Nuclear magnetic relaxation of spin<Emphasis Type="Italic">I</Emphasis>=1/2 scalar coupled to a quadrupolar nucleus in the presence of cross-correlation effects

The rigorous treatment of relaxation for the dipolar-multipolarAX spin system (I=1/2,S>1/2) in the presence of the dipolarI-S coupling, anisotropy chemical shift and quadrupolar interaction ofS spin is proposed. The calculations of the spin evolution under the relaxation Hamiltonian are based on the second-order time-dependent perturbation theory and are carried out in the operator representation. For this task the double commutator identities of the type [[I _±S _z ⁿ ,A _q ^μp ]A _?q ^μp ] and [[I _zS _z ⁿ ,A _q ^μp ]A _?q ^μp. ] are derived. The fist-order differential equations for the evolution of longitudinal two-spin orderI _zS _z ⁿ , z=magnetization ofS spinS _z ⁿ and coherences <I _±S _z ⁿ > in the spin systemIS with scalar coupling between spin 1/2 and quadrupolar spinS>1/2 were obtained. These equations are used to get equations for the evolutions of each component of the multiplet structure of spinI. The imaginary part of the cross-correlation spectral density function and indirect spin-spin coupling Hamiltonian are taken into account. Equations for the longitudinal components of theI spin spectrum in the presence of cross-correlation effects were obtained also. Longitudinal and transverse relaxation times and cross-relaxation times in the presence of cross-correlation D-CSA, Q-CSA, Q-D were analyzed.     

Stability of Coulomb systems

The stability of m ₁ ⁺ m ₂ ⁺ m ₃ ^? m ₄ ^? Coulomb systems formed by particles of unit charge against dissociation is considered as a function of the particle mass. It is shown that, from the stability of the m ₁ ⁺ m ₂ ⁺ m ₃ ^? three-particle system, it follows that the m ₁ ⁺ m ₂ ⁺ m ₃ ^? m ₄ ^? four-particle system containing an additional particle of mass satisfying the condition m ₄ ^? ? m ₃ ^? is stable. The results of calculations of the stability domain for m ₁ ⁺ m ₂ ⁺ m ₃ ^? systems asymmetric in particle masses are reported. The stability of 39 asymmetric exotic four-particle molecules and mesic molecules against dissociation is established.     

Dominant decays of scalar leptoquarks and scalar gluons in the minimal four-color symmetry model

Fermionic and weak decays of the scalar leptoquarks S = S ₁ ⁽⁺⁾ , S ₁ ^(?) , and S _m and the scalar gluons F = F ₁ and F ₂ predicted by the minimal model involving four-color symmetry and the Higgs mechanism of quark-and lepton-mass splitting are considered. The widths and the branching ratios are calculated for these decays, and the results are analyzed versus the couplings and masses of decaying particles. It is shown that, at relatively small mass splittings Δm within scalar doublets (Δm < m _W), the fermionic decays S ₁ ⁽⁺⁾ → tl _j ⁺ , S ₁ ^(?) → v _i \(\tilde b\), S _m → t \(\tilde \nu \) _j, F ₁ → t \(\tilde b\), and F ₂ → t \(\tilde t\), which are characterized by few-GeV widths for m _S, m _F < 1 TeV and decay branching ratios close to unity, are dominant, but that, for Δm > m _W, the weak decays S → S′W and F → F’W compete with the above fermionic decays. In the case of m _S < m _t, the processes S ₁ ⁽⁺⁾ → cl _j ⁺ , S ₁ ^(?) → v _i \(\tilde b\), S _m → bl _j ⁺ , and S _m → c \(\tilde \nu \) _j, whose total branching ratios are Br(S ₁ ⁽⁺⁾ → cl ⁺) ≈ Br(S ₁ ^(?) → v \(\tilde b\)) ≈ 1, Br(S _m → bl ⁺) ≈ 0.9, and Br(S _m → c \(\tilde \nu \)) ≈ 0.1, appear to be dominant decays of scalar leptoquarks. Searches for these decays at LHC and the Tevatron are of interest.     

Depolarizing collisions in ytterbium vapor: Isotropic and anisotropic relaxation

Isotropic depolarizing collisions are studied using a stimulated photon echo with a specific polarization of the excitation radiation pulses in a mixture of ytterbium with krypton for the J = 1 ? J = 0 transition of ¹⁷⁴Yb. The difference between the relaxation rates of orientation and alignment γ _b ⁽²⁾ ? γ _b ⁽¹⁾ of the ³ P ₁(6s6p) ¹⁷⁴Yb level is measured as a function of the krypton pressure. The collision photon echo at the J = 1 ? J = 0 transition induced by the anisotropic relaxation is studied for the Yb + Xe mixture. The power of the collision echo increases from zero with the addition of a buffer gas to ytterbium, reaches an optimal level, and decreases with an increase in the buffer gas pressure. The polarization of this collision-induced echo differs from the polarization of the conventional echo. The experimental results are in qualitative agreement with theoretical predictions.     

Nonergodic state of relaxation ferroelectric Cd<Subscript>2</Subscript>Nb<Subscript>2</Subscript>O<Subscript>7</Subscript> in a constant electric field

The temperature dependence of the residual polarization of the nonergodic relaxation state (NERS) obtained from the measurements of pyroelectric current during zero-field heating (ZFH) in the temperature interval from 10 to 295 K is investigated for the Cd₂Nb₂O₇ relaxation system in two cases: (1) after sample cooling in a constant electric field E (FC) from T = 295 K to a preset temperature, which is much lower than the “freezing” temperature of the relaxation state (T _f ≈ 182 K), field removal, and subsequent cooling in zero field (ZFC) to T = 10 K and (2) after ZFC from T = 295 K to the same temperature below T _f , application of the same field, and FC to T = 10 K. The behavior of the P _r ^FC (T) and P _r ^ZFC (T) dependences is analyzed. In the field E < 2 kV/cm, the P _r ^ZFC curves as functions of 1/T have a broad low-intensity peak in the region T ≈ T _f , which vanishes in stronger fields, when the P _r ^FC (1/T) curves intersect at T ≈ T _f and have no anomalies. The difference in the behavior of P _r ^ZFC (T) and P _r ^FC (T) indicates the difference in the nature of NERS formed during ZFC and FC of the system upon a transition through T _f . In the ZFC mode, NERS exhibits glasslike behavior; in the FC regime, features of the ferroelectric behavior even in the weak field. Analogous variations of P _r ^ZFC (T) and P _r ^FC (T) in a classical ferroelectric KDP are also given for comparison.     

Influence of the dimension of a polycrystalline film and the optical anisotropy of crystallites on the effective dielectric constant of the film

The dimension D of a polycrystalline film and the optical anisotropy m = ε_z/ε_x of uniaxial crystallites with the principal components ε_x = ε_y and ε_z of the tensor of the dielectric constant have been shown to produce a strong influence on the effective dielectric constant ε_D^* and the effective refractive index n_D^* = (ε_D^*)^1/2 of the film in the optical transparency region, as well as on the boundaries of the intervals B_Dl ≤ ε_D^* ≤ B_Du. The intervals Δ₂(m) = B_2l–B_2u and Δ₃(m) = B_3l–B_3u are separated by a gap for m in the range 1 < m < 2, whereas the theoretical dependence ε₂^*(m) is separated by a gap from the interval Δ₃(m) for m in the range 1 < m < 4. This is confirmed by a comparison of the experimental (n_oP) and theoretical (n_D^*) ordinary refractive indices for uniaxial polycrystalline films of the conjugated polymer poly(p-phenylene vinylene) (PPV) with uniaxial crystallites and appropriate values of m. In the visible transparency region of the PPV films with a change in m(λ) in the range 2 < m(λ) < 3 due to the dependence of the components ε_x,z(λ) on the light wavelength λ, the refractive indices n_oP²(λ) = ε_oP(λ) are consistent with the theoretical values of ε₂^*(λ) and lie outside the interval Δ₃(m). For m(λ) > 3 near the electronic absorption band of the crystallites, the values of ε_oP(λ) lie in the region of the overlap of the intervals Δ₂(m) and Δ₃(m). The boundaries mc of the range 1 < m < m_c are determined, for which the interval Δ₂(m) is separated by a gap from the dependences ε₃^*(m) corresponding to the effective medium theory with spherical crystallites and hierarchical models of a polycrystal, as well as from the proposed new dependence ε₃^*(m).     

Probabilities of forbidden magnetic-dipole transitions in the hydrogen atom and hydrogen-like ions

Explicit formulasfor strongly forbidden magnetic-dipole transitiions between states njl and n′jl in the hydrogen atom and light hydrogen-like ions are derived. The expressions for transition probabilities are presented in the form W _{n′jl; njl} ^(M1) = D _n′n ^lj αm _e (αZ)¹⁰ (in relativistic units), where m _e is the electron mass, α is the fine-structure constant, and Z is the nuclear charge; the constants D _n′n ^lj are presented in an analytical form. Before now, only the D ₂₁ ^01/2 coefficient corresponding to the 1s _1/2–2s _1/2 transition was known in explicit form. The results obtained can be used in designing an experiment on parity violation in the hydrogen atom.     

High-frequency EPR of Cr<Superscript>2+</Superscript> ions in CdGa<Subscript>2</Subscript>S<Subscript>4</Subscript>

High-frequency broad-band (65–240 GHz) EPR is used to study impurity centers of bivalent chromium in a CdGa₂S₄ crystal. It is found that the EPR spectra correspond to tetragonal symmetry. The spin Hamiltonian H = βB · g · S + B ₂ ⁰ O ₂ ⁰ + B ₄ ⁰ O ₄ ⁰ + B ₄ ⁴ O ₄ ⁴ with the parameters B ₂ ⁰ =23659±2 MHz, B ₄ ⁰ =1.9±1 MHz, |B ₄ ⁴ |=54.2±2 MHz, g_‖=1.93±0.02, and g_⊥=1.99±0.02 is used to describe the observed spectra. It is concluded that chromium ions occupy one of the tetrahedrally coordinated cation positions.     

Long-range spin correlations in a honeycomb spin model with a magnetic field

We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h _α ? J. Such a perturbation treated in the lowest nonvanishing order over h _α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s ^z (t, r)s ^z (0, 0)》 ∝ h _z ² f(t, r), where f(t, r) ∝ [max(t, Jr)]^–4. We have studied the effects of the next order of perturbation in h _z and found an additional term of the order h _z ⁴ in the correlation function 《s ^z (t, r)s ^z (0, 0)》 which scales as h _z ⁴ cosγ/r ³ at Jt? r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by the weak imaginary vector potential A _x ∝ i h _z ² .     

Electronic structure of α-Al<Subscript>2</Subscript>O<Subscript>3</Subscript>: Ab initio simulations and comparison with experiment

Al₂O₃ films 150 Å thick are deposited on silicon by the ALD technique, and their x-ray (XPS) and ultraviolet (UPS) photoelectron spectra of the valence band are investigated. The electronic band structure of corundum (α-Al₂O₃) is calculated by the ab initio density functional method and compared with experimental results. The α-Al₂O₃ valence band consists of two subbands separated with an ionic gap. The lower band is mainly formed by oxygen 2s states. The upper band is formed by oxygen 2p states with a contribution of aluminum 3s and 3p states. A strong anisotropy of the effective mass is observed for holes: m _h⊥ ^* ≈ 6.3m ₀ and m _h‖ ^* ≈ 0.36m ₀. The effective electron mass is independent of the direction m _e‖ ^* ≈ m _e⊥ ^* ≈ 0.4m ₀.     

Dipole moment functions for electronic transitions from ion-pair states of the second tier of molecular iodine

The emission spectra caused by the transitions from the ion-pair states and f0 _g ⁺ and G1_g of the I₂ molecule are obtained by excitation of individual rovibronic levels of the molecule by the method of optical-optical double resonance. The emission spectra from the state F0 _u ⁺ populated due to collisions I₂(f) + I₂(X) are also measured. By modeling the experimental emission spectra, the dipole moment functions for the electronic transitions f _g ⁺ -B0 _u ⁺ , A0 _u ⁺ , and B″0 _u ⁺ ; G1_g-A0 _u ⁺ and B″0 _u ⁺ ; and F0 _u ⁺ -X0 _g ⁺ and a′0 _g ⁺ of the iodine molecule are reconstructed.     

Violation of light beam reversibility principle in optical media with a random quasi-zero refractive index

The relic abundance of light millicharged particles (MCPs) with the electric charge e′ = 5 × 10^–5 e and with the mass slightly below or above the electron mass is calculated. The abundance depends on the mass ratio η = m _X /m _e and for η < 1 can be high enough to allow MCPs to be the cosmological dark matter or to make a noticeable contribution to it. On the other hand, for η ? 1 the cosmological energy density of MCPs can be quite low, Ω _X h ₀ ² ≈ 0.02 for scalar MCPs, and Ω _X h ₀ ² ≈ 0.001 for spin 1/2 fermions. But even the lowest value of Ω _X h ₀ ² is in tension with several existing limits on the MCP abundances and parameters. However, these limits have been derived under some natural or reasonable assumptions on the properties of MCPs. If these assumptions are relaxed, a patch in the mass–charge plot of MCPs may appear, permitting them to be dark matter particles.     

The nature of the lower excited state of the special pair of bacterial photosynthetic reaction center of <Emphasis Type="Italic">Rhodobacter Sphaeroides</Emphasis> and the dynamics of primary charge separation

Quantum-chemical calculations of the structure in the ground and lower singlet excited states and the vibrations (in the ground state) of special pair P of photosynthetic reaction center of purple bacteria (RCPb) Rhodobacter Sphaeroides, consisting of two bacteriochlorophyll molecules P_A and P_B, have been carried out. It is shown that excitation of the special pair is followed by fast relaxation dynamics, accompanied by the transformation of the initial P* state into the P_A^δ+P_B^δ- state (δ ~ 0.5) with charge separation. This behavior is due to the presence of several nonplanar vibrations with participation of the acetyl group of macrocycle P_В in the nuclear wave packet on the potential surface of the P* state; these vibrations facilitate destabilization of the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) of the macrocycle P_A and formation of the P_A^δ+P_B^δ- state. The structural transformations in the P* state are due to its linking character in the contact region of the acetyl group-containing pyrrole rings of P_A and P_B. The transition from the P* state to specifically the P_A^δ+P_B^δ- state is related to the fact that the acetyl group P_A is involved in the intermolecular hydrogen bond with amino acid residue His^L168; for this reason, this group and the pyrrole ring linked with it can hardly participate in structural transformations. The electronic matrix element Н₁₂ of the electron transfer from the special pair in the P_A^δ+P_B^δ- state to a molecule of accessory bacteriochlorophyll В_А greatly exceeds that for the transfer to В_B. This circumstance and the fact that the P_A^δ+P_B^δ- state is energetically more favorable than the P* state facilitate the preferred directionality of the electron transfer in RCPb Rhodobacter Sphaeroides with participation of the cofactors located in its subunit L.     

Isotopically invariant dunham parameters and the potential function of the HCl molecule

The isotopically invariant Dunham parameters U _mj , Δ _mj ^H and Δ _mj ^Cl were determined by simultaneously fitting the line centers of vibration-rotation transitions of six isotopic HCl forms in the ground electronic state. Fitting included relations between U _mj values. The parameters of the isotopically invariant potential of HCl were determined using independent U _m0 and U _m1 values. The contributions to the vibrational terms of H³⁵Cl caused by violation of the Born-Oppenheimer approximation were calculated.     

Low-energy Ce spin excitations in CeFeAsO and CeFeAsO<Subscript>0.84</Subscript>F<Subscript>0.16</Subscript>

We use inelastic neutron scattering to study the low-energy spin excitations of polycrystalline samples of nonsuperconducting CeFeAsO and superconducting CeFeAsO_0.84F_0.16. Two sharp dispersionless modes are found at 0.85 and 1.16 meV in CeFeAsO below the Ce antiferromagnetic (AF) ordering temperature of T _N ^Ce ? 4 K. On warming to above T _N ^Ce ? 4 K, these two modes become one broad dispersionless mode that disappears just above the Fe ordering temperature T _N ^Fe ? 140 K. For superconducting CeFeAsO_0.84F_0.16, where Fe static AF order is suppressed, we find a weakly dispersive mode center at 0.4 meV that may arise from short-range Ce-Ce exchange interactions. Using a Heisenberg model, we simulate powder-averaged Ce spin wave excitations. Our results show that we need both Ce spin wave and crystal electric field excitations to account for the whole spectra of low-energy spin excitations.     

Hyperfine Interactions in Pb<Superscript>3+</Superscript>F<Stack><Subscript>8</Subscript><Superscript>−</Superscript></Stack>F<Stack><Subscript>a</Subscript><Superscript>−</Superscript></Stack> clusters in fluorite crystals

The parameters of hyperfine interactions in Pb³⁺F ₈ ^? F _a ^? tetragonal clusters of MeF₂ crystals (Me=Ca, Sr, Ba) are interpreted. The contributions of the spin polarization to the parameters of the proper hyperfine interaction and additional (ligand) hyperfine interactions are calculated in the approximation of weak binding between a charge-compensating ion F _a ^? and a cubic fragment in the tetragonal cluster. It is demonstrated that correct inclusion of the contributions from the spin polarization to the ligand isotropic hyperfine interaction for the F _a ^? ion leads to anomalously large parameters of this interaction for MeF₂ crystals. These results are in agreement with experimental data.     

The effect of phase noise of bichromatic radiation upon resonances of coherent population trapping

We consider the effect of the noise difference phase of a bichromatic field upon coherent population trapping resonances in the simplest three-level system in Λ configuration. The quasi-stationary solution of Bloch optical equations, which was found with some assumptions, shows that the presence of exciting short-correlated fluctuations of the phase of radiation reduces the contrast of the resonance line without affecting its spectral width. For the Gaussian phase noise the contrast suppression factor is χ = exp[?? _rms ² ], where ? _rms ² is phase dispersion. The experimental results obtained earlier by our group are analyzed.     

The Structure of Radiative Tunnel Recombination Sites in Emulsion Microcrystals of AgBr(I)

To identify the structure of emissive tunnel recombination sites in the emulsion microcrystals of silver bromide AgBr(I) with iodine contaminations and to determine the role of an emulsion medium in their formation, the temperature dependence of the luminescence spectra in the range from 77 to 120 K, the kinetics of the growth of the maximum luminescence intensity value at λ ≈ 560 nm, and the luminescence flash spectrum stimulated by the infrared light are investigated. Two types of the AgBr_{1 – x}(I _x ) (x = 0.03) microcrystals—namely, obtained in an aqueous solution and on a gelatin substrate—are used in the studies. It is established that the emissive tunnel recombination sites with a luminescence maximum at λ ≈ 560 nm in AgBr_{1 – x}(I _x ) (x = 0.03) are the {(I _a ^- I _a ^- )Ag _i ⁺ } donor–acceptor complexes with the I _a ^- iodine ions located in neighbor anionic sites of the AgBr(I) crystal lattice, next to which the Ag _i ⁺ interstitial silver ion is positioned. With an increase in the temperature, the {(I _a ^- I _a ^- )Ag _i ⁺ } sites undergo structural transformation into the {(I _a ^- I _a ^- )Ag_in⁺} sites, where n = 2, 3, …. Moreover, the {(I _a ^- I _a ^- )Ag _in ⁺ } sites (n = 2) after the capture of an electron and hole also provide the tunnel recombination with a luminescence maximum at λ ≈ 720 nm. The influence of an emulsion medium consists in that gelatin interacts with the surface electron-localization sites, i.e., the interstitial silver ions Ag _in ⁺ , n = 1, 2, and forms the complexes {Ag _in ⁰ G⁺} (n = 1, 2) with them. The latter are deeper electron traps with a small capture cross section as compared to the Ag _in ⁺ sites (n = 1, 2) and that manifest themselves in that the kinetics of the luminescence growth in AgBr(I) to a stationary level at λ ≈ 560 nm is characterized by the presence of “flash firing.” At the same time, the luminescence flash stimulated by IR light, for which the Ag _in ⁺ (n = 1, 2) electron-localization sites are responsible, is absent. It is supposed that the electrons localized on the {Ag _in ⁺ G⁺} complexes (n = 2) retain the capability for emissive tunnel recombination with holes localized on paired iodine sites with a luminescence maximum at λ ≈ 750 nm.     

Determination of the effective nuclear charge for free ions of transition metals from experimental spectra

The refined set of values of the effective nuclear charge (\(\bar Z_{ef} \)) and the set of one-electron spin-orbital constants (ξ _3d ^teor ) are obtained for ions of transition metals with the help of a semiempirical method of calculation of the spectrum of free ions with allowance for the spin-orbital interaction. The effective nuclear charge, which is a variable theoretical parameter, was determined from a comparison of theoretically calculated ion absorption spectra with experimental ones. The form of the potential for the calculation of the spin-orbital constant was chosen such that the calculated value ξ _3d ^teor would coincide with the experimental one ξ _3d ^exp . The calculated set of values \(\bar Z_{ef} \), ξ _3d ^teor } can be used in semiempirical calculations of energy levels of 3d ions (ions with an incomplete 3d shell).