scholarly journals Shell-structure and asymmetry effects in level densities

2021 ◽  
Author(s):  
A. G. Magner ◽  
A. I. Sanzhur ◽  
S. N. Fedotkin ◽  
A. I. Levon ◽  
S. Shlomo
Keyword(s):  
Shell Structure ◽  
Level Density ◽  
Fermi Gas ◽  
Saddle Point Method ◽  
Density Parameter ◽  
Excitation Energies ◽  
Periodic Orbit Theory ◽  
Shell Effects ◽  
Opposite Case ◽  
Energy Formula

Level density [Formula: see text] is derived for a nuclear system with a given energy [Formula: see text], neutron [Formula: see text], and proton [Formula: see text] particle numbers, within the semiclassical extended Thomas–Fermi and periodic-orbit theory beyond the Fermi-gas saddle-point method. We obtain [Formula: see text], where [Formula: see text] is the modified Bessel function of the entropy [Formula: see text], and [Formula: see text] is related to the number of integrals of motion, except for the energy [Formula: see text]. For small shell structure contribution one obtains within the micro–macroscopic approximation (MMA) the value of [Formula: see text] for [Formula: see text]. In the opposite case of much larger shell structure contributions one finds a larger value of [Formula: see text]. The MMA level density [Formula: see text] reaches the well-known Fermi gas asymptote for large excitation energies, and the finite micro-canonical limit for low excitation energies. Fitting the MMA [Formula: see text] 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 [Formula: see text], which differs significantly from that of neutron resonances.

Analysis of pairing phase transition in Sn-isotopes within semiclassical approach

2020 ◽  
Vol 29 (09) ◽  
pp. 2050071
Author(s):  
Saniya Monga ◽  
Harjeet Kaur ◽  
Sudhir R. Jain
Keyword(s):  
Phase Transition ◽  
Shell Structure ◽  
Level Density ◽  
Critical Temperatures ◽  
Periodic Orbit Theory ◽  
Level Densities ◽  
Shell Effects ◽  
Particle Level ◽  
Pairing Correlations ◽  
Orbit Theory

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 [Formula: see text]- 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 [Formula: see text]-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 [Formula: see text] 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.

scholarly journals Nuclear level densities away from line of β-stability

2021 ◽  
Author(s):  
Tanmoy Ghosh ◽  
Bhoomika Maheshwari ◽  
Sangeeta Arora ◽  
Gaurav Saxena ◽  
Bijay Agrawal
Keyword(s):  
Single Particle ◽  
Level Density ◽  
Mass Range ◽  
Density Parameter ◽  
Structural Effects ◽  
Mass Model ◽  
Nuclear Level ◽  
Level Densities ◽  
Shell Effects ◽  
Order Of Magnitude

Abstract The variation of total nuclear level densities (NLDs) and level density parameters with proton number Z are studied around the β-stable isotope, Z0, for a given mass number. We perform our analysis for a mass range A=40 to 180 using the NLDs from popularly used databases obtained with the single-particle energies from two different microsopic mass-models. These NLDs which include microscopic structural effects such as collective enhancement, pairing and shell corrections, do not exhibit inverted parabolic trend with a strong peak at Z0 as predicted earlier. We also compute the NLDs using the single-particle energies from macroscopic-microscopic mass-model. Once the collective and pairing effects are ignored, the inverted parabolic trends of NLDs and the corresponding level density parameters become somewhat visible. Nevertheless, the factor that governs the (Z-Z0) dependence of the level density parameter, leading to the inverted parabolic trend, is found to be smaller by an order of magnitude. We further find that the (Z-Z0) dependence of NLDs is quite sensitive to the shell effects.

SEMICLASSICAL SHELL STRUCTURE OF MOMENTS OF INERTIA IN DEFORMED FERMI SYSTEMS

2010 ◽  
Vol 19 (04) ◽  
pp. 735-746 ◽  
Author(s):  
A. G. MAGNER ◽  
A. M. GZHEBINSKY ◽  
A. S. SITDIKOV ◽  
A. A. KHAMZIN ◽  
J. BARTEL
Keyword(s):  
Free Energy ◽  
Shell Structure ◽  
Mean Field ◽  
Field Approximation ◽  
Moment Of Inertia ◽  
Mean Field Approximation ◽  
Perfect Agreement ◽  
Periodic Orbit Theory ◽  
Shell Effects ◽  
The Moment

The collective moment of inertia is derived analytically within the cranking model in the adiabatic mean-field approximation at finite temperature. Using the nonperturbative periodic-orbit theory the semiclassical shell-structure components of the collective moment of inertia are obtained for any potential well. Their relation to the free-energy shell corrections are found semiclassically as being given through the shell-structure components of the rigid-body moment of inertia of the statistically equilibrium rotation in terms of short periodic orbits. Shell effects in the moment of inertia disappear exponentially with increasing temperature. For the case of the harmonic-oscillator potential one observes a perfect agreement between semiclassical and quantum shell-structure components of the free energy and the moment of inertia for several critical bifurcation deformations and several temperatures.

scholarly journals Spallation of 56Fe by 1.0 GeV Protons

2019 ◽  
Vol 26 ◽  
pp. 25
Author(s):  
N. G. Nicolis ◽  
G. S. Souliotis ◽  
A. Asimakopoulou
Keyword(s):  
Gamma Rays ◽  
Cross Sections ◽  
Level Density ◽  
Fermi Gas ◽  
Nuclear Potential ◽  
Density Parameter ◽  
Nuclear Decay ◽  
Intermediate Mass ◽  
Spallation Reactions ◽  
Intranuclear Cascade

Mass, charge and isotopic distributions observed in spallation reactions of 56Fe with 1 GeV protons are analysed in the framework of the intranuclear cascade code ISABEL  coupled with the sequential binary decay code MECO. The code MECO provides a description of the equilibrated nuclear decay by the emission of gamma-rays, light-mass particles and clusters as well as intermediate mass fragments emitted in their ground, excited bound and excited unbound states (continuum) according to a generalized Weisskopf formalism. A good overall description of the experimental data is obtained with a global Fermi gas level density parameter and inverse cross sections based on the Christensen and Winther nuclear potential. Multifragmentation decay events are simulated with the code SMM and their influence on the above observables is discussed.

Width of fission-fragment mass yield at simple statistical approach

2018 ◽  
Vol 27 (01) ◽  
pp. 1850002
Author(s):  
V. Yu. Denisov ◽  
O. A. Belyanovska ◽  
V. P. Khomenkov ◽  
I. Yu. Sedykh ◽  
K. M. Sukhyy
Keyword(s):  
Energy Level ◽  
Fission Fragment ◽  
Statistical Approach ◽  
Level Density ◽  
Simple Expression ◽  
Density Parameter ◽  
Mass Yield ◽  
Excitation Energies ◽  
Level Density Parameter ◽  
Fragment Mass

Simple expression for the temperature dependence of the width of fission-fragment mass yields is obtained for high excitation energies. The width depends on the number of nucleons in nuclei, the volume and surface terms of the energy level density parameter, the temperature and the stiffness parameter of the potential related to mass-asymmetric degree of freedom. The contribution of the surface term of the energy level density parameter into the width is important at temperatures [Formula: see text][Formula: see text]MeV.

scholarly journals Ignatyuk damping factor: A semiclassical formula

2019 ◽  
Vol 28 (08) ◽  
pp. 1950061 ◽  
Author(s):  
Nishchal R. Dwivedi ◽  
Saniya Monga ◽  
Harjeet Kaur ◽  
Sudhir R. Jain
Keyword(s):  
Level Density ◽  
Model Fitting ◽  
Damping Factor ◽  
Density Parameter ◽  
Nuclear Level Density ◽  
Nuclear Level ◽  
Gamma Energy ◽  
Level Density Parameter ◽  
Shell Effects ◽  
Semiclassical Methods

Data on nuclear-level densities extracted from transmission data or gamma energy spectrum store the basic statistical information about nuclei at various temperatures. Generally, this extracted data goes through model fitting using computer codes like CASCADE. However, recently established semiclassical methods involving no adjustable parameters to determine the level density parameter for magic and semi-magic nuclei give a good agreement with the experimental values. One of the popular ways to paramaterize the level density parameter which includes the shell effects and its damping was given by Ignatyuk. This damping factor is usually fitted from the experimental data on nuclear-level density and it comes around 0.05 [Formula: see text]. In this work, we calculate the Ignatyuk damping factor for various nuclei using semiclassical methods.

GROSS-SHELL EFFECTS IN THE DISSIPATIVE NUCLEAR DYNAMICS

2012 ◽  
Vol 21 (05) ◽  
pp. 1250034 ◽  
Author(s):  
J. P. BLOCKI ◽  
A. G. MAGNER ◽  
I. S. YATSYSHYN
Keyword(s):  
Collective Motion ◽  
Mean Field ◽  
Shell Correction ◽  
Nuclear Model ◽  
Quantum Gas ◽  
Excitation Energies ◽  
Nuclear Dynamics ◽  
Friction Coefficients ◽  
Periodic Orbit Theory ◽  
Shell Effects

The order-to-chaos transition in the dynamics of the quantum gas of independent particles was studied within the nuclear model based on the time-dependent mean-field approach. The excitation of the quantum gas in the Woods–Saxon potential with a small diffuseness of its surface rippled according to the Legendre polynomials P2 and P3 are obtained for a slow and small amplitude collective motion. We found strong correlations between time-derivatives of the excitation energies (one-body friction coefficients) and shell-correction energies as functions of the particle number. Semiclassical estimates of the friction coefficients were obtained within the periodic orbit theory by using the uniform approximation.

A COMPOSITE NUCLEAR-LEVEL DENSITY FORMULA WITH SHELL CORRECTIONS

1965 ◽  
Vol 43 (8) ◽  
pp. 1446-1496 ◽  
Author(s):  
A. Gilbert ◽  
A. G. W. Cameron
Keyword(s):  
Lower Energy ◽  
Level Density ◽  
Energy Levels ◽  
Fermi Gas ◽  
Experimental Information ◽  
Shell Correction ◽  
Nuclear Level Density ◽  
Excitation Energies ◽  
Nuclear Level ◽  
Level Densities

At low excitation energies a "constant nuclear temperature" representation of nuclear-level densities is used, and at high excitation energies the regular Fermi gas formula is adopted. A method is developed for determining the parameters of the Fermi gas formula by using both the pairing and the shell-correction energies found by Cameron and Elkin for their semiempirical atomic mass formula in its exponential form. This procedure determines level densities at neutron-binding-energy excitations subject to an average factor error of 1.8. Methods are also developed for determining the parameters for the lower-energy formula in such a way that it best fits the lower-energy levels and joins smoothly to the Fermi gas formula. Correlations of the resulting parameters with shell and pairing effects are found. A composite prescription is given for calculating level densities in nuclei for which no experimental information is known. Tables give level density parameters for a wide variety of nuclei for which some experimental information is known. Some of the derivations of the Fermi gas formula in the literature were found to be slightly incorrect, so new derivations are presented in Appendixes.

scholarly journals The nuclear level density parameter

2019 ◽  
Vol 11 (20) ◽  
pp. 35-46
Author(s):  
Rasha S. Ahmed
Keyword(s):  
Level Density ◽  
State Density ◽  
Density Parameter ◽  
Nuclear Level Density ◽  
Excitation Energies ◽  
Nuclear Level ◽  
Level Density Parameter ◽  
Experimental Works ◽  
Experimental Values ◽  
Energy Dependent

The nuclear level density parameter  in non Equi-Spacing Model (NON-ESM), Equi-Spacing Model (ESM) and the Backshifted Energy Dependent Fermi Gas model (BSEDFG) was determined for 106 nuclei; the results are tabulated and compared with the experimental works. It was found that there are no recognizable differences between our results and the experimental -values. The calculated level density parameters have been used in computing the state density as a function of the excitation energies for 58Fe and 246Cm nuclei. The results are in a good agreement with the experimental results from earlier published work.

scholarly journals Fission dynamics with microscopic level densities

2018 ◽  
Vol 169 ◽  
pp. 00019
Author(s):  
Jørgen Randrup ◽  
Daniel Ward ◽  
Gillis Carlsson ◽  
Thomas Døssing ◽  
Peter Möller ◽  
...  
Keyword(s):  
Potential Energy ◽  
Energy Surface ◽  
Local Level ◽  
Level Density ◽  
Deformation Energy ◽  
Excitation Energies ◽  
Level Densities ◽  
Mass Distributions ◽  
Shell Effects ◽  
The Individual

Working within the Langevin framework of nuclear shape dynamics, we study the dependence of the evolution on the degree of excitation. As the excitation energy of the fissioning system is increased, the pairing correlations and the shell effects diminish and the effective potential-energy surface becomes ever more liquid-drop like. This feature can be included in the treatment in a formally well-founded manner by using the local level densities as a basis for the shape evolution. This is particularly easy to understand and implement in the Metropolis treatment where the evolution is simulated by means of a random walk on the five-dimensional lattice of shapes for which the potential energy has been tabulated. Because the individual steps between two neighboring lattice sites are decided on the basis of the ratio of the statistical weights, what is needed is the ratio of the local level densities for those shapes, evaluated at the associated local excitation energies. For this purpose, we adapt a recently developed combinatorial method for calculating level densities which employs the same single-particle levels as those that were used for the calculation of the pairing and shell contributions to the macroscopic-microscopic deformation-energy surface. For each nucleus under consideration, the level density (for a fixed total angular momentum) is calculated microscopically for each of the over five million shapes given in the three-quadratic-surface parametrization. This novel treatment, which introduces no new parameters, is illustrated for the fission fragment mass distributions for selected uranium and plutonium cases.

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