Level Density Parameter Research Articles

Entropies, level-density parameters and fission probabilities along the triaxially- and axially-symmetric fission paths in 296Lv

We investigate the variation of statistical properties of the fissile nucleus, especially entropy, and nuclear level density, along different fission paths. The calculations were focused on comparing axial and triaxial trajectories leading to fission of 296Lv. We observe that change of shell effects and their suppression rates with deformation can substantially influence fission dynamics. Furthermore, the fission process exhibits iso-entropic behavior at high excitation energies, while pronounced entropy variations are observed at lower energies. We derive a deformation-dependent level density parameter that plays a critical role in estimating the survival probability of a superheavy nucleus. The competition between different fission paths was further studied by employing a master equation approach, thereby demonstrating the critical role of entropy and thermodynamic properties in shaping fission dynamics within multidimensional deformation spaces.

Bayesian uncertainty quantification for synthesizing superheavy elements

To improve the theoretical prediction power for synthesizing superheavy elements beyond Og, a Bayesian uncertainty quantification method is employed to evaluate the uncertainty of the calculated evaporation residue cross sections (ERCS) for the first time. The key parameters of the dinuclear system model (DNS-sysu), such as the diffusion parameter a, the damping factor Ed, and the level-density parameter ratio af/an are systematically constrained by the Bayesian analysis of recent ERCS data. One intriguing behaviour is shown that the optimal incident energies (OIE) corresponding to the largest ERCS weakly depend on the fission process. We also find that these parameters are strongly correlated and the uncertainty propagation considering the parameters independently is not reasonable. The 2σ confidence level of posterior distributions for a=0.586−0.002+0.002 fm, Ed=25.65−3.41+3.43 MeV, and af/an=1.081−0.021+0.021 are obtained. Furthermore, the confidence levels of the ERCS and OIE for synthesizing Z = 119 via the reactions Cr54+243Am, Ti50+249Bk, and V51+248Cm are predicted. This work sets the stage for future analyses to explore the OIE and reaction systems for the synthesis of superheavy elements.

Enhanced capability of model fitting to nuclear level density and heat capacity: testing on 93−98Mo nuclei

We propose an improved fitting approach that improves reliability in studying the nuclear level density (NLD) and thermodynamic quantities. The proposed method, which relies on the fact that experimental fluctuations or outliers, if they exist, should not be involved in the fitting process, is validated with a set of data artificially generated with anomalous data points being intentionally inserted. In order to showcase the advantages of the proposed technique, we have applied it to re-investigate the back-shifted Fermi gas (BSFG) level density parameters and thermodynamic quantities, particularly the heat capacities, of 93−98Mo isotopes. We have found that the range of values for the level density parameter of 93Mo (approximately from 8.5 to 9.0 MeV−1) is notably smaller than that obtained for the other isotopes of Mo (approximately from 10.5 to 11.5 MeV−1). This observation is different from previous predictions, in which the values of level density parameter of all Mo isotopes are in the same range. This is because among the Mo isotopes under examination, 93Mo (N = 51 neutrons) has the smallest number of valence neutrons, namely only a single neutron away from the closed N = 50 shell. In addition, thanks to the proposed method, we have discussed the effects of data fluctuations on the BSFG NLDs and thermodynamic quantities of 93−98Mo isotopes, from which our recommendation for future works is announced. On top of that, we should notice that the proposed approach can be further applied to any work involving the fitting of a phenomenological model to empirical data.

Neutron and fission decay width of superheavy compound nuclei

We have systematically studied the level density parameter, nuclear level density and decay width of neutron and fission of superheavy nuclei. This paper is validated by comparing with available experiments for [Formula: see text]U and [Formula: see text]Pu. The angular dependence of level density parameter, level densities and ratio of [Formula: see text] and [Formula: see text] the thermal excitation energy (U) have been studied in the superheavy region [Formula: see text]. The role of entrance channel parameter on decay width of neutron and fission has been studied both in cold and hot fusion reactions in the superheavy region [Formula: see text]. Systematic variation of [Formula: see text] and [Formula: see text] is observed in both the cases. Finally, predicted [Formula: see text] for the synthesis of superheavy nuclei [Formula: see text] and 120.

Comprehensive analysis of uncertainty quantification for the 58Ni(n, p)58Co reaction cross section* *Project supported by the Scientific and Industrial Research (CSIR), Government of India (File No 09/013(882)/2019-EMR-1) for providing senior research fellowships, the IUAC-UGC, Government of India (Sanction No. IUAC/XIII.7/UFR- 71353), and Institutions of Eminence (IoE) BHU (Grant No. 6031).

In this study, we measured the 58Ni(n, p)58Co reaction cross section with neutron energies of 1.06, 1.86, and 2.85 MeV. The cross section was measured using neutron activation techniques and γ-ray spectroscopy, and it was compared with cross section data available in the EXFOR. Furthermore, we calculated the covariance matrix of the measured cross section for the aforementioned nuclear reaction. The uncertainties of the theoretical calculation for 58Ni(n, p)58Co reaction cross section were calculated via Monte Carlo method. In this study, we used uncertainties in the optical model and level density parameters to calculate uncertainties in the theoretical cross sections. The theoretical calculations were performed by using TALYS-1.96. In this study, we aim to analyze the effect of uncertainties of the nuclear model input as well as different experimental variables used to obtain the values of reaction cross section.

Statistical investigation of the angular momentum dependence of the nuclear level density parameter

The nuclear level density (NLD) parameter is crucial for calculating cross-sections in nuclear physics, astrophysics, reactor design, and medical physics. Spin and parity, along with excitation energy, are fundamental properties of an excited nuclear level. Previous investigations into the NLD’s dependence on spin and parity have primarily used approximate methods like parity equidistribution and Gaussian distribution of spins. However, the specific impact of spin and parity on the NLD parameter, a key component in NLD formulation, has not been extensively studied. We examined the spin and parity dependence of the NLD parameter. Our findings demonstrate that the NLD parameter’s dependency on both excitation energy and angular momentum can be accurately characterized by a Laplace distribution, highlighting the complex interplay of these factors in nuclear physics.

Evaluation of neutron cross sections of 48Ti based on the Unified-Monte-Carlo-B method* *Supported by the National Key Research and Development (R&D) Program (2022YFA1602403) and Continuous Support Basic Scientific Research Project BJ010261223282

A cross section evaluation of neutron induced reactions on 48Ti is undertaken using the Unified Monte Carlo-B (UMC-B) approach. The evaluation concentrates on estimating the covariance and the use of the UMC-B allows avoiding the deficiencies of linear regression brought by the traditional least squares method. Eight main neutron and charged particle emission reactions from n+48Ti in the fast neutron energy region below 20 MeV are studied in this work. The posterior probability density function (PDF) of each neutron cross section is obtained in a UMC-B Bayesian approach by convoluting the model PDFs sampled based on model parameters and the likelihood functions for the experimental data. Nineteen model parameters including level density, pair corrections, optical model and Kalbach matrix element parameter are stochastically sampled with the assumption of normal distributions to estimate the model uncertainty. The Cholesky factorization approach is applied to consider potential parameter correlations. Finally, the posterior covariance matrices are generated using the UMC-B generated weights. The new evaluated results are compared with the CENDL-3.2, ENDF/B-VIII.0, JEFF-3.3, TENDL-2021 and JENDL-5 evaluations and differences are discussed.

Investigation of 90,92Zr(n,γ)91,93Zr in the s-process nucleosynthesis

Abstract The neutron capture rates and Maxwellian-averaged cross-sections (MACS) for 90Zr(n,γ)91Zr and 92Zr(n,γ)93Zr processes have been computed within the framework of Talys v1.96. The effects of phenomenological nuclear level density (NLD) parameters and the gamma strength functions (GSFs) on Maxwellian-averaged cross-sections and neutron capture rates are examined both quantitatively and qualitatively. The present model-based computed data for MACS and reaction rates gives a good comparison with the existing literature. The fine-tuning of the statistical model’s nuclear properties (level density and gamma-ray strength) to reproduce experimental data will allow the detailed investigation of the s-process network.

Evidence on the high energy behavior of nuclear level density parameter

The nuclear level density parameter (NLDP) plays an important and crucial role in the most widely used phenomenological models that calculate the nuclear level density (NLD) based on the Fermi gas model (FGM). NLDP can be affected by various effects that have been ignored during the FGM calculations. The dependence of NLDP on excitation energy has been predicted by various references and using various relationships that are mainly tested and normalized at low energies by experimental data of low levels. In this research, using nuclear reaction codes and experimental data of the evaporation spectrum of heavy ion 32S + 74Ge reaction leading to 106Cd compound nucleus (CN) at high excitation energies, high energy behaviour of NLDP is investigated and compared with different relationship predictions. By calculating and reducing the contribution of non-equilibrium mechanisms, it is suggested that NLDP behaves increasing and then decreasing at high energies (almost Gaussian-like behavior), contrary to the predictions of all conventional energy-dependent NLDP relations.

Pre-equilibrium Effects on Alpha Particle Induced Reactions on Niobium Isotope from Threshold upto 100MeV using the Computer Code COMPLET

Excitation functions (EF) for four reactions of the type 93Nb (α, xn); x = 1-4 were studied. This study provides current evidences about the dominance of pre-equilibrium processes at high energies followed by compound nucleus equilibration at low energies. The main objective of the work is to look pre-equilibrium emission induced by alpha particle energies up to 100 MeV on Niobium through describing, analyzing and interpreting the theoretical results of cross sections obtained from computer code COMPLET by comparing with experimental data obtained from EXFOR library. COMPLET code has been used for the analysis using the initial exciton number n0 = 4(4p+oh) and level density parameter ACN/10. A general agreement was found for all reactions.

Nuclear level density in the statistical semiclassical micro-macroscopic approach

Level density ρ is derived for a finite system with strongly interacting nucleons at a given energy E, neutron N, and proton Z particle numbers, projection of the angular momentum M, and other integrals of motion, within the semiclassical periodic-orbit theory (POT) beyond the standard Fermi-gas saddle-point method. For large particle numbers, one obtains an analytical expression for the level density which is extended to low excitation energies U in the statistical micro-macroscopic approach (MMA). The interparticle interaction averaged over particle numbers is taken into account in terms of the extended Thomas - Fermi component of the POT. The shell structure of spherical and deformed nuclei is taken into account in the level density by the Strutinsky shell correction method through the mean-field approach used near the Fermi energy surface. The MMA expressions for the level density ρ reaches the well-known macroscopic Fermi-gas asymptote for large excitation energies U and the finite combinatoric power-expansion limit for low energies U. We compare our MMA results for the averaged level density with the experimental data obtained from the known excitation energy spectra by using the sample method under statistical and plateau conditions. Fitting the MMA ρ to these experimental data on the averaged level density by using only one free physical parameter - inverse level density parameter K - for several nuclei and their long isotope chain at low excitation energies U one obtains the results for K. These values of K might be much larger than those deduced from neutron resonances. The shell, isotopic asymmetry, and pairing effects are significant for low excitation energies.

Production routes analysis of PET agent 72As from alpha and proton induced reaction using different level density models

This study evaluated the production routes of the medically essential radioisotope 72As from the stable isotopes of gallium, germanium, arsenic, and selenium, where four alpha-induced reactions: 69Ga(α, n)72As, 71Ga(α, 3n)72As, 70Ge(α, np)72As, and 72Ge(α, nt)72As and five proton-induced reactions: 72Ge(p, n)72As, 73Ge(p, 2n)72As, 74Ge(p, 3n)72As, 75As(p, nt)72As, and 74Se(p, 2np)72As are evaluated using three phenomenological and one microscopic nuclear level density models in different energy ranges. The investigation compares the calculated results based on the chosen models and the experimental data collected from the EXFOR data library. Statistical factors H, D, and R were also computed to determine the level density model with the best fit to the experimental data. Some level density parameters were adjusted to enrich the fits further, and integral yield vs energy was calculated using the best-fitted models.

A Comparison between Ericson's Formulae Results and Experimental Data Using New Formulae of Single Particle Level Density

The partial level density PLD of pre-equilibrium reactions that are described by Ericson’s formula has been studied using different formulae of single particle level density . The parameter was used from the equidistant spacing model (ESM) model and the non- equidistant spacing model (non-ESM) and another formula of are derived from the relation between and level density parameter . The formulae used to derive are the Roher formula, Egidy formula, Yukawa formula, and Thomas –Fermi formula. The partial level density results that depend on from the Thomas-Fermi formula show a good agreement with the experimental data.

Neutron multiplicity measurement and investigation of nuclear dissipation and shell effects in Si30+W182,184,186 reactions

Background: Enhanced prescission neutron multiplicity (${\ensuremath{\nu}}_{\mathrm{pre}}$) over statistical model calculations assuming Bohr-Wheeler fission width is explained using Kramers' fission width incorporating dissipative effects. The dissipation strength obtained from such studies reported significant effect of the neutron shell closure of $N=126$ of the fissioning system as well as nuclear temperature. The dependence of dissipation strength on shell effect and temperature is also attributed to the choice of input parameters in the statistical model calculations.Purpose: We investigate the role of $N/Z$, shell effect, collective enhancement of level density (CELD), and excitation energy on ${\ensuremath{\nu}}_{\mathrm{pre}}$ in reactions forming isotopes of the Ra nucleus.Methods: The neutron multiplicity excitation function is measured for the $^{30}\mathrm{Si}+^{182,184,186}\mathrm{W}$ reactions populating $^{212,214,216}\mathrm{Ra}$ nuclei using the National Array of Neutron Detectors (NAND) at the Inter-University Accelerator Centre, New Delhi. Among these compound nuclei, $^{214}\mathrm{Ra}$ has a major neutron shell closure of $N=126$. Measured ${\ensuremath{\nu}}_{\mathrm{pre}}$ are analyzed within the framework of a statistical model incorporating dynamical hindrance in nuclear fission due to dissipation, shell corrections in the fission barrier and level density, and CELD.Results: Experimental ${\ensuremath{\nu}}_{\mathrm{pre}}$ show a marginal isotopic dependence at all excitation energies. ${\ensuremath{\nu}}_{\mathrm{pre}}$ values do not show any noticeable effect of neutron magic number $N=126$. Dissipation strength of $\ensuremath{\beta}=8\phantom{\rule{4pt}{0ex}}{\mathrm{zs}}^{\ensuremath{-}1}$ ($5.27\phantom{\rule{4pt}{0ex}}\mathrm{MeV}/\ensuremath{\hbar}$) reasonably reproduces the experimental ${\ensuremath{\nu}}_{\mathrm{pre}}$ excitation functions for all three nuclei in the measured energy range. Appreciable variations in presaddle neutron emissions are observed when shell effect or CELD is excluded in the calculations. Even though both the shell and CELD are found to impact primarily in the presaddle sector, they alter the excitation energy and multiplicity in the saddle-to-scission sector as well in a complementary manner.Conclusions: A temperature independent dissipation coefficient is observed to reproduce the experimental results in this study throughout the excitation energy range measured. Shell corrections in fission barrier and level density parameters and CELD in fission and particle evaporation widths also influence the neutron multiplicities. The observed effect of CELD in the presaddle phase is attributed to the large enhancement of level density at the saddle due to its large deformation and consequent enhancement of fission width.

Fission as a relevant probe of the nuclear level density away from β-stability

Fission at moderate to high excitation energy is proposed as an innovative approach to study the evolution of the nuclear level density (NLD) away from β-stability. A four-dimensional dynamical Langevin model, implementing various prescriptions of the asymptotic level-density parameter a˜, is employed to demonstrate the relevance of considering typical fission observables, and namely the pre- and post-scission neutron multiplicities, to investigate the evolution of a˜ with N and Z. The richness of fission is shown to offer an alternative route, that is very complementary to the conventional fusion-evaporation method from which no consensus emerged yet. In particular, to investigate the isospin-dependence of the NLD, the present calculations lead us to propose a series of fusion-induced fission measurements based on Ca + Pb collisions which are readily available at current experimental facilities. This set of reactions can be further enhanced with today, as well as future, radioactive beams.

Impact of the quenching of shell effects with excitation energy on nuclear level density

We investigate the nature and impact of shell effects on nuclear level density (NLD) and particle emission probability as a function of temperature in a microscopic theoretical framework of Statistical Model for nuclei ranging from neutron deficient to neutron rich isotopes of Z= 27−35. Critical temperatures are traced for neighbouring even, odd, closed shell and mid−shell nuclei which respond to excitations differently due to their varying stability and structural effects. Importance of the shell effects and shell correction energy is reflected significantly in NLD variation which slowly diminishes with increasing excitation energy indicating the quenching of shell effects. The enhancement of LD parameter with the deformation and rotation and the fade out of enhancement with increasing excitations has been shown. The weakening of magicity of N=28 near the proton drip line has been observed in the inverse level density parameter ‘K’(= A/a) and β variation though it is usually uncommon to see this effect in excited nuclei. Variation of our calculated NLD for odd 69As and even 70Ge exhibits structural effects and agrees very well with the variation of experimental values. Our evaluated level density parameter ‘a’ values are compared with RIPL-2 (Reference Input Parameter Library) data which show good agreement.

Survival probability of compound nuclei in heavy-ion fusion reaction

We have developed an empirical formula to calculate the survival probability of superheavy nuclei by analyzing about 95 fusion experiments, which were classified into four categories based on the deformation parameters of a projectile–target system. Every category is analyzed using ten different entrance channel parameters; one of these displays the smoothest variation. That channel is Z 2/A, where Z and A are the atomic number and mass number, respectively. Further, the predicted empirical relation is improved by the inclusion of the fission barrier, separation energy, level density parameter, center of mass energy, and fusion barrier height for the Z 2/A term. Furthermore, the evaporation residue cross-section is maximum at a certain beam energy, called the optimal energy. Thus, finding the survival probability at the optimal energy is important in the synthesis of a superheavy nucleus. We have developed an empirical formula for the survival probability at the optimal energy to facilitate future superheavy nucleus synthesis.

Preequilibrium models for 58Ni (n, xp) reaction in Neutrons at 8, 9, 9.4, 11 and 14.8 MeV using the EMPIRE and TALYS codes

In this study, the calculations of proton emission spectra produced by 58Ni (n, xp) reaction are used in the framework of preequilibrium models with the EMPIRE and TALYS codes. Exciton Model predictions combined with the Kalbach angular distributions systematics and statistical Multi-step Direct (MSD) with Multi-step Compound (MSC) processes preequilibrium models were used. Also, some necessary parameters as optical model, level density, level density a-parameter and single-particle level density parameter have been investigated for our calculations. The comparison with experimental data shows clear improvement over the Exciton and MSD with MSC models calculations.

Microscopic-macroscopic level densities for low excitation energies

Level density ρ(E,Q) is derived within the micro-macroscopic approximation (MMA) for a system of strongly interacting Fermi particles with the energy E and additional integrals of motion Q, in line with several topics of the universal and fruitful activity of A. S. Davydov. Within the extended Thomas Fermi and semiclassical periodic orbit theory beyond the Fermi-gas saddle-point method, we obtain ρ∝Iν(S)/Sν, where Iν (S) is the modified Bessel function of the entropy S. For small shell-structure contribution, one finds ν = κ/2 + 1, where κ is the number of additional integrals of motion. This integer number is a dimension of Q, Q = {N, Z, …} for the case of two-component atomic nuclei, where N and Z are the numbers of neutrons and protons, respectively. For much larger shell structure contributions, one obtains ν = κ /2 + 2. The MMA level density ρ reaches the well-known Fermi gas asymptote for large excitation energies and the finite micro-canonical combinatoric limit for low excitation energies. The additional integrals of motion can also be the projection of the angular momentum of a nuclear system for nuclear rotations of deformed nuclei, number of excitons for collective dynamics, and so on. Fitting the MMA total level density ρ(E, Q) for a set of the integrals of motion Q = {N, Z}, to experimental data on a long nuclear isotope chain for low excitation energies, one obtains the results for the inverse level-density parameter K, which differs significantly from those of neutron resonances due to shell, isotopic asymmetry, and pairing effects.

Broken axial symmetry as essential feature for a consistent modelling of various observables in heavy nuclei

Although most nuclear spectroscopy as well as atomic hyperfine structure data do not deliver accurate information on nuclear axiality the ad-hoc assumption of symmetry about one axis found widespread use in nuclear model calculations. In the theoretical interpretation of nuclear properties as well as in the analysis of experimental data triaxiality was considered – if at all – only for some, often exotic, nuclides. A breaking of axial symmetry combined to a spin-independent moment of inertia results in a surprisingly simple heuristic triaxial parametrization of the yrast sequence in all heavy nuclei, including well deformed ones. No additional fit parameters are needed in detailed studies of the mass and charge dependence of the electric dipole strength in the range of and outside of giant dipole resonances. Allowing triaxiality also avoids the introduction of an arbitrary level density parameter ã to fit the accurate values observed in n-capture experiments and ã can be taken from nuclear matter studies. A combination of this value to the yrast energies no longer based on axiality and the related I(I+1) rule results in agreement to data independent of spin. And predictions for radiative neutron capture as derived on the basis of non-axiality are improved as well. The experimentally favoured broken axial symmetry is in accord to HFB and MC-shell model calculations already for nuclei in the valley of stability.