Relativistic quasiparticle time blocking approximation. II. Pygmy dipole resonance in neutron-rich nuclei

Theoretical studies of low-lying dipole strength in even-even spherical nuclei within the relativistic quasiparticle time blocking approximation (RQTBA) are presented. The RQTBA developed recently as an extension of the self-consistent relativistic quasiparticle random phase approximation (RQRPA) enables one to investigate effects of coupling of two-quasiparticle excitations to collective vibrations within a fully consistent calculation scheme based on covariant energy density functional theory. Dipole spectra of even-even $^{130}$Sn -- $^{140}$Sn and $^{68}$Ni -- $^{78}$Ni isotopes calculated within both RQRPA and RQTBA show two well separated collective structures: the higher-lying giant dipole resonance (GDR) and the lower-lying pygmy dipole resonance (PDR) which can be identified by a different behavior of the transition densities of states in these regions.Comment: 28 pages, 13 figure

On the Solution of the Number-Projected Hartree-Fock-Bogoliubov Equations

The numerical solution of the recently formulated number-projected Hartree-Fock-Bogoliubov equations is studied in an exactly soluble cranked-deformed shell model Hamiltonian. It is found that the solution of these number-projected equations involve similar numerical effort as that of bare HFB. We consider that this is a significant progress in the mean-field studies of the quantum many-body systems. The results of the projected calculations are shown to be in almost complete agreement with the exact solutions of the model Hamiltonian. The phase transition obtained in the HFB theory as a function of the rotational frequency is shown to be smeared out with the projection.Comment: RevTeX, 11 pages, 3 figures. To be published in a special edition of Physics of Atomic Nuclei (former Sov. J. Nucl. Phys.) dedicated to the 90th birthday of A.B. Migda

Relativistic Mean Field Approach and the Pseudo-Spin Symmetry

Based on the Relativistic Mean Field (RMF) approach the existence of the broken pseudo-spin symmetry is investigated. Both spherical RMF and constrained deformed RMF calculations are carried out employing realistic Lagrangian parameters for spherical and for deformed sample nuclei. The quasi - degenerate pseudo-spin doublets are confirmed to exist near the fermi surface for both spherical and deformed nuclei.Comment: 9 pages RevTex, 4 p.s figures, to appear in Phys. Rev. C as R.

Gravitational GUT Breaking and the GUT-Planck Hierarchy

It is shown that non-renormalizable gravitational interactions in the Higgs sector of supersymmetric grand unified theories (GUT's) can produce the breaking of the unifying gauge group $G$ at the GUT scale $M_{\rm GUT} \sim 10^{16}$~GeV. Such a breaking offers an attractive alternative to the traditional method where the superheavy GUT scale mass parameters are added ad hoc into the theory. The mechanism also offers a natural explanation for the closeness of the GUT breaking scale to the Planck scale. A study of the minimal SU(5) model endowed with this mechanism is presented and shown to be phenomenologically viable. A second model is examined where the Higgs doublets are kept naturally light as Goldstone modes. This latter model also achieves breaking of $G$ at $M_{\rm GUT}$ but cannot easily satisfy the current experimental proton decay bound.Comment: 11 pages, REVTeX, 1 figure included as an uuencoded Z-compressed PostScript file. Our Web page at http://physics.tamu.edu/~urano/research/gutplanck.html contains ready to print PostScript version (with figures) as well as color version of plot

Covariant response theory beyond RPA and its application

The covariant particle-vibration coupling model within the time blocking approximation is employed to supplement the Relativistic Random Phase Approximation (RRPA) with coupling to collective vibrations. The Bethe-Salpeter equation in the particle-hole channel with an energy dependent residual particle-hole (p-h) interaction is formulated and solved in the shell-model Dirac basis as well as in the momentum space. The same set of the coupling constants generates the Dirac-Hartree single-particle spectrum, the static part of the residual p-h interaction and the particle-phonon coupling amplitudes. This approach is applied to quantitative description of damping phenomenon in even-even spherical nuclei with closed shells $^{208}$Pb and $^{132}$Sn. Since the phonon coupling enriches the RRPA spectrum with a multitude of ph$\otimes$phonon states a noticeable fragmentation of giant monopole and dipole resonances is obtained in the examined nuclei. The results are compared with experimental data and with results of the non-relativistic approach.Comment: 12 pages, 4 figures, Proceedings of the NSRT06 Conferenc

Cranked Hartree-Fock-Bogoliubov Calculation for Rotating Bose-Einstein Condensates

A rotating bosonic many-body system in a harmonic trap is studied with the 3D-Cranked Hartree-Fock-Bogoliubov method at zero temperature, which has been applied to nuclear many-body systems at high spin. This method is a variational method extended from the Hartree-Fock theory, which can treat the pairing correlations in a self-consistent manner. An advantage of this method is that a finite-range interaction between constituent particles can be used in the calculation, unlike the original Gross-Pitaevskii approach. To demonstrate the validity of our method, we present a calculation for a toy model, that is, a rotating system of ten bosonic particles interacting through the repulsive quadrupole-quadrupole interaction in a harmonic trap. It is found that the yrast states, the lowest-energy states for the given total angular momentum, does not correspond to the Bose-Einstein condensate, except a few special cases. One of such cases is a vortex state, which appears when the total angular momentum $L$ is twice the particle number $N$ (i.e., $L=2N$).Comment: accepted to Phys. Rev.

Exact vortex nucleation and cooperative vortex tunneling in dilute BECs

With the imminent advent of mesoscopic rotating BECs in the lowest Landau level (LLL) regime, we explore LLL vortex nucleation. An exact many-body analysis is presented in a weakly elliptical trap for up to 400 particles. Striking non-mean field features are exposed at filling factors >>1 . Eg near the critical rotation frequency pairs of energy levels approach each other with exponential accuracy. A physical interpretation is provided by requantising a mean field theory, where 1/N plays the role of Planck's constant, revealing two vortices cooperatively tunneling between classically degenerate energy minima. The tunnel splitting variation is described in terms of frequency, particle number and ellipticity.Comment: 4 pages,4 figure

Nuclear Chemical and Mechanical Instability and the Liquid-Gas Phase Transition in Nuclei

The thermodynamic properties of nuclei are studied in a mean field model using a Skryme interaction. Properties of two component systems are investigated over the complete range of proton fraction from a system of pure neutrons to a system of only protons. Besides volume, symmetry, and Coulomb effects we also include momentum or velocity dependent forces. Applications of the results developed are then given which include nuclear mechanical and chemical instability and an associated liquid/gas phase transition in two component systems. The velocity dependence leads to further changes in the coexistence curve and nuclear mechanical and chemical instability curves.Comment: 21 pages, 9 figures, Results are changed due to error in progra