Orbital angular momentum crosstalk of single photons propagation in a slant non-Kolmogorov turbulence channel

We analyze the orbital angular momentum (OAM) crosstalk of single photons propagation through low-order atmospheric turbulence. The probability models of the orbital angular momentum crosstalk for single photons propagation in the channel with the non-Kolmogorov turbulence tilt, coma, and astigmatism and defocus aberration have been established. It is found, for α = 11/3, that the turbulent tilt is the dominant aberration which causes the orbital angular momentum crosstalk, the coma is second and the astigmatism is third, but the defocus aberration has no impact on OAM. The results also indicate that the regularities of orbital angular momentum crosstalk caused by the tilt, the coma and the astigmatism are almost the same, respectively. The crosstalk probability of the orbital angular momentum increases as the azimuth mode index p of Laguerre-Gaussian (LG) beam increases, the turbulent strength C_n² enhances, the orbital angular momentum quantum number rises, the diameter of circular sampling aperture D and the channel zenith angle θ increase.     

Theoretical Investigation into Production of Double-Λ Hypernuclei from Stopped Ξ − on 6Li

We have investigated theoretically a feasible nuclear reaction to produce light double-Λ hypernuclei by choosing a suitable target. In the reaction from stopped Ξ ^? on ⁶Li target light doubly-strange nuclei, ${^5_{\Lambda\Lambda}{\rm H}}$ and ${^6_{\Lambda\Lambda}{\rm He}}$ , are produced: we have calculated the formation ratio of ${^5_{\Lambda\Lambda}{\rm H}}$ to ${^6_{\Lambda\Lambda}{\rm He}}$ for Ξ ^? absorptions from 2S, 2P and 3D orbitals of Ξ ^?–⁶Li atom by assuming a d?α cluster model for ⁶Li. From this cluster model the d?α relative wave functions has a node due to Pauli exclusion among nucleons belonging to d and α clusters. Two kinds of d?α wave functions, namely 1s relative wave function with a phenomenological one-range Gaussian (ORG) potential and that of an orthogonality-condition model (OCM) are used. It is found that the probability of ${^5_{\Lambda\Lambda}{\rm H}}$ formation is larger than that of ${^6_{\Lambda\Lambda}{\rm He}}$ for all absorption orbitals: in the case of the major 3D absorption their ratio is 1.08 for ORG and 1.96 for OCM. The dominant low momentum component of the d?α relative wave function favors the ${^5_{\Lambda\Lambda}{\rm H}}$ formation with a low Q value compared to the ${^6_{\Lambda\Lambda}{\rm He}}$ formation with a high Q value. We have also calculated momentum distributions of emitted particles, d and n, displaying continuum spectra for single-Λ hypernuclei, ${^4_{\Lambda}{\rm H}}$ and ${^5_{\Lambda}{\rm He}}$ , and line spectra for the ${^5_{\Lambda\Lambda}{\rm H}}$ and ${^6_{\Lambda\Lambda}{\rm He}}$ nuclei. Thus, our present theoretical analysis would be a significant contribution to experiments in the strangeness ?2 sector of hypernuclear physics.     

Structure of geodesics in the regular Hayward black hole space-time

The regular Hayward model describes a non-singular black hole space-time. By analyzing the behaviors of effective potential and solving the equation of orbital motion, we investigate the time-like and null geodesics in the regular Hayward black hole space-time. Through detailed analyses of corresponding effective potentials for massive particles and photons, all possible orbits are numerically simulated. The results show that there may exist four orbital types in the time-like geodesics structure: planetary orbits, circular orbits, escape orbits and absorbing orbits. In addition, when \(\ell \), a convenient encoding of the central energy density \(3/8\pi \ell ^{2}\), is 0.6M, and b is 3.9512M as a specific value of angular momentum, escape orbits exist only under \(b>3.9512M\). The precession direction is also associated with values of b. With \(b=3.70M\) the bound orbits shift clockwise but counter-clockwise with \(b=5.00M\) in the regular Hayward black hole space-time. We also find that the structure of null geodesics is simpler than that of time-like geodesics. There only exist three kinds of orbits (unstable circle orbits, escape orbits and absorbing orbits).     

Equatorial circular orbits in Kerr–anti-de Sitter spacetimes

Equatorial circular orbits of test particles in the Kerr–anti-de Sitter black-hole and naked-singularity spacetimes are analyzed and their properties like the existence, orientation and stability are discussed. Due to the attractive cosmological constant ( $\varLambda <0$ ), all particles moving along equatorial orbits are still bound in the gravitational field of the central object. In general, there are two families of equatorial circular orbits. Particles moving along minus-family orbits possess negative angular momentum and, thus, they are counterrotating from the point of view of the locally non-rotating frames (LNRF). Particles moving along plus-family orbits possess, in most cases, positive angular momentum and belong to corotating particles from the point of view of the LNRF. Nevertheless, in stationary regions inside black holes and also near naked singularities with appropriately chosen value of the cosmological constant and rotational parameter $a<1.299$ , there are also counterrotating plus-family circular orbits. Moreover, in spacetimes with $a<1.089$ , some of these orbits are characterized by negative specific energy, indicating the bounding energy of the particle, moving along such an orbit, higher than its rest energy. In black-hole spacetimes, all such orbits are radially unstable, but in naked-singularity spacetimes, stable counterrotating orbits with negative specific energy exist.     

Stability of Black Holes and Black Branes

We establish a new criterion for the dynamical stability of black holes in D ≥ 4 spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamical stability is equivalent to the positivity of the canonical energy, ${\mathcal{E}}$ , on a subspace, ${\mathcal{T}}$ , of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon. This is shown by proving that—apart from pure gauge perturbations and perturbations towards other stationary black holes— ${\mathcal{E}}$ is nondegenerate on ${\mathcal{T}}$ and that, for axisymmetric perturbations, ${\mathcal{E}}$ has positive flux properties at both infinity and the horizon. We further show that ${\mathcal{E}}$ is related to the second order variations of mass, angular momentum, and horizon area by ${\mathcal{E} = \delta^2 M -\sum_A \Omega_A \delta^2 J_A - \frac{\kappa}{8\pi}\delta^2 A}$ , thereby establishing a close connection between dynamical stability and thermodynamic stability. Thermodynamic instability of a family of black holes need not imply dynamical instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that for any black brane corresponding to a thermodynamically unstable black hole, sufficiently long wavelength perturbations can be found with ${\mathcal{E} < 0}$ and vanishing linearized ADM quantities. Thus, all black branes corresponding to thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of ${\mathcal{E}}$ on ${\mathcal{T}}$ is equivalent to the satisfaction of a “ local Penrose inequality,” thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability. Although we restrict our considerations in this paper to vacuum general relativity, most of the results of this paper are derived using general Lagrangian and Hamiltonian methods and therefore can be straightforwardly generalized to allow for the presence of matter fields and/or to the case of an arbitrary diffeomorphism covariant gravitational action.     

Nucleon and {\Delta} Elastic and Transition Form Factors

We present a unified study of nucleon and \({\Delta}\) elastic and transition form factors, and compare predictions made using a framework built upon a Faddeev equation kernel and interaction vertices that possess QCD-like momentum dependence with results obtained using a symmetry-preserving treatment of a vector \({\otimes}\) vector contact-interaction. The comparison emphasises that experiments are sensitive to the momentum dependence of the running couplings and masses in the strong interaction sector of the Standard Model and highlights that the key to describing hadron properties is a veracious expression of dynamical chiral symmetry breaking in the bound-state problem. Amongst the results we describe, the following are of particular interest: \({G_{E}^{p}(Q^{2})/G_{M}^{p}(Q^{2})}\) possesses a zero at Q ² = 9.5 GeV²; any change in the interaction which shifts a zero in the proton ratio to larger Q ² relocates a zero in \({G_{E}^{n}(Q^{2})/G_M^{n}(Q^{2})}\) to smaller Q ²; there is likely a value of momentum transfer above which \({G_{E}^{n} > G_{E}^{p}}\) ; and the presence of strong diquark correlations within the nucleon is sufficient to understand empirical extractions of the flavour-separated form factors. Regarding the \({\Delta(1232)}\) -baryon, we find that, inter alia: the electric monopole form factor exhibits a zero; the electric quadrupole form factor is negative, large in magnitude, and sensitive to the nature and strength of correlations in the \({\Delta(1232)}\) Faddeev amplitude; and the magnetic octupole form factor is negative so long as rest-frame P- and D-wave correlations are included. In connection with the \({N \to \Delta}\) transition, the momentum-dependence of the magnetic transition form factor, \({G_{M}^{*}}\) , matches that of \({G_{M}^{n}}\) once the momentum transfer is high enough to pierce the meson-cloud; and the electric quadrupole ratio is a keen measure of diquark and orbital angular momentum correlations, the zero in which is obscured by meson-cloud effects on the domain currently accessible to experiment. Importantly, within each framework, identical propagators and vertices are sufficient to describe all properties discussed herein. Our analysis and predictions should therefore serve as motivation for measurement of elastic and transition form factors involving the nucleon and its resonances at high photon virtualities using modern electron-beam facilities.     

Supremum of the Airy2 Process Minus a Parabola on a Half Line

Let $\mathcal {A}_{2}(t)$ be the Airy₂ process. We show that the random variable $$\sup_{t\leq\alpha} \bigl\{\mathcal {A}_2(t)-t^2 \bigr\}+\min\{0,\alpha \}^2 $$ has the same distribution as the one-point marginal of the Airy_2→1 process at time α. These marginals form a family of distributions crossing over from the GUE Tracy-Widom distribution F _GUE(x) for the Gaussian Unitary Ensemble of random matrices, to a rescaled version of the GOE Tracy-Widom distribution F _GOE(4^1/3 x) for the Gaussian Orthogonal Ensemble. Furthermore, we show that for every α the distribution has the same right tail decay $e^{-\frac{4}{3} x^{3/2} }$ .     

Meson spectra and mass splitting of \eta_{c}^{} - J/ \psi calculated with a regularized quark potential

The complete Breit potential contains the terms of spin-spin, spin-orbit, orbit-orbit, and tensor force interactions which become singular at short distance. Most of previous calculations of the non-relativistic potential quark model considered only the spin-spin interaction and substituted the $ \delta$ (r) -function by the Gaussian or Yukawa potential in coordinate space. Recently, a method to regularize the Breit potential consists of subtracting terms that cancel the singularity at the origin but leave the intermediate- and long-distance behavior unchanged. Motivated by this work we regularize the Breit potential by multiplying the singular terms in momentum space identically by the form factor [ $ \mu^{2}_{}$ /(q ² + $ \mu^{2}_{}$ )]² of the momentum transfer q , where the screened mass μ increases with the reduced mass of the meson. With the regularized Breit potential we calculate the masses of 30 common mesons and the new $ \eta_{b}^{}$ meson. We find that the calculated masses from light to heavy mesons agree well with experimental data. The inclusion of such a dependence of the reduced mass in the potential regularization improves the spin-spin splittings of $ \eta_{c}^{}$ -J/ $ \psi$ and $ \eta_{b}^{}$ - $ \Upsilon$ (1S) . The spin-orbit and tensor force interactions in the Breit potential lead to the splittings of $ \chi_{{c0}}^{}$ , $ \chi_{{c1}}^{}$ , and $ \chi_{{c2}}^{}$ .     

Lattice QCD Towards Nuclear Forces

Recent studies of nuclear forces based on lattice QCD are presented. Not only the central potential but also the tensor potential is deduced from the Nambu?CBethe?CSalpeter wave function measured with lattice QCD. This method is applied to various kinds of nuclear potentials, such as ${V_{NN}, V_{\Lambda N}, V_{p{\Xi}^0},V_{\Lambda\Lambda-N\Xi-\Sigma\Sigma}}$ (coupled-channel potential), and ${V^{\{{\bf {27},{8}_s,{1},{10},\overline{10},{8}_a}\}}}$ (flavor representation potential). The energy dependence and the angular momentum dependence of the quenched V _NN is studied. A challenge for three-nucleon force from lattice QCD is also presented.     

Nuclear magnetic moments for J~π=2_1~+ state of ~(10)Be with ab initio Monte Carlo shell model calculation

The magnetic moment of 2+1 state for 10Be are calculated and investigated in terms of single particle orbits for protons and neutrons under the framework of ab initio Monte Carlo shell model method in an emax = 3 model space. The reduced matrix elements of orbital and spin angular momentum are evaluated. It is found that the orientations of orbital angular momentum in diferent single particle orbits are consistent. Conversely,the orientations of spin in diferent single particle orbits tend to be chaotic. The nuclear magnetic moment of 2+1 state for 10Be is obtained as 1.006N and is discussed in regards to the contribution of orbital and spin angular momentum both for protons and neutrons. The corresponding g-factor is also given.     

Gyromagnetic ratios of collective states of166Er

The static hyperfine field ofB _hf ^4.2k (ErHo) = 739(18)T of a ferromagnetic holmium single crystal polarized in an external magnetic field of ± 0.48T at ～4.2K was used for integral perturbed γ-γ angular correlation (IPAQ measurements of the g-factors of collective states of¹⁶⁶Er. The 1,200y ^166m Ho activity was used which populates the ground state band and the γ vibrational band up to high spins. The results: $$\begin{gathered} g(4_g^ + ) = + 0.315(16) \hfill \\ g(6_g^ + ) = + 0.258(11) \hfill \\ g(8_g^ + ) = + 0.262(47)and \hfill \\ g(6_\gamma ^ + ) = + 0.254(32) \hfill \\ \end{gathered}$$ exhibit a significant reduction of the g-factors with increasing rotational angular momentum. The followingE2/M1 mixing ratios of interband transitions were derived from the angular correlation coefficients: $$\begin{gathered} 5_\gamma ^ + \Rightarrow 4_g^ + :\delta (810keV) = - (36_{ - 7}^{ + 11} ) \hfill \\ 7_\gamma ^ + \Rightarrow 6_g^ + :\delta (831keV) = - (18_{ - 2}^{ + 3} )and \hfill \\ 7_\gamma ^ + \Rightarrow 8_g^ + :\delta (465keV) = - (63_{ - 12}^{ + 19} ). \hfill \\ \end{gathered}$$ The results are discussed and compared with theoretical predictions.     

Frame-dragging fields and spin 1 gravitomagnetic radiation

Experimental results published in 2004 (Ciufolini and Pavlis in Nature 431:958–960, 2004) and 2011 (Everitt et al. in Phys Rev Lett 106:221101, 1–5, 2011) have confirmed the frame-dragging phenomenon for a spinning earth predicted by Einstein’s field equations. Since this is observed as a precession caused by the gravitomagnetic (GM) field of the rotating body, these experiments may be viewed as measurements of a GM field. The effect is encapsulated in the classic steady state solution for the vector potential field $\zeta $ of a spinning sphere–a solution applying to a sphere with angular momentum J and describing a field filling space for all time (Weinberg in Gravitation and Cosmology, Wiley, New York, 1972). In a laboratory setting one may visualise the case of a sphere at rest $(\zeta =0, \text{ t}<0)$ , being spun up by an external torque at $\text{ t}=0$ to the angular momentum J: the $\zeta $ field of the textbook solution cannot establish itself instantaneously over all space at $\text{ t}=0$ , but must propagate with the velocity c, implying the existence of a travelling GM wave field yielding the textbook $\zeta $ field for large enough t (Tolstoy in Int J Theor Phys 40(5):1021–1031, 2001). The linearized GM field equations of the post-Newtonian approximation being isomorphic with Maxwell’s equations (Braginsky et al. in Phys Rev D 15(6):2047–2060, 1977), such GM waves are dipole waves of spin 1. It is well known that in purely gravitating systems conservation of angular momentum forbids the existence of dipole radiation (Misner et al. in Gravitation, Freeman & Co., New York, 1997); but this rule does not prohibit the insertion of angular momentum into the system from an external source–e.g., by applying a torque to our laboratory sphere.     

Confinement, average forces, and the Ehrenfest theorem for a one-dimensional particle

The topics of confinement, average forces, and the Ehrenfest theorem are examined for a particle in one spatial dimension. Two specific cases are considered: (i) A free particle moving on the entire real line, which is then permanently confined to a line segment or ‘a box’ (this situation is achieved by taking the limit V ₀?→?∞ in a finite well potential). This case is called ‘a particle-in-an-infinite-square-well-potential’. (ii) A free particle that has always been moving inside a box (in this case, an external potential is not necessary to confine the particle, only boundary conditions). This case is called ‘a particle-in-a-box’. After developing some basic results for the problem of a particle in a finite square well potential, the limiting procedure that allows us to obtain the average force of the infinite square well potential from the finite well potential problem is re-examined in detail. A general expression is derived for the mean value of the external classical force operator for a particle-in-an-infinite-square-well-potential, $\hat{F}$ . After calculating similar general expressions for the mean value of the position ( $\hat{X}$ ) and momentum ( $\hat{P}$ ) operators, the Ehrenfest theorem for a particle-in-an-infinite-square-well-potential (i.e., $\mathrm{d}\langle\hat{X}\rangle/\mathrm{d}t=\langle\hat{P}\rangle/M$ and $\mathrm{d}\langle\hat{P}\rangle/\mathrm{d}t=\langle\hat{F}\rangle$ ) is proven. The formal time derivatives of the mean value of the position ( $\hat{x}$ ) and momentum ( $\hat{p}$ ) operators for a particle-in-a-box are re-introduced. It is verified that these derivatives present terms that are evaluated at the ends of the box. Specifically, for the wave functions satisfying the Dirichlet boundary condition, the results, $\mathrm{d}\langle\hat{x}\rangle/\mathrm{d}t=\langle\hat{p}\rangle/M$ and $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t=\mathrm{b.t.}+\langle\hat{f}\rangle$ , are obtained where b.t. denotes a boundary term and $\hat{f}$ is the external classical force operator for the particle-in-a-box. Thus, it appears that the expected Ehrenfest theorem is not entirely verified. However, by considering a normalized complex general state that is a combination of energy eigenstates to the Hamiltonian describing a particle-in-a-box with v(x)?=?0 ( $\Rightarrow\hat{f}=0$ ), the result that the b.t. is equal to the mean value of the external classical force operator for the particle-in-an-infinite-square-well-potential is obtained, i.e., $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t$ is equal to $\langle\hat{F}\rangle$ . Moreover, the b.t. is written as the mean value of a quantity that is called boundary quantum force, f _B. Thus, the Ehrenfest theorem for a particle-in-a-box can be completed with the formula $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t=\langle{{f_\mathrm{B}}}\rangle$ .     

Spectral signs of the internal heavy-atom effect in aliphatic carbonyl compounds

The CNDO/S method has been applied to the internal effect of Si on the electronic spectrum of the acetone molecule; there is a considerable bathochromic shift and an increase in the \(S_0 \to S_{n\pi ^ * } \) intensity for theα-silyl ketones, while theβ-silyl ketons give only an increase in the intensity of \(S_0 \to S_{n\pi ^ * } \) absorption relative to acetone. The heavy atom substantially alters \(f_{S_0 \to T_{n\sigma ^* } } \) and \(\tau _{T_{n\sigma ^* } }^0 \) but has little effect on \(f_{S_0 \to T_{n\pi ^* } } \) and \(\tau _{T_{n\pi ^* } }^0 \) .     

One-range Addition Theorems for Noninteger n Slater Functions using Complete Orthonormal Sets of Exponential Type Orbitals in Standard Convention

By the use of complete orthonormal sets of ${\psi ^{(\alpha^{\ast})}}$ -exponential type orbitals ( ${\psi ^{(\alpha^{\ast})}}$ -ETOs) with integer (for α ^* = α) and noninteger self-frictional quantum number α ^*(for α ^* ≠ α) in standard convention introduced by the author, the one-range addition theorems for ${\chi }$ -noninteger n Slater type orbitals ${(\chi}$ -NISTOs) are established. These orbitals are defined as follows $$\begin{array}{ll}\psi _{nlm}^{(\alpha^*)} (\zeta ,\vec {r}) = \frac{(2\zeta )^{3/2}}{\Gamma (p_l ^* + 1)} \left[{\frac{\Gamma (q_l ^* + )}{(2n)^{\alpha ^*}(n - l - 1)!}} \right]^{1/2}e^{-\frac{x}{2}}x^{l}_1 F_1 ({-[ {n - l - 1}]; p_l ^* + 1; x})S_{lm} (\theta ,\varphi )\\ \chi _{n^*lm} (\zeta ,\vec {r}) = (2\zeta )^{3/2}\left[ {\Gamma(2n^* + 1)}\right]^{{-1}/2}x^{n^*-1}e^{-\frac{x}{2}}S_{lm}(\theta ,\varphi ),\end{array}$$ where ${x=2\zeta r, 0<\zeta <\infty , p_l ^{\ast}=2l+2-\alpha ^{\ast}, q_l ^{\ast}=n+l+1-\alpha ^{\ast}, -\infty <\alpha ^{\ast} <3 , -\infty <\alpha \leq 2,_1 F_1 }$ is the confluent hypergeometric function and ${S_{lm} (\theta ,\varphi )}$ are the complex or real spherical harmonics. The origin of the ${\psi ^{(\alpha ^{\ast})} }$ -ETOs, therefore, of the one-range addition theorems obtained in this work for ${\chi}$ -NISTOs is the self-frictional potential of the field produced by the particle itself. The obtained formulas can be useful especially in the electronic structure calculations of atoms, molecules and solids when Hartree–Fock–Roothan approximation is employed.     

The tomography of quark-gluon plasma by vector mesons

The fireball formed in a heavy ion collision is characterized by the impact parameter vector $\vec b$ , which is orthogonal to the beam direction and can be determined from the multiplicity and the angular distribution of the reaction products. By appropriate rotations the $\vec b$ vectors of each collision can be oriented into a fixed direction. Using the measured values of the momentum distributions of the vector mesons an integral equation can be formulated for the unknown emission densities $(E_M (\vec r))$ and for the unknown absorption densities $(\Delta \mu _M (\vec r,p))$ of the different vector mesons $M( \equiv \omega ^0 ,\rho ^0 ,\phi ^0 ,\psi ^0 ,\psi ^{0'} ,\Upsilon )$ .     

Localization for a Random Walk in Slowly Decreasing Random Potential

We consider a continuous time random walk X in a random environment on ?⁺ such that its potential can be approximated by the function V:?⁺→? given by $V(x)=\sigma W(x) -\frac {b}{1-\alpha}x^{1-\alpha}$ where σW a Brownian motion with diffusion coefficient σ>0 and parameters b, α are such that b>0 and 0<α<1/2. We show that P-a.s. (where P is the averaged law) $\lim_{t\to\infty} \frac{X_{t}}{(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}}=1$ with $C^{*}=\frac{2\alpha b}{\sigma^{2}(1-2\alpha)}$ . In fact, we prove that by showing that there is a trap located around $(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}$ (with corrections of smaller order) where the particle typically stays up to time t. This is in sharp contrast to what happens in the “pure” Sinai’s regime, where the location of this trap is random on the scale ln² t.     

Annihilation-type charmless radiative decays of B meson in non-universal Z′ model

We study charmless pure annihilation type radiative B decays within the QCD factorization approach. After adding the vertex corrections to the naive factorization approach, we find that the branching ratios of $\overline{B}^{0}_{d}\to\phi\gamma$ , $\overline{B}^{0}_{s}\to\rho^{0}\gamma$ and $\overline{B}^{0}_{s}\to\omega\gamma$ within the standard model are at the order of $\mathcal{O}(10^{-12})$ , $\mathcal{O}(10^{-10})$ and $\mathcal{O}(10^{-11})$ , respectively. The smallness of these decays in the standard model makes them sensitive probes of flavor physics beyond the standard model. To explore their physics potential, we have estimated the contribution of Z′ boson in the decays. Within the allowed parameter space, the branching ratios of these decay modes can be enhanced remarkably in the non-universal Z′ model: The branching ratios can reach to $\mathcal{O}(10^{-8})$ for $\overline{B}_{s}^{0}\to \rho^{0}(\omega)\gamma$ and $\mathcal{O}(10^{-10})$ for the $\overline{B}_{d}^{0}\to \phi \gamma$ , which are large enough for LHC-b and/or Super B-factories to detect those channels in near future. Moreover, we also predict large CP asymmetries in suitable parameter space. The observation of these modes could in turn help us to constrain the Z′ mass within the model.     

Gyromagnetic ratio of the 2+ rotational state of184W and observation of a large hyperfine anomaly with respect to183Wg in iron

Theg-factor of the 2⁺ rotational state of¹⁸⁴W was redetermined by an IPAC measurement in an external magnetic field of 9.45 (5)T as: $$g_{2^ + } (^{184} W) = + 0.289(7).$$ In the evaluation the remeasured half-life of the 2⁺ state: $$T_{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} (2^ + ) = 1.251(12)ns$$ was used. TDPAC-measurements with a sample of carrierfree¹⁸⁴Re in high purity iron gave the hyperfine fields: $$B_{300 K}^{hf} (^{184} W_2 + \underline {Fe} ) = 70.1(21)T$$ and $$B_{40 K}^{hf} (^{184} W_{2^ + } \underline {Fe} ) = 71.8(22)T.$$ A comparison with the hyperfine field known from a spin echo experiment with¹⁸³W _g Fe leads to the hyperfine anomaly: $$^{184} W_{2^ + } \Delta ^{183} W_g = + 0.145(36).$$ The hyperfine splitting observed in a Mössbauer source experiment with another sample of carrierfree^184m Re in high purity iron indicates that the smaller splitting, measured previously by a Mössbauer absorber experiment is due to the high tungsten concentration in the absorber. The new value for theg-factor of the 2⁺ state together with the result of the Mössbauer experiment allow an improved calibration for our recent investigation of theg _R -factors of the 4⁺ and 6⁺ rotational states. The recalculated values are: $$g_{4^ + } (^{184} W) = + 0.293(23)$$ and $$g_{6^ + } (^{184} W) = + 0.299(43).$$ The remeasured 792-111 keVγ-γ angular correlation $$W(\Theta ) = 1 - 0.034(4) \cdot P_2 + 0.325(6) \cdot P_4 $$ gives for the mixing ratio of theK-forbidden 792keV transition: $$\delta ({{E2} \mathord{\left/ {\vphantom {{E2} {M1}}} \right. \kern-\nulldelimiterspace} {M1}}) = - \left( {17.6\begin{array}{*{20}c} { + 1.8} \\ { - 1.5} \\ \end{array} } \right).$$ A detailed investigation of the attenuation ofγ-γ angular correlations in liquid sources of¹⁸⁴Re and^184m Re revealed the reason for erroneous results of early measurements of the 2⁺ g _R -factor: The time dependence of the perturbation is not of a simple exponential type. It contains an unresolved strong fast component.