Semiempirical investigation of perturbations of the g factors of electronic-vibrational-rotational levels of hydrogen: III. The r 3Π g − and s 3Δ g − states of the H2 and D2 molecules

The g factors of rovibrational levels of the (4d)r ³Π _g ^? and (4d)s ³Δ _g ^? states of the H₂ and D₂ molecules have been obtained for the first time. These values were found within the nonadiabatic model taking into account the interaction of the 4dπ³Π_g and 4dδ³Δ_g states in the pure precession approximation using semiempirical values of the expansion coefficients of the wave function in an adiabatic basis, which was obtained for the first time for the states of the triplet 4d complex of terms of the hydrogen molecules, and the results of numerical calculation of the overlap integrals of the vibrational wave functions of these states. It is established that the interference effects of the interaction between the 4dπ³Π _g ^? and 4dδ³Δ _g ^? states lead to significant (up to 7 times for the r ³Π _g ^? state of the H₂ and D₂ molecules and 70 and 8 times for the s ³Δ _g ^? state of the H₂ and D₂ molecules, respectively) differences between the nonadiabatic values of the g factors and the corresponding adiabatic values. It is found that the perturbed values of the g factors are much closer to the values corresponding to the case of Hund’s d coupling of angular momenta than to the values corresponding to the b coupling. It is established that the perturbations of the g factors of rovibrational levels of the states of the 4d complex of terms are much greater (up to 2 times for the ³Π _g ^? states and 350 times for the ³Δ _g ^? states) than the perturbations of the same characteristics for the 3d complex of terms of the hydrogen molecule with the same vibrational and rotational quantum numbers.     

Probabilities of rovibronic transitions in the I 1Π g − , J 1Δ g − →C 1Π ± u systems of bands of the deuterium molecule

Probabilities of spontaneous rovibronic transitions I ¹Π _g ^? , v′ J′, J ¹Δ _g ^? , v′, J′→C ¹Π _u ^± , v″, J″ of the D₂ molecule (for vibrational and rotational quantum numbers v′=v″=0–3 and J′=1–9, J″=J′±1) have been obtained for the first time. They were determined using (1) the previously proposed nonadiabatic model, which takes into account the electron-rotational interaction of the upper levels; (2) the coefficients of expansion of wave functions of perturbed states in the Born-Oppenheimer basis, which were found from the experimental data on rovibronic terms; and (3) semiempirical b initio data on electronic transition dipole moments of the 3dπ¹Π_g→2pπ¹Π_u and 3dπδ¹Δ_g→2pπ¹Π_u transitions. The dependences of the transition probabilities on J′ for the same bands of both hydrogen isotopomers H₂ and D₂ were found to be identical. They represent monotone functions for R and P branches and functions with a maximum (minimum) for Q branches. The ratios of transition probabilities of different isotopomers for different branches of the same systems of bands and for the same branches of different systems of bands were found to be correlated. The semiempirical values obtained in the paper agree with the experimental values within the limits of the errors of their determination. The nonempirical values of transition probabilities agree with the experiment considerably worse.     

Comparison of semiempirical and ab initio absolute probabilities of rovibronic transitions for the I 1Π g − , J 1Δ g − →C 1Π u ± system of bands of the H2 molecule

The absolute values of probabilities of the I ¹Π _g ^? , v′, J′; J ¹ Δ _g ^? , v′, J′→C ¹Π _u ^± , v″, J″ spontaneous transitions in the H₂ molecule (for the vibrational and rotational quantum numbers v′=v″=0–3, J′=1–6, and J″=J′, J′ ±1) are calculated by using ab initio and semiempirical data on the dipole moments of the 3dπ ¹Π_g, 3dδ¹Δ_g→2pπ¹Π_u electronic transitions. In both cases, the calculations are performed both in the adiabatic approximation and with an allowance for the nonadiabatic effect of electronic-rotational interaction. The coefficients of expansion of the wave functions of perturbed rovibronic states in the Born-Oppenheimer basis functions used in the calculations were obtained in the approximation of pure precession from experimental values of the terms. It was found that the values of transition probabilities based on the ab initio calculations systematically exceed the corresponding semiempirical data by a factor of 1.2–1.9 for the I ¹Π_g→C ¹Π _u ^± transition and by a factor of 1.4–1.6 for the J ¹Δ _g ^? →C ¹Π _u ^± transition. It was established that the difference between the ab initio and semiempirical values of electronic transition moments virtually has no effect on the dependence of the transition probabilities on the vibrational quantum numbers. The discrepancies between the results of adiabatic and nonadiabatic calculations are significant and reach two orders of magnitude, which is indicative of the important role of perturbations in the probabilities of the transitions considered.     

Ordering of atoms in 3d sublattice of the intermetallic quasibinary system Dy(Fe1−xMnx)2

Methods of x-ray analysis and nuclear -resonance (Mössbauer effect) have been used to study the distribution of iron and manganese atoms in the intermetallic quasibinary system Dy(Fe_1–xMn_x)₂, which is isostructural to the Laves phase C15. Ordering of atoms of transition metals has been found in 3d sublattice of intermetallic compounds Dy(Fe_1–xMn_x)₂ with the formation of a triple superstructure having the stoichiometric composition Dy(Fe_0·.25Mn_0·.75)₂.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 55–60, June, 1986.     

Analysis of the hadronic light-by-light contributions to the muon g − 2

We calculate the hadronic light-by-light contributions to the muon g − 2. We use both 1/N_c and chiral counting to organize the calculation. Then we calculate the leading and next-to-leading order in the 1/N_c expansion low energy contributions using the Extended Nambu-Jona-Lasinio model as hadronic model. We do that to all orders in the external momenta and quark masses expansion. Although the hadronic light-by-light contributions to muon g − 2 are not saturated by these low energy contributions we estimate them conservatively. A detailed analysis of the different hadronic light-by-light contributions to muon g − 2 is done. The dominant contribution is the twice anomalous pseudoscalar exchange diagram. The final result we get is a_μ^{light-by-light} = (−9.2 ± 3.2) × 10⁻¹. This is between two and three times the expected experimental uncertainty at the forthcoming BNL muon g − 2 experiment.     

Status of the lepton g − 2 and effects of hadronic corrections

The electron and muon anomalous magnetic moments (AMM) are measured in experiments and studied in the Standard Model (SM) with the highest precision accessible in particle physics. The comparison of the measured quantity with the SM prediction for the electron AMM provides the best determination of the fine structure constant. The muon AMM is more sensitive to the appearance of New Physics effects and, at present, there appears to be a three- to four-standard deviation between the SM and experiment. The lepton AMMs are pure relativistic quantum correction effects and therefore test the foundations of relativistic quantum field theory in general, and of quantum electrodynamics (QED) and SM in particular, with highest sensitivity. Special attention is paid to the studies of the hadronic contributions to the muon AMM which constitute the main source of theoretical uncertainties of the SM.     

Hadronic contributions to (g−2) of the leptons and to the effective fine structure constant α(M Z 2 )

The new experiment planned at Brookhaven to measure the anomalous magnetic moment of the muona _μ≡(g _μ?2)/2 will improve the present accuracy of 7 ppm by about a factor of 20. This requires a careful reconsideration of the theoretical uncertainties of theg?2 predictions, which are dominated by the error of the contribution from the light quarks to the photon vacuum polarization. This issue is cruicial also for the precise determination of the running fine structure constant at theZ-peak as LEP/SLC experiments continue to increase their precision. In this paper we present an updated analysis of the hadronic vacuum polarization using all presently availablee ⁺e^? data. This seems to be justified because previous work on the subject was based to some extent on preliminary or incomplete experimental data. Contributions from different energy ranges are presented separately forg?2 of the muon and the τ-lepton and for α(M _Z ² ). We obtain the resultsa _μ ^had* =(725±16)×10^?10 anda _τ ^had* =(351±10)×10^?8, where the asterisk indicates the dressed (renormalization group improved) value. For the effective fine structure constant atM _Z=91.1888 GeV we obtainΔα _had ⁽⁵⁾ =0.0280±0.0007 and α(M _Z ² )^?1=128.896±0.090. Further improvement in the accuracy of theoretical predictions which depend on the hadronic vacuum polarization requires more precise measurements ofe ⁺e^? cross-sections at energies below about 12 GeV in future experiments.     

Ionic conductivity and crystal structure for the Li3−2xCr2−xTax(PO4)3 system

The monoclinic phase (P2₁/n) was formed for 0≤x≤0.6 and the NASICON-type rhombohedral phase (R3̄c) was obtained for the region 0.8≤x≤1.2 in the Li_3−2xCr_2−xTa_x(PO₄)₃ system. The activation energy for Li⁺ migration was ca. 0.45 eV for the monoclinic structure and ca. 0.36 eV for the rhombohedral structure. The maximum conductivity of 8.4×10⁻⁶ S cm⁻¹ at 298 K was obtained for x=0.8 of the Li_3−2xCr_2−xTa_x(PO₄)₃ system. The conductivity of LiCrTa(PO₄)₃ was enhanced about three to five times by the addition of the lithium salt due to the improvement of the sinterablity. The maximum conductivity was 2.4×10⁻⁵ S cm⁻¹ at 298 K for LiCrTa(PO₄)₃–0.2Li₃BO₃.     

Ultrasonic studies of the high Tc superconductor (La1−xSrx)2CuO4−δ

We synthesized (La_1−xSr_x)₂CuO_4−δ crystals with 0 ≦ x ≦ 0.4 by the sintering method, and obtained several samples with good homogeneity, high onset superconducting transition temperature T_c ≲ 38 K and narrow transition width ΔT_c. For the sample with the maximum T_c among them, ultrasonic measurements were performed. In the curve of the sound velocity change ΔV_s(T) versus temperature T, there was observed an anomalously large decrease of sound velocity as T decreases in the range 150 K < T < 240 K. Furthermore, in the plots of the ultrasonic attenuation coefficient α(T) as a function of T, there were observed a broad and large peak located at T ∼ 100 K and a small peak located at T ∼ 200 K. These results show the existence of an optical mode of the energy ℏω_op/k_B ∼ 100 K and, probably, also of that of ∼ 200 K. On the basis of these experimental results of elastic properties, we suggest the origin of high T_c of this material.     

Discovery of deeply bound π− states in the208Pb(d,3He) reaction

Narrow lines were observed around 133 MeV excitation energy in the²⁰⁸Pb(d,³He) reaction atT _d=300 MeV/u using the Fragment Separator System at GSI. They are assigned to the deeply boundπ ^??²⁰⁷Pb states with configurations of $\left( {2p} \right)_{\pi ^ - } $ (3p_1/2, 3p_3/2) _n ^?1 .     

Tensor Force Manifestations in ab Initio Study of the 2H(d, γ)4He, 2H(d, p)3H, and 2H(d, n)3He Reactions

The ²H(d, γ)⁴He capture reaction and the ²H(d, p)³H and ²H(d, n)³He transfer reactions at very low energies are studied in an extended microscopic cluster model with a realistic nucleon–nucleon force. Our results show that the tensor force in realistic interactions plays an essential and indispensable role to reproduce the very low-energy astrophysical S factor of these reactions.     

Tensor force manifestations in ab initio study of the 2H(d,γ)4He, 2H(d,p)3H, and 2H(d,n)3He reactions

The (2)H(d,p)(3)H, (2)H(d,n)(3)He, and (2)H(d,γ)(4)He reactions are studied at low energies in a multichannel ab initio model that takes into account the distortions of the nuclei. The internal wave functions of these nuclei are given by the stochastic variational method with the AV8' realistic interaction and a phenomenological three-body force included to reproduce the two-body thresholds. The obtained astrophysical S factors are all in very good agreement with the experiment. The most important channels for both transfer and radiative capture are identified by comparing to calculations with an effective central force. They are all found to dominate thanks to the tensor force.     

Phase diagram and domain structure of the Rb2 x Tl2(1− x )Cd2(SO4)3 solid solutions

From measurements of temperature dependences of the birefringence and from observations of the domain structure the x, T–phase diagram for the Rb_{2 x} Tl_{2(1? x )}Cd₂(SO₄)₃ solid solutions have been obtained. Ferroelastic domain structure and movement of phase boundaries have been studied in the course of phase transitions in Rb_{2 x} Tl_{2(1? x )}Cd₂(SO₄)₃ crystals. Possible reasons for the appearance of mechanically non-compatible (‘forbidden’) ferroelastic domain walls are given.     

High-resolution spectroscopy of the a4Σ−3/2 − X12Π3/2 system of gold monosulphide in the near infrared

ABSTRACT

We have recorded the a⁴Σ^? _3/2 ? X₁ ²Π_3/2 (0,0), (1,0), and (2,0) bands of gaseous gold monosulphide (AuS) at sub-Doppler resolution in the near-infrared region. The molecules were made in a hollow cathode discharge source by the reaction of sputtered gold with carbonyl sulphide. The high resolution of the laser excitation spectrum enabled the determination of molecular constants describing the rotational and ¹⁹⁷Au hyperfine structure in both states, as well as the spin–rotation interaction in the a⁴Σ^? _3/2 state. The natures of the two electronic states are discussed in the context of the observed hyperfine structure.     

Influence of space charges on the dielectric behaviour of (Li2B4O7)1−x(WO3)x-glasses

The dielectric behaviour of (Li₂B₄O₇)_1−x(WO₃)_x glass samples is to a large extent governed by space charges. A detailed analysis of the effective dielectric constant ϵ_eff and the loss tangent tan δ reveals the intrinsic dielectric properties of the materials. At large WO₃-contents (0.44<x<0.55) we find a characteristic temperature in ϵ(T) which coincides with a phase transition temperature in crystalline WO₃, suggesting a reconstruction of the local environment of many tungsten atoms near to their WO₃-crystalline state.     

Estimation of the energy spectrum of cosmic ray electrons at the atmospheric depth (3.8–7.4)g.cm−2

Analytical calculations have been done to estimate the energy spectra of the secondary electrons originated from the decay of charged and neutral pions initiated on the upper atmosphere from the primary nucleon–air interactions in the energy range (4–100) GeV. The calculations are valid up to an atmospheric depth of about (3.8–7.4) g.cm^–2. The derived results are compared with the observed electron fluxes available from the balloon flight experiments of MASS2, HEAT, magnetic spectrometer system of Golden et al., instrument using scintillating fibers of Nishimura et al., and BETS.     

Determination of the reaction-matrix elements of the D(d,n)3He and D(d,p)3H reactions forE d ≤500 keV

All available data of the mirror fusion reactions D(d, n)³He and D(d, p)³H have been subjected to a new analysis in order to extract the matrix elements of all 16 transitions necessary for inclusion of alll2 waves. Their energy dependence was assumed to be governed solely by Coulomb penetrabilities. The Levenberg-Marquardt algorithm was used to fit all experimental data. The experimental data are reproduced satisfactorily. The results compare well with anR-matrix analysis and with refined resonating group calculations. No suppression of quintet entrance-state transitions and therefore no neutron suppression in polarized fusion can be derived from this analysis.This work was funded by the German Federal Ministers for Research and Technology (BMFT) under the contract numbers 06-OK-153 and 06-OK-272     

Correlation between the magnetic and electrical properties of the (VS)x(Fe2O3)2−x oxysulfide system

The correlation between the magnetic and electrical properties of the (VS)_x(Fe₂O₃)_2?x (0.9<x<1.25) oxysulfide solid solutions has been studied. The crossover of conductivity from the semimetallic to semiconducting type is accompanied by changes in the magnetic susceptibility, which are characteristic of the transition from delocalized to localized electrons. For x=1.25, a region of the ferromagnetic ordering has been established in the temperature range 90–120 K.