Configuration mixing of angular-momentum projected triaxial relativistic mean-field wave functions

The framework of relativistic energy density functionals is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum projected wave functions, generated by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The effects of triaxial deformation and of $K$-mixing is illustrated in a study of spectroscopic properties of low-spin states in $^{24}$Mg.Comment: 15 pages, 11 figures, 4 tables, accepted for publication in Phys. Rev.

Beyond the relativistic mean-field approximation (II): configuration mixing of mean-field wave functions projected on angular momentum and particle number

The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the relativistic mean-field + Lipkin-Nogami BCS equations, with a constraint on the mass quadrupole moment. The model employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a density-independent $\delta$-interaction in the pairing channel. Illustrative calculations are performed for $^{24}$Mg, $^{32}$S and $^{36}$Ar, and compared with results obtained employing the model developed in the first part of this work, i.e. without particle-number projection, as well as with the corresponding non-relativistic models based on Skyrme and Gogny effective interactions.Comment: 37 pages, 10 figures, submitted to Physical Review

Contact-allergy time

The most commonly used techniques for the in vivo evaluation of the cellular immune response include intracutaneous testing with microbial recall antigens or sensitization with neoantigens. The reliability of these tests for the individual patient usually is low due to the lack of standardization and quantification. Moreover only the efferent branch of the immune response can be judged. The dinitrochlorobenzene-contact allergy time (DNCB-CAT) is a quantitative approach for the assessment of the cellular immune response. 2% DNCBointment is applied on the upper arm in a 1 cm2 area. On the following days patch-testing with 0.05% DNCB-ointment is done on the homolateral forearm in alternating localizations till an allergic contact dermatitis reaction appears. As assessed in patients with malignant melanoma (MM, n=\\5) and with lymphoproliferative disorders (LD, η = 25), the DNCB-CAT correlates with the age of the patients and can be expressed by a formula given by the age (years) χ factor (MM = 0.16; LD = 0.17) + constant figure (MM = 5.5; LD = 4.3). There was no significant difference between the two groups or subgroups investigated. By DNCB-CAT quantitative analysis of the cellular immune response in vivo is possible. It is an appropriate model for further investigations of the cellular immunity under different clinical, histological, prognostic, and therapeutic aspects

Modeling and analysis of pinhole occulter experiment

The objectives were to improve pointing control system implementation by converting the dynamic compensator from a continuous domain representation to a discrete one; to determine pointing stability sensitivites to sensor and actuator errors by adding sensor and actuator error models to treetops and by developing an error budget for meeting pointing stability requirements; and to determine pointing performance for alternate mounting bases (space station for example)

Triaxial Angular Momentum Projection and Configuration Mixing calculations with the Gogny force

We present the first implementation in the $(\beta,\gamma)$ plane of the generator coordinate method with full triaxial angular momentum and particle number projected wave functions using the Gogny force. Technical details about the performance of the method and the convergence of the results both in the symmetry restoration and the configuration mixing parts are discussed in detail. We apply the method to the study of $^{24}$Mg, the calculated energies of excited states as well as the transition probabilities are compared to the available experimental data showing a good overall agreement. In addition, we present the RVAMPIR approach which provides a good description of the ground and gamma bands in the absence of strong mixing.Comment: 40 pages,14 figure

Lipkin translational-symmetry restoration in the mean-field and energy-density-functional methods

Based on the 1960 idea of Lipkin, the minimization of energy of a symmetry-restored mean-field state is equivalent to the minimization of a corrected energy of a symmetry-broken state with the Peierls-Yoccoz mass. It is interesting to note that the "unphysical" Peierls-Yoccoz mass, and not the true mass, appears in the Lipkin projected energy. The Peierls-Yoccoz mass can be easily calculated from the energy and overlap kernels, which allows for a systematic, albeit approximate, restoration of translational symmetry within the energy-density formalism. Analogous methods can also be implemented for all other broken symmetries.Comment: 15 LaTeX pages, 8 eps figures, submitted to Journal of Physics

Beyond the relativistic mean-field approximation: configuration mixing of angular momentum projected wave functions

We report the first study of restoration of rotational symmetry and fluctuations of the quadrupole deformation in the framework of relativistic mean-field models. A model is developed which uses the generator coordinate method to perform configuration mixing calculations of angular momentum projected wave functions, calculated in a relativistic point-coupling model. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the constrained relativistic mean-field + BCS equations in an axially deformed oscillator basis. A number of illustrative calculations are performed for the nuclei 194Hg and 32Mg, in comparison with results obtained in non-relativistic models based on Skyrme and Gogny effective interactions.Comment: 32 pages, 14 figures, submitted to Phys. Rev.

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

Density Functional Theory: Methods and Problems

The application of density functional theory to nuclear structure is discussed, highlighting the current status of the effective action approach using effective field theory, and outlining future challenges.Comment: 10 pages, 14 figures, invited talk at INT workshop on Nuclear Forces and the Quantum Many-Body Problem, Seattle, October 200