The hyperspherical-expansion approach and shell models

By means of Talmi integrals the matrix elements of nuclear interaction in the set of radial differential equations of the hyperspherical-expansion approach are related to the elements of usual shell models. The introduced average field equated to the diagonal element of the core reproduces the form of the effective (two-body) cut-off oscillator. The corresponding eigenvalue problem with a flat (heavy nuclei) and rounded (light nuclei) alternative for the well is solved and compared with the phenomenological relations: the asymptotic saturation can be achieved for the flat well. Using these results the starting set is transformed into the set of integral equations by means of the Green's functions. Then it is, successively, reduced to the eigenvalue equations of usual shell models identical for both the well alternatives. Compared with the usual models some improvements apply and the oscillator length is given automatically.     

Shape coexistence in the neutron deficient Pb isotopes and the configuration-constrained shell correction approach

Calculations of shape-isomeric states in neutron deficient lead isotopes have been performed using the configuration-constrained shell correction method with a Woods-Saxon average potential and a monopole pairing interaction. This approach enables us to decompose the ground state potential energy surface in separate parts characterized uniquely by the number of occupied intruder orbitals. The calculations reproduce the positions of the excited 0⁺ intruder states. The isotope¹⁹⁶Pb is discussed in detail.     

Energy- andN-averagings in the shell correction method

It is shown that a difference exists between the mean values of the total single-particle energies obtained by averaging over the nucleon numberN and over the phase-space distributions (the energy-averaging) due to the symmetry of the single-particle Hamiltonian. This difference could lead to significant corrections in fitting the nuclear masses involving the droplet model.     

基于自适应扩散模型的单帧红外条纹非均匀性校正算法

针对红外焦平面成像系统存在列向条纹非均匀性的现象,采用了一种基于自适应PM扩散模型的非均匀校正新算法。首先,综合利用图像梯度信息和局部灰度统计信息,自适应计算PM模型的扩散阈值;然后将每列像素的PM模型估计值作为该列像素的期望值;最后采用最陡下降法迭代计算得到每列像元的校正参数,并对结果进行循环校正以提高校正效果。实验结果表明:该算法可以保护图像边缘信息,与同类算法相比,能够更有效地抑制条纹非均匀性,并且能够防止图像产生鬼影。     

An improved particle correction procedure for the particle level set method

The particle level set method [D. Enright, R. Fedkiw, J. Ferziger, I. Mitchell, A hybrid particle level set method for improved interface capturing, J. Comput. Phys. 183 (2002) 83–116.] can substantially improve the mass conservation property of the level set method by using Lagrangian marker particles to correct the level set function in the under-resolved regions. In this study, the limitations of the particle level set method due to the errors introduced in the particle correction process are analyzed, and an improved particle correction procedure is developed based on a new interface reconstruction scheme. Moreover, the zero level set is “anchored” as the level set functions are reinitialized; hence the additional particle correction after the level set reinitialization is avoided. With this new scheme, a well-defined zero level set can be obtained and the disturbances to the interface are significantly reduced. Consequently, the particle reseeding operation will barely result in the loss of interface characteristics and can be applied as frequently as necessary. To demonstrate the accuracy and robustness of the proposed method, two extreme particle reseeding strategies, one without reseeding and the other with reseeding every time step, are applied in several benchmark advection tests and the results are compared with each other. Three interfacial flow cases, a 2D surface tension driven oscillating droplet, a 2D gas bubble rising in a quiescent liquid, and a 3D drop impact onto a liquid pool are simulated to illustrate the advantages of the current method over the level set and the original particle level set methods with regard to the smoothness of geometric properties and mass conservation in real physical applications.     

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.     

Mechanistic models of the ion-solvation shell system

The eigenfrequencies of solvation shell oscillations with respect to the ion are estimated in various approximations describing the ion–solvation shell system. The results of comparisonwith experiments suggest that the most appropriate is the model in which the solvated ion is considered to be a spherical rotator formed either by the entire solvation shell or by a layer of solvent molecules adjacent to the outer boundary of the solvation shell.     

Semiclassical elementary particle models

Some simple models of elementary particles are discussed; they may be described as semiclassical, quark, shell models. Particles are assumed to be composed of spherical concentric charged shells. Three basic types of shell are allowed, quantum numbers are associated with each type such as to establish a quantum number correspondence between the shell types and the (p, n, ) quarks. Particles are identified through the quantum numbers of their constituent shells (quarks).The basic assumptions underlying the models considered are relationships between the electromagnetic energy associated with elementary particles (quark systems) and particle masses. The electromagnetic energy is represented classically; the models are semiclassical in that the shell radii are related to particle Compton wavelengths.Particle mass and magnetic moment formulas are derived, possible values for quark masses are suggested, and possible connections of the models considered with particle symmetry schemes are discussed.     

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.     

Relativistic shell models and meson-exchange currents

We discuss the connection between nonrelativistic pair exchange currents and relativistic mean field theories. Heavy mesons, especially the σ-meson, are shown to yield strong enhancements to the matrix element of “odd” Dirac operators, such as γ and γ₄γ₅, in complete analogy to the strong enhancements obtained in relativistic mean field theories. For isoscalar operators, there is a cancelling contribution from ω-pair diagrams, called “backflow” in relativistic theories, but for isovector operators the equivalent ρ-pair diagram is very weak. Agreement between traditional nonrelativistic calculations and experiment is worsened by the introduction of heavy-meson pair diagrams. The situation can be improved on adding vertex form factors and short-range correlation functions that reduce the heavy-meson pair contribution by about a factor of two. The differences between the two approaches are emphasized and experimental tests are discussed.     

On two-dimensionalization of three-dimensional turbulence in shell models

Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have been studied and reproduced. Within the framework of shell models we have obtained the following results: (i) progressive steepening of the energy spectrum with increased strength of the rotation, and, (ii) depletion in the energy flux of the forward forward cascade, sometimes leading to an inverse cascade. The presence of extended self-similarity and self-similar PDFs for longitudinal velocity differences are also presented for the rotating 3D turbulence case.     

Single image non-uniformity correction using compressive sensing

A non-uniformity correction (NUC) method for an infrared focal plane array imaging system was proposed. The algorithm, based on compressive sensing (CS) of single image, overcame the disadvantages of “ghost artifacts” and bulk calculating costs in traditional NUC algorithms. A point-sampling matrix was designed to validate the measurements of CS on the time domain. The measurements were corrected using the midway infrared equalization algorithm, and the missing pixels were solved with the regularized orthogonal matching pursuit algorithm. Experimental results showed that the proposed method can reconstruct the entire image with only 25% pixels. A small difference was found between the correction results using 100% pixels and the reconstruction results using 40% pixels. Evaluation of the proposed method on the basis of the root-mean-square error, peak signal-to-noise ratio, and roughness index (ρ) proved the method to be robust and highly applicable.     

Discrete and continuum spectra in the unified shell model approach

A new version of the nuclear shell model unifies the consideration of the discrete spectrum, where the results reproduce the standard shell model, and continuum. The ingredients of the method are the non-Hermitian effective Hamiltonian, energy-dependent one-body and two-body decay amplitudes, and self-consistent treatment of thresholds. The results for helium and oxygen isotope chains reproduce the data well.     

Stochastic approach to nuclear shell model

We propose a Quantum Monte Carlo diagonalization method for solving the quantum many-body interacting systems. Not only the ground state but also low-lying excited states are obtained with their wave functions. Consequently the level structure of low-lying states can be studied with realistic interactions. After testing this method with⁴⁸Cr, we report that the doubly closed shell probability of⁵⁶Ni is shown to be only 53% in a full pf shell calculation, in contrast to the corresponding probability of⁴⁸Ca which reaches 86%. The most recent results on³²Mg are presented. Presented by T. Otsuka at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997. This work was supported in part by Grant-in-Aid for Scientific Research (B) (No. 08454058) from the Ministry of Education, Science and Culture.     

Inverse cascade regime in shell models of two-dimensional turbulence

We consider shell models that display an inverse energy cascade similar to two-dimensional turbulence (together with a direct cascade of an enstrophylike invariant). Previous attempts to construct such models ended negatively, stating that shell models give rise to a "quasiequilibrium" situation with equipartition of the energy among the shells. We show analytically that the quasiequilibrium state predicts its own disappearance upon changing the model parameters in favor of the establishment of an inverse cascade regime with Kolmogorov scaling. The latter regime is found where predicted, offering a useful model to study inverse cascades.