55017968
Series solutions for the Dirac equation in Kerr-Newman space-time
The Dirac equation is solved for an electron in a Kerr–Newman geometry using an adaptation of the procedure of Chandrasekhar. The corresponding eigenfunctions obtained can be represented as series of Jacobi polynomials. The spectrum of eigenvalues can be calculated using continued fraction techniques. Representations for the eigenvalues and eigenfunctions are obtained for various ranges of the parameters appearing in the Kerr–Newman metric. Some comments concerning the bag model of nucleons are made.
121892369
Lie theory and the wave equation in space–time. I. The Lorentz group
In this article we begin a study of the relationship between separation of variables and the conformal symmetry group of the wave equation ψtt −Δ3ψ=0 in space–time. In this first article we make a detailed study of separation of variables for the Laplace operator on the one and two sheeted hyperboloids in Minkowski space. We then restrict ourselves to homogeneous solutions of the wave equation and the Lorentz subgroup SO(3,1) of the conformal group SO(4,2). We study the various separable bases by using the methods of integral geometry as developed by Gel’fand and Graev. In most cases we give the spectral analysis for these bases, and a number of new bases are developed in detail. Many of the special function identities derived appear to be new. This preliminary study is of importance when we subsequently study models of the Hilbert space structure for solutions of the wave equation and the Klein–Gordon equation ψtt−Δ3ψ=λψ.
120822220
Separation of variables in Einstein spaces. I. Two ignorable and one null coordinate
Computes and classifies all Einstein spaces and their corresponding coordinate systems such that the Hamilton-Jacobi equation admits a separation of variables with two ignorable and one essential null coordinates. The authors find that all such spaces correspond to plane-fronted gravitational waves of Petrov type N. They also give necessary conditions which a general space-time must have in order to admit coordinates of the type studied. Furthermore, the integrability conditions for Helmholtz (Schrodinger) separability are completely solved.
120819205
Subgroups of Lie groups and separation of variables
Separable systems of coordinates for the Helmholtz equation ΔdΨ =EΨ in pseudo‐Riemannian spaces of dimension d have previously been characterized algebraically in terms of sets of commuting second order symmetry operators for the operator Δd. They have also been characterized geometrically by the form that the metric ds2=gik(x)dxidxk can take. We complement these characterizations by a group theoretical one in which the second order operators are related to continuous and discrete subgroups of G, the symmetry group of Δd. For d=3 we study all separable coordinates that can be characterized in terms of the Lie algebra L of G and show that they are of eight types, seven of which are related to the subgroup structure of G. Our method clearly generalizes to the case d≳3. Although each separable system corresponds to a pair of commuting symmetry operators, there do exist pairs of commuting symmetries S1,S2 that are not associated with separable coordinates. For subgroup related operators we show in detail just...
123571163
A classification of second‐order raising operators for Hamiltonians in two variables
We develop a group theoretic method based on results of Winternitz et al. to compute and classify all first‐ and second‐order raising and lowering operators admitted by Hamiltonians of the form H¯=−(1/2)Δ2+V(x,y). The key to our results, which generalize to higher dimensions, is a proof that H¯ admits a second‐order raising operator only if the Schrodinger equation separates in Cartesian, polar, or elliptic coordinates.
120256112
CLEBSCH--GORDAN COEFFICIENTS AND SPECIAL FUNCTION IDENTITIES. II. THE ROTATION AND LORENTZ GROUPS IN 3-SPACE.
It is shown that the construction of concrete models of Clebsch‐Gordan decompositions for tensor products of irreducible group representations leads to a wide variety of special function identities. In this paper the representation theory of the rotation and Lorentz groups in 3‐space is used to give elegant derivations of identities involving Languerre, Gegenbauer, hypergeometric, and generalized hypergeometric functions. Some of these identities may be new in this general form.
118717401
Simultaneous observations of extensive air showers and underground muons at Soudan 2
We have built a small proportional tube air shower array on the surface above the Soudan 2 proton decay detector in Soudan, Minnesota, USA. This array, in coincidence with the underground detector, allows simultaneous surface and underground observations of high energy cosmic ray showers. These observations, still in their initial stages, may eventually be able to provide information about the composition of cosmic ray primaries in the knee'' region of the energy spectrum. 4 refs.
18536843
Measurement of the underground atmospheric muon charge ratio using the MINOS Near Detector
The magnetized MINOS Near Detector, at a depth of 225 mwe, is used to measure the atmospheric muon charge ratio. The ratio of observed positive to negative atmospheric muon rates, using 301 days of data, is measured to be 1.266±0.001(stat)_(-0.014)^(+0.015)(syst). This measurement is consistent with previous results from other shallow underground detectors and is 0.108±0.019(stat+syst) lower than the measurement at the functionally identical MINOS Far Detector at a depth of 2070 mwe. This increase in charge ratio as a function of depth is consistent with an increase in the fraction of muons arising from kaon decay for increasing muon surface energies
14782259
First direct observation of muon antineutrino disappearance.
This Letter reports the first direct observation of muon antineutrino disappearance. The MINOS experiment has taken data with an accelerator beam optimized for ν(μ) production, accumulating an exposure of 1.71 × 10²⁰ protons on target. In the Far Detector, 97 charged current ν(μ) events are observed. The no-oscillation hypothesis predicts 156 events and is excluded at 6.3σ. The best fit to oscillation yields |Δm²| = [3.36(-0.40)(+0.46)(stat) ± 0.06(syst)] × 10⁻³ eV², sin²(2θ) = 0.86(-0.12)(+0.11)(stat) ± 0.01(syst). The MINOS ν(μ) and ν(μ) measurements are consistent at the 2.0% confidence level, assuming identical underlying oscillation parameters.
17785120
The silicon tracker of the beam test engineering model of the GLAST large-area telescope
The silicon tracker for the engineering model of the GLAST Large Area Telescope(LAT) has at least two unique features: it employs self triggering readout electronics, dissipating less than 200 mu-W per channel and to date represents the largest surface of silicon microstrip detectors assembled in a tracker (2.7 m{sup 2}). It demonstrates the feasibility of employing this technology for satellite based experiments, in which low power consumption, large effective areas and high reliability are required. This note describes the construction of this silicon tracker, which was installed in a beam test of positrons, hadrons and tagged photons at SLAC in December of 1999 and January of 2000.
1159458
Study of quasielastic scattering using charged-current νμ -iron interactions in the MINOS near detector
Kinematic distributions from an inclusive sample of 1.41×10^6 charged-current ν_μ interactions on iron, obtained using the MINOS near detector exposed to a wide-band beam with peak flux at 3 GeV, are compared to a conventional treatment of neutrino scattering within a Fermi gas nucleus. Results are used to guide the selection of a subsample enriched in quasielastic ν_μFe interactions, containing an estimated 123,000 quasielastic events of incident energies 1<E_ν<8  GeV, with ⟨E_ν⟩=2.79  GeV. Four additional subsamples representing topological and kinematic sideband regions to quasielastic scattering are also selected for the purpose of evaluating backgrounds. Comparisons using subsample distributions in four-momentum transfer Q^2 show the Monte Carlo model to be inadequate at low Q^2. Its shortcomings are remedied via inclusion of a Q^2-dependent suppression function for baryon resonance production, developed from the data. A chi-square fit of the resulting Monte Carlo simulation to the shape of the Q^2 distribution for the quasielastic-enriched sample is carried out with the axial-vector mass M_A of the dipole axial-vector form factor of the neutron as a free parameter. The effective M_A which best describes the data is 1.23^(+0.13)_(−0.09)(fit)^(+0.12)_(−0.15)(syst)  GeV.