Level densities of heaviest nuclei

The intrinsic level densities of superheavy nuclei in the α-decay chains of ^296,298,300120 are calculated using the single-particle spectra obtained with the modified two-center shell model. The role of the shell and pairing effects on the level density as well as their quenching with excitation energy are studied. The extracted level density parameter is expressed as a function of mass number, ground-state shell correction, and excitation energy. The results are compared with the phenomenological values of level density parameters used to calculate the survival of excited heavy nuclei.     

Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme interactions and from relativistic mean field theory. VWK consists of the Thomas-Fermi part plus a pure, perturbative ?² correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of ?⁴ order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g., ²⁰⁸Pb turns out to be only ∼−6 MeV what is about a factor two or three off the generally accepted value. As an ad hoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.     

Single particle models in the shell correction approach

We investigate the dependence of the shell correction energy on the parameters as they occur in the Nilsson model and the single particle model with a Woods-Saxon potential. We give criteria, how these parameters should be chosen in order that the shell correction energies become fairly model-independent. The different models yield now a value of about ?20 MeV for²⁰⁸Pb, substantially larger than in previous work. Its relation to the remainder of the mass formula fit is discussed. We find that shell energies have an extremum. The minimum occurs close to the conventional parameter values (except the potential diffuseness of the protons) and close to the minimum of the total binding energy. The minimum in shell energy corresponds to a maximum bunching of single particle states. The gross properties of these extremal shells agree considerably better with the experimental spectra (for both the neutrons and the protons) than those of conventional model parameters.     

Shell energy in the heaviest nuclei using the Green’s function oscillator expansion method

The Greens function oscillator expansion method and the generalized Strutinsky smoothing procedure are applied to shell corrections in the heaviest elements. A macroscopic-microscopic method with a finite deformed Woods-Saxon potential is used. The stability condition for the shell correction is discussed in detail and the parameters defining the smoothing procedure are carefully determined. It is demonstrated that the spurious contribution to the total binding energy due to the unphysical particle gas that appears in the standard method can be as large as 1.5 MeV for weakly bound neutron-rich superheavy nuclei, but the effect on energy differences (e.g., alpha-decay values) is fairly small.     

Effects of shell correction on α decay properties

The shell correction effects on the α decay properties of heavy and superheavy nuclei have been studied in a macroscopic-microscopic manner. The macroscopic part is constructed from the generalized liquid drop model(GLDM), whereas the microscopic part, namely, the shell correction energy, brings about certain effects on the potential barriers and half-lives under a WKB approximation, which is emphasized in this work. The results show that the shell effects play a significant role in the estimation of the α decay half-lives within the actinide region.Predictions of the α decay half-lives are then generated for superheavy nuclei, which will provide useful information for future experiments.     

Inclusion of the continuum effects in thermodynamical calculations of nuclear binding energy shell corrections

The contribution of the resonances in a realistic finite potential well to the nuclear binding energy shell corrections is considered. A simple expression for the shell correction based on the thermodynamical method is suggested and the sensitivity of the thermodynamical method to an extension of the continuum states is investigated.     

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.     

Evaluation of nuclear shell correction energies for realistic level schemes by temperature smearing method

Calculations of shell correction energies by the temperature smearing method for realistic single particle level schemes of finite depth potentials are described and discussed. It is found that the method provides unique values of the shell correction energies for the various shapes relevant in the fission of actinide nuclei including those shapes where breakdown of the usual Gaussian energy smearing procedure was observed.     

Shell corrections for finite depth potentials

An improved version of the shell correction method is suggested valid for use with finite depth potentials without referring to unbound part of the spectrum. The improved values for the shell corrections are quite stable with respect to the variation of free parameters. Comparison with earlier calculations is given.     

The shell correction and self-consistent deformation energies

The Hartree-Fock deformation energy of the nucleus is represented as the sum of two terms one of which (E^σ) is due to the re-distribution of the nuclear density and depends on the microscopically non-self-consistent parameters σ of the nuclear shape. The other component (E^π) is related to the coherent distortion of the quasiparticle wave functions in the occupied states and is the same as the deformation energy considered in theories of microscopic vibrations for a fixed quasiparticle distribution. Quantities averaged over the particle-hole distribution are introduced which satisfy the condition of statistical self-consistency. It is shown that the shell correction energy represents the averaged effect of the re-distribution of the single-particle states. Finally, corrections are formulated for the shell-model potential which does not satisfy the condition of statistical self-consistency.     

Fusion hindrance and roles of shell effects in superheavy mass region

We present the first attempt of systematically investigating the effects of shell correction energy for a dynamical process, which includes fusion, fusion–fission and quasi-fission processes. In the superheavy mass region, for the fusion process, shell correction energy plays a very important role and enhances the fusion probability when the colliding partner has a strong shell structure. By analyzing the trajectory in three-dimensional coordinate space with the Langevin equation, we reveal the mechanism of the enhancement of the fusion probability caused by ‘cold fusion valleys’. The temperature dependence of shell correction energy is considered.     

Shell structure for deformed nuclear shapes

Eigenvalues for the harmonic oscillator without l·s or l² terms suggest a deformed shell structure for nuclei with axes ratios 2 : 1 and deformation ? = 0.6 with corresponding nucleon “magic numbers” 2, 4, 10, 16, 28, 40, 60, 80 110 and 140, subject to small modifications due to spin-orbit and other correction terms. Experimental evidence of reasonably stable highly deformed structures corresponding to nucleon numbers 16, 20, 28, 40 and 60 (64) is presented. Attempts to calculate the corresponding potential energy surfaces using the Strutinsky shell correction method are described.     

激光辐照下充压柱壳的破坏能量阈值数值模拟

采用有限元方法模拟了激光辐照下充压柱壳的热力学响应,计算了不同工况下结构的瞬态温度场和应力场,根据材料强度准则判断了柱壳的破坏时刻,并提出了一种预测激光辐照下充压柱壳破坏能量阈值的数值方法。研究了壳体厚度和内压大小对柱壳破坏能量阈值的影响,并给出了典型工况下柱壳破坏能量阈值同壳体厚度以及充压大小的关系。数值计算结果表明：破坏能量密度阈值与壳体厚度、内压大小近似成线性关系,壳体厚度比内压大小对柱壳的激光破坏能量阈值影响更大。     

激光辐照下充压柱壳的破坏能量阈值数值模拟

采用有限元方法模拟了激光辐照下充压柱壳的热力学响应,计算了不同工况下结构的瞬态温度场和应力场,根据材料强度准则判断了柱壳的破坏时刻,并提出了一种预测激光辐照下充压柱壳破坏能量阈值的数值方法。研究了壳体厚度和内压大小对柱壳破坏能量阈值的影响,并给出了典型工况下柱壳破坏能量阈值同壳体厚度以及充压大小的关系。数值计算结果表明:破坏能量密度阈值与壳体厚度、内压大小近似成线性关系,壳体厚度比内压大小对柱壳的激光破坏能量阈值影响更大。     

Generalization of the Independent Pair Model to degenerate nuclear states

The equations of the Independent Pair Model for finite nuclei are generalized to nuclear states non describable by a single shell model configuration. As an application of these generalized equations to excited states, the energy of the excitedT=0,J ^π=0⁺ -state of⁴He has been calculated by an approximate solution. Using a spin-averaged square well potential with hard core and Serber exchange character, with all parameters beeing determined from two-nucleon data, the calculation yields an excitation energy of 21.58 MeV compared to the experimental value of about 20.1 MeV.     

Gamma-gamma angular correlation studies in97Tc

The rapid rotation of even-even nuclei is investigated. The characteristic properties of Zn, Mo, Sn, Te, Xe, Ba, Ce and Nd isotopes for high spin are presented. Microscopic calculations are based on the modified oscillator average potential including the quadrupole axial (?) and nonaxial (γ) deformations. The potential energy surfaces of the nuclei are obtained by the shell correction method. The nuclear shape determined by the potential energy surface as a function of angular momentum is predicted.     

Shell effect and capture cross sections in the synthesis of superheavy nuclei

The shell effect is included in the improved isospin dependent quantum molecular dynamics model in which the shell correction energy of the system is calculated by using the deformed two-center shell model.A switch function is introduced to connect the shell correction energy of the projectile and the target with that of the compound nucleus during the dynamical fusion process.It is found that the calculated capture cross sections reproduce the experimental data quantitatively at the energy near the Coulomb...     

Microscopic quadrupole and hexadecapole moments of rare earth nuclei

The theoretical calculations of multipole moments of even-even rare earth nuclei are presented. The potential energy surface is evaluated by the shell correction method. The condition ensuring the equality of the density distribution of the macroscopic liquid droplet part of the potential energy and the density generated by the single particle potential is added. A single particle Nilsson potential is used. New, less stiff potential surfaces versusε ₄ are obtained while the multipole moments calculated at the equilibrium deformations agree well with experimental data.     

Energy trapping in power transmission through a circular cylindrical elastic shell by finite piezoelectric transducers

We study the transmission of electric energy through a circular cylindrical elastic shell by acoustic wave propagation and piezoelectric transducers. Our mechanics model consists of a circular cylindrical elastic shell with finite piezoelectric patches on both sides of the shell. A theoretical analysis using the equations of elasticity and piezoelectricity is performed. A trigonometric series solution is obtained. Output voltage and transmitted power are calculated. Confinement and localization of the vibration energy (energy trapping) is studied which can only be understood from analyzing finite transducers. It is shown that when thickness-twist mode is used the structure shows energy trapping with which the vibration can be confined to the transducer region. It is also shown that energy trapping is sensitive to the geometric and physical parameters of the structure.