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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 36 (1974), S. 157-170 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In various tabulations of such spectroscopic coefficients as the matrix elements of tensor operators or fractional parentage coefficients, it is found that many entries are unexpectedly zero. A survey is made of all cases that occur in the atomicf shell and that involve the 7-dimensional vector representation of the groupG 2. Direct explanations are given in terms of the group structure of the electronic configurations that comprise the shell. The techniques used depend on a splitting of the state space into “spin-up” and “spin-down” parts, and, for other cases, the extensive use of the methods of second quantization. TheF terms of the atomicf shell are found to split into three classes. The separation that this classification provides for the twoF terms belonging to the irreducible representation (31) ofG 2 coincides with Racah's separation. An improved separation of theH states of (31) is described.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 278 (1976), S. 117-121 
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The use of intrinsic states to resolve multiplicity difficulties in nuclear shell theory has been extended to the atomic case. If Slater determinantal product states are cast in the role of intrinsic states, it is often possible to produce final states that approximate to the physical states better than those determined by the group-theoretical procedures of Racah. The standard multiplicity separations for electrons of various azimuthal quantum numbersl can also be reproduced in many cases by a judicious choice of an intrinsic state. The usefulness of the method is limited principally by the fact that orthogonal intrinsic states do not necessarily yield orthogonal final states.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Foundations of physics 13 (1983), S. 51-59 
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Desarguesian nature of angular-momentum theory is illustrated by drawing correspondences between relations satisfied by then-j symbols and various collinearity properties of the appropriate diagrams. No examples of Pappus' theorem have been found. A relation is suggested between the operations of angular-momentum theory and Hilbert's constructions for the addition and multiplication of points on a line.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 111 (1999), S. 5706-5729 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Matrix elements of all two-electron and three-electron operators that are scalar with respect to the icosahedral group I have been tabulated for the icosahedral configurations hN. These operators represent the Coulomb interaction between electrons occupying h orbitals, and also the effects (to the lowest orders of perturbation theory) of configuration interaction on the levels of hN. States and operators are labelled by the irreducible representations (irreps) of the continuous groups SO(3) and SO(5) in addition to the irreps of I. An alternative scheme is introduced in which the irreps W of SO(5) are retained, but the orbital angular-momentum quantum numbers L associated with SO(3) are replaced by the irreps of the permutation groups S5 and S6, the latter corresponding to the interchanges (possibly nonfeasible) of the six fivefold axes of an icosahedron among themselves. The kaleidoscope operator K, which rotates the weight space of SO(5) by π/2, is an element of S5 and S6, and can be used to characterize the operators. The energy matrices in the second scheme are particularly simple, the scalar or pseudoscalar nature of the operators with respect to S5 leading to block forms either on the diagonal or off the diagonal, respectively. Operators of the former kind are invariant under the K operation and, in the hypothetical absence of the pseudoscalars, would lead to every level of icosahedral type T1 being degenerate with a level of type T2. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 2616-2622 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Generalized 6j symbols for G2 in which all four triangular conditions involve the seven-dimensional irreducible representation (irrep) (10) are multiplicity-free. Algebraic expressions depending on the highest weights of the accompanying irreps are found by using generalizations of the Racah-Wigner algebra. A rule is given for generalizing the SO(3) phase factors. The results are applied to finding algebraic expressions for a class of isoscalar factors for SO(7)&supuline;G2.
    Type of Medium: Electronic Resource
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