Angular momentum and energy dependence of fission andn,p,4He emission from194Hg compound nucleus

Spin and temperature dependence of the fission and particle emission is studied for¹⁹⁴Hg. The compound nucleus is described using the Strutinsky shell correction approach extended for finite angular momenta and temperature. The shell corrections to the potential energy, free energy and the angular momentum are calculated using the Woods-Saxon average field. Results are compared with the experimental data and show a good qualitative agreement. It is found that the inclusion of the shell effects is necessary to understand the decay properties of¹⁹⁴Hg even for temperatures as high as 1.5–2.0 MeV.     

Shape Transitions and Jacobian Instability in Excited Krypton Isotopes

Shape transitions as a function of angular momentum in even–even krypton isotopes with A?=?72–84 have been investigated using the cranked Nilsson–Strutinsky method. The Jacobi shape transition from noncollective oblate to super or hyperdeformed collective prolate or triaxial shape taking place in rotating nuclei as in the case of gravitating rotating stars is studied in krypton isotopes. The cranked Nilsson–Strutinsky method with a method of tuning the angular velocity to get the fixed spins is used in the calculations. Our results show that all the krypton isotopes considered in this study are the good candidates for detecting the Jacobi shape transition. Shape evolutions as a function of spin and temperature with thermal fluctuations are studied using the Landau theory of phase transitions. The constants appearing in the Landau expression for the free energy are determined by using the free energy surfaces at ω?=?0 calculated by the Strutinsky method. We show that in the presence of thermal fluctuations, the averaged shapes obtained for the considered isotopes differ from the most probable shapes. The sharp Jacobi transitions are modified due to the effect of thermal fluctuations.     

Dependence of mass fission asymmetry on the compound excitation energy

The influence of the excitation energy of compound fissioning nucleus on the potential deformation energy as a function of the fission and asymmetry coordinates has been investigated. The Fermi distribution of nucleons at a certain temperature is assumed and taken into account in the Strutinsky shell-correction method. It has been found that the structure of the potential energy surface becomes smoother with increasing excitation energy and shell effects disappear at a compound-nuclear temperature of 2.0 to 2.5 MeV.     

Stability of Strutinsky Shell Correction Energy in Relativistic Mean Field Theory

The single-particle spectrum obtained from the relativistic mean field （RMF） theory is used to extract the shell correction energy with the Strutinsky method. Considering the delicate balance between the plateau condition in the Strutinsky smoothing procedure and the convergence for the total binding energy, the proper space sizes used in solving the RMF equations are investigated in detail by taking ^208 Pb as an example. With the proper space sizes, almost the same shell correction energies are obtained by solving the RMF equations either on basis space or in coordinate space.     

Calculation of charge vibration in fission with Strutinsky shell correction

The Strutinsky shell correction method has been applied to the two spheroid model to study charge vibrations in fission. The investigation is carried out by calculating the potential energy surface with respect to three degrees of freedom: charge vibration from the uniform value and the deformations of the two fragments. The results suggest that the effect of shells at Z = 50 and N = 82 do not cause large deviations from the liquid drop model charge density around mass 132; their effect is much more pronounced in the fragment excitation energy. The results also suggest that the fragment excitation and kinetic energies for a given mass ratio are markedly charge density dependent. Some features inherent to this treatment with respect to characteristic periods of individual degrees of freedom have been discussed.     

The equivalence of the Strutinsky type smoothing and the temperature averaging method

The Fermi gas model of the nucleus at high temperatures can be used to define a ground state shell correction. We demonstrate analytically that the shell correction so obtained is the same as that obtained from the Strutinsky type method.     

Shell structure in nuclei

A review of shell structure for spherical and a variety of deformed nuclei is presented. The microscopic-macroscopic method of Strutinsky is used to calculate potential energy surfaces with the pure harmonic oscillator and the modified harmonic oscillator. New sets of “magic numbers” for a variety of different prolate, oblate and axially asymmetric shapes are generated. Experimental evidence for the special stability caused by these shell effects is presented with special emphasis on the lightest and heaviest nuclei where the effects are most pronounced. The radial diffuseness parameter is treated as a Strutinsky variable and its significance in extrapolating into the superheavy region considered. The calculation of shell effects for high spin states is also reviewed.     

微观描述热核裂变寿命（英文）

有关热核裂变的研究与反应堆中的诱发裂变,天体环境中的裂变,以及超重元素的合成等密切相关。热核裂变的研究通常是基于Bohr-Wheeler 的统计裂变理论。而统计模型的研究十分依赖唯像的能级密度和位能面。因此,提出基于微观的有限温度的能量密度泛函理论计算热核的裂变寿命。可以微观自洽地计算出温度相关的裂变位垒高度,曲率,集体质量参数。基于虚自由能法,从低温到高温的裂变寿命可以由一个统一的框架给出。展示了在裂变研究中温度相关裂变位垒的重要性,并讨论了微观描述热核裂变的前景。The studies of thermal fission rates are relevant to novel reactors, astrophysical environments, and survival probabilities of compound superheavy nuclei. This has been conventionally studied by the Bohr-Wheeler statistical model that depends on phenomenological level densities and fission barriers. In this context, we propose to study the thermal fission rates based on microscopic temperature dependent nuclear energy density functional theory. The microscopic temperature dependent fission barrier heights and curvatures, and collective mass parameters can be self-consistently obtained. The fission lifetimes from low to high temperatures can be given by the imaginary free energy method in a consistent framework. Microscopic temperature dependent fission barriers play an essential role in fission studies.     

Nuclear shapes and interaction potentials of two colliding208Pb nuclei at finite temperature

The effect of nuclear and Coulomb interactions on the shapes of two colliding²⁰⁸Pb nuclei at finite temperature is investigated. The complex potential energy density derived by Faessler and collaborators and the kinetic energy density and entropy density for two Fermi spheres at finite temperature are used to calculate the free energy of the²⁰⁸Pb +²⁰⁸Pb system in the energy density formalism. Shell corrections are added to the free energy in the framework of the Strutinsky method. The total free energy is minimized with respect to the quadrupole deformation and the diffuseness to determine the density distribution of²⁰⁸Pb nucleus at certain distanceR and temperatureT assuming the deformed Woods-Saxon shape for each nucleus. It is found that the nucleus acquires larger deformation and diffuseness as the temperature increases. The interaction potential between two²⁰⁸Pb nuclei is calculated from the minimized free energy. The total (nuclear + Coulomb) potential is found to decrease with increasing temperature, whereas the real part of the nuclear potential becomes more repulsive as the temperature increases.     

Semiclassical model of a one-dimensional quantum dot

A one-dimensional quantum dot at zero temperature is used as an example for developing a consistent semiclassical method. The method can also be applied to systems of higher dimension that admit separation of variables. For electrons confined by a quartic potential, the Thomas-Fermi approximation is used to calculate the self-consistent potential, the electron density distribution, and the total energy as a function of the electron number and the effective electron charge representing the strength of interaction between electrons. Use is made of scaling with respect to the electron number. An energy quantization condition is derived. The oscillating part of the electron density and both gradient and shell corrections to the total electron energy are calculated by using the results based on the Thomas-Fermi model and analytical expressions derived in this study. The dependence of the shell correction on the interaction strength is examined. Comparisons with results calculated by the density functional method are presented. The relationship between the results obtained and the Strutinsky correction is discussed.     

A secondary minimum in the potential energy surface of Ca

Strutinsky type calculations are extended to lighter nuclei. Secondary minima in the potential energy surface generally considered to account for the existence of fission isomers occur also in the lighter mass region. Results for ⁴⁰Ca are compared with experimental evidences.     

High spin properties of 124Ba

The ¹²⁴Ba nucleus is investigated on the basis of the method of statistical mechanics by assuming the nucleons to move in triaxially deformed Nilsson potential. The variation in the Fermi energies of protons and neutrons is studied as a function of spin and temperature. The Fermi energies determined as a function of angular momentum is used to study the dependence of shell correction on angular momentum using the Strutinsky smoothing procedure. The most important observation is that the shell correction is almost the same for all spins for ¹²⁴Ba. The spin cutoff parameter and the single particle level density parameter are studied as a function of spin and temperature. Constant entropy lines drawn by plotting the excitation energy against angular momentum are found to be roughly at constant energy above the yrast line and are almost equally spaced. It is observed that no yrast traps are present for ¹²⁴Ba.     

Shell effects in a paired nucleus for finite excitation energies

Shell effects are considered as functions of the excitation energy of the nucleus. The effects of pairing are included and studied in the BCS approximation. Some numerical results, based on the single-particle spectrum of a Woods-Saxon potential, are given. In the limit of zero excitation the shell correction to the energy is compared with the results obtained by the Strutinsky method.     

Strutinsky smoothing and the partition function approach

The Strutinsky shell correction is analytically shown to be equivalent to the shell correction obtained from the partition function approach, provided certain restrictions on the Strutinsky smoothing parameter are met.     

The shape of fast-rotating nuclei in the region of subshellN=82

The fast rotating erbium nuclei in the vicinity ofN=82 are investigated in the framework of the Strutinsky shell-correction method using the Woods-Saxon potential including non-axial hexadecapole deformations. The equilibrium deformation and moment of inertia are calculated for different spin values. The influence of nuclear temperature on the shell-effects is also discussed.     

General theory of microscopic dynamical response in surface probe microscopy: from imaging to dissipation

We present a general theory of atomistic dynamical response in surface probe microscopy when two solid surfaces move with respect to each other in close proximity, when atomic instabilities are likely to occur. These instabilities result in a bistable potential energy surface, leading to temperature dependent atomic scale topography and damping (dissipation) images. The theory is illustrated on noncontact atomic force microscopy and enables us to calculate, on the same footing, both the frequency shift and the excitation signal amplitude for tip oscillations. We show, using atomistic simulations, how dissipation occurs through reversible jumps of a surface atom between the minima when a tip is close to the surface, resulting in dissipated energies of 1.6 eV. We also demonstrate that atomic instabilities lead to jumps in the frequency shift that are smoothed out with increasing temperature.