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1994 (1)
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1Author    B. C. Sanctuary, M. Angala, S. K. Rish, N. AnRequires cookie*
 Title    Theory of NQR Pulses  
 Abstract    Pulses applied to spin systems with I > 1/2 in the absence of any external fields, the NQR case, are fundamentally different from NMR pulses. In particular, both rotating and counter-rotating components of the rf field must be kept in NQR, whereas only the "in phase" component need be retained in NMR. NQR pulses are illustrated for 7 = 3 / 2 in an axially symmetric electric field gradient (EFG). 
  Reference    Z. Naturforsch. 49a, 71—7 (1994); received October 27 1993 
  Published    1994 
  Keywords    NQR, Pulse, Density matrix, NMR 
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 TEI-XML for    default:Reihe_A/49/ZNA-1994-49a-0071.pdf 
 Identifier    ZNA-1994-49a-0071 
 Volume    49 
2Author    D. J. Isbister, D. H. ChaplinRequires cookie*
 Title    The Influence of the Skin Effect on the Amplitude of Single Pulse Gamma Detected NMR on Oriented Nuclei Signals  
 Abstract    The effects of skin depth on gamma detected single pulse Nuclear Magnetic Resonance on Oriented Nuclei (NMRON) signals are theoretically explored for narrow, intermediate and broad line metallic samples, using the density matrix approach describing a pure Zeeman system. It is shown that the skin effect distortion of the signal can dominate over intermediate to broadline distortions for that range of experimental conditions generally applicable to ferromagnetic hosts. In particular, the skin effect distortions of the first maximum, obtained when the excitation pulse width is lengthened, are significant and can determine the accuracy of calibration of the radiofrequency "(rf)" field amplitude at the resonating nuclei when assigning an average turn angle to this maximum. 
  Reference    Z. Naturforsch. 45a, 43—49 (1990); received July 7 1989 
  Published    1990 
  Keywords    NMRON, Zeeman interactions, Skin effect, Density matrix 
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 TEI-XML for    default:Reihe_A/45/ZNA-1990-45a-0043.pdf 
 Identifier    ZNA-1990-45a-0043 
 Volume    45 
3Author    JohnE. HarrimanRequires cookie*
 Title    Electron Densities, Momentum Densities, and Density Matrices  
 Abstract    Relationships among electron coordinate-space and momentum densities and the one-electron charge density matrix or Wigner function are examined. A knowledge of either or both densities places constraints on possible density matrices. Questions are approached in the context of a finite-basis-set model problem in which density matrices are elements in a Euclidean vector space of Hermitian operators or matrices, and densities are elements of other vector spaces. The maps (called "collapse") of the operator space to the density spaces define a decomposition of the operator space into orthogonal subspaces. The component of a density matrix in a given subspace is deter-mined by one density, both densities, or neither. Linear dependencies among products of basis functions play a fundamental role. Algorithms are discussed for finding the subspaces and construct-ing an orthonormal set of functions spanning the same space as a linearly dependent set. Examples are presented and additional investigations suggested. 
  Reference    Z. Naturforsch. 48a, 203—210 (1993); received October 8 1991 
  Published    1993 
  Keywords    Electron density, Momentum density, Density matrix 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0203.pdf 
 Identifier    ZNA-1993-48a-0203 
 Volume    48 
4Author    Hartmut Schmider, VedeneH. Smith, Wolf WeyrichRequires cookie*
 Title    On the Inference of the One-Particle Density Matrix from Position and Momentum-Space Form Factors  
 Abstract    A modification of a recently developed method for the least-squares reconstruction of a one-par-ticle reduced density matrix from experimentally accessible expectation values is applied to the test systems of atomic beryllium and neon. The improvement of the resulting matrices through inclusion of electron correlation is demonstrated. Their quality is judged by comparison of the moments of the position and momentum densities and of the spherically averaged density matrix in a suitable representation. 
  Reference    Z. Naturforsch. 48a, 211—220 (1993); received June 3 1992 
  Published    1993 
  Keywords    Density matrix, Reconstruction, Least-squares fit, Beryllium, Neon 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0211.pdf 
 Identifier    ZNA-1993-48a-0211 
 Volume    48 
5Author    VedeneH. Schmider, Smith, Wolf WeyrichRequires cookie*
 Title    Hartmut  
 Abstract    A recently developed method for the least-squares reconstruction of one-particle reduced density matrices from one-particle expectation values has been applied to isotropic Compton profiles of neon from the literature. The resulting densities in momentum and position space are compared with the ones obtained from ab-initio calculations. 
  Reference    Z. Naturforsch. 48a, 221—226 (1993); received June 3 1992 
  Published    1993 
  Keywords    Density matrix, Compton profile, Least-squares fit, Atomic orbitals, Reconstruction 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0221.pdf 
 Identifier    ZNA-1993-48a-0221 
 Volume    48 
6Author    DouglasM. CollinsRequires cookie*
 Title    Entropy Maximizations on Electron Density  
 Abstract    Incomplete and imperfect data characterize the problem of constructing electron density represen-tations from experimental information. One fundamental concern is identification of the proper protocol for including new information at any stage of a density reconstruction. An axiomatic approach developed in other fields specifies entropy maximization as the desired protocol. In particular, if new data are used to modify a prior charge density distribution without adding extraneous prejudice, the new distribution must both agree with all the data, new and old, and be a function of maximum relative entropy. The functional form of relative entropy is a = — g In (g/z), where g and x respectively refer to new and prior distributions normalized to a common scale. Entropy maximization has been used to deal with certain aspects of the phase problem of X-ray diffraction. Varying degrees of success have marked the work which may be roughly assigned to categories as direct methods, data reduction and analysis, and image enhancement. Much of the work has been expressed in probabilistic language, although image enhancement has been somewhat more physical or geometric in description. Whatever the language, entropy maximization is a specific and deterministic functional manipulation. A recent advance has been the description of an al-gorithm which, quite deterministically, adjusts a prior positive charge density distribution to agree exactly with a specified subset of structure-factor moduli by a constrained entropy maximization. Entropy on an iV-representable one-particle density matrix is well defined. The entropy is the expected form, and it is a simple function of the one-matrix eigenvalues which all must be non-neg-ative. Relationships between the entropy functional and certain properties of a one-matrix are discussed, as well as a conjecture concerning the physical interpretation of entropy. Throughout this work reference is made to informational entropy, not the entropy of thermodynamics. 
  Reference    Z. Naturforsch. 48a, 68—74 (1993); received May 26 1992 
  Published    1993 
  Keywords    Charge density, Correlation energy, Density matrix, Entropy maximization, Hohenberg-Kohn theorem 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0068.pdf 
 Identifier    ZNA-1993-48a-0068 
 Volume    48 
7Author    Jean-Louis CalaisRequires cookie*
 Title    Momentum Distribution and Charge Density in Solid-State Theory  
 Abstract    We present a discussion of a number of conceptual and methodological aspects associated with the theoretical characterization and computation of charge densities and momentum distributions in solids. The main ambition has been to stress properties that both exact and approximate quantities must possess. We have also attempted to point out conceptual and computational trends which would seem to be of importance for the future of the subject. 
  Reference    Z. Naturforsch. 48a, 151—158 (1993); received May 14 1992 
  Published    1993 
  Keywords    Solid-state theory, Charge density, Momentum density, Density matrices, Hartree-Fock approximation, Density functional theory 
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 TEI-XML for    default:Reihe_A/48/ZNA-1993-48a-0151.pdf 
 Identifier    ZNA-1993-48a-0151 
 Volume    48