Simplified Vacuum Energy Expressions for Radial Backgrounds and Domain Walls

We extend our previous results of simplified expressions for functional determinants for radial Schr\"odinger operators to the computation of vacuum energy, or mass corrections, for static but spatially radial backgrounds, and for domain wall configurations. Our method is based on the zeta function approach to the Gel'fand-Yaglom theorem, suitably extended to higher dimensional systems on separable manifolds. We find new expressions that are easy to implement numerically, for both zero and nonzero temperature.Comment: 30 page

Nuclear Propelled Vessels and Neutrino Oscillation Experiments

We study the effect of naval nuclear reactors on the study of neutrino oscillations. We find that the presence of naval reactors at unknown locations and times may limit the accuracy of future very long baseline reactor-based neutrino oscillation experiments. At the same time we argue that a nuclear powered surface ship such as a large Russian ice-breaker may provide an ideal source for precision experiments. While the relatively low reactor power would in this case require a larger detector, the source could be conveniently located at essentially any distance from a detector built at an underground location near a shore in a region of the world far away from other nuclear installations. The variable baseline would allow for a precise measurement of backgrounds and greatly reduced systematics from reactor flux and detector efficiency. In addition, once the oscillation measurement is completed, the detector could perform geological neutrino and astrophysical measurements with minimal reactor background.Comment: 4 pages, 2 figure

Re-Examination of Possible Bimodality of GALLEX Solar Neutrino Data

The histogram formed from published capture-rate measurements for the GALLEX solar neutrino experiment is bimodal, showing two distinct peaks. On the other hand, the histogram formed from published measurements derived from the similar GNO experiment is unimodal, showing only one peak. However, the two experiments differ in run durations: GALLEX runs are either three weeks or four weeks (approximately) in duration, whereas GNO runs are all about four weeks in duration. When we form 3-week and 4-week subsets of the GALLEX data, we find that the relevant histograms are unimodal. The upper peak arises mainly from the 3-week runs, and the lower peak from the 4-week runs. The 4-week subset of the GALLEX dataset is found to be similar to the GNO dataset. A recent re-analysis of GALLEX data leads to a unimodal histogram.Comment: 14 pages, 8 figure

Strong ellipticity and spectral properties of chiral bag boundary conditions

We prove strong ellipticity of chiral bag boundary conditions on even dimensional manifolds. From a knowledge of the heat kernel in an infinite cylinder, some basic properties of the zeta function are analyzed on cylindrical product manifolds of arbitrary even dimension.Comment: 16 pages, LaTeX, References adde

Optimal MRI sequences for 68Ga-PSMA-11 PET/MRI in evaluation of biochemically recurrent prostate cancer.

BackgroundPET/MRI can be used for the detection of disease in biochemical recurrence (BCR) patients imaged with 68Ga-PSMA-11 PET. This study was designed to determine the optimal MRI sequences to localize positive findings on 68Ga-PSMA-11 PET of patients with BCR after definitive therapy. Fifty-five consecutive prostate cancer patients with BCR imaged with 68Ga-PSMA-11 3.0T PET/MRI were retrospectively analyzed. Mean PSA was 7.9 ± 12.9 ng/ml, and mean PSA doubling time was 7.1 ± 6.6 months. Detection rates of anatomic correlates for prostate-specific membrane antigen (PSMA)-positive foci were evaluated on small field of view (FOV) T2, T1 post-contrast, and diffusion-weighted images. For prostate bed recurrences, the detection rate of dynamic contrast-enhanced (DCE) imaging for PSMA-positive foci was evaluated. Finally, the detection sensitivity for PSMA-avid foci on 3- and 8-min PET acquisitions was compared.ResultsPSMA-positive foci were detected in 89.1% (49/55) of patients evaluated. Small FOV T2 performed best for lymph nodes and detected correlates for all PSMA-avid lymph nodes. DCE imaging performed the best for suspected prostate bed recurrence, detecting correlates for 87.5% (14/16) of PSMA-positive prostate bed foci. The 8-min PET acquisition performed better than the 3-min acquisition for lymph nodes smaller than 1 cm, detecting 100% (57/57) of lymph nodes less than 1 cm, compared to 78.9% (45/57) for the 3-min acquisition.ConclusionPSMA PET/MRI performed well for the detection of sites of suspected recurrent disease in patients with BCR. Of the MRI sequences obtained for localization, small FOV T2 images detected the greatest proportion of PSMA-positive abdominopelvic lymph nodes and DCE imaging detected the greatest proportion of PSMA-positive prostate bed foci. The 8-min PET acquisition was superior to the 3 min acquisition for detection of small lymph nodes

Kaluza-Klein Pistons with non-Commutative Extra Dimensions

We calculate the scalar Casimir energy and Casimir force for a $R^3\times N$ Kaluza-Klein piston setup in which the extra dimensional space $N$ contains a non-commutative 2-sphere, $S_{FZ}$. The cases to be studied are $T^d\times S_{FZ}$ and $S_{FZ}$ respectively as extra dimensional spaces, with $T^d$ the $d$ dimensional commutative torus. The validity of the results and the regularization that the piston setup offers are examined in both cases. Finally we examine the 1-loop corrected Casimir energy for one piston chamber, due to the self interacting scalar field in the non-commutative geometry. The computation is done within some approximations. We compare this case for the same calculation done in Minkowski spacetime $M^D$. A discussion on the stabilization of the extra dimensional space within the piston setup follows at the end of the article.Comment: 22 page

Bose-Einstein condensation in arbitrarily shaped cavities

We discuss the phenomenon of Bose-Einstein condensation of an ideal non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the finite extension of the cavity on all thermodynamical quantities, especially on the critical temperature of the system, is considered. We use two main methods which are shown to be equivalent. The first deals with the partition function as a sum over energy levels and uses a Mellin-Barnes integral representation to extract an asymptotic formula. The second method converts the sum over the energy levels to an integral with a suitable density of states factor obtained from spectral analysis. The application to some simple cavities is discussed.Comment: 10 pages, LaTeX, to appear in Physical Review

Solar Neutrinos from CNO Electron Capture

The neutrino flux from the sun is predicted to have a CNO-cycle contribution as well as the known pp-chain component. Previously, only the fluxes from beta+ decays of 13N, 15O, and 17F have been calculated in detail. Another neutrino component that has not been widely considered is electron capture on these nuclei. We calculate the number of interactions in several solar neutrino detectors due to neutrinos from electron capture on 13N, 15O, and 17F, within the context of the Standard Solar Model. We also discuss possible non-standard models where the CNO flux is increased.Comment: 4 pages, 1 figure, submitted to Phys. Rev. C; v2 has minor changes including integration over solar volume and addition of missing reference to previous continuum electron capture calculation; v3 has minor changes including addition of references and the correction of a small (about 1%) numerical error in the table