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Register a new userUnified description of 0+ states in a large class of nuclear collective models
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A remarkably simple regularity in the energies of 0+ states in a broad class of collective models is discussed. A single formula for all 0+ states in flat-bottomed infinite potentials that depends only on the number of dimensions and a simpler expression applicable to all three IBA symmetries in the large boson number limit are presented. Finally, a connection between the energy expression for 0+ states given by the X(5) model and the predictions of the IBA near the critical point is explored.
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The energies of subsets of excited 0+ states in geometric collective models are investigated and found to exhibit intriguing regularities. In models with an infinite square well potential, it is found that a single formula, dependent on only the number of dimensions, describes a subset of 0+ states. The same behavior of a subset of 0+ states is seen in the large boson number limit of the Interacting Boson Approximation (IBA) model near the critical point of a first order phase transition, in contrast to the fact that these 0+ state energies exhibit a harmonic behavior in all three limiting symmetries of the IBA. Finally, the observed regularities in 0+ energies are analyzed in terms of the underlying group theoretical framework of the different models.
In this work, we define a set of analytic tools to describe the dynamic response of the magnetization to small perturbations, which can be used on its own or in combination with micromagnetic simulations and does not require saturation. We present a general analytic description of the ferromagnetic high frequency susceptibility tensor to describe angular as well as frequency dependent ferromagnetic resonance spectra and account for asymmetries in the line shape. Furthermore, we expand this model to reciprocal space and show how it describes the magnon dispersion. Finally we suggest a trajectory dependent solving tool to describe the equilibrium states of the magnetization.
Contractions of orthogonal groups to Euclidean groups are applied to analytic descriptions of nuclear quantum phase transitions. The semiclassical asymptotic of multipole collective Hamiltonians are also investigated.
Low mass star-forming regions are more complex than the simple spherically symmetric approximation that is often assumed. We apply a more realistic infall/outflow physical model to molecular/continuum observations of three late Class 0 protostellar sources with the aims of (a) proving the applicability of a single physical model for all three sources, and (b) deriving physical parameters for the molecular gas component in each of the sources. We have observed several molecular species in multiple rotational transitions. The observed line profiles were modelled in the context of a dynamical model which incorporates infall and bipolar outflows, using a three dimensional radiative transfer code. This results in constraints on the physical parameters and chemical abundances in each source. Self-consistent fits to each source are obtained. We constrain the characteristics of the molecular gas in the envelopes as well as in the molecular outflows. We find that the molecular gas abundances in the infalling envelope are reduced, presumably due to freeze-out, whilst the abundances in the molecular outflows are enhanced, presumably due to dynamical activity. Despite the fact that the line profiles show significant source-to-source variation, which primarily derives from variations in the outflow viewing angle, the physical parameters of the gas are found to be similar in each core.
If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Greens operator can be constructed in terms of a continued fraction. As an illustrative example we discuss the Coulomb Greens operator in Coulomb-Sturmian basis representation. Based on this representation, a quantum mechanical approximation method for solving Lippmann-Schwinger integral equations can be established, which is equally applicable for bound-, resonant- and scattering-state problems with free and Coulombic asymptotics as well. The performance of this technique is illustrated with a detailed investigation of a nuclear potential describing the interaction of two $alpha$ particles.
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