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.

Some Properties of $\pi$ Meson in Nuclear Matter with Finite Density

In the GCM we study some properties of meson as the Goldstone bosons in a nuclear matter with finite density. Using the effective action in a nuclear matter, we calculate the decay constant and mass as functions of the chemical potential. The relation between the chemical potential and the density of a nuclear matter is firstly given here. We find that and monotonously decrease as nuclear matter density increases. The result is consistent with the usual assumption that the chiral symmetry is gradually restored as the density of a nuclear matter increases.

Retrospective Analysis of the Performance of a New-Generation Dual Pump Phaco System Using Two Sizes of Phaco Tips in Cases with Different Nuclear Hardness

Purpose: To evaluate the performance of a phacoemulsification system in terms of effective (EPT) and total phaco time (TPT) using 20G and 21G phaco tips. Methods: Retrospective comparative study including 143 consecutive cataractous eyes undergoing phacoemulsification cataract surgery with the Visalis 500 device. The 20G and 21G phaco tips were used in 46 and 97 eyes, respectively. The EPT and TPT values were evaluated. Results: Median TPT was 11.25 s and 17.50 s in the 20G and 21G groups, respectively (p = 0.0011). Median EPT values were 3.15 s and 5.00 s in the 20G and 21G groups, respectively (p = 0.0032). TPT and EPT were significantly lower in 3/3+ cataract eyes compared to 4/4+ using both tips (p < 0.001). Conclusions: The Visalis 500 allows cataract surgery with reduced TPT and EPT, even in hard cataracts. The use of the 20G phaco tip provides an additional benefit in terms of reduction of phaco time.

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.

An analytical formula for fluctuations in nuclear charge density

The experimental charge densities of atomic nuclei show fluctuations in their distributions. This paper investigates the limits of accuracy of two-parameter Fermi and three-parameter Fermi distributions in describing the charge density. An improved analytical function for density distribution is proposed, which allows for density fluctuation. The experimental charge densities of 40Ca, 60Ni, 100Mo, 152Sm and 208Pb, representing the various shapes of density fluctuation, are used to assess the accuracy of the proposed formula. The proposed function reproduces the experimental charge densities with significant improvement in accuracy over other commonly used formulae. A compilation of charge density distribution parameters of 73 nuclei is presented based on the proposed formula.

Experimental nuclear charge density and theoretical description of theabove-barrier light heavy-ion fusion process

Theoretical modeling of nucleus-nucleus collisions is often based on the nucleus-nucleus potential.One of the advanced methods for constructing this potential is the semi-microscopical double-folding model with M3 YParis NN-forces.Proton and neutron densities are significant components of this model.The correct nucleon density(ND) must reproduce the experimental nuclear charge density(NCD).However,those who deal with modeling the fusion process typically disregard this circumstance.We aim to achieve a good description of both the nuclear charge density and above-barrier fusion cross sections of even-even light nuclei with Z=N.We consider several versions of NDs available in literature and construct our own approximation for the ND of the even-even spherical nuclei^(12)C,^(16)O,and^(40)Ca,abbreviated as FE-density(Fermi+exponential).We carefully compare the NCDs resulting from different versions of NDs with the experimental NCDs.After finding the nucleus-nucleus potential using the double-folding model with the density dependent M3 Y-Paris NN-forces and FE densities,we evaluate the abovebarrier fusion cross sections for five reactions,^(12)C+^(12)C,^(12)C+^(16)O,^(16)O+^(16)O,^(16)O+^(40)Ca,and^(40)Ca+^(40)Ca,and40Ca+40Ca,for which experimental data are available.The cross sections are calculated using two approaches:a) the barrier penetration model and b) the trajectory model with surface friction(TM).To find the transmission coefficients for the TM,the Langevin equations are employed.For all considered reactions,our TM typically reproduces the above-barrier experimental cross sections within 10-15%.The only adjustable parameter of the model,the optimal friction strength KRm,is found to be approximately 90 zs·GeV-1for the light reactions12C+12C,12C+16O,and16O+16O and approximately 15zs·GeV-1for the heavy reactions16O+40Ca and40Ca+40Ca.The latter findings are in reasonable agreement with the systematics found previously.Thus,the FE-recipe allows highly accurate and simultaneous reproduction of both the nuclear charge density and above-barrier fusion cross sections of five reactions involving12C,160,and40Ca nuclei.

Global dynamical correlation energies in covariant density functional theory： Cranking approximation

Tje global dynamical correlation energies for 575 even even nuclei with proton numbers ranging from Z = 8 to Z = 108 calculated with the covariant density functional theory using the PC-PK1 parametrization are presented. The dynamical correlation energies include the rotational correction energies obtained with the cranking approximation and the quadrupole vibrational correction energies. The systematic behavior of the present correlation energies is in good agreement with that obtained from the projected generator coordinate method using the SLy4 Skyrme force although our values are systematically smaller. After including the dynamical correlation energies, the root- mean-square deviation predicted by the PC-PK1 for the 575 even-even nuclei masses is reduced from 2.58 MeV to 1.24 MeV.

Investigation of neutron density distribution of^208Pb nucleus when the proton density is constrained to its experimental distribution

In this study,two novel improvements for the theoretical calculation of neutron distributions are presented.First,the available experimental proton distributions are used as a constraint rather than inferred from the calculation.Second,the recently proposed distribution formula,d3pF,is used for the neutron density,which is more detailed than the usual shapes,for the first time in a nuclear structure calculation.A semi-microscopic approach for binding energy calculation is considered in this study.However,the proposed improvements can be introduced to any other approach.The ground state binding energy and neutron density distribution of 208Pb nucleus are calculated by optimizing the binding energy considering three different distribution formulae.The implementation of the proposed improvements leads to qualitative and quantitative improvements in the calculation of the binding energy and neutron density distribution.The calculated binding energy agrees with the experimental value,and the calculated neutron density exhibits fluctuations within the nuclear interior,which corresponds with the predictions of self-consistent approaches.

Quark distributions in nuclei and nuclear effects on nucleon structure functions

Extended quark distribution functions are presented obtained by fitting a large amount of experimental data of the l-A DIS process on the basis of an improved nuclear density model. The experimental data of l-A DIS processes with A≥ 3 in the region 0.0010 ≤ x ≤ 0.9500 are quite satisfactorily described by using the extended formulae. Our knowledge of the influence of nuclear matter on the quark distributions is deepened.

Wind Power Probability Density Prediction Based on Quantile Regression Model of Dilated Causal Convolutional Neural Network

Aiming at the wind power prediction problem,a wind power probability prediction method based on the quantile regression of a dilated causal convolutional neural network is proposed.With the developed model,the Adam stochastic gradient descent technique is utilized to solve the cavity parameters of the causal convolutional neural network under different quantile conditions and obtain the probability density distribution of wind power at various times within the following 200 hours.The presented method can obtain more useful information than conventional point and interval predictions.Moreover,a prediction of the future complete probability distribution of wind power can be realized.According to the actual data forecast of wind power in the PJM network in the United States,the proposed probability density prediction approach can not only obtain more accurate point prediction results,it also obtains the complete probability density curve prediction results for wind power.Compared with two other quantile regression methods,the developed technique can achieve a higher accuracy and smaller prediction interval range under the same confidence level.

Effects of nuclear deformation on the form factor for direct dark matter detection

For the detection of direct dark matter, in order to extract useful information about the funda- mental interactions from the data, it is crucial to properly determine the nuclear form factor. The form factor for the spin-independent cross section of collisions between dark matter particles and the nucleus has been thoroughly studied by many authors. When the analysis was carried out, the nuclei were always supposed to be spherically symmetric. In this work, we investigate the effects of the deformation of nuclei from a spherical shape to an ellipticM one on the form factor. Our results indicate that as long as the ellipticity is not too large, such deformation will not cause any substantial effects. In particular, when the nuclei are randomly orientated in room-temperature circumstances, one can completely neglect them.

Shape evolution of 72,74Kr with temperature in covariant density functional theory

The rich phenomena of deformations in neutron-deficient krypton isotopes, such as shape evolution with neutron number and shape coexistence, have attracted the interest of nuclear physicists for decades. It is interesting to study such shape phenomena using a novel way, e.g. by thermally exciting the nucleus. In this work, we develop the finite temperature covariant density functional theory for axially deformed nuclei with the treatment of pairing correlations by the BCS approach, and apply this approach for the study of shape evolution in 72,74Kr with increasing temperature. For 72Kr, with temperature increasing, the nucleus firstly experiences a relatively quick weakening in oblate deformation at temperature T-0.9 MeV, and then changes from oblate to spherical at T-2.1 MeV. For 74Kr, its global minimum is at quadrupole deformation β2--0.14 and abruptly changes to spherical at T-1.7 MeV. The proton pairing transition occurs at critical temperature 0.6 MeV following the rule Tc =0.6△p （0）, where △p（0） is the proton pairing gap at zero temperature. The signatures of the above pairing transition and shape changes can be found in the specific heat curve. The single-particle level evolutions with temperature are presented.

Shell corrections with finite temperature covariant density functional theory

The temperature dependence of the shell corrections to the energy sEsell,entropy T8S sell,and free en-ergy oFshell is studied by employing the covariant density functional theory for closed-shell nuclei.Taking 144Sm as an example,studies have shown that,unlike the widely-used exponential dependence exp(-E*/Ed),8Eshell exhibits a non-monotonous behavior,ie.,first decreasing 20%approaching a temperature of 0.8 MeV,and then fading away exponentially.Shell corrections to both free energy 8F shell and entropy T8S shell can be approximated well using the Bohr-Mottelson forms T/sinh(t)and[rcoth(r)-1]/sinh(r),respectively,in which Tx T.Further studies on the shell corrections in other closed-shell nuclei,100Sn and 208 Pb,are conducted,and the same temperature dependen-cics are obtained.

Global analysis of Skyrme forces with higher-order density dependencies

The density-dependent term in Skyrme forces is essential to simulate three-body and many-body correlations beyond the low-momentum two-body interaction. We speculate that a single density term may be insumcient and a higher-order density dependent term is added. The present work investigates the influence of higher-order density dependencies based on extended UNEDF0 and SkM＊ forces. Global descriptions of nuclear masses and charge radii are presented. The extended UNEDF0 force gives a global rms error on binding energies of 1.29 MeV. The influence on fission barriers and equation of state are also investigated. Perspectives to improve Skyrme forces are discussed, including global center-of-mass corrections and Lipkin-Nogami pairing corrections.

Generalized time-dependent generator coordinate method for induced fission dynamics

The generalized time-dependent generator coordinate method(TD-GCM)is extended to include pairing correlations.The correlated GCM nuclear wave function is expressed in terms of time-dependent generator states and weight functions.The particle–hole channel of the effective interaction is determined by a Hamiltonian derived from an energy density functional,while pairing is treated dynamically in the standard BCS approximation with time-dependent pairing tensor and single-particle occupation probabilities.With the inclusion of pairing correlations,various time-dependent phenomena in open-shell nuclei can be described more realistically.The model is applied to the description of saddle-to-scission dynamics of induced fission.The generalized TD-GCM charge yields and total kinetic energy distribution for the fission of 240Pu,are compared to those obtained using the standard time-dependent density functional theory(TD-DFT)approach,and with available data.

Isoscaling properties for neutron-rich fragments in highly asymmetric heavy ion collision systems

Traditionally,isoscaling has been interpreted and applied within the framework of the grand canonical ensemble,based on the assumption that fragment production occurs following the attainment of a statistical equilibrium state.However,the influence of the symmetry energy can lead to differences in the neutron and density distribution in neutron-rich nuclei.This in turn may impact the iso scaling parameters(usually denoted byαandβ).We examine the isoscaling properties for neutron-rich fragments produced in highly asymmetric systems on inverse kinematics,namely^(40,48)Ca and ^(58,64)Ni+^(9)Be at 140 MeV per nucleon.We evaluate α and β values and sort them as a function of the neutron excess I≡N-Z.The significant differences in a extracted from fragments within different ranges of I emphasize the importance of understanding the dependence of isoscaling parameters on fragments generated in various collision regions.Furthermore,the|β(N)|/α(Z)value for a specific fragment in small size and highly iso spin asymmetry systems can serve as a probe to detect the variations in neutron density and proton density in different regions of the nucleus and indicate the limitations of theoretical models in investigating these issues.

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.

Theoretical Studies of Proton Radioactivity

In the paper, we will discuss the most recent theoretical approaches developed by our group,to understand the mechanisms of decay by one proton emission, and the structure and shape of exotic nuclei at the limits of stability.