A stochastic model for transient magnetic fields as observed by perturbed angular distribution of gamma rays

A stochastic model is introduced to study the transient magnetic field (TF) experienced by the nuclei of fast ions traversing a ferromagnetic medium. The field is assumed to arise primarily from the bound electrons of the ion, polarized by the internal magnetic field of the ferromagnetic specimen. Spin-flip scattering is considered to be the dominant mechanism for polarization transfer from the host to the ion. Electron capture and loss mechanisms are also taken into account in a phenomenological manner. An analytical expression is derived for the TF which depends on the electron capture and loss cross-sections. The result for the perturbation factor is shown to be more general than that derived by Abragam and Pound and reduces to their result in the appropriate limit.     

Time windows of various nuclear methods for the observation of spin dynamical processes

The applications of various hyperfine tools to the study of spin dynamical processes are reviewed. A few typical line shapes in the context of the Mössbauer effect and μSR derived from stochastic model calculations are discussed and the interplay of time scales associated with various processes in relation to the time window of a given probe is assessed.     

Income distribution dependence of poverty measure: A theoretical analysis

Using a modified deprivation (or poverty) function, in this paper, we theoretically study the changes in poverty with respect to the ‘global’ mean and variance of the income distribution using Indian survey data. We show that when the income obeys a log-normal distribution, a rising mean income generally indicates a reduction in poverty while an increase in the variance of the income distribution increases poverty. This altruistic view for a developing economy, however, is not tenable anymore once the poverty index is found to follow a pareto distribution. Here although a rising mean income indicates a reduction in poverty, due to the presence of an inflexion point in the poverty function, there is a critical value of the variance below which poverty decreases with increasing variance while beyond this value, poverty undergoes a steep increase followed by a decrease with respect to higher variance. Identifying this inflexion point as the poverty line, we show that the pareto poverty function satisfies all three standard axioms of a poverty index [N.C. Kakwani, Econometrica 43 (1980) 437; A.K. Sen, Econometrica 44 (1976) 219] whereas the log-normal distribution falls short of this requisite. Following these results, we make quantitative predictions to correlate a developing with a developed economy.     

Structural studies on molecular complexes,I: Crystal and molecular structure of 9-aminoacridine-sulfamethoxypyridazine (1∶1), C13H10N2·C11H12N4O3S

The crystal structure of the molecular complex of the antiseptic 9-aminoacridme and the sulfa drug sulfamethoxypyridazine (11), C₁₃H₁₀N₂·C₁₁H₁₂N₄O₃S, has been determined by X-ray diffraction methods. The crystals are orthorhombic: Pbca (No. 61),a=16.321(1),b=16.951(1),c=16.331(1) Å,Z=8,F(000)=1984, andV _c =4518.1(5) ų. The structural parameters have been refined to a finalR value of 0.046 for 3134 observed reflections. The results of X-ray analysis show that the structure contains an acridinium-sulfanilamidate ion pair. A hydrogen atom is transferred from the sulfonamide nitrogen atom to the nitrogen atom of the acridine ring, and an N(acridinium)-HN(sulfonamide) hydrogen bond is formed. A slight folding of the acridine moiety is observed.     

Study of time-dependent hyperfine interactions by PAC,Mössbauer effect, μSR and NMR: A review of stochastic models

Time-dependent hyperfine interactions constitute a useful nuclear tool for probing interactions in condensed matter. The hyperfine coupling between, say, a nucleus and its surrounding electrons in an atom, is rendered time dependent when the atom becomes a component of a many-body system. The time dependence can arise from a variety of effects, e.g., interaction of the electronic shell of the nucleus with phonons, magnons, other electrons, etc., or modulation of the electronic environment of the nucleus owing to defect kinetics, etc. The experimental methods usually employed for studying hyperfine interactions consist of the perturbed angular correlation (PAC) of -rays, the Mössbauer effect, nuclear magnetic resonance (NMR), or muon spin rotation (SR). The aim of this review is to provide a common theoretical basis for analyzing time-dependent hyperfine spectra by the above-mentioned techniques. This is achieved by expressing the experimentally measured quantity in each case in terms of an object termed the perturbation factor. With a view to calculating the latter, the time-dependent hyperfine interaction is modelled in terms of a stochastic hamiltonian. Two distinct kinds of stochastic models are considered, and their applications illustrated within a random-phase-like approximation. Various physical examples are then investigated. These include fluctuating electric quadrupolar and magnetic dipolar interactions. Comparison of the computed plots of the perturbation factor brings out the similarities and dissimilarities between the PAC, Mössbauer, SR and NMR techniques.     

Interaction Between Pd(RaaiR′)Cl<Subscript>2</Subscript> and Adenine: Reaction Dynamics and Mechanism [RaaiR′ = 1-alkyl-2-(arylazo)imidazole]

Nucleophilic substitution of Pd(RaaiR′)Cl₂ [RaaiR′=1-alkyl-2-(arylazo)imidazole, p-R—C₆H₄— N=N—C₃H₂NN-1-R′; where R= H(a)/Me(b)/Cl(c) and R′ = Et(1)/Bz(2)] with adenine (A) in MeCN–water (1:1) at 298 K, to form [Pd(A)₂]Cl₂, has been studied spectrophotometrically under pseudo-first-order conditions and the analyses support a nucleophilic association path. The reaction follows the rate law, rate = {a+k [A] ₀²[Pd(RaaiR′)Cl₂]: first-order in Pd(RaaiR′)Cl₂ and second-order in A. The rate increases as follows: Pd(RaaiEt)Cl₂(1) < Pd(RaaiBz)Cl₂(2) and Pd(MeaaiR′)Cl₂(b) < Pd(HaaiR′)Cl₂(a) < Pd(ClaaiR′)Cl₂(c). External addition of Cl⁻ (LiCl) suppresses the rate (rate 1/[Cl⁻]). The activation parameters, H⁰ and S⁰ of the reactions were calculated from the Eyring plot and support the proposed mechanism.