Back-shifted Fermi Gas Research Articles

Thermal properties of $$^{172}\mathrm{Yb}$$ and $$^{162}\mathrm{Dy}$$ isotopes in the back-shifted Fermi gas model with temperature-dependent pairing energy

Thermodynamic properties of $$^{172}\mathrm{Yb}$$ and $$^{162}\mathrm{Dy}$$ isotopes are investigated using the back-shifted Fermi-gas (BSFG) model with the energy-dependent level density parameter and the temperature-dependent pairing energy. The temperature dependency of pairing energy is applied using the mean order parameter of the exact Ginzburg–Landau (EGL) theory. The level density, entropy, temperature and heat capacity of $$^{172}\mathrm{Yb}$$ and $$^{162}\mathrm{Dy}$$ isotopes are calculated using these approaches and the results are compared with each other as well as with experimental data to examine the validity of these models. The results obtained by the present study indicate that the BSFG model with the temperature-dependent pairing energy is in better agreement with the experimental data, compared to the BSFG model with the energy-dependent level density parameter, for $$^{172}\mathrm{Yb}$$ and $$^{162}\mathrm{Dy}$$ isotopes.

Nuclear level densities and γ -ray strength functions of Ta180,181,182

Particle-$\gamma$ coincidence experiments were performed at the Oslo Cyclotron Laboratory with the $^{181}$Ta(d,X) and $^{181}$Ta($^{3}$He,X) reactions, to measure the nuclear level densities (NLDs) and $\gamma$-ray strength functions ($\gamma$SFs) of $^{180, 181, 182}$Ta using the Oslo method. The Back-shifted Fermi-Gas, Constant Temperature plus Fermi Gas, and Hartree-Fock-Bogoliubov plus Combinatorial models where used for the absolute normalisations of the experimental NLDs at the neutron separation energies. The NLDs and $\gamma$SFs are used to calculate the corresponding $^{181}$Ta(n,$\gamma$) cross sections and these are compared to results from other techniques. The energy region of the scissors resonance strength is investigated and from the data and comparison to prior work it is concluded that the scissors strength splits into two distinct parts. This splitting may allow for the determination of triaxiality and a $\gamma$ deformation of $14.9^{\circ} \pm 1.8^{\circ}$ was determined for $^{181}$Ta.

Calculation of 89Y(p,x)86,88,89gZr, 86g,87g,88gY, 85gSr, and 84Rb reaction cross sections based on level density

Excitation functions based on level density were calculated for proton-induced on yttrium-89 using the TALYS-1.8 code. Hence, production cross-section of the 89Y(p,x)86,88,89gZr, 86g,87g,88gY, 85gSr, and 84gRb were computed up to 50 MeV. In this study, the constant temperature model alongside the Fermi Gas model (CGCM) was employed as a default model. For this reason, the a-parameter as an essential parameter in the Fermi Gas formula was modified to obtain the best result. Besides, the Back-shifted Fermi Gas Model (BSFGM) and the Generalized Superfluid Model (GSM) are presented to the deliberation. The outcomes of cross-sections were compared with the experimental data approaching regarding desired consequences.

Nuclear level density and thermal properties of 270110, 278112, and 290116 superheavy isotopes in low excitation energies

The level density parameter α is calculated using the semiclassical approach for 270 110, 278 112, and 290 116 superheavy isotopes. The Woods-Saxon potential is considered for the interaction of nucleons inside a nucleus. Thermal properties of these isotopes, including the entropy, the nuclear temperature, and the heat capacity are calculated within the framework of microcanonical ensemble and the back-shifted Fermi gas model with one adjustable parameter E 1 . The process of breaking the first Cooper pair and cooling of the 270 110, 278 112, and 290 116 superheavy isotopes have also been observed.

Evaluated the level density for proton induced nuclear resonances in (P+48Ti) reaction using different models

The experimental proton resonance data for the reaction P+48Ti have been used to calculate and evaluate the level density by employed the Gaussian Orthogonal Ensemble, GOE version of RMT, Constant Temperature, CT and Back Shifted Fermi Gas, BSFG models at certain spin-parity and at different proton energies. The results of GOE model are found in agreement with other, while the level density calculated using the BSFG Model showed less values with spin dependence more than parity, due the limitation in the parameters (level density parameter, a, Energy shift parameter, E1and spin cut off parameter, σc). Also, in the CT Model the level density results depend mainly on two parameters (T and ground state back shift energy, E0), which are approximately constant in their behavior with the proton energy compared with GOE model. The RMT estimation used to calculate the corrections of the incompleteness proton resonance measurement data by using two methods; the conventional analysis method, which depends on the resonance widths and the updated, developed, tested and applied a new analysis method, which depends mainly on the resonance spacings. The spacing analysis method is found much less sensitive to non-statistical phenomena than is the width analysis method. Where the analysis of a given data set via these two independent analysis methods indicated the increasing in the reliability of the determination of the missing fraction of levels, the observed fraction f between 0.87+0.13−0.11 – 0.68+0.12−0.12 for different spin-parity of this reaction and then the distinguishability in the level density calculations can be achieved. The modified Porter Thomas distribution along with the maximum likelihood function have been used to get the missing levels corrections for 5 proton resonance sequences in the present reaction. To estimate the present long-range correlations for pure sequence of levels the mean square of the deviation of the cumulative number of levels from a fitted straight line represented by the Dyson and Mehta Δ3 statistic has been employed for spin parity 12+, and calculated the <Δ3> against the cumulative number of proton levels.

Investigation of gamma strength functions and level density models effects on photon induced reaction cross–section calculations for the fusion structural materials 46,50Ti, 51V, 58Ni and 63Cu

Scientists have been focused on fusion reactor studies to overcome the increasing energy demand. The materials, which have the potential to be used in fusion reactors must be resistant to the harmful effects of radiation in the manner of material itself. Selection of the appropriate materials to be used in nuclear reactors has a crucial importance to achieve the maximum efficiency and security. Ti, V, Ni and Cu are known as some of the constructional fusion materials. Existence of many knowledge about those materials provides countless advantages to the researchers and one of them is the cross–section, which basically means the probability of a nuclear reaction's occurrence. In addition to the cross–section, there exist some other parameters, which could be pointed as gamma strength function and level density models that affect the theoretical calculations. In this study, photon induced reaction cross–sections of 46,50Ti, 51V, 58Ni and 63Cu target isotopes have been calculated by using TALYS 1.8 code with different gamma strength functions in the giant dipole resonance region. For gamma strength functions Kopecky-Uhl generalised Lorentzian Model, Brink-Axel Lorentzian Model, Hartree-Fock BCS tables, Hartree-Fock-Bogolyubov tables and Goriely's Hybrid Model have been employed. To appoint the best gamma strength function model, the relative variance calculations have been performed. Also, reaction cross–sections have been recalculated by using the best gamma strength function models through the different level density options. Constant Temperature Fermi Gas Model, Back Shifted Fermi Gas Model and Generalised Super Fluid Model have been employed for level density calculations. Experimental data for the investigated reactions have been taken from EXFOR library and used for comparisons of the obtained calculation results.

Theoretical calculations of production cross–sections for the 201Pb, 111In 18F and 11C radioisotopes at proton induced reactions

Production of radioisotopes that used in medical diagnosis and treatment are mostly based on the nuclear reactions. The cross–section data are important to understand nuclear reaction mechanisms. In this study TALYS 1.8 code has been used to calculate production cross–sections of 201Pb, 111In, 18F and 11C radioisotopes at proton induced reactions. Constant Temperature Fermi Gas Model (CTFGM), Back Shifted Fermi Gas Model (BSFGM) and Generalised Super Fluid Model (GSM) have been employed as a level density models for computations. Relative variance calculations have been carried out to determine the best level density model. In addition to cross–section calculations, total activities of radioisotopes have been presented. Production cross–section calculation results have been compared with experimental data taken from Experimental Nuclear Reaction Database (EXFOR).

Measurement of $$^{96}\rm{Zr}(n,\gamma)^{97}Zr$$ 96 Z r ( n , γ ) 97 Z r reaction cross section at the neutron energies of 0.61 and 1.05 MeV and covariance analysis for the uncertainty

The $$^{96}\rm{Zr}(n,\gamma)^{97}Zr$$ reaction cross sections relative to $$^{197}\rm{Au}(n,\gamma)^{198}Au$$ monitor reaction with the neutron energies of 0.61 and 1.05 MeV from the 7Li(p,n)7Be reaction have been measured for the first time by using the activation and off-line $\gamma$ -ray spectrometric technique. The error analysis of the experimental data was done by considering the partial uncertainties in various attributes and the correlations between those attributes were reported through covariance analysis. The present experimental cross sections have been compared with the theoretical prediction by TALYS-1.8 using the back-shifted Fermi gas model and Brink-Axel Lorentzian $\gamma$ -ray strength functions. The TALYS-1.8 calculations well predicted the present experimental cross sections at both neutron energies. The spectrum averaged neutron capture cross sections of 96Zr obtained in the present work have also been compared with the evaluated cross sections from ENDF/B-VIII.0, JENDL-4, JEFF-3.3, CENDL-3.1 and TENDL-2015 libraries. They are found to be in close agreement with the TENDL-2015 and CENDL-3.1 libraries at the neutron energies of 0.61 and 1.05 MeV.

Investigation of level density parameter effects on (p,n) and (p,2n) reaction cross–sections for the fusion structural materials 48Ti, 63Cu and 90Zr

The materials used in fusion reactor must be resistance to the harmful effects of radiation in the manner of material itself. Selection of the appropriate materials used in nuclear reactor has a crucial importance to achieve the maximum efficiency and security. Ti, Cu and Zr are known to be employed as first wall materials in fusion reactors. In this study, level density parameter effects on (p,n) and (p,2n) reaction cross–section calculations have been investigated by employing different level density models within TALYS 1.8 computer code for 48Ti, 63Cu and 90Zr selected as target materials. Also, for these isotopes (p,n) and (p,2n) reaction cross–section calculations have been done by using two different level density models of EMPIRE 3.2 code. For calculations; Constant Temperature Fermi Gas Model, Back Shifted Fermi Gas Model, Generalised Super Fluid Model and Microscopic level densities (temperature dependent Hartree Fock Bogolyubov, Gogny Force) from Hilaire's combinatorial tables have been used from TALYS 1.8. In addition, Generalised Superfluid Model and Hartree Fock Bogolyubov Model have been selected for calculations from EMPIRE 3.2 code. To appoint the best level density model, the relative variance analyses have been done. The cross–section calculations have been repeated via TALYS 1.8 level density models by changing the a parameter replacing with the obtained one from the best level density model result and value taken from the literature for each isotope. To analyze and comment about the outcomes of the study, a comparison of the results have been done with each other and the experimental data taken from the literature.

Overview and evaluation of different nuclear level density models for the 123I radionuclide production

The 123I radionuclide (T1/2 = 13.22 h, β+ = 100%) is one of the most potent gamma emitters for nuclear medicine. In this study, the cyclotron production of this radionuclide via different nuclear reactions namely, the 121Sb(α,2n), 122Te(d,n), 123Te(p,n), 124Te(p,2n), 124Xe(p,2n), 127I(p,5n) and 127I(d,6n) were investigated. The effect of the various phenomenological nuclear level density models such as Fermi gas model (FGM), Back-shifted Fermi gas model (BSFGM), Generalized superfluid model (GSM) and Enhanced generalized superfluid model (EGSM) moreover, the three microscopic level density models were evaluated for predicting of cross sections and production yield predictions. The SRIM code was used to obtain the target thickness. The 123I excitation function of reactions were calculated by using of the TALYS-1.8, EMPIRE-3.2 nuclear codes and with data which taken from TENDL-2015 database, and finally the theoretical calculations were compared with reported experimental measurements in which taken from EXFOR database.

Photon Induced Reaction Cross-Section Calculations of Several Structural Fusion Materials

In this paper; photo-neutron cross-sections have been computed for 27Al, 28,29Si, 52Cr, 54,56Fe isotopes by using nuclear reaction codes TALYS 1.6 and EMPIRE 3.1 with different level density models. Constant Temperature Fermi Gas, Back Shifted Fermi Gas and Generalized Superfluid Models have been employed from TALYS 1.6 whereas Generalized Super Fluid Model was the only model employed from EMPIRE 3.1 reaction codes. Obtained results have been analyzed with experimental values taken from the EXFOR database.

The cross section calculation of 112Sn(α,γ)116Te reaction with different nuclear models at the astrophysical energy range

The theoretical cross section calculations for the astrophysical p process are needed because most of the related reactions are technically very difficult to be measured in the laboratory. Even if the reaction was measured, most of the measured reactions have been carried out at the higher energy range from the astrophysical energies. Therefore, almost all cross sections needed for p process simulation have to be theoretically calculated or extrapolated to the astrophysical energies. \(^{112}\hbox {Sn}(\alpha ,\gamma )^{116}\hbox {Te}\) is an important reaction for the p process nucleosynthesis. The theoretical cross section of \(^{112}\hbox {Sn}(\alpha ,\gamma )^{116}\hbox {Te}\) reaction was investigated for different global optical model potentials, level density, and strength function models at the astrophysically interested energies. Astrophysical S factors were calculated and compared with experimental data available in the EXFOR database. The calculation with the optical model potential of the dispersive model by Demetriou et al., and the back-shifted Fermi gas level density model and Brink-Axel Lorentzian strength function model best served to reproduce experimental results at an astrophysically relevant energy region. The reaction rates were calculated with these model parameters at the p process temperature and compared with the current version of the reaction rate library Reaclib and Starlib.

Collective effects in deuteron induced reactions of aluminum

Cross sections of 27Al(d,x)22Na, 27Al(d,x)24Na, and 27Al(d,x)27Mg reactions are calculated by using TALYS 1.6 computer code with different nuclear level density models, which are composite Gilbert–Cameron model, back-shifted Fermi gas model, generalized superfluid model, and recently proposed collective semi-classical Fermi gas model in the energy range of 3–180MeV. The results are compared with the experimental data taken from EXFOR library. In these deuteron induced reactions, collective effects are investigated by means of nuclear level density models. Collective semi-classical Fermi gas model including the collective effects via the level density parameter represents the best agreement with the experimental data compared to the other level density models, especially in the low deuteron bombarding energies where the collective effects dominate.

γ strength function and level density of Pb208 from forward-angle proton scattering at 295 MeV

Gamma strength functions (GSFs) and level densities (LDs) are essential ingredients of statistical nuclear reaction theory with many applications in astrophysics, reactor design, and waste transmutation. The aim of the present work is a test of systematic parametrizations of the GSF recommended by the RIPL-3 data base for the case of $^{208}$Pb. The upward GSF and LD in $^{208}$Pb are compared to gamma decay data from an Oslo-type experiment to examine the validity of the Brink-Axel (BA) hypothesis. The E1 and M1 parts of the total GSF are determined from high-resolution forward angle inelastic proton scattering data taken at 295 MeV at RCNP, Osaka, Japan. The total LD in $^{208}$Pb is derived from the $1^-$ LD extracted with a fluctuation analysis in the energy region of the isovector giant dipole resonance. The E1 GSF is compared to parametrizations recommended by the RIPL-3 data base showing systematic deficiencies of all models in the energy region around neutron threshold. The new data for the poorly known spinflip M1 resonance call for a substantial revision of the model suggested in RIPL-3. The total GSF derived from the present data is larger in the PDR energy region than the Oslo data but the strong fluctuations due to the low LD resulting from the double shell closure of $^{208}$Pb prevent a conclusion on a possible violation of the BA hypothesis. Using the parameters suggested by RIPL-3 for a description of the LD in $^{208}$Pb with the back-shifted Fermi gas model, remarkable agreement between the two experiments spanning a wide excitation energy range is obtained. Systematic parametrizations of the E1 and M1 GSF parts need to be reconsidered at low excitation energies. The good agreement of LD provides an independent confirmation of the approach underlying the decomposition of GSF and LDs in Oslo-type experiments.

Nuclear level density of even-even nuclei with temperature-dependent pairing energy

The influence of using a temperature-dependent pairing term on the back-shifted Fermi gas (BSFG) model of nuclear level density of some even-even nuclei has been investigated. We have chosen an approach to determine the adjustable parameters from theoretical calculations, directly. The exact Ginzburg-Landau (EGL) theory was used to determine the temperature-dependent pairing energy as back-shifted parameter of the BSFG model. The level density parameter of the BSFG model has been determined through the Thomas-Fermi approximation. The level densities of 96Mo, 106,112Cd, 106,108Pd, 164Dy, 232Th, 238U and heat capacities of 96Mo and 164Dy nuclei were calculated. Good agreement between theory and experiment was observed.

Back shifted Fermi gas model with temperature dependent pairing energy: Thermal properties of 98Mo

The effect of using a temperature dependent pairing term in back-shifted Fermi-gas (BSFG) formula of nuclear level density has been studied. We have used the mean order parameter formula of modified Ginzburg–Landau (MGL) theory as a simple possible choice for temperature dependency of the pairing term. The level density and heat capacity of [Formula: see text]Mo have been calculated with this formalism and compared with the experimental data. We observed good agreement between the heat capacity of this model and the experimental data.

Deexcitation Modes in Spallation Nuclear Reactions

Spallation nuclear reactions in the range of 0.2 to 1.2 GeV are studied using the CRISP code. A new approach for the deexcitation stage of the compound nucleus was introduced. For the calculations of the level densities, this approach is based on the Back-shifted Fermi gas model (BSFG), which takes into account pairing effects and shell corrections, whereas the calculation of the fission barriers were performed by means of the Extended Thomas-Fermi plus Strutinsky Integral (ETFSI) method, which is a high-speed approximation to the Hartree-Fock method with pairing correlations treated as in the usual BCS plus blocking approach. This procedure is more appropriate to calculate level densities for exotic nuclei. Satisfactory results were obtained and compared with experimental data obtained in the GSI experiments. As another important result, we highlight some directions for the development of a qualitatively superior version of the CRISP code with the implementation of more realistic and suitable physical models to be applied in stable and exotic nuclei that participate in the process. This new version of the code includes several substantial changes in the decay of the hot compound nucleus which allow satisfactory agreement with the experimental data and a reduction of the adjustment parameters.

Nuclear-level densities in the 49V and 57Co nuclei on the basis of evaporated-neutron spectra in (p, n) and (d, n) reactions

The spectra of neutrons from the reactions 49Ti(p, n)49V and 57Fe (p, n)57Co were measured in the range of proton energies between 8 and 11 MeV along with their counterparts from the reactions 48Ti(d, n)49V and 56Fe (d, n)57Co at the deuteron energies of 2.7 and 3.8 MeV. These measurements were conducted with the aid of a time-of-flight fast-neutron spectrometer on the basis of the EGP-15 pulsed tandem accelerator of the Institute for Physics and Power Engineering (IPPE, Obninsk). An analysis of measured data was performed within the statistical equilibrium and preequilibrium models of nuclear reactions. The respective calculations based on the Hauser–Feshbach formalism of statistical theory were carried out with nuclear-level densities given by the generalized superfluid model of the nucleus, the backshifted Fermi-gas model, and the Gilbert–Cameron composite formula. The nuclear-level densities of 49V and 57Co and their energy dependences were determined. The results were discussed together with available experimental data and data recommended by model systematics.

Studying Nuclear Level Densities of 238U in the Nuclear Reactions within the Macroscopic Nuclear Models

Abstract In this work the nuclear level density parameters of 238U have been extracted in the back-shifted Fermi gas model (BSFGM), as well as the constant temperature model (CTM), through fitting with the recent experimental data on nuclear level densities measured by the Oslo group. The excitation functions for 238U(p,2nα)233Pa, and 238U(p,4n)235Np reactions and the fragment yields for the fragments of the 238U(p,f) reaction have been calculated using obtained level density parameters. The results are compared to their corresponding experimental values. It was found that the extracted excitation functions and the fragment yields in the CTM coincide well with the experimental values in the low-energy region. This finding is according to the claim made by the Oslo group that the extracted level densities of 238U show a constant temperature behaviour.

Nuclear level density predictions

Simple formulas depending only on nuclear masses were previously proposed for the parameters of the Back-Shifted Fermi Gas (BSFG) model and of the Constant Temperature (CT) model of the nuclear level density, respectively. They are now applied for the prediction of the level density parameters of all nuclei with available masses. Both masses from the new 2012 mass table and from different models are considered and the predictions are discussed in connection with nuclear regions most affected by shell corrections and nuclear structure effects and relevant for the nucleosynthesis.