Theoretical evaluation of the overall values of unnormalized discrepancy indices for truncated data in crystals obeying Wilson distributions

Theoretical expressions for the local values of six types of unnormalized R-indices are derived for an imperfectly related incomplete model of a crystal (centrosymmetric and non-centrosymmetric) with truncated data which is characterized by a truncation limit y _t. These indices depend on the parameters σ ₁, D and y _t. In the situations of practical interest (i.e., σ ₁ ² >0·3 and y _t<0·2) R-indices for the centro-symmetric case decrease as y _tincreases while these for the non-centro-symmetric case remain more or less constant. Contribution No. 569     

Overall values of conventional discrepancy indices for crystals with heavy atoms. Part II. Results for monoclinic and orthorhombic crystals when the heavy-atom part alone constitutes the model

Theoretical expressions of 〈y _N〉, 〈|y _N − σ₁ y _P ^c |〉 and 〈|y _N ² −σ ₁ ² (y _P ^c )²|〉 (wherey _N andy _P ^c are the normalized structure amplitudes of the structure and the model respectively) are derived in terms of the heavy atom contributionσ ₁ ² for monoclinic and orthorhombic crystals containing a few (i.e., 1 or 2) heavy atoms of the same kind per asymmetric unit by taking the heavy atom part alone as the model. Results are obtained for both the related and unrelated cases. The local values of 〈y _N〉 and 〈|y _N ⁿ − σ ₁ ⁿ (y _P ^c ) ⁿ |〉, (n=1, 2) calculated from these expressions can be used to calculate the overall values of the conventionalR-indicesR(F) andR(I) for the related and unrelated cases. These overall values could be used to check the correctness of heavy atoms located in the structure. Contribution No. 550     

Parton distributions,small-x physics and the spin structure of the nucleon

Several theoretical aspects in leading (1-loop) and higher (2-loop) order as well as various approaches of extracting leading twist-2 parton distributions from structure function measurements are discussed and summarized. Their implications for the small-x region (x⩽10⁻²) are analyzed and compared with alternative approaches where higher twist contributions (‘fans’) are added to the twist-2 LO terms in the evolution equations. The second part of these lectures deals with longitudinally polarized parton distributions related to the structure functiong ₁, in particular with various scenarios to explain the total spin structure of nucleons, including the gluon anomaly as well. Specific (realistic) tests for discriminating between these alternatives are discussed as well asx-dependent expectations, in particular for neutron targets in connection with the Bjorken sum rule. Furthermore, various theoretical expectations and sum rules for the transverse (chiral-even) structure functiong ₂ are presented and very recent developments of transverse chiral-odd (‘transversity’) distributions are briefly discussed.     

Spectra and structure of energy levels of Pr3+ in crystals of yttrium and gadolinium oxyorthosilicates

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 62, No. 6, pp. 123–129, November–December, 1995.     

Probability distributions for the overlaps and self-correlations of the pure states of ann-vector model

The probability distributions for the overlaps between and the self-correlations of the pure states of the Stanleyn-vector model with infinite-range interactions are derived. These probability distributions represent two new order parameters for the model and are intimately related to the parameters which arise naturally within the replica formalism for the treatment of the corresponding quenched random-bond model. In contrast to then = 1 Ising case, the probability distributions are nontrivial whenn > 1 and an additional parameter for self-correlation has to be introduced.     

Calculating the intensities of absorption bands of the IR spectrum for benzylidene methylamine and its deuteroanalogs

To whom correspondence should be addressd.     

Photoionization of the ground1 S e and twenty lowest excited states of the Ne-like Fe16+

TheR-matrix method is used to calculate cross-sections for the photoionization of Ne-like Fe¹⁶⁺ from ground 2s ²2p ⁶¹ S ^e and excited states belonging to 2s2p ⁶ 3l and 2s ²2p ⁵ 3l configurations. Configuration interaction wavefunctions are used to represent two target states of Fe¹⁷⁺ ion retained in theR-matrix expansion. The cross-sections are obtained as a function of kinetic energy (ε _k) of the ejected electron from 10 to 24 Ry. For low kinetic energy the cross-sections show series of Rydberg states which converge onto² S ^e threshold Fe¹⁷⁺. The calculations are carried out in the LS coupling.     

Electronic structure and magnetism of R(Fe,Si)12 (R = Y, Nd)

The newly developed full-potential linearized augmented plane wave (LAPW) and local orbitals (lo) based on standard APW methods are briefly introduced, and the structure and magnetic properties of R(Fe, Si)₁₂ compounds (R = Y, Nd) are calculated using the method. The distribution of Si at different sites is analyzed based on total energy of one crystal unit with structure having been optimized. The characters of magnetic moments, total density of states (TDOS) and partial density of states (PDOS) for different crystal sites Si occupies are obtained and analyzed. The results show that the total magnetic moments of RFe₁₀Si₂ (R = Y, Nd) are larger than those of RFe₁₀ M ₂ (M = Ti, V, Cr, Mn, Mo and W) and the hybridization mechanism is seen as follows. Si(8j) reduce the magnetic moments of Fe at three sites, however, Si(8f) mainly reduce the magnetic moments of Fe(8i) and Fe(8j) atoms. The Curie temperature is markedly enhanced by the introduction of Si atoms according to spin fluctuation of DOS at Fermi level.     

Quantum-chemical calculation of the electronic structure and excited states of ZnS and CdS clusters

Conclusion The calculations performed give, on the whole, rather promising results, though they have some drawbacks. For example, the values obtained for oscillator strengths seem to be underestimated, as a consequence of the insufficiently large number of excited configurations taken into account. This can be improved by using special algorithms for dealing with matrices of large dimensions. The authors thank V. V. Sviridov and S. V. Gaponenko for initiation of the present work. The work was carried out under financial support from the Fundamental Research Fund of the Republic of Belarus. Institute of Molecular and Atomic Physics of the Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal, Prikladnoi Spektroskopii, Vol. 63, No. 5, pp. 714–722, September–October 1996.     

Polarization of the Fluorescence Excited in the P- and R Branches of the Vibronic Lines of Jet-Cooled Complex Molecules

A model is suggested to calculate the degree of polarization of the fluorescence of jet-cooled polyatomic molecules excited within the P- and R branches of the rotational contour of the vibronic line by light not providing resolution of the rotational structure. These dependences are calculated and compared with experimental data for molecules belonging to different types of asymmetric tops with different intramolecular orientation of the fluorescence transition dipole moment: anthracene; anthracene + Ar; 1,4-diaminoanthraquinone; indole; tetracene, and triphendioxazine.     

Zeros of the helicity amplitudes of Σ−-p and Λ-p elastic scattering

The forces of interaction as reflected in the cosθ plane analytic structures of the helicity amplitudes of Σ⁻-p and Λ-p scattering are optimally exploited using the conformal mapping technique of Cutkosky and coworkers. A suitable parametrization of these amplitudes in the mapped variable is then chosen so that it can see the zeros better. These zeros are then located by making a good fit to the differential scattering cross-section curves. The effect of these zeros upon the cross-sections is discussed. Values for the phase shifts and coupling parameters between channels of fixedJ values are also computed.     

Photoionization of Al IV (neon-type) from its ground 2s 22p 6 1 S e and excited 2s 22p 53p 3,1 P 0 3 S e states using the R-matrix method

The R-matrix method is used to calculate the total photoionization cross-sections from the ground 2s ²2p ^{6 1} S ^e and the first three excited 2s ²2p ⁵3p ^3,1 S ^e states of Al IV, for photon energies ranging from the first ionization threshold to just above the second threshold of the residual ion Al V. The two lowest LS terms of Al V − 2s ²2p ^{5 2} P ⁰, 2s2p ^{6 2} S ^e, 2s2p ^{6 2} S ^e, represented by sophisticated configuration interaction wavefunctions, are included in the R-matrix calculation. The resulting cross-sections are affected by Rydberg series of resonances converging to the 2s2p ^{6 2} S ^e excited threshold.