120717466
Matrix operator symmetries of the Dirac equation and separation of variables
The set of all matrix‐valued first‐order differential operators that commute with the Dirac equation in n‐dimensional complex Euclidean space is computed. In four dimensions it is shown that all matrix‐valued second‐order differential operators that commute with the Dirac operator in four dimensions are obtained as products of first‐order operators that commute with the Dirac operator. Finally some additional coordinate systems for which the Dirac equation in Minkowski space can be solved by separation of variables are presented. These new systems are comparable to the separation in oblate spheroidal coordinates discussed by Chandrasekhar [S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford U.P., Oxford, 1983)].
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.
17212560
Superintegrability on the two-dimensional hyperboloid. II
In this work we examine the basis functions for classical and quantum mechanical systems on the two-dimensional hyperboloid that admit separation of variables in at least two coordinate systems. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup spherical coordinate cases, and the details of the structure of the quadratic symmetry algebras.
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...
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.
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.
36369065
Comparisons of annual modulations in MINOS with the event rate modulation in CoGeNT
The CoGeNT Collaboration has recently published results from a fifteen month data set which indicate an annual modulation in the event rate similar to what is expected from weakly interacting massive particle interactions. It has been suggested that the CoGeNT modulation may actually be caused by other annually modulating phenomena, specifically the flux of atmospheric muons underground or the radon level in the laboratory. We have compared the phase of the CoGeNT data modulation to that of the concurrent atmospheric muon and radon data collected by the MINOS experiment which occupies an adjacent experimental hall in the Soudan Underground Laboratory. The results presented are obtained by performing a shape-free χ^2 data-to-data comparison and from a simultaneous fit of the MINOS and CoGeNT data to phase-shifted sinusoidal functions. Both tests indicate that the phase of the CoGeNT modulation is inconsistent with the phases of the MINOS muon and radon modulations at the 3.0σ level.
55946508
Fluorocarbon evaporative cooling developments for the ATLAS pixel and semiconductor tracking detectors
We report on the development of evaporative fluorocarbon cooling for the ATLAS Pixel and SemiConductor Tracker (SCT) detectors. Data are presented from cooling studies on representative prototype Pixel and SCT detector thermo-structures, using perfluoro-npropane (C3F8), -butane (C4F10), trifluoro-iodo-methane (CF3I) and custom C3F8/C4F10 mixtures. Thermophysical properties were calculated for custom mixtures. For most of the structures tested at full projected power dissipation, operation of silicon detector substrates at temperatures below –7oC (required for 10 year lifetime in the radiation environment of LHC) should be possible, albeit in some cases with increases in inner diameter (I.D.) of the coolant tubes from those of the present series of prototypes. Heat transfer coefficients in the range 2-5.103 Wm-2K-1 have been measured in a 3.6 mm I.D. heated tube dissipating 100 Watts close to the full equivalent power (~110 W) of a barrel SCT detector “stave” over a range of power dissipations and mass flows in the above fluids. Aspects of full-scale evaporative cooling circulator design for the ATLAS experiment are discussed, together with plans for future development.
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.
16147937
New constraints on muon-neutrino to electron-neutrino transitions in MINOS
This paper reports results from a search for ν_μ → ν_e transitions by the MINOS experiment based on a 7×10^(20) protons-on-target exposure. Our observation of 54 candidate ν_e events in the far detector with a background of 49.1±7.0(stat)±2.7(syst) events predicted by the measurements in the near detector requires 2sin^2(2θ_(13))sin^2θ_(23)<0.12(0.20) at the 90% C.L. for the normal (inverted) mass hierarchy at δ_(CP)=0. The experiment sets the tightest limits to date on the value of θ_(13) for nearly all values of δ_(CP) for the normal neutrino mass hierarchy and maximal sin^2(2θ_(23)).
110729769
ATLAS pixel detector electronics and sensors
The silicon pixel tracking system for the ATLAS experiment at the Large Hadron Collider is described and the performance requirements are summarized. Detailed descriptions of the pixel detector electronics and the silicon sensors are given. The design, fabrication, assembly and performance of the pixel detector modules are presented. Data obtained from test beams as well as studies using cosmic rays are also discussed.