 1  Author
 B. C. Sanctuary, M. Angala, S. K. Rish, N. An  Requires 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 counterrotating 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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 default:Reihe_A/49/ZNA199449a0071.pdf    Identifier
 ZNA199449a0071    Volume
 49  
2  Author
 D. J. Isbister, D. H. Chaplin  Requires 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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 ZNA199045a0043    Volume
 45  
3  Author
 JohnE. Harriman  Requires cookie*   Title
 Electron Densities, Momentum Densities, and Density Matrices    Abstract
 Relationships among electron coordinatespace and momentum densities and the oneelectron 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 finitebasisset 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 determined 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 constructing 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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 default:Reihe_A/48/ZNA199348a0203.pdf    Identifier
 ZNA199348a0203    Volume
 48  
5  Author
 VedeneH. Schmider, Smith, Wolf Weyrich  Requires cookie*   Title
 Hartmut    Abstract
 A recently developed method for the leastsquares reconstruction of oneparticle reduced density matrices from oneparticle 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 abinitio calculations.   
Reference
 Z. Naturforsch. 48a, 221—226 (1993); received June 3 1992   
Published
 1993   
Keywords
 Density matrix, Compton profile, Leastsquares fit, Atomic orbitals, Reconstruction   
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 ZNA199348a0221    Volume
 48  
6  Author
 DouglasM. Collins  Requires cookie*   Title
 Entropy Maximizations on Electron Density    Abstract
 Incomplete and imperfect data characterize the problem of constructing electron density representations 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 Xray 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 algorithm which, quite deterministically, adjusts a prior positive charge density distribution to agree exactly with a specified subset of structurefactor moduli by a constrained entropy maximization. Entropy on an iVrepresentable oneparticle density matrix is well defined. The entropy is the expected form, and it is a simple function of the onematrix eigenvalues which all must be nonnegative. Relationships between the entropy functional and certain properties of a onematrix 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, HohenbergKohn theorem   
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