretical dependence of IR on energy was confirmed-the IR smoothly increases with increasing energy.The comparison showed a noticeable difference(more than 3.85 times) in the experimental IR relative to all theoretical estimates.

Cross section of reaction ^(181)Ta(p,nγ)^(181)W and the influence of the spin cut-off parameter on the cross section

In this work, the program Cindy was modified to calculate the formation cross section of each energy level of residual nucleus lSlw resulting from the reaction lSlTa（p,n2/）lSlw. The concerned cross sections calculated at proton energy Ep=4.5-8.5 MeV agreed well with experimental results. The influence of the spin cut-off parameter in the energy level density model on the cross section was studied. The obtained results show that the influence of spin cut-off is obvious for lower energy levels.