Cage motion of a probe atom in a vacancy complex in Pt

The perturbation function of a Cd probe atom bound in a hydrogen-decorated vacancy complex in Pt is found to exhibit dynamical relaxation at 294 K, as measured by the technique of perturbed γ-γ angular correlations. Based on other characteristics of the complex, a model is proposed for the structure of the complex. In the undecorated state, it consists of a probe atom at the center of a tetrahedron of vacancies in the fcc structure. In the decorated state at low temperature, the probe atom returns to one of the four vacant lattice sites. The relaxation at room temperature is attributed to motion of the probe atom in a cage formed by the four vacant sites.     

Atom transport in random two sublattice structures: analogue of the random alloy sum rule

A simple and often used model of atom transport by the vacancy mechanism on two physically distinct interpenetrating sublattices assumes that each atom–vacancy exchange frequency depends only on the species of the atom and the sublattice from which it jumps. In the kinetic theory of this model, the phenomenological coefficients can be expressed as sums of partial correlation functions, each labelled by the sublattices associated with the atoms making the first and last jumps in the sequence of correlated jumps which it represents. A sum rule, a set of exact relations among these partial correlation functions, is derived for the model, assuming arbitrary vacancy content and any number of chemical species. It reduces to a widely used sum rule for the random lattice gas [L.K. Moleko and A.R. Allnatt, Phil. Mag. A 58 677 (1988)] in the limit that atom jump frequencies are made independent of sublattice. For the two sublattice model at very low vacancy contents, a more powerful sum rule is also derived; it is essentially the same as that of Belova and Murch [Defect Diffus. Forum 194/199 547 (2001)]. The efficiencies of the three sum rules are briefly compared. The low vacancy concentration sum rule is illustrated by numerical simulations for a binary two sublattice system.     

Neutron scattering by anharmonic crystals and the effect of sublattice displacements

A theory has been given for the scattering of neutrons by anharmonic crystals, for which terms of the typeV ⁽³⁾ (k _1j1; —k _1j1;o _j) which contribute to the sublattice displacements are not neglected. Using the standard perturbation theory in the interaction picture or Green’s function method, an expression has been derived for the differential scattering cross-section which brings in the shift and the width of the phonons in one-phonon energy exchange processes. It is shown that the sublattice displacements will modify the phase factor arising from the scattering by any atom in the unit cell, and the Debye-Waller factor also gets altered both by the sublattice displacements as well as by higher order terms arising from anharmonicity. It is shown that the differential scattering cross-section contains a term linearly depending on the third order anharmonicity coefficientV ⁽³⁾ (k _1j1;k _2j2;k _3j3) and neutron scattering by crystals should provide a useful method for evaluating the third order anharmonicity coefficients.     

Hyperfine interactions of 111Cd in TiO2 (Rutile) studied by perturbed angular correlations

The time-differential perturbed angular correlation for ¹¹¹Cd nuclei has been measured after ¹¹¹In implantation into polycrystalline TiO₂. The observed perturbation functions are characterized by a well-defined electric field gradient with the quadrupole coupling constant ν_Q = 105(1) MHz and the asymmetry parameter η = 0.18(1). We attribute these hyperfine parameters to ¹¹¹Cd on the (distorted) substitutional cation site in rutile. The PAC results are compared with those in SnO₂ rutile as well as with X-ray diffraction, RBS channeling experiments and point charge model calculations including relaxation of the probe atom surrounding.     

PAC Measurements on New Ferromagnetic Compound Pd2TiSn

Magnetic hyperfine field (mhf) acting on ¹⁸¹Ta at the Ti site has been investigated in the alloy Pd₂TiSn by Perturbed Angular Correlation (PAC) measurements using the (133–482) keV – cascade in ¹⁸¹Ta following the ^– decay of ¹⁸¹Hf. The magnetic hyperfine field was measured as a function of temperature in the range of 45–1000K. The magnetization measurements were carried out with a vibrating sample magnetometer. The interpretation of the experimental results is based on the assumption that the probe nuclei occupy both the regular Ti sites as well as the Ti atom sites randomly distributed on the Pd sublattice.     

Photonic dark matter portal and quantum physics

We study a model of dark matter in which the hidden sector interacts with standard model particles via a hidden photonic portal.We investigate the effects of this new interaction on the hydrogen atom,including the Stark,Zeeman and hyperfine effects.Using the accuracy of the measurement of energy,we obtain an upper bound for the coupling constant of the model as f≤10~(-12).We also calculate the contribution from the hidden photonic portal to the anomalous magnetic moment of the muon as α_μ≤ 2.2 × 10~(-23)(for the dark particle mass scale 100MeV),which provides an important probe of physics beyond the standard model.     

Polarized velocity selective spectroscopy of atomic rubidium using counterpropagating beams

A scheme to obtain dispersion-like profiles using polarized velocity selective spectroscopy is presented. A circularly polarized pump laser beam whose frequency is scanned, and a linearly polarized, probe beam locked to a resonant frequency in the atom cross at a rubidium absorption cell. The transmitted intensities of the probe beam, with mutually perpendicular polarization directions are detected as the frequency of the pump beam is scanned. The sum of these two signals gives absorption profiles, while the difference results in dispersion profiles. This scheme is tested in the D₂ manifold of atomic rubidium. Weaker cross-over lines are found to be present and the slopes of their dispersion profiles are found to be opposite to those of the atomic transitions. This allowed an unambiguous determination of the atomic lines in both ⁸⁵Rb and ⁸⁷Rb, something that is particularly useful for the identification of the repumping transition in neutral atom trapping experiments. The dispersion profiles obtained are also suitable for frequency locking to atomic transitions or cross-over lines in both isotopes.     

Numerical analysis of the π+π− atom lifetime in ChPT

We apply Chiral perturbation theory at one loop to analyze the general formula for the π⁺π⁻ atom lifetime derived recently in the framework of QCD [A. Gall et al., Phys. Lett. B 462 (1999) 335]. The corresponding analytic expression is investigated numerically, and compared with recent work in the literature.     

Angular dependence of the PAC spectrum in a quenched single crystal of cadmium

To examine the orientation and magnitude of the electric field gradient (EFG) created by a vacancy at the¹¹¹In probe site, PAC spectra were measured in a Cd single crystal as a function of the crystal orientation after a quenching and aging treatment at 120 K. The results are compared with calculated spectra based on a point charge model of the EFG created by a vacancy at the site of the probe atom.     

Spectral characteristics of cold rubidium atoms in a dark magneto-optical trap

Spectral characteristics of rubidium atoms confined in a dark magneto-optical trap (DMOT) are measured, including probe absorption spectra and atom density as a function of the cooling and repumping laser frequencies. The trap can capture and cool more than 2.5 × 10⁸ rubidium atoms, confining them in a hyperfine state weakly perturbed by the laser beams used to form the trap. The optical density of the trapped atomic cloud approaches 9. A qualitative model of the DMOT operation is presented, based on the experimental results obtained.     

Excitation of autoionization resonances in collisions of helium atoms with fast ions

A theoretical model of collisions between fast ions and atoms is proposed which describes the effect of projectiles on the excitation of autoionization resonances. The model takes into account the change in the binding energy of electrons in a target atom induced by the field of a projectile, the effect of the field of the atom on the kinematics of the ion scattering, as well as the effect of the intermediate (1snl)¹ L states on the two-electron excitation mechanism. The charge dependence of the excitation cross section of the (2s ²)¹ S and (2s2p)¹ P resonances is found to be weaker than in the first order of the perturbation theory and is in qualitative agreement with experimental data. The reasons for the emergence of such a charge dependence are analyzed.     

On stochastic complex beam-beam interaction models with Gaussian colored noise

This paper is to continue our study on complex beam-beam interaction models in particle accelerators with random excitations Y. Xu, W. Xu, G.M. Mahmoud, On a complex beam-beam interaction model with random forcing [Physica A 336 (2004) 347-360]. The random noise is taken as the form of exponentially correlated Gaussian colored noise, and the transition probability density function is obtained in terms of a perturbation expansion of the parameter. Then the method of stochastic averaging based on perturbation technique is used to derive a Fokker-Planck equation for the transition probability density function. The solvability condition and the general transforms using the method of characteristics are proposed to obtain the approximate expressions of probability density function to order ε.Also the exact stationary probability density and the first and second moments of the amplitude are obtained, and one can find when the correlation time equals to zero, the result is identical to that derived from the Stratonovich-Khasminskii theorem for the same model under a broad-band excitation in our previous work.     

PAC Probes as Diffusion Tracers in Solids

Perturbed angular correlation (PAC) probe atoms have been used as tracers to study diffusion in solids. The method works for diffusion on a sublattice for which the point symmetry is noncubic and the electric field gradient (EFG) at the probe nucleus reorients in each jump. Such motion leads to relaxation of the nuclear quadrupole interaction. Precise values of the tracer jump frequency have been obtained from fits of measured PAC perturbation functions. Results obtained to date are reviewed for Cd tracer atoms in rare-earth indides such as LaIn3 that have the L1₂ crystal structure, for which each jump on the In-sublattice reorients the EFG by 90°. New results are presented for LaSn3 and prospects for future studies are outlined.     

NMR study of Li diffusion in β-LiAl

Diffusion of a Li atom in an anode material β-LiAl was studied over the composition range of 48.0–50.2 at % Li by the ⁷Li magnetic relaxation times. Dependence of T₁ upon temperature and the resonance frequency was successfully explained by a vacancy diffusion on the Li sublattice involving a distribution of the activation energy for migration, E_a. The central value of E_a was almost independent of the composition (? 13.8 kJ mol^-1), while the width of distribution increased with increase of the number of substituted Li on the Al sublattice. The obtained diffusion constants, extrapolated to 415°C, were larger by a factor of 1.8–3.4 than those obtained by the electrochemical method.     

Silicon diffusion in molybdenum disilicide: correlation effects

Correlation factors for silicon diffusion by a vacancy mechanism in the silicon sublattice of the tetragonal MoSi₂ structure have been calculated by combining an analytical and a Monte Carlo approach. The ratio of the silicon diffusivity perpendicular to the tetragonal axis to that parallel to the tetragonal axis is also deduced. An effect of forward correlation of tracer atom jumps in the silicon sublattice with the corresponding partial correlation factor of 1.5 appears at small frequencies of silicon atom jumps along the tetragonal axis with respect to the jump frequencies in the silicon layer perpendicular to the tetragonal axis of the MoSi₂ structure. The anisotropy of silicon diffusion in MoSi₂ measured by Salamon et al. is explained in terms of correlation effects of silicon diffusion on its own sublattice.     

Dispersion relations for stark energy shifts in hydrogen atom

On the basis of an approximate but nonperturbative expression for the energy shift δE in the ground state of the hydrogen atom in the presence of an electric field of strength , we deduce that δE has a branch point at = 0, and an asymptotic behavior ln as → ∞. These properties lead to a twice-subtracted dispersion relation for δE as a function of . The dispersion relations in conjunction with the WKB approximation and the perturbation series allow us to (i) deduce the large-n behavior of the coefficient of ⁿ in the perturbation series for δE( ) including 1/n corrections and (ii) obtain the energy shift and the level width of the ground state for a large range of values of . The agreement with the earlier numerical calculations is very satisfactory.     

Nuclear quadrupolar relaxation and the dynamics of pairs of atoms in liquids

We have developed a model calculation for the electrical field gradient correlation function on a probe atom in the liquid, c_EFG(t)=20(0)V₂₀(t)>. In this model, symmetry of the liquid is introduced explicitly and the distribution function for therelative coordinate r_i(t) between the probe atom and particle i is calculated using Smoluchowski's diffusion equation with a mean force potential Φ(r)=k_BT In g(r). The results for c_EFG(t) can be characterized by two correlation times, , the shorter one being responsible for the small values of R_Q in pure liquid metals, the longer one producing the increase of R_Q in alloys. Also good agreement is found with recent results for c_efg(t) from molecular dynamics studies.     

Resonant decay of a two state atom interacting with a massless non-relativistic quantised scalar field

We consider a model Hamiltonian derived from the interaction of an atom with a non-relativistic massless quantized field. The model atom has two states, and the interaction is linear in the field operator. We do not make the rotating wave approximation and there is no infrared cutoff. We prove that the excited state of the atom with no photons present decays at an approximately exponential rate in accordance with the predictions of time dependent perturbation theory. The proof requires some analyticity and regularity assumptions on the interaction between atom and field. These imply in particular that the interaction goes to zero at least as fast ask ², ask0, wherek is the photon momentum.     

Investigation of gamma radiation induced changes in local structure of borosilicate glass by TDPAC and EXAFS

Gamma radiation induced changes in local structure around the probe atom (Hafnium) were investigated in sodium barium borosilicate (NBS) glass, used for immobilization of high level liquid waste generated from the reprocessing plant at Trombay, Mumbai. The (NBS) glass was doped with ¹⁸¹Hf as a probe for time differential perturbed angular correlation (TDPAC) spectroscopy studies, while for studies using extended X-ray absorption fine structure (EXAFS) spectroscopy, the same was doped with 0.5 and 2 % (mole %) hafnium oxide. The irradiated as well as un-irradiated glass samples were studied by TDPAC and EXAFS techniques to obtain information about the changes (if any) around the probe atom due to gamma irradiation. TDPAC spectra of unirradiated and irradiated glasses were similar and reminescent of amorphous materials, indicating negligible effect of gamma radiation on the microstructure around Hafnium probe atom, though the quaqdrupole interaction frequency (ω _Q) and asymmetry parameter (η) did show a marginal decrease in the irradiated glass compared to that in the unirradiated glass. EXAFS measurements showed a slight decrease in the Hf-O bond distance upon gamma irradiation of Hf doped NBS glass indicating densification of the glass matrix, while the cordination number around hafnium remains unchanged.     

On the perturbation theory of critical phenomena

It is shown how, using the ideas of Brezin, Le Guillou and Zinn-Justin, one may obtain the critical properties of the φ⁴ model from renormalised perturbation theory without the use of the Callan-Symanzik equation and an associated approximation