Propagation-invariant beams with quantum pendulum spectra: from Bessel beams to Gaussian beam-beams

We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly-periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they resemble transversely propagating one-dimensional Gaussian wavepackets (Gaussian beam-beams). Pendulum beams are the eigenfunctions of an operator which interpolates between the squared angular momentum operator and the linear momentum operator. The analysis reveals connections with Mathieu beams, and insight into the paraxial approximation.Comment: 4 pages, 3 figures, Optics Letters styl

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

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

Genetic parameters for animal mortality in pasture-based, seasonal-calving dairy and beef herds

peer-reviewedIn the absence of informative health and welfare phenotypes, breeding for reduced animal mortality could improve overall health and welfare, provided genetic variability in animal mortality exists. The objective of the present study was to estimate genetic (and other) variance components for animal mortality in pasture-based, seasonal-calving dairy and beef herds across multiple life stages as well as to quantify the genetic relationship in mortality among life stages. National mortality records were available for all cattle born in the Republic of Ireland. Cattle were grouped into three life stages based on age (0 to 30 days, 31 to 365 days, 366 to 1095 days) whereas females with ≥1 calving event were also grouped into five life stages, based on parity number (1, 2, 3, 4, and 5), considering both the initial 60 days of lactation and a cow's entire lactation period, separately. The mean mortality prevalence ranged from 0.70 to 5.79% in young animals and from 0.53 to 3.86% in cows. Variance components and genetic correlations were estimated using linear mixed models using 21,637 to 100,993 records. Where heritability estimates were different from zero, direct heritability estimates for mortality in young animals (≤1095 days) ranged from 0.006 to 0.040, whereas the genetic standard deviation ranged from 0.015 to 0.034. The contribution of a maternal genetic effect to mortality in young animals was evident up to 30 days of age in dairy herds, but this was only the case in preliminary analysis of stillbirths in beef herds. Based on the estimated genetic standard deviation in the present study, the incidence of mortality in young animals could be reduced through breeding by up to 3.4 percentage units per generation. For cows, direct heritability estimates for mortality, where different from zero, ranged from 0.003 to 0.049. The genetic standard deviation for mortality in cows ranged from 0.005 to 0.016 during the initial 60 days of lactation and ranged from 0.011 to 0.032 during the cow's entire lactation. Genetic correlations among the age groups as well as between the age groups and cow parities had high standard errors. Genetic correlations among the cow parities were moderate to strongly positive (ranging from 0.66 to 0.99) and mostly different from zero. Results from the present study can be used to inform genetic evaluations for mortality in young animals and in cows as well as the potential genetic gain achievable

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

Effective shell model Hamiltonians from density functional theory: quadrupolar and pairing correlations

We describe a procedure for mapping a self-consistent mean-field theory (also known as density functional theory) into a shell model Hamiltonian that includes quadrupole-quadrupole and monopole pairing interactions in a truncated space. We test our method in the deformed N=Z sd-shell nuclei Ne-20, Mg-24 and Ar-36, starting from the Hartree-Fock plus BCS approximation of the USD shell model interaction. A similar procedure is then followed using the SLy4 Skyrme energy density functional in the particle-hole channel plus a zero-range density-dependent force in the pairing channel. Using the ground-state solution of this density functional theory at the Hartree-Fock plus BCS level, an effective shell model Hamiltonian is constructed. We use this mapped Hamiltonian to extract quadrupolar and pairing correlation energies beyond the mean field approximation. The rescaling of the mass quadrupole operator in the truncated shell model space is found to be almost independent of the coupling strength used in the pairing channel of the underlying mean-field theory.Comment: 15 pages, 5 figure

Relativistic Nuclear Energy Density Functionals: adjusting parameters to binding energies

We study a particular class of relativistic nuclear energy density functionals in which only nucleon degrees of freedom are explicitly used in the construction of effective interaction terms. Short-distance (high-momentum) correlations, as well as intermediate and long-range dynamics, are encoded in the medium (nucleon density) dependence of the strength functionals of an effective interaction Lagrangian. Guided by the density dependence of microscopic nucleon self-energies in nuclear matter, a phenomenological ansatz for the density-dependent coupling functionals is accurately determined in self-consistent mean-field calculations of binding energies of a large set of axially deformed nuclei. The relationship between the nuclear matter volume, surface and symmetry energies, and the corresponding predictions for nuclear masses is analyzed in detail. The resulting best-fit parametrization of the nuclear energy density functional is further tested in calculations of properties of spherical and deformed medium-heavy and heavy nuclei, including binding energies, charge radii, deformation parameters, neutron skin thickness, and excitation energies of giant multipole resonances.Comment: 53 pages, 23 figures, accepted for publication in Physical Review

The Geometry of a qq-Deformed Phase Space

The geometry of the $q$-deformed line is studied. A real differential calculus is introduced and the associated algebra of forms represented on a Hilbert space. It is found that there is a natural metric with an associated linear connection which is of zero curvature. The metric, which is formally defined in terms of differential forms, is in this simple case identifiable as an observable.Comment: latex file, 26 pp, a typing error correcte