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.

THE INTERNAL EXCITATION OF THE GAS OF INDEPENDENT PARTICLES IN A TIME DEPENDENT POTENTIAL

2011 ◽  
Vol 20 (02) ◽  
pp. 292-298 ◽  
Author(s):  
J. P. BLOCKI ◽  
A. G. MAGNER ◽  
I. S. YATSYSHYN
Keyword(s):  
Small Amplitude ◽  
Equilibrium Shape ◽  
Mean Field ◽  
Time Dependent ◽  
Nuclear Model ◽  
Quantum Gas ◽  
Excitation Energies ◽  
Shell Effects ◽  
Internal Excitation ◽  
Classical Gas

The order-to-chaos transition in the dynamics of independent classical and quantum gas of particles was studied by means of the computer simulations within the nuclear model based on the time-dependent mean-field approach. The excitation of the classical gas for containers whose surfaces are rippled according to Legendre polynomials P2, P3 is followed for twenty periods of oscillations. For different vibration frequencies of small amplitude vibrations of such a container near the spherical equilibrium shape we obtained for the classical gas much smaller excitation energies than those predicted by the wall formula. With increasing equilibrium deformation they become significantly larger and for P3 vibrations they are close to the wall formula limit. Notable shell effects were found in the excitation energies of the quantum gas in the Woods-Saxon potential with the corresponding relatively sharp (diffuseness equals to 0.1 fm) moving surfaces for small-amplitude slow vibrations.

scholarly journals TEMPERATURE DEPENDENCE OF THE NUCLEAR ENERGY IN RELATIVISTIC MEAN-FIELD THEORY

2005 ◽  
Vol 14 (03) ◽  
pp. 505-511 ◽  
Author(s):  
B. NERLO-POMORSKA ◽  
K. POMORSKI ◽  
J. SYKUT ◽  
J. BARTEL
Keyword(s):  
Single Particle ◽  
Level Density ◽  
Mean Field Theory ◽  
Mean Field ◽  
Correction Method ◽  
Shell Correction ◽  
Shell Effects ◽  
Relativistic Mean Field ◽  
Single Particle Level ◽  
Particle Level

Self-consistent relativistic mean-field (RMF) calculations with the NL3 parameter set were performed for 171 spherical even-even nuclei with 16≤A≤224 at temperatures in the range 0≤T≤4 MeV . For this sample of nuclei single-particle level densities are determined by analyzing the data obtained for various temperatures. A new shell-correction method is used to evaluate shell effects at all temperatures. The single-particle level density is expressed as function of mass number A and relative isospin I and compared with previous estimates.

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.

SEMICLASSICAL ORIGIN OF SHELL STRUCTURES IN DEFORMED NUCLEI: DEPENDENCE ON SURFACE DIFFUSENESS AND EFFECT OF SPIN-ORBIT COUPLINGS

2004 ◽  
Vol 13 (01) ◽  
pp. 191-202 ◽  
Author(s):  
KEN-ICHIRO ARITA
Keyword(s):  
Periodic Orbit ◽  
Mean Field ◽  
Orbit Coupling ◽  
Shell Structures ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Periodic Orbit Theory ◽  
Shell Effects ◽  
Surface Diffuseness ◽  
Type Potential

Shell structures in nuclear mean field potentials are analyzed using semiclassical periodic-orbit theory. rα-type potential model is taken as an approximation of Woods-Saxon model, and spin-orbit coupling is also taken into account. Using this model, we examine shell structure as functions of deformation, nuclear size (diffuseness), and spin-orbit coupling strength. Significant roles of periodic orbit bifurcations for strong deformed shell effects are clarified. Special attentions will be paid to bifurcations of the 'bridge orbits', which emerge from symmetric orbits and then submerge in other symmetric orbits by varying a potential parameter.

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.

scholarly journals Swarm shedding in networks of self-propelled agents

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jason Hindes ◽  
Victoria Edwards ◽  
Klimka Szwaykowska Kasraie ◽  
George Stantchev ◽  
Ira B. Schwartz
Keyword(s):  
Network Topology ◽  
Collective Motion ◽  
Mean Field Theory ◽  
Mean Field ◽  
Interaction Strength ◽  
Central Question ◽  
Agent Interaction ◽  
Sparse Networks ◽  
Swarm Pattern ◽  
Limited Sensing

AbstractUnderstanding swarm pattern formation is of great interest because it occurs naturally in many physical and biological systems, and has artificial applications in robotics. In both natural and engineered swarms, agent communication is typically local and sparse. This is because, over a limited sensing or communication range, the number of interactions an agent has is much smaller than the total possible number. A central question for self-organizing swarms interacting through sparse networks is whether or not collective motion states can emerge where all agents have coherent and stable dynamics. In this work we introduce the phenomenon of swarm shedding in which weakly-connected agents are ejected from stable milling patterns in self-propelled swarming networks with finite-range interactions. We show that swarm shedding can be localized around a few agents, or delocalized, and entail a simultaneous ejection of all agents in a network. Despite the complexity of milling motion in complex networks, we successfully build mean-field theory that accurately predicts both milling state dynamics and shedding transitions. The latter are described in terms of saddle-node bifurcations that depend on the range of communication, the inter-agent interaction strength, and the network topology.

FISSION TIME OF α-INDUCED REACTIONS MEASURED BY THE CRYSTAL BLOCKING TECHNIQUE

2010 ◽  
Vol 19 (05n06) ◽  
pp. 1227-1235 ◽  
Author(s):  
V. A. DROZDOV ◽  
D. O. EREMENKO ◽  
O. V. FOTINA ◽  
S. Yu. PLATONOV ◽  
O. A. YUMINOV ◽  
...  
Keyword(s):  
Fission Fragment ◽  
Statistical Approach ◽  
Reliable Information ◽  
Fission Barrier ◽  
Large Set ◽  
Angular Anisotropy ◽  
Excitation Energies ◽  
Shell Effects ◽  
Pu Isotopes ◽  
Nuclear Dissipation

A large set of experimental observables for the 232 Th , 235 U (α, xnf ) reactions has been analyzed within the dynamic-statistical approach with allowance for the nuclear dissipation phenomenon, the double humped structure of fission barrier, and also the temperature damping of shell effects. The energy dependences of the lifetime effect (experimentally measured by the crystal blocking technique) along the corresponding data on the fission fragment angular anisotropy and also fission probabilities of U and Pu isotopes produced in the reactions were chosen for the analysis. Reliable information on the nuclear viscosity at the low excitation energies (< 30 MeV) was obtained.

scholarly journals Low-Cost Molecular Excited States from a State-Averaged Resonating Hartree-Fock Approach

2019 ◽  
Author(s):  
Jacob Nite ◽  
Carlos A. Jimenez-Hoyos
Keyword(s):  
Excited States ◽  
Configuration Interaction ◽  
Low Cost ◽  
Computational Cost ◽  
Mean Field ◽  
Chem Phys ◽  
Spin Projection ◽  
Excitation Energies ◽  
Hartree Fock ◽  
Orbital Relaxation

Quantum chemistry methods that describe excited states on the same footing as the ground state are generally scarce. In previous work, Gill et al. (J. Phys. Chem. A 112, 13164 (2008)) and later Sundstrom and Head-Gordon (J. Chem. Phys. 140, 114103 (2014)) considered excited states resulting from a non-orthogonal configuration interaction (NOCI) on stationary solutions of the Hartree–Fock equations. We build upon those contributions and present the state-averaged resonating Hartree–Fock (sa-ResHF) method, which differs from NOCI in that spin-projection and orbital relaxation effects are incorporated from the onset. Our results in a set of small molecules (alanine, formaldehyde, acetaldehyde, acetone, formamide, and ethylene) suggest that sa-ResHF excitation energies are a notable improvement over configuration interaction singles (CIS), at a mean-field computational cost. The orbital relaxation in sa-ResHF, in the presence of a spin-projection operator, generally results in excitation energies that are closer to the experimental values than the corresponding NOCI ones.

scholarly journals Low-Cost Molecular Excited States from a State-Averaged Resonating Hartree-Fock Approach

2019 ◽  
Author(s):  
Jacob Nite ◽  
Carlos A. Jimenez-Hoyos
Keyword(s):  
Excited States ◽  
Configuration Interaction ◽  
Low Cost ◽  
Computational Cost ◽  
Mean Field ◽  
Chem Phys ◽  
Spin Projection ◽  
Excitation Energies ◽  
Hartree Fock ◽  
Orbital Relaxation

Quantum chemistry methods that describe excited states on the same footing as the ground state are generally scarce. In previous work, Gill et al. (J. Phys. Chem. A 112, 13164 (2008)) and later Sundstrom and Head-Gordon (J. Chem. Phys. 140, 114103 (2014)) considered excited states resulting from a non-orthogonal configuration interaction (NOCI) on stationary solutions of the Hartree–Fock equations. We build upon those contributions and present the state-averaged resonating Hartree–Fock (sa-ResHF) method, which differs from NOCI in that spin-projection and orbital relaxation effects are incorporated from the onset. Our results in a set of small molecules (alanine, formaldehyde, acetaldehyde, acetone, formamide, and ethylene) suggest that sa-ResHF excitation energies are a notable improvement over configuration interaction singles (CIS), at a mean-field computational cost. The orbital relaxation in sa-ResHF, in the presence of a spin-projection operator, generally results in excitation energies that are closer to the experimental values than the corresponding NOCI ones.

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