Level Density Formula Research Articles

An Application of Interacting Boson Fermion-Fermion Model (IBFFM) for <sup>134</sup>Cs Nucleus

This work concerns the calculations of interacting boson fermion-fermion model (IBFFM) for the odd-odd nucleus <sup>134</sup>Cs. The energy levels (positive and negative parity states), electric transition probability B(E2), magnetic transition probability B(M1), quadrupole and magnetic dipole moments have been studied in this work. The IBFFM results are compared with the available experimental data. In the present work, the IBFFM pattern of total and parametric dependent level densities for the odd-odd nucleus <sup>134</sup>Cs is investigated and compared to the pattern found in previous investigations in the framework of combinatorial and spectral distribution approaches. When comparing the theoretical values with the available experimental values, it was found that there is a good match between them. This is due to the values of the Hamiltonian parameters that were found accurately, so this IBFFM model is considered one of the effective models in studying the nuclear structure of odd-odd nuclei. The level density of the odd-odd nucleus <sup>196</sup>Au is investigated in the interacting boson-fermion-fermion model (IBFFM) which accounts for collectivity and complex interaction between quasiparticle and collective modes. The IBFFM spin-dependent level densities show high-spin reduction with respect to Bethe formula. This can be well accounted for by a modified spin-dependent level density formula.

A Comparison Between the Theoretical Cross Section Based on the Partial Level Density Formulae Calculated by the Exciton Model with the Experimental Data for (_79^197)Au nucleus

In this paper, the theoretical cross section in pre-equilibrium nuclear reaction has been studied for the reaction at energy 22.4 MeV. Ericson’s formula of partial level density PLD and their corrections (William’s correction and spin correction) have been substituted in the theoretical cross section and compared with the experimental data for nucleus. It has been found that the theoretical cross section with one-component PLD from Ericson’s formula when doesn’t agree with the experimental value and when . There is little agreement only at the high value of energy range with the experimental cross section. The theoretical cross section that depends on the one-component William's formula and on-component corrected to spin PLD formula doesn't agree with the experimental cross section. But in case of theoretical cross section based on two-component Ericson's and William's PLD formulae it has been found that there is acceptable agreement when the exciton number is taken .

A Comparison Between the Theoretical Cross Section Based on the Partial Level Density Formulae Calculated by the Exciton Model with the Experimental Data for (_79^197)Au nucleus

في هذا البحث، تمت دراسة المقطع العرضي النظري لتفاعلات قبل التوازن للتفاعل بطاقة 22.4 MeV. حيث تم تعويض صيغة اركسون للمركبة الواحدة لكثافة الحالات الجزئية PLDوتصحيحاتها ( تصحيح وليم, وتصحيح البرم) بالمقطع العرضي النظري وقورنت النتائج مع النتائج العملية لنواة الذهب . حيث وجد ان المقطع العرضي النظري مع صيغة اركسون لمركبة واحدة لا يتفق مع للمقطع العرضي العملي عندما وعندما هناك اتفاق بسيط عند القيم الكبيرة للطاقة. المقطع العرضي النظري المعتمد على صيغة كثافة الحالات الجزئية PLD المصححة بتصحيح وليم لحالة المركبة الواحدة و صيغة المركبة الواحدة المصححة للزخم الزاوي لا يتطابقان مع القيم العملية. ولكن في حالة المقطع العرضي النظري المعتمد على صيغتي اركسون و وليم ذواتا المركبتين وجد ان هناك تطابق جيد لصيغتي اركسون و وليم عندما n=5.

O16–18+O16 and O16,18+C12,13 fusion-evaporation reactions at near-Coulomb-barrier energies from statistical model calculations

Fusion-evaporation reactions of carbon and oxygen isotopes at near-Coulomb-barrier energies are important subjects in nuclear-reaction studies. They are closely related to nucleosynthesis in astrophysics and may provide novel opportunities to study the $\ensuremath{\alpha}$-clustering effect in light nuclei. In this work, the $^{16\ensuremath{-}18}\mathrm{O}+^{16}\mathrm{O}$ and $^{16,18}\mathrm{O}+^{12,13}\mathrm{C}$ fusion-evaporation reactions are studied by using the statistical model based on the Hauser-Feshbach formalism. It is found that the statistical model with the original Gilbert-Cameron level-density formula typically underestimates the $\ensuremath{\alpha}$-emission cross sections. To overcome this problem, we introduce for the residual nuclei a new level-density formula with the correction term inspired by theoretical considerations on the $\ensuremath{\alpha}$-clustering effect. Compared with the original Gilbert-Cameron level-density formula, our statistical-model calculations with the new level-density formula show significant improvements.

Microscopie Calculations of Nuclear Level Densities and Astrophysical Applications

A new level density formula based on a microscopic calculation of the thermodynamic quantities using the deformed Hartree-Fock-BCS method is proposed. In the microscopic approach shell, pairing and deformation effects on the thermodynamic quantities are treated consistently. The final level density formula is shown to be in close agreement with experimental neutron resonance spacings and low energy states. The impact of the newly-determined level densities on nuclear reaction cross sections and rates of relevance in astrophysics applications is presented.

Microscopic description of average level spacing in even-even nuclei

A microscopic theoretical approach to the average level spacing at the neutron binding energy in even-even nuclei is proposed. The approach is derived based on the Bardeen-Cooper-Schrieffer (BCS) theory at finite temperature and projection M of the total angular momentum J, which is often used to describe the superfluid properties of hot rotating nuclei. The exact relation of the J-dependent total level density to the M-dependent state densities, based on which the average level spacing is calculated, was employed. The numerical calculations carried out for several even-even nuclei have shown that in order to reproduce the experimental average level spacing, the M-dependent pairing gaps as well as the exact relation of the J-dependent total level density formula should be simultaneously used.

Influence of nuclear deformation on level density parameter

By using semiclassical method and considering deformed Woods–Saxon mean field potential, single-particle level density g, level density parameter a, and nuclear level density have been calculated for some deformed nuclei with deformation parameters ([Formula: see text], [Formula: see text]). Significant difference between deformed and spherical level density parameter and nuclear level density were observed. The effect of [Formula: see text] on level density parameter was notable. A simple formula for single-particle level density has been introduced.

Statistical properties ofPu243, andPu242(n,γ)cross section calculation

The level density and gamma-ray strength function (gammaSF) of 243Pu have been measured in the quasi-continuum using the Oslo method. Excited states in 243Pu were populated using the 242Pu(d,p) reaction. The level density closely follows the constant-temperature level density formula for excitation energies above the pairing gap. The gammaSF displays a double-humped resonance at low energy as also seen in previous investigations of actinide isotopes. The structure is interpreted as the scissors resonance and has a centroid of omega_{SR}=2.42(5)MeV and a total strength of B_{SR}=10.1(15)mu_N^2, which is in excellent agreement with sum-rule estimates. The measured level density and gammaSF were used to calculate the 242Pu(n,gamma) cross section in a neutron energy range for which there were previously no measured data.

Neutron spectra of 57Fe(p, n)57Co and 56Fe(d, n)57Co reactions and the density of 57Co levels

Neutron spectra of the 57Fe(p, n)57Co reaction are measured in the proton energy range of 8–11 MeV and for 56Fe(d, n)57Co reaction in the deuteron energy ranges of 2.7 and 3.8 MeV. Measurements are performed with the time-of-flight spectrometer for fast neutrons on the EGP-15 pulsed tandem accelerator at the Leipunsky Institute for Physics and Power Engineering (IPPE). The data are analyzed using the statistical equilibrium and preequilibrium models of nuclear reactions. Computations are performed using Hauser-Feshbach formalism of the statistical theory with the generalized superfluid nucleus model, the back-shifted Fermi gas model, and the Gilbert-Cameron formula for the nuclear level density. The nuclear level density for 57Co, its energy dependence, and the model parameters are determined. The resulting data are discussed with respect to existing experimental data and model system recommendations.

Level density andγ-ray strength function in the odd-oddNp238nucleus

The level density and $\ensuremath{\gamma}$-ray strength function in the quasicontinuum of $^{238}\mathrm{Np}$ have been measured using the Oslo method. The level-density function follows closely the constant-temperature level-density formula and reaches $43\ifmmode\times\else\texttimes\fi{}{10}^{6}$ levels per MeV at ${S}_{n}=5.488$ MeV of excitation energy. The $\ensuremath{\gamma}$-ray strength function displays a two-humped resonance at low-energy as also seen in previous investigations of Th, Pa, and U isotopes. The structure is interpreted as the scissors resonance and has an average centroid of ${\ensuremath{\omega}}_{\mathrm{SR}}=2.26(5)$ MeV and a total strength of ${B}_{\mathrm{SR}}=10.8(12){\ensuremath{\mu}}_{N}^{2}$, which is in excellent agreement with sum-rule estimates. The scissors resonance is shown to have an impact on the $^{237}\mathrm{Np}$${(n,\ensuremath{\gamma})}^{238}$Np cross section.

Investigation of the Appropriate Partial Level Density Formula for Pre-Equilibrium Nuclear Exciton Model

Ericson formula represents the first formula, which was suggested to describe the partial level density (PLD) formula in pre-equilibrium region of the nuclear reactions. Then a number of corrections were added to this formula in order to make it more suitable to physical meaning. In this paper, there are two aims to be done: the first aim is to study the correspondence between one and two-components formulae in Ericson, Pauli, and pairing corrections; the second aim is to compare and study the results of Comprehensive formula, which contents with all corrections, with Ericson, Pauli, and pairing formulae. The Comprehensive formula was suggested to simulate the reality. To achieve these aims the 56Fe and 90Zr nuclei were chosen and the results showed that the difference between one and two-components formulae was too small which can be neglected. Furthermore, the results strongly recommended that for cross section calculations of the nuclear reaction, one must use Comprehensive formula rather than Pauli formula.

Level studies of 71 Ge via 71 Ga (P, nγ) 71 Ge reaction and density of discrete levels in 71 Ge

The excited states of 71Ge have been investigated via the 71Ga (P, n) 71Ge reaction with the proton beam energies from 2.5 to 4.3 MeV. The parameters of the nuclear level density formula have been determined from the extensive and complete level scheme for 71Ge. The Bethe formula for the back-shifted Fermi gas model and the constant temperature model are compared with the experimental level densities. Key words: Level schemes of 71Ge, 71Ga (P, n) 71Ge reaction, angular distribution, Fermi gas model.

Isospin dependence of nuclear level density of 28Al considering symmetry energy and pairing corrections

In this study, the single-particle level densities are calculated by using the isospin dependent nuclear level density (NLD) formula. The calculations are performed using the experimental data for 28Al achieved from 27 Al(n γ)28Al resonances. Considering the symmetry energy and parity corrections, the NLDs at the excitation energy, E = 20MeV are calculated and the maximum possible isospin in the range from ground state up to this excitation energy is estimated. The first correction led to reduced level densities and the later resulted in decreased densities for some of the levels while increased densities for the others. It is observed that the maximum level density occurs for T = 1 and at low energies for which the experimental data are available there is a good agreement between calculated and experimental data.

Nuclear level densities in 47V, 48V, 49V, 53Mn, and 54Mn from neutron evaporation spectra

The spectra of neutrons from the (p, n) reactions on 47Ti, 48Ti, 49Ti, 53Cr, and 54Cr nuclei were measured in the proton-energy range 7–11 MeV. The measurements were performed with the aid of a fast-neutron spectrometer by the time-of-flight method over the base of the EGP-15 tandem accelerator of the Institute for Physics and Power Engineering (IPPE, Obninsk). Owing to a high resolution and a high stability of the time-of-flight spectrometer used, low-lying discrete levels could be identified reliably along with a continuum section of neutron spectra. An analysis of measured data was performed within the statistical equilibrium and preequilibrium models of nuclear reactions. The relevant calculations were performed by using the exact formalism of Hauser-Feshbach statistical theory supplemented with the generalized model of a superfluid nucleus, the back-shifted Fermi gas model, and the Gilbert-Cameron composite formula for the nuclear level density. The nuclear level densities for 47V, 48V, 49V, 53Mn, and 54Mn were determined along with their energy dependences and model parameters. The results are discussed together with available experimental data and recommendations of model systematics.

Level studies of 93Mo via 93Nb(p, nγ)93Mo reaction and density of discrete levels in 93Mo

The excited states of 93Mo have been investigated via the 93Nb(P,n?)93Mo reaction with proton beam energies of 2.5-4.3 MeV. The parameters of the nuclear level density formula were determined from the extensive and complete level scheme of 93Mo. The Bethe formula for the back-shifted Fermi gas model and the constant temperature model are compared with experimental level densities.

Calculation of Generalized Level Densities for Nuclei in Mass Region 20 < A < 50

In this study, a relation between generalized level density and standard level density is derived. Using this relation and Bethe formula of Fermi gas model for standart level density we obtained a generalized nuclear level density formula for nucleus. Generalized level densities were calculated for some nuclei in mass region between 20 and 50 for different q values close to 1. Our results explain experimental data better than those of Gilbert-Cameron (GC) and Rohr, which are two of the leading compilations in evaluating nuclear level density.

Level studies of 73As via 73Ge(p, nγ)73As reaction and density of discrete levels in 73As

The excited states of 73As have been investigated via the 73Ge(p, n?)73As reaction with the proton beam energies from 2.5-4.3 MeV. The parameters of the nuclear level density formula have been determined from the extensive and complete level scheme for 73As. The Bethe formula for the back-shifted Fermi gas model and the constant temperature model are compared with the experimental level densities.

Global and local level density models

Four different level density models, three phenomenological and one microscopic, are consistently parameterized using the same set of experimental observables. For each of the phenomenological models, the Constant Temperature Model, the Back-shifted Fermi gas Model and the Generalized Superfluid Model, a version without and with explicit collective enhancement is considered. Moreover, a recently published microscopic combinatorial model is compared with the phenomenological approaches and with the same set of experimental data. For each nuclide for which sufficient experimental data exists, a local level density parameterization is constructed for each model. Next, these local models have helped to construct global level density prescriptions, to be used for cases for which no experimental data exists. Altogether, this yields a collection of level density formulae and parameters that can be used with confidence in nuclear model calculations. To demonstrate this, a large-scale validation with experimental discrete level schemes and experimental cross sections and neutron emission spectra for various different reaction channels has been performed.

Phenomenological Nuclear Level Densities using the KTUY05 Nuclear Mass Formula for Applications Off-Stability

A new parametrization for the phenomenological nuclear level density taking account of the shell and pairing energies of the recent nuclear mass formula of Koura, Tachibana, Uno, and Yamada (KTUY05) a is proposed. Such a level density formula is often required to calculate nuclear reaction cross sections for nuclei off-stability, especially for fission systems and astrophysical applications. With the phenomenological level density formula of Gilbert-Cameron with the energy dependent level density parameter of Ignatyuk, a smooth dependence of the asymptotic level density parameter a* on the mass number is obtained. At low energies, systematics for the constant temperature model are also derived by connecting the Fermi gas level density and the discrete level information available for more than 1,000 nuclei. Some comparisons with the discrete level data and the microscopic model are made to validate our approach, and it is concluded that the parametrization obtained can be used for nuclear reaction calculations on stable or unstable nuclei within a reasonable uncertainty.

Unified model of nuclear mass and level density formulas

Nuclear ground and excited state properties are described by using parameter systematics on mass and level density formulas. The formulas are based on an analytical expression of the single-particle state density by introducing the shell-pairing correlation in a new way. Main features are the shell, pairing, and deformation effects on the droplet model near the ground state, which are washed out at higher excitation energies. The main aim of the paper is to provide in the analytical framework the improved energy dependent shell, pairing, and deformation corrections generalized to the collective enhancement factors, which offer a systematic prescription over a great number of nuclear reactions. The new formulas are shown to be in close agreement with not only the empirical nuclear mass data but also the measured slow neutron resonance spacings and experimental systematics observed in the excitation energy dependent properties.