Abstract
We introduce the concept of the envelope dyadic Green's function (EDGF) and present a formalism to study the propagation of electromagnetic fields with slowly varying amplitude (EMFSVA) in dispersive anisotropic media with two dyadic constitutive parameters: the dielectric permittivity and the magnetic permeability. We find the matrix elements of the EDGFs by applying the formalism for uniaxial anisotropic metamaterials. We present the relations for the velocity of the EMFSVA envelopes which agree with the known definition of the group velocity in dispersive media. We consider examples of propagation of the EMFSVA passing through active and passive media with the Lorentz and the Drude type dispersions, demonstrating beam focusing in hyperbolic media and superluminal propagation in media with inverted population. The results of this paper are applicable to the propagation of modulated electromagnetic fields and slowly varying amplitude fluctuations of such fields through frequency dispersive and dissipative (or active) anisotropic metamaterials. The developed approach can be also used for the analysis of metamaterial-based waveguides, filters, and delay lines.

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Abstract

Abstract
The free energy of an alpha particle is calculated using the local density approximation in the harmonic oscillator basis. The effective two-body interactions are generated from the lowest order constrained variational (LOCV) calculation for nuclear matter at finite temperature, with the Reid and ?-Reid potentials. The Fermi?Dirac distribution is used to calculate the entropy and the occupation probability of each state of alpha particle at a given temperature. The effective mass is treated as a variational parameter. Our zero temperature results with the ?-Reid interaction agree well with the experimental saturation data of alpha particle and the other many-body techniques. The flashing temperature of ˜5 MeV is found, which is consistent with experimental evidence. It is concluded that a similar liquid?gas phase transition to that of nuclear matter is most probable in the alpha particle and heavier nuclei. PACS Nos.: 21.65+f, 21.10-k, 21.10Dr, 21.60-n

Abstract
The ground state properties of light closed shell nuclei, i.e. 4He, 12C, 16O, 28Si, 32S, 40Ca and 56Ni are studied by using the channel-dependent effective two-body interactions (CDEI's). The CDEI's are generated through the lowest-order constrained variational (LOCV) calculation for asymmetric nuclear matter with the charge-dependent Av18 bare nucleon–nucleon potential. The work is performed on the harmonic oscillator basis, and the local density approximation is applied to create the relative and the center of mass dependent effective two-body potential. Unlike nuclear matter, and similar to our previous calculations with the Reid68 interaction, while the Av18 potential under binds above nuclei up J max = 2 channel, it gives ground state binding energies closer to the experimental data with respect to the ?- Reid68 and the Reid68 potentials. There are not much difference between the results of Av18 interaction with J max = 5, and those of Reid68Day potential which has been define up to J max = 5. The different CDEI's up to J max = 5 are discussed and the results of our calculations are compared with the other theoretical approaches and experimental data. Finally, it is shown that the contributions of higher partial waves (J>2) are not very important and the two-body kinetic energy in J = 1 channel is roughly twice as that of J = 0 which is not the case for the two-body potential energy.

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