119430316
Complete sets of commuting operators and O (3) scalars in the enveloping algebra of SU (3)
We consider the ``missing label'' problem for basis vectors of SU(3) representations in a basis corresponding to the group reduction SU(3)⊃O(3)⊃O(2). We prove that only two independent O (3) scalars exist in the enveloping algebra of S U (3), in addition to the obvious ones, namely the angular momentum L2 and the two SU(3) Casimir operators C(2) and C(3). Any one of these two operators (of third and fourth order in the generators) can be added to C(2), C(3), L2, and L3 to form a complete set of commuting operators. The eigenvalues of the third and fourth order scalars X(3) and X(4) are calculated analytically or numerically for many cases of physical interest. The methods developed in this article can be used to resolve a missing label problem for any semisimple group G, when reduced to any semisimple subgroup H.
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.
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...
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)].
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.
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.
122216729
Underground Muons from the Direction of Cygnus X-3 during the January 1991 Radio Flare
Abstract Muons recorded in the Soudan 2 underground nucleon decay detector from January 1989 to February 1991 have been examined for any correlation with the radio flares of Cygnus X-3 observed during this period. On two nearby days during the radio flare of January 1991 a total of 32 muons within 2.0° of the Cygnus X-3 direction were observed when 11.4 were expected.
123128720
Observation of a shadow of the Moon in the underground muon flux in the Soudan 2 detector
A shadow of the Moon, with a statistical significance of 5{sigma}, has been observed in the underground muon flux at a depth of 2090 mwe using the Soudan 2 detector. The angular resolution of the detector is well described by a Gaussian with a sigma {<=}0.3 degree sign . The position of the shadow confirms that the alignment of the detector is known to better than 0.15 degree sign and has remained stable during ten years of data taking. (c) 2000 The American Physical Society.
123121317
The CLEO III silicon tracker
Abstract The Cornell Electron Storage Ring is being upgraded to B-factory luminosities. The CLEO detector is also being upgraded with a new charged particle tracking system and with the addition of a ring imaging Cerenkov particle identification system. A major part of the tracking system upgrade is the construction of a new four-layer double-sided silicon tracker with 93% solid angle coverage and new readout electronics. The status of the silicon tracker including production tests and the expected performance of the final system are discussed.
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)).
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.