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Register a new userSelf-consistent anisotropic oscillator with cranked angular and vortex velocities
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Authors
G. Rosensteel
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The Kelvin circulation is the kinematical Hermitian observable that measures the true character of nuclear rotation. For the anisotropic oscillator, mean field solutions with fixed angular momentum and Kelvin circulation are derived in analytic form. The cranking Lagrange multipliers corresponding to the two constraints are the angular and vortex velocities. Self-consistent solutions are reported with a constraint to constant volume.
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The survey of different configurations near Fermi surface of 138Nd results in 12 lowest configurations, at both positive- and negative-deformations. These are calculated to be the energetically lowest configurations. The results show that, for both EDFs, the rotational states based on positive-minimum, which is at gamma~35, are lower than the respective configurations with negative-deformation. The general trends of the spin-versus-omega curve, and the energy-versus-spin curve reproduce well those of the experimental data. Further, for the observed bands `T1-T8, the calculated results using SLy4L allows the configurations of the observed bands to be assigned. The calculations predict transitional quadrupole moments, which can be used to compare with future experimental data. The current cranked self-consistent mean-field calculations of the near-yrast high-spin rotational bands in 138Nd reproduce well the experimental data. The results suggest that the experimentally observed bands can be assigned to the calculated bands with various configurations at the positive-deformation. The predictions of the current calculations are complementary to that of the well-know macroscopic-microscopic calculations, both of which await future experiment to verify.
The present thesis aims at studying the properties of symmetric nuclear and pure neutron matter from a Greens functions point of view, including two-body and three-body chiral forces. An extended self-consistent Greens function formalism is defined to consistently incorporate three-body forces in the many-body calculations. The effect of three-nucleon interactions is included via the construction of a dressed two-body density dependent force. This is obtained performing an average of the leading order three-body terms in the chiral effective field theory expansion. The dressed force corresponds to the use of an in-medium propagator in the average which takes into account the correlations characterizing the system at each stage of the many-body calculation. The total energy of the system is obtained by means of a modified Galitskii-Migdal-Koltun sumrule to correctly account for the effect of three-body forces. Microscopic as well as macroscopic properties of symmetric nuclear and pure neutron matter are analyzed in detailed.
We study relativistic nuclear matter in the $sigma - omega$ model including the ring-sum correlation energy. The model parameters are adjusted self-consistently to give the canonical saturation density and binding energy per nucleon with the ring energy included. Two models are considered, mean-field-theory where we neglect vacuum effects, and the relativistic Hartree approximation where such effects are included but in an approximate way. In both cases we find self-consistent solutions and present equations of state. In the mean-field case the ring energy completely dominates the attractive part of the energy density and the elegant saturation mechanism of the standard approach is lost, namely relativistic quenching of the scalar attraction. In the relativistic Hartree approach the vacuum effects are included in an approximate manner using vertex form factors with a cutoff of 1 - 2 GeV, the range expected from QCD. Due to the cutoff, the ring energy for this case is significantlysmaller, and we obtain self-consistent solutions which preserve the basic saturation mechanism of the standard relativistic approach.
By employing the angular momentum projection technique we propose a method to reliably calculate the quantum spectrum of nuclear collective rotation. The method utilizes several cranked mean-field states with different rotational frequencies and they are superposed in the sense of the configuration mixing or the generator coordinate method, after performing the projection; the idea was originally suggested by Peierls-Thouless in 1962. It is found that the spectrum as a result of the configuration mixing does not essentially depend on chosen sets of cranking frequencies if the number of mean-field states utilized in the mixing is larger than a certain small value. We apply this method to three examples employing the Gogny D1S effective interaction and show that it is useful to study high-spin rotational bands by means of the angular momentum projection method.
We extend the self-consistent Greens functions formalism to take into account three-body interactions. We analyze the perturbative expansion in terms of Feynman diagrams and define effective one- and two-body interactions, which allows for a substantial reduction of the number of diagrams. The procedure can be taken as a generalization of the normal ordering of the Hamiltonian to fully correlated density matrices. We give examples up to third order in perturbation theory. To define nonperturbative approximations, we extend the equation of motion method in the presence of three-body interactions. We propose schemes that can provide nonperturbative resummation of three-body interactions. We also discuss two different extensions of the Koltun sum rule to compute the ground state of a many-body system.
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