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In this paper we describe an approach to Casimir Force problems that is ultimately generalizable to all fields, boundary conditions, and cavity geometries. This approach utilizes locally defined reflection amplitudes to express the energy per unit area of any Casimir interaction. To demonstrate this approach we solve a number of Casimir Force problems including the case of uniaxial boundary conditions in a parallel-plate cavity., 9 pages, 5 figures, Equation 18 has been corrected, [v1] contained a typo

Double beta decay of $^{128}\mathrm{Te}$ has been confirmed and the ratio of half-lives for \ensuremath{\beta}\ensuremath{\beta} decay of $^{130}\mathrm{Te}$ and $^{128}\mathrm{Te}$ has been precisely determined as ${\mathit{T}}_{1/2}^{130}$/${\mathit{T}}_{1/2}^{128}$=(3.52\ifmmode\pm\else\textpm\fi{}0.11)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ by ion-counting mass spectrometry of Xe in ancient Te ores, using techniques that reduce interferences due to trapped Xe. We have also detected excesses of $^{126}\mathrm{Xe}$ originating in high energy reactions of cosmic ray muons and their secondaries on Te; such reactions make minor contributions to the measured $^{128}\mathrm{Xe}$ excesses in the Te ores. The Xe measurements, combined with common Pb dating of the ores, yield a $^{130}\mathrm{Te}$ half-life of (2.7\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{21}$ yr and thus a $^{128}\mathrm{Te}$ half-life of (7.7\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}${10}^{24}$ yr, the longest radioactive decay lifetime measured to date. These results give limits on the effective Majorana mass of the neutrino (1.1--1.5 eV) and right-handed currents (\ensuremath{\Vert}〈\ensuremath{\eta}〉\ensuremath{\Vert}5.3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$) comparable to the best obtained from direct neutrinoless \ensuremath{\beta}\ensuremath{\beta}-decay searches. They also imply new limits on unconventional Majorons not constrained by measurements of the ${\mathit{Z}}^{0}$ decay width.

Double beta decay of $^{128}\mathrm{Te}$ has been confirmed and the ratio of half-lives for \ensuremath{\beta}\ensuremath{\beta} decay of $^{130}\mathrm{Te}$ and $^{128}\mathrm{Te}$ has been determiend as $^{130}\mathrm{Te}_{1/2}$${/}^{128}$${\mathrm{Te}}_{1/2}$=(3.52\ifmmode\pm\else\textpm\fi{}0.11)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ by ion-counting mass spectrometry of Xe in ancient Te ores. The Xe measurements, combined with common Pb dating, yield a $^{130}\mathrm{Te}$ half-life of (2.7\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{21}$ yr and thus a $^{128}\mathrm{Te}$ half-life of (7.7\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}${10}^{24}$ yr. These results give limits on the effective Majorana mass of the neutrino (1.1-1.5 eV) and right-handed currents (\ensuremath{\Vert}〈\ensuremath{\eta}〉\ensuremath{\Vert}g5.3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8)}$ comparable to the best obtained from direct neutrinoless \ensuremath{\beta}\ensuremath{\beta}-decay searches. They also imply new limits on nonstandard Majorons not constrained by measurements of the ${\mathit{Z}}^{0}$ decay width.

The rotations around the vertical axis associated with the normal mode oscillations of the Earth and those induced by the seismic and other disturbances have been very difficult to observe directly. Such observations will provide additional information for 3D modeling of the Earth and for understanding earthquakes and other underground explosions. In this paper, we describe the design of an instrument capable of measuring the rotational motions associated with the seismic oscillations of the Earth, including the lowest frequency normal mode at ν ≈ 3.7 × 10 −4 Hz. The instrument consists of a torsion balance with a natural frequency of ν 0 ≈ 1.6 × 10 −4 Hz, which is observed by an autocollimating optical lever of high angular resolution and dynamic range. Thermal noise limits the sensitivity of the apparatus to amplitudes of ≈ 1.5 × 10 −9 rad at the lowest frequency normal mode and the sensitivity improves as ν −3/2 with increasing frequency. Further improvements in sensitivity by about two orders of magnitude may be achieved by operating the balance at cryogenic temperatures. Alternatively, the instrument can be made more robust with a reduced sensitivity by increasing ν 0 to ≈10 −2 Hz. This instrument thus complements the ongoing effort by Igel and others to study rotational motions using ring laser gyroscopes and constitutes a positive response to the clarion call for developments in rotation seismology by Igel, Lee, and Todorovska [H. Igel, W.H.K. Lee and M.I. Todorovska, AGU Fall Meeting 2006, Rotational Seismology Sessions: S22A,S23B, Inauguration of the International Working Group on Rotational Seismology (IWGoRS) ].

Most of the powerful astronomical objects discovered over the past three decades appear to be energised by the accretion of matter on to condensed massive bodies residing in their centres. X-ray binaries, active galactic nuclei, extragalactic double radio sources displaying relativistic jets and other such interesting phenomena are some examples for which an important part of the gravitational energy associated with the inflow of matter is radiated away as non-thermal particles and quanta. Excellent overviews of the relevant astronomical literature and of the physical processes related with accretion flows on to black holes are provided by Rees [1], Begelman et al.[2] and by Frank et al. [3]. In recent years the evidence for the existence of both supermassive black holes (M BH ~ 106 — 108 M ⊙) and stellar mass black holes is accumulating rapidly [4–7].

Propagation of cosmic rays is discussed with the intent of deriving results relevent to the origin of cosmic rays. Starting from a brief description of the methods for demodulating the effects of the solar wind on the spectra of particles, we describe an accurate method for correcting for spallation effects on the cosmic-ray nuclei during their transport from the sources subsequent to their acceleration. We present the composition of cosmic rays at the sources and discuss its implications to their origin. We discuss briefly the effects of stochastic acceleration in the interstellar medium on the relative spectra of primaries and secondaries in cosmic rays and show that the observation of decreasing relative abundance of secondaries with increasing energy rules out such phenomena for galactic cosmic rays. The spectrum of cosmic-ray electrons is discussed in terms of contributions from a discrete set of sources situated at various distances from the solar system on the galactic plane. We show that unless there are at least 3.104 sources actively accelerating cosmis rays in the Galaxy the spectrum of electrons would have a premature cut-off at high energies. Finally we point out some important questions that need to be clearly resolved for making further progress in the field.

Damping of the ΔB = 2 n− n oscillations due to the removal of the degeneracy in interactions with ambient nuclear and electromagnetic fields is discussed. These considerations are then applied to the experiments performed deep underground to yield a lower limit to the oscillation time of ≈5 × 107 s with 90% confidence. Some astrophysical consequences of such oscillations are briefly mentioned.

Cosmic rays origin, discussing nuclear, electron and electromagnetic components, supernovae, pulsars, white dwarfs and gas motions in Galactic Center

Calculations of the longitudinal development of air showers initiated by protons and heavy primaries are made. A comparison of the characteristics indicates that the separation of the heavy nucleus and proton-initiated showers is difficult. The size dependence of the number of muons of energy greater than 1, 220, and 660 GeV is shown to be consistent with the existence of a rigidity cutoff of galactic cosmic rays at ~ 105 GV, followed by an extragalactic component of protons at higher energies. The lateral distribution of 220-GeV muons in air showers is shown to be consistent with a mean transverse momentum of less than 1 GeV per pion.

A radio survey of X-ray emitting globular clusters has been conducted at 327 MHz and the results are presented. Fourteen radio sources are detected within the total area encompassed by one tidal radius of the clusters. Statistically, there is no excess of radio sources in these fields, but two sources are found which may be associated with the globular clusters NGC 5272 and NGC 6656. Significant differences in positional coincidence, radio flux density, and size of the radio sources are found with some of the earlier radio observation of similar nature. The nature of a double-lobed radio structure detected for the X-ray source 1E 1339.9+28 is discussed. 28 refs.