No-core shell model

Large-basis no-core shell model (LBNCSM). 

For the large-basis no-core shell model calculations see Navratil et al. (2000), and for coupled cluster calculations Bishop et al. (1990), Heisenberg and Mihaila (1999) as well as Wloch et al. (2005). 

According to the core-shell model, the growing particle is actually heterogeneous rather than homogeneous, and it consists of an expanding polymer-rich (monomer-starved) core surrounded by a monomer-rich (polymer-starved) outer spherical shell. It is the outer shell that serves as the major locus of polymerization and Smith-Ewart (on-off) mechanism prevails while virtually no polymerization occurs in the core because of its monomer-starved condition. Reaction within an outer shell or at the particle surface would be most likely to be operative for those polymerizations in which the polymer is insoluble in its own monomer or under conditions where the polymerization is diffusion-controlled such that a propagating radical cannot diffuse into the center of the particle. 

The SANS data were modeled [34, 35] as a system of particles with an inner core radius (/ core) and outer shell radius (/ sheii) assuming that there are no orientational correlations, using the same methodology [26, 27, 34] as that developed for aqueous aggregates. For dilute solutions, interparticle interactions may be neglected [4] and several particle shapes were used. The best fits were given by a spherical core-shell model with a Schultz distribution [35] of particle sizes, with a breadth (polydispersity) parameter (Z) and an aggregation number (i.e. the number of molecules per micelle) A agg- A comparison of independently calibrated... 

Figure 2.8 Shell model of ionic polarizability (a) unpolarized ion (no displacement of shell) (b) polarized (displaced shell) (c) interactions 1, core-core 2, shell-shell 3, core-shell.

Shell model calculations predict a quasi-shell closure at 96Zr. Therefore, it is of interest to measure g-factors of states in 97Zr and test whether they can be described by simple shell model configurations. The 1264.4 keV level has a half-life of 102 nsec, and its g-factor was measured by the time-differential PAC method at TRISTAN [BER85a]. The result, g-0.39(4), is consistent with the Schmidt value of 0.43, which assumes no core polarization and the free value for the neutron g factor, g g free. This indicates that the 1264.4 keV level is a very pure single-particle state, thus confirming the shell model prediction of a quasi-shell closure at 96Zr. 

The SANS data were modelled as a system in which core-shell micelles interact in a solvent medium and, assuming no orientational correlations, the differential scattering cross section is given by... 

The above potential is based on a rigid-ion-model (RIM), as no effect of atomic polarization is taken into account. A shell model (SM) was also developed, which considers a split core-shell structure for polarizable O atoms. As usual [23], core and shell are coupled by an elastic spring of force constant k, and are characterized by different electric charges zqc and ZQs- In addition to k, and zqs, also the core-shell displacement, is to be optimized, and contributes three positional parameters (unless reduced by symmetry) for eaeh O atom in the asymmetric unit. When an O atom is involved in the two-body interaction, the repulsive and, possibly, dispersive energy is eomputed by reference to the 0 shell position. All other atoms and interactions are treated as for the RIM case. 

Most interesting is the large increase in reinforcement even for small bound rubber thicknesses. Let us briefly discuss the advantages of the model. They find that the results obtained are realistic for small as well as intermediate filler concentrations, i.e. they are in accordance with experiments at least qualitatively. For the core-shell systems they have provided exact calculations of intrinsic moduli for various special forms of core-shell elasticity, i.e. soft spheres, hard spheres with soft surfaces, etc. These results contain no fit parameters and in principle both compressible and incompressible media are accessible. 

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