Narrow Results

By using semiclassical method and considering Woods–Saxon and Coulomb potentials, the level density parameter a was calculated for three superheavy nuclei ²⁷⁰110, ²⁷⁸112 and ²⁹⁰116. Obtained results showed that the value of level density parameter of these nuclei is near to the simple relation a ≈ A/10. In framework of the dinuclear system model, the effects of level density parameter on the probability of the formation of a compound nucleus, the ratio of neutron emission width and fission width, and evaporation residue cross-section of three cold fusion reactions ⁶²Ni+²⁰⁸Pb, ⁷⁰Zn+²⁰⁸Pb and ⁸²Se+²⁰⁸Pb, leading to superheavy elements were investigated. The findings indicate that the level density parameter play a significant role in calculations of heavy-ion fusion–fission reactions. The obtained results in the case of a = A/12 have larger values in comparison with calculated level density parameter with Woods–Saxon potential (a_WS) and a = A/10. The theoretical results of the evaporation residue cross-section are very sensitive to the choice of level density parameter. The calculated values with a_WS are in good agreement with experimental values.

A theoretical study of nuclear level density of Thorium nuclei that exist on and off the beta-stability line is carried out using Talys 1.6. The level density parameter a and spin cut-off factor $\sigma$ for Thorium isotopes ${}^{216-270}$Th are estimated. The values of both these parameters decrease towards the neutron drip line and the proton drip line. Cross-sections for $(n,p)$ and $(n,\alpha )$ reactions for Thorium isotopes are also calculated. The estimated and experimental values of cross-sections for ${}^{232}$Th are comparable. These evaluated data are useful in understanding the mechanism of nuclear reactions taking place under extreme conditions including those in nucleosynthesis.

Level density models have an undeniable importance for a better perception on the nature of nuclear reactions, which influences our life via various ways. Many novel and advanced medical application use radioisotopes, which are produced with nuclear reactions. By considering the connection between the level density models and the importance of theoretical calculations for the production routes of medically important isotopes, this study is performed to investigate the level density model effects on the production cross-section calculations of ${}^{62}$Zn, ${}^{68}$Ga, ${}^{77}$Kr, ${}^{103}$Pd, ${}^{111}$In, ${}^{124}$I and ${}^{211}$At radioisotopes via some alpha particle induced and neutron emitting reactions. For theoretical calculations; frequently used computation tools, such as TALYS and EMPIRE codes, are applied. Obtained theoretical results are then compared with the experimental data, taken from Experimental Nuclear Reaction Data (EXFOR) library. For a better interpretation of the results, a mean weighted deviation calculation for each investigated reaction is performed in addition to a visual comparison of the graphical representations of the outcomes.

We investigate one-neutron and two-neutron emission from ¹³²Sn and its neighboring isotopes due to thermal excitation. The rotational states of ¹³²Sn at different temperatures are investigated. The effects of separation energy and thermal excitation energy on neutron emission probability are studied.

Properties of shell model Hamiltonians, and in particular the tri-diagonal matrices obtained with the Lanczos procedure are exploited to determine the density of states and to estimate the ground-state energies. It will be shown that with a few parameters that are adjusted to the moments up to fourth order of the Hamiltonian, one can model the resultant tri-diagonal matrices. An estimate of the ground state energy can quickly be obtained from the modeled matrices, and the density of states for the full matrix can quickly be obtained using the WKB approximation. The accuracy of the ground state is dependent on high moments, six and greater.

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 ${}^{98}$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.

The nuclear level densities and single particle entropies are predicted for nuclei in the mass region $50<A<74$ within a framework of statistical theory of hot nuclei method. In this method, particle-number and energy conservation as well as nuclear pairing correlations are included in the partition function of grand canonical ensemble. The suppression of pairing correlations is distinctly noticed in temperature dependence of entropies between the critical temperatures $T_C\approx 0.7$ MeV and $T_C\approx 1.0$ MeV for ${}^{50,51}V$, ${}^{61,62}Ni$ and ${}^{73,74}\mathrm{\text{Ge}}$ isotopes of the elements. These structural thermodynamic entropies are interpreted as a remarkable signature of the superfluid to normal phase transition connected to the vanishing of pairing gap. The calculated level densities are compared with recent experimental values. In addition, the single particle entropy of intermediate-mass nuclei is depicted as half of the entropy of mid-shell nuclei in the rare-earth region. As a consequence, the $N=28$ shell closure of ${}^{51}$V carries low entropy at low excitation energy presents an interesting analogy to the $Z=28$ shell closure of ${}^{61}$Ni. Merely, in the case of odd–even ${}^{73}\mathrm{\text{Ge}}$ has higher entropy than the even–even ${}^{74}\mathrm{\text{Ge}}$ nucleus.

Nuclear level densities of ${}^{207}$Pb and ${}^{89}$Y are calculated using the Lipkin–Nogami (LN) method and Bradeen–Cooper–Schrieffer (BCS) model. It is revealed that the calculated nuclear level densities are highly matched with the experimental data of Oslo group. The excitation energy and entropy are calculated for mentioned nuclei. In the case of two studied nuclei the characteristic of being magic for the number of neutrons or protons causes the decrease of the excitation energy and entropy contribution of magic system at low temperatures.

Aims of this work are: (i) Investigation of the production of some radioisotopes that could be used in nuclear battery technology with neutron-induced reaction processes, (ii) Estimation of the cross-section curves of $(n,\gamma )$ reactions for astrophysical processes in the energy region between 1eV and 1MeV, (iii) Determination of suitable level density models for the $(n,\gamma )$ reaction processes. Additionally, the obtained results were compared with the experimental data and recommended data. Based on the calculated results, to eliminate lack of nuclear data in the literature, we recommend new experiments for some reaction processes to be performed by the experimenters. Moreover, for the $(n,\gamma )$ reaction processes, suitable level density models were proposed.

The accurate knowledge of the nuclear level density is crucial for understanding the nuclear structure and for numerous applications including astrophysical reactions. In this review paper, we discuss the shell-model description of the nuclear level density, the use of the statistical moments method and underlying physics. The level density found with the moments method is shown to agree with the results of the exact diagonalization of the Hamiltonian matrix. The statistical approach is also compared to other standard methods for deriving level densities. The role of specific interaction matrix elements is reviewed in connection to the behavior of the level densities as these evolve. Chaotization and thermalization processes, collective enhancement and phase transitions are discussed with changing strengths of specific groups of two-body interaction matrix elements. The popular phenomenological constant temperature model is compared to the moments method and the effective temperature parameter of the model for different isotopes is discussed.

We demonstrate that pairing phase transition (superfluid to normal) can be described quite generally in terms of the thermodynamical properties after verifying the obtained level densities with the available experimental data for ${}^{118,122}Sn$- isotopes. Periodic-orbit theory conveniently connects the oscillatory part of level density to the underlying classical periodic orbits and hence, leads to the shell effects in the single-particle level density. Such methods incorporated with pairing effects can be used effectively to study the phase transitions in $Sn$-isotopes. In addition to this, an interplay between pairing correlations and the shell effects has been understood by analyzing the results obtained for the critical temperatures and shell structure energies for ${}^{102-138}Sn$ isotopes. A relation between variation in critical temperatures caused by shell effects and the shell structure energies determined with and without pairing effects has been established. Furthermore, the systematics of the heat capacity (giving a clear signature of pairing phase transition) as function of temperature for these nuclei are investigated as well.

In this work, we calculate the level density parameter for several nuclei by deploying the semiclassical trace formula for spherically symmetric harmonic oscillator potential with spin-orbit interactions, which describes the quantum shell effects in terms of the classical periodic orbits. With the usage of recently proposed Laplace like formula of level density parameter by Canbula et al., the effects of collective rotations and vibrations as well as deformations in nuclei are incorporated. The comparison of our results with the experimental ones show a good agreement. Later on, the study is also extended to the calculation of nuclear level density and survival probability in several superheavy nuclei (SHN).

Level density $\rho (E,N,Z)$ is derived for a nuclear system with a given energy $E$, neutron $N$, and proton $Z$ particle numbers, within the semiclassical extended Thomas–Fermi and periodic-orbit theory beyond the Fermi-gas saddle-point method. We obtain $\rho \propto I_{\nu }(S)/S^{\nu }$, where $I_{\nu }(S)$ is the modified Bessel function of the entropy $S$, and $\nu$ is related to the number of integrals of motion, except for the energy $E$. For small shell structure contribution one obtains within the micro–macroscopic approximation (MMA) the value of $\nu =2$ for $\rho (E,N,Z)$. In the opposite case of much larger shell structure contributions one finds a larger value of $\nu =3$. The MMA level density $\rho$ reaches the well-known Fermi gas asymptote for large excitation energies, and the finite micro-canonical limit for low excitation energies. Fitting the MMA $\rho (E,N,Z)$ to experimental data on a long isotope chain for low excitation energies, due mainly to the shell effects, one obtains results for the inverse level density parameter $K$, which differs significantly from that of neutron resonances.

For a sustainable nuclear energy program using fission reactors, the reduction or elimination of long-lived radioactive waste is essential. The hazardous Long-Lived Fission Products (LLFP), which are by-products of the operation of nuclear reactors, need to be converted to short-lived or stable nuclei. For nuclear transmutation, the knowledge of reaction cross-sections is important. The cross-section and half-life for the proton-induced transmutation of the LLFP, ${}^{126}$Sn, produced as nuclear waste from the reactor have been calculated. The cross-section for the (p,n) reaction on unstable ${}^{126}$Sn has been calculated using phenomenological as well as microscopic models of optical potentials and level densities in the framework of the statistical nuclear model using the latest version of the code TALYS-1.96. The Koning–Delaroche (KD) and Jeukenne–Lejeune–Mahaux–Bruyeres (JLMB) optical models, as well as back-shifted Fermi gas model (BFM) and Hartree–Fock (HF) level density, based on the Skyrme force from Gorielys tables, have been used. The renormalized optical model parameters and level density models obtained by comparing cross-sections with data for protons incident on stable ${}^{112,114,115,116,117,118,119,120,122,124}$Sn isotopes were extended to make a prediction of (p,n) cross-section on unstable ${}^{126}$Sn isotope. The excitation function obtained using JLMB-HF calculation for ${}^{126}$Sn reveals a peak at an incident proton energy of 8.5MeV with a corresponding cross-section of 269mb. It would be of interest to perform experiments for measurements of cross-section where data are unavailable, especially in the peak regions and beyond, to validate the predictions of this work. It is found that for a proton flux of $6.25\times 10^{14}$s${}^{-1}$cm${}^{-2}$, and a peak cross-section calculated using JLMB-HF calculation, the effective half-life of transmutation of ${}^{126}$Sn is about 65 years, thus justifying its feasibility.

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 ${}^{236}$U and ${}^{240}$Pu. The angular dependence of level density parameter, level densities and ratio of ${\mathrm{\Gamma }}_n$ and ${\mathrm{\Gamma }}_f$ the thermal excitation energy (U) have been studied in the superheavy region $104\le Z\le 118$. 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 $104\le Z\le 118$. Systematic variation of ${\mathrm{\Gamma }}_n$ and ${\mathrm{\Gamma }}_f$ is observed in both the cases. Finally, predicted ${\mathrm{\Gamma }}_n/{\mathrm{\Gamma }}_{\mathrm{\text{tot}}}$ for the synthesis of superheavy nuclei $Z=119$ and 120.

It is now well established that at moderate excitation energies the nucleus temperature does not vary with increasing excitation energy. We show that, as a consequence, two nuclei with different temperatures brought into contact show a rather surprising energy-sorting mechanism where the hotter nucleus transfers all its excitation energy to the colder one. The scission configuration of the fission process offers a unique possibility to observe this phenomenon. The energy sorting mechanism is clearly reflected by the mean number of prompt neutrons as a function of the fragment mass and by the dependence of the local even-odd effect with mass asymmetry.

Level densities of 2⁺ and 1⁻ states in ⁴⁰Ca have been extracted from high energy-resolution (p,p′) experiments performed using the K600 magnetic spectrometer at iThemba LABS, South Africa. The success of the method depends on the accurate determination of various background components underneath the giant resonance. It was found that using the nearly model-independent method of Discrete Wavelet Transform (DWT) background determination using bi-orthogonal wavelets of high order of vanishing moments proved sufficient for the extraction of level density in the excitation energy region of the Isoscalar Giant Quadrupole Resonance (ISGQR) and Isovector Giant Dipole Resonance (IVGDR). Comparison of the experimentally extracted 2⁺ and 1⁻ level densities with Back-Shifted Fermi Gas Model (BSFG), Hartree-Fock Bogoliubov (HFB) and Hartree-Fock-Bardeen-Cooper Schriffer (HF-BCS) theoretical model predictions were made. Future interests in the use of radioactive-ion beams of different intensities will provide opportunities in elucidating this important property experimentally for more exotic calcium isotopes.