Spherical-shell model

The spherical shell model can only account for tire major shell closings. For open shell clusters, ellipsoidal distortions occur [47], leading to subshell closings which account for the fine stmctures in figure C1.1.2(a ). The electron shell model is one of tire most successful models emerging from cluster physics. The electron shell effects are observed in many physical properties of tire simple metal clusters, including tlieir ionization potentials, electron affinities, polarizabilities and collective excitations [34]. 

In the context of the spherical shell model for nearly-free electrons, assuming that Au, Sc, and Ti contribute with 1,3,5 delocalized valence electrons, respectively, it appears that AueSc+ and Au5Ti+ are magic clusters with 8 valence electrons. However, for the other TM impurities, delocalization of valence charge is restricted to the 4s electrons if this model is forced to explain the observed drops of intensity, at n=5 and 7. We obtain the experimental magic numbers ° of Au TM+ clusters without resorting to the empirical shell-model of delocalized electrons. 

Conventional spherical shell model calculations have been undertaken to describe 90 88zr and 90 88y in these large scale calculations valence orbitals included If5/2 2P3/2 2Pl/2 and 199/2 The d5/2 orbital was included for 98Y and for high-spin calculations in 98Zr. Restrictions were placed on orbital occupancy so that the basis set amounted to less than 2b,000 Slater determinants. Calculations were done with a local, state independent, two-body interaction with single Yukawa form factor. Predicted excitation energies and electromagnetic transition rates are compared with recent experimental results. 

Spherical shell-model calculations were undertaken of these nuclei, in order to gain information on their nuclear structure. The calculations reported here were done with a local, state independent two-body interaction with a single Yukawa form factor,... 

Before discussing the recent developments of the model, let me remind you of the main components of the DDM (1) The starting point is the spherical shell model of Mayer and Jensen, where the single-particle level energies are taken from the experimental spectra of odd-A nuclei with one particle (or hole) outside a closed shell. There is a single level scheme for all nuclei. Our version can be found in Table I of [KUM77]. 

For the nuclei studied in this experiment the dominant decay mode is Gamow-Teller beta decay.Partial halflives corresponding to Gamow-Teller beta decay calculated in a spherical shell model formalism [Bro85] are shown in Table I.The calculated lifetimes are with one exception(17C) all shorter than the measured lifetimes. 

Depending upon the membrane geometry, film models can be of two types (a) Uniform flat sheet model, which assumes the membrane to be a planar film and (b) Spherical shell model in which an emulsion globule is characterized as a double shell with the membrane around a single internal phase droplet. Planar geometry models have been used [15-17]. Kremesec and Slattery considered the overall mass transfer resistance as a sum of the resistance through continuous, membrane, and internal phases [17]. 

The spherical shell model was first proposed by Cahn and Li [3]. They suggested that the mass transfer rate through the film is directly related to the solute concentration difference, AC across the film. The rate equation then becomes ... 

The calculations were carried out with the spherical shell-model code OXBASH [15]. A complete set of calculations for all A = 205-212 nuclei of Fig. 1 was performed with both a surface-delta interaction (SDI) [16] and a combination of realistic interactions based on G-matrix... 

Ceulemans, A., CompemoUe, S., Lijnen, E. Hiatus in the spherical shell model of fuUerenes. Phys. Chem. Chem. Phys. 6,238 (2004)... 

Most spectroscopic quadrupole moments are considerably larger than the single-particle values of the spherical shell model. This is true even for... 

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