Electron density distribution in paramagnetic chromium A gamma ray diffraction study

High accuracy single crystal structure factors, complete up to sin amp; 61553; amp; 61548; amp; 61472; amp; 61501; amp; 61472; amp; 61489; amp; 61486; amp; 61495; amp; 61496; amp; 61472; amp; 61485; amp; 61489; amp; 61484; amp; 61472; have been measured from paramagnetic chromium at 333 K using 316.5 keV gamma radiation. A detailed description of the electron density distribution is derived in terms of a multipolar atomic deformation model. There is pronounced charge asphericity in the valence region arising from preferential occupancy of the t2g subshell. The 3d charge distribution is contracted by 12.6 relative to the free atom, in accordance with magnetic synchrotron x ray and neutron measurements. By contrast, the atomic crystal scattering factor deduced from experiment is found to be in contradiction with earlier experimental and theoretical work. Achievement of a reliable Debye Waller factor is of vital importance in this context. There is no evidence for an anharmonic term in the atomic potential. Real space and energetic features of the charge density topology are used to characterize the directed metallic bonds. Special attention is paid to the form factor approximation in diffraction data analysis

Reassessment of the electron density in Cu2O using gamma ray diffraction

The electron density distribution in Cu2O has been critically reexamined to test controversial conclusions from earlier experimental and theoretical studies. The electron density is derived via multipole refinement of high quality single crystal diffraction data, collected at room temperature with 316.5 keV gamma radiation. Four gamma lines in the energy range 200 600 keV have been used to extrapolate extinction free low order structure factors. The remaining extinction corrections refine to a crystal mosaicity identical to the observed one. There is no support for anharmonic contributions to the thermal parameters. Important features of the derived electron density are i a partially filled dz2 orbital, ii an incomplete ionization of Cu and O, iii no interstitial Cu Cu charge pileup, thereby refuting the covalent bonding hypothesi

Electron density distribution in paramagnetic chromium A gamma ray diffraction study

High accuracy single crystal structure factors, complete up to sin amp; 61553; amp; 61548; amp; 61472; amp; 61501; amp; 61472; amp; 61489; amp; 61486; amp; 61495; amp; 61496; amp; 61472; amp; 61485; amp; 61489; amp; 61484; amp; 61472; have been measured from paramagnetic chromium at 333 K using 316.5 keV gamma radiation. A detailed description of the electron density distribution is derived in terms of a multipolar atomic deformation model. There is pronounced charge asphericity in the valence region arising from preferential occupancy of the t2g subshell. The 3d charge distribution is contracted by 12.6 relative to the free atom, in accordance with magnetic synchrotron x ray and neutron measurements. By contrast, the atomic crystal scattering factor deduced from experiment is found to be in contradiction with earlier experimental and theoretical work. Achievement of a reliable Debye Waller factor is of vital importance in this context. There is no evidence for an anharmonic term in the atomic potential. Real space and energetic features of the charge density topology are used to characterize the directed metallic bonds. Special attention is paid to the form factor approximation in diffraction data analysis

Probabilities from envariance?

Zurek claims to have derived Born's rule noncircularly in the context of an ontological no-collapse interpretation of quantum states, without any "deus ex machina imposition of the symptoms of classicality." After a brief review of Zurek's derivation it is argued that this claim is exaggerated if not wholly unjustified. In order to demonstrate that Born's rule arises noncircularly from deterministically evolving quantum states, it is not sufficient to assume that quantum states are somehow associated with probabilities and then prove that these probabilities are given by Born's rule. One has to show how irreducible probabilities can arise in the context of an ontological no-collapse interpretation of quantum states. It is argued that the reason why all attempts to do this have so far failed is that quantum states are fundamentally algorithms for computing correlations between possible measurement outcomes, rather than evolving ontological states.Comment: To appear in IJQI; 9 pages, LaTe

On the controversy concerning the definition of quark and gluon angular momentum

A major controversy has arisen in QCD as to how to split the total angular momentum into separate quark and gluon contributions, and as to whether the gluon angular momentum can itself be split, in a gauge invariant way, into a spin and orbital part. Several authors have proposed various answers to these questions and offered a variety of different expressions for the relevant operators. I argue that none of these is acceptable and suggest that the canonical expression for the momentum and angular momentum operators is the correct and physically meaningful one. It is then an inescapable fact that the gluon angular momentum operator cannot, in general, be split in a gauge invariant way into a spin and orbital part. However, the projection of the gluon spin onto its direction of motion i.e. its helicity is gauge invariant and is measured in deep inelastic scattering on nucleons. The Ji sum rule, relating the quark angular momentum to generalized parton distributions, though not based on the canonical operators, is shown to be correct, if interpreted with due care. I also draw attention to several interesting aspects of QED and QCD, which, to the best of my knowledge, are not commented upon in the standard textbooks on Field Theory.Comment: 41 pages; Some incorrect statements have been rectified and a detailed discussion has been added concerning the momentum carried by quarks and the Ji sum rule for the angular momentu

Radiative processes in external gravitational fields

Kinematically forbidden processes may be allowed in the presence of external gravitational fields. These ca be taken into account by introducing generalized particle momenta. The corresponding transition probabilities can then be calculated to all orders in the metric deviation from the field-free expressions by simply replacing the particle momenta with their generalized counterparts. The procedure applies to particles of any spin and to any gravitational fields. transition probabilities, emission power, and spectra are, to leading order, linear in the metric deviation. It is also shown how a small dissipation term in the particle wave equations can trigger a strong backreaction that introduces resonances in the radiative process and deeply affects the resulting gravitational background.Comment: 5 pages, 1 figur

Complications and Monitoring – Guidelines on Parenteral Nutrition, Chapter 11

Compared to enteral or hypocaloric oral nutrition, the use of PN (parenteral nutrition) is not associated with increased mortality, overall frequency of complications, or longer length of hospital stay (LOS). The risk of PN complications (e.g. refeeding-syndrome, hyperglycaemia, bone demineralisation, catheter infections) can be minimised by carefully monitoring patients and the use of nutrition support teams particularly during long-term PN. Occuring complications are e.g. the refeeding-syndrome in patients suffering from severe malnutrition with the initiation of refeeding or metabolic, hypertriglyceridemia, hyperglycaemia, osteomalacia and osteoporosis, and hepatic complications including fatty liver, non-alcoholic fatty liver disease, cholestasis, cholecystitis, and cholelithiasis. Efficient monitoring in all types of PN can result in reduced PN-associated complications and reduced costs. Water and electrolyte balance, blood sugar, and cardiovascular function should regularly be monitored during PN. Regular checks of serum electrolytes and triglycerides as well as additional monitoring measures are necessary in patients with altered renal function, electrolyte-free substrate intake, lipid infusions, and in intensive care patients. The metabolic monitoring of patients under long-term PN should be carried out according to standardised procedures. Monitoring metabolic determinants of bone metabolism is particularly important in patients receiving long-term PN. Markers of intermediary, electrolyte and trace element metabolism require regular checks

The Angular Momentum Operator in the Dirac Equation

The Dirac equation in spherically symmetric fields is separated in two different tetrad frames. One is the standard cartesian (fixed) frame and the second one is the diagonal (rotating) frame. After separating variables in the Dirac equation in spherical coordinates, and solving the corresponding eingenvalues equations associated with the angular operators, we obtain that the spinor solution in the rotating frame can be expressed in terms of Jacobi polynomials, and it is related to the standard spherical harmonics, which are the basis solution of the angular momentum in the Cartesian tetrad, by a similarity transformation.Comment: 13 pages,CPT-94/P.3027,late

The Mathematical Structure of Arrangement Channel Quantum Mechanics

A non-Hermitian matrix Hamiltonian H appears in the wavefunction form of a variety of many-body scattering theories. This operator acts on an arrangement channel Banach or Hilbert space 1(;\u27 = Ell ncr where ,r is the N-particle Hilbert space and a are certain arrangement channels. Various aspects of the spectral and semigroup theory for H are considered. The normalizable and weak (wavelike) eigenvectors ofH are naturally characterized as either physical or spurious. Typically H is scalar spectral and equivalent to H on an H-invariant subspace of physical solutions. If the eigenvectors form a basis, by constructing a suitable biorthogonal system, we show that H is scalar spectral on \u27C. Other concepts including the channel space observables, trace class and trace, density matrix and Moller operators are developed. The sense in which the theory provides a representation of N-particle quantum mechanics and its equivalence to the usual Hilbert space theory is clarified