Coherent state triplets and their inner products

It is shown that if H is a Hilbert space for a representation of a group G, then there are triplets of spaces F_H, H, F^H, in which F^H is a space of coherent state or vector coherent state wave functions and F_H is its dual relative to a conveniently defined measure. It is shown also that there is a sequence of maps F_H -> H -> F^H which facilitates the construction of the corresponding inner products. After completion if necessary, the F_H, H, and F^H, become isomorphic Hilbert spaces. It is shown that the inner product for H is often easier to evaluate in F_H than F^H. Thus, we obtain integral expressions for the inner products of coherent state and vector coherent state representations. These expressions are equivalent to the algebraic expressions of K-matrix theory, but they are frequently more efficient to apply. The construction is illustrated by many examples.Comment: 33 pages, RevTex (Latex2.09) This paper is withdrawn because it contained errors that are being correcte

The coupling of valence shell and particle-hole degrees of freedom in a partial random phase approximation

It is well known that the random phase approximation breaks down in the absence of a substantial energy gap between occupied and unoccupied single-particle states. Particle-hole excitations are then inevitably accompanied by substantial rearrangements of the particles in the neighbourhood of the Fermi surface. To accommodate this situation, a partial RPA is introduced which corresponds to replacing only the particle-hole degrees of freedom by bosons but leaving the valence space degrees of freedom intact. The PRPA is therefore a mapping of the many-fermion dynamics into the dynamics of a coupled boson-valence space. In application of the PRPA, algebraic methods, of either a fermionic or Lie algebra type, can be introduced, if desired, to facilitate the treatment of the valence space degrees of freedom. Results of applications are presented in which the valence space particles are treated in the rotational and SU(3) models, and are coupled strongly to giant dipole and quadrupole resonances.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26774/1/0000326.pd

New perspective on the U(n) Wigner-Racah calculus. I. Vector coherent state theory and construction of Gel'fand bases

Using a vector coherent state theory, it is shown that the construction of Gel'fand bases for the unitary group is particularly simple. The very specific rules for construction of the states greatly facilitate the subsequent computation of matrix elements of the generators of the u(n) Lie algebra.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48816/2/jav20i9p2241.pd

Canonical orthonormal Wigner supermultiplet basis

The explicit construction of an orthonormal basis for states of good spin, isospin and SU(4) Wigner supermultiplet symmetry is given in a Bargmann representation space. A complete set of quantum labels is provided by a Sp(3, R) contains/implies U(3) complementary symmetry.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48815/2/jav20i2p257.pd

Meteorological source variability in atmospheric gravity wave parameters derived from a tropical infrasound station

Gravity waves are an important part of the momentum budget of the atmosphere. Despite this, parameterizations of gravity wave spectra in atmospheric models are poorly constrained. Gravity waves are formed by jet streams, flow over topography and convection, all of which produce pressure perturbations as they propagate over the Earth’s surface, detectable by microbarometer arrays used for sensing infrasound. In this study, observations of gravity waves between 2007 and 2011 at an infrasound station in the Ivory Coast, West Africa are combined with meteorological data to calculate parameters such as intrinsic phase speed and wavenumber. Through spectral analysis, the seasonal and daily variations in all gravity wave parameters are examined. The gravity wave back azimuth varies with the migration of the Inter-Tropical Convergence Zone, a region of intense convection, supporting previous studies. Daily variations in gravity wave arrivals at the station can be linked to two distinct convective cycles over the land and ocean. This was achieved by combining the gravity wave parameters with lightning strikes detected by the Met Office’s Arrival Time Difference lightning detection system. Noise generated by turbulence in the middle of the day was found to attenuate smaller pressure amplitude gravity waves, artificially amplifying the daily variations in some gravity wave parameters. Detection of daily and seasonal variations in gravity wave parameters has the potential be used to improve the representation of gravity wave spectra in atmospheric models

STM Imaging of Flux Line Arrangements in the Peak Effect Regime

We present the results of a study of vortex arrangements in the peak-effect regime of 2H-NbSe_2 by scanning tunneling microscopy. By slowly increasing the temperature in a constant magnetic field, we observed a sharp transition from collective vortex motion to positional fluctuations of individual vortices at the temperature which coincides with the onset of the peak effect in ac-susceptibility. We conclude that the peak effect is a disorder driven transition, with the pinning energy winning from the elastic energy.Comment: 4 pages, 4 figures included Manuscript has been submitte

Charge-radius change and nuclear moments in the heavy tin isotopes from laser spectroscopy: Charge radius of 132^{132}Sn

NESTER ACCLaser spectroscopy measurements have been carried out on the neutron-rich tin isotopes with the COMPLIS experimental setup. Using the $5s^25p^2$ $^3P_0 \rightarrow 5s^25_p6s$ $^3P_1$ optical transition, hyperfine spectra of $^{126-132}$Sn and $^{125,127,129-131}Sn^m$ were recorded for the first time. The nuclear moments and the mean square charge radius variation ($\delta) were extracted. From the quadrupole moment values, these nuclei appear to be spherical. The magnetic moments measured are thus compared with those predicted by spherical basis approaches. From the measured$\delta, the absolute charge radii of these isotopes were deduced in particular that of the doubly magic $^{132}$Sn nucleus. The comparison of the results with several mean-field-type calculations have shown that dynamical effects play an important role in the tin isotopes

Recent results on neutron rich tin isotopes by laser spectroscopy

Laser spectroscopy measurements have been performed on neutron rich tin isotopes using the COMPLIS experimental setup. The nuclear charge radii of the even-even isotopes from A=108 to 132 are compared to the results of macroscopic and microscopic calculations. The improvements and optimizations needed to perform the isotope shift measurement on $^{134}$Sn are presented