The ratio of the charm structure functions F k c (k = 2, L) at low x in deep inelastic scattering with respect to the expansion method

We study the expansion method for the gluon distribution function at low x values and calculate the charm structure functions in the LO and NLO analysis. Our results provide a compact formula for the ratio R ^c = F _L ^c /F ₂ ^c , which is approximately independent of x and the details of the parton distribution function at low x values. This ratio could be a good probe of the charm structure function F ₂ ^c in the proton deduced from the reduced charm cross sections at DESY HERA. These results show that the charm structure functions obtained are in agreement with HERA experimental data and other theoretical models.     

F 2 c at low x

We study the heavy-quark contributions to the proton structure function F ₂(x,Q ²) at next-to-leading order using compact formulas at small values of Bjorken??s x variable. The formulas provide a good agreement with the modern HERA data for F ₂ ^c (x,Q ²).     

Vacuum condensates in supersymmetric gluodynamics

We analyse the restrictions imposed by supersymmetric Ward identities on the dimension-six condensates in supersymmetric gluodynamics. It is shown that the system of the Ward identities admits a nonzero value for the four-fermion condensate \(\left\langle {\left( {\lambda \sigma _\mu T^a \bar \lambda } \right)^2 } \right\rangle _0 \) while 〈f ^abc F _μν ^a F _νρ ^b F _ρμ ^c 〉₀ must vanish.     

Polarized deuteron structure functions at small x

We investigate shadowing corrections to the polarized deuteron structure functions g ₁ ^d and b₁. In the kinematic domain of current fixed target experiments we observe that shadowing effects in g ₁ ^d are approximately twice as large as for the unpolarized structure function F ₂ ^d . Furthermore, we find that b₁ is surprisingly large at x < 0.1 and receives dominant contributions from coherent double scattering.     

Mößbauereffekt in157Gd und155Gd

Using the Mössbauer technique electric hyperfine interactions of the first excited non-rotational states at 64 keV in¹⁵⁷Gd and at 86.5 keV in¹⁵⁵Gd have been determined in GdF₃ and GdCl₃· 6H₂O. For the ratio of quadrupolmoments the ratiosQ ₆₄ ¹⁵⁷ /Q _g ¹⁵⁷ =1.74±0.04,Q _86.5 ¹⁵⁵ /Q _g ¹⁵⁷ =?0.07 ± 0.21 andQ _g ¹⁵⁵ /Q _g ¹⁵⁷ =0.78 ± 0.06 were found. In addition isomer shifts were observed from which a ratio δ〈r²〉 ₆₄ ¹⁵⁷ /δ〈r²〉 _86.5 ¹⁵⁵ =?2.6±0.15 can be inferred.     

The primary and secondary acceptors in bacterial photosynthesis III. Characterization of the quinone radicals Q A − ⋅ and Q B − ⋅ by EPR and ENDOR

Electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) techniques were used to investigate the electronic structure of the primary (Q _A ^?? ) and secondary (Q _B ^?? ) ubiquinone electron acceptors in reaction centers (RCs) of the photosynthetic bacteriumRhodobacter sphaeroides. To reduce the EPR linewidth, the high-spin Fe²⁺ present in native RCs was replaced by diamagnetic Zn²⁺. Experiments were performed both on frozen solutions and single crystals at microwave frequencies of 9, 35 and 94 GHz. Differences in the EPR/ENDOR spectra were observed for Q _A ^?? and Q _B ^?? , which are attributed to different environments of the quinones in the RC. The differences exhibited themselves in: (i) the g-tensors, (ii) the¹⁷O and¹³C hyperfine coupling (hfc) constants of the quinones labeled at the carbonyl group, (iii) the¹H-hfcs of the quinone ring and (iv) the exchangeable protons hydrogen bonded to the carbonyl oxygens. From these results and from H/D exchange experiments, the following conclusions were drawn: both Q _A ^?? and Q _B ^?? have at least two hydrogen bonds of different strengths to the carbonyl oxygens. The hydrogen bonds for Q _A ^?? are stronger and more asymmetric than for Q _B ^?? . For Q _A ^?? the stronger bond (to O₄) was assigned to His(M219) and the weaker (to O₁) to Ala(M260). For Q _B ^?? the stronger bond (to O₄) was assigned to His(L190), with several weaker bonds (to O₁) to Ser(L223), Ile(224) and Gly(L225). From the temperature dependence of the hfcs of the exchangeable protons some dynamic properties of the RC were deduced. Hfcs with more distant nitrogens were observed by electron spin echo envelope modulation (ESEEM). For Q _A ^?? they were assigned to N_δ of His(M219) and to the peptide backbone nitrogen of Ala(M260) and for Q _B ^?? to N_δ of His(L190). These interactions indicate the extent of the electron wave function, which is important for the understanding of the electron transfer mechanism. Based on the magnetic resonance results, the function of the quinone acceptors in the reaction center is discussed.     

Constraints on gluon evolution at smallx

The BFKL and the unified angular-ordered equations are solved to determine the gluon distribution at smallx. The impact of kinematic constraints is investigated. Predictions are made for observables sensitive to the gluon at smallx. In particular comparison is made with measurements at the HERA electron-proton collider of the proton structure functionF ₂(x, Q ²) as a function of lnQ ², the charm componentF _c ² (X, Q ²) and diffractiveJ/Ψ photoproduction.     

Constraints on gluon evolution at smallx

The BFKL and the unified angular-ordered equations are solved to determine the gluon distribution at smallx. The impact of kinematic constraints is investigated. Predictions are made for observables sensitive to the gluon at smallx. In particular comparison is made with measurements at the HERA electron-proton collider of the proton structure functionF ₂(x, Q ²) as a function of lnQ ², the charm componentF _c ² (X, Q ²) and diffractiveJ/?? photoproduction.     

The parton distribution functions of the photon and the structure functionF 2 γ (x,Q 2)

We present new parametrisations of the parton distribution functions of the photon including the first parametrisation in next-to-leading order QCD. We take into account some recent theoretical considerations pertaining to the gluon content of the photon,g ^γ. We argue that if an evolution is started at very lowQ ² and a fit to allF ₂ ^γ data performed with no constraints on the gluon distribution, then physically unreasonable gluon distributions may result. Our results support recent indications thatQ ₀ ² ≤1 GeV² is too low a value from which to start a perturbative evolution. Starting our evolution atQ ₀ ² =5.3 GeV², we evolve up inQ ² using a modified version of Rossi's Ansatz. The limited lever arm inQ ² leads to limited sensitivity to the QCD scale parameter Λ, though there is a preference for low values in the 0.1–0.2 GeV range. We also present new parametrisations of the singular asymptotic quark and gluon distribution functions of the photon which we believe are more accurate than those in current use.     

BFKL Pomeron in the reaction γ ⊥ * (Q 2)p→ρ ⊥ 0 p at large Q 2 and W

The reaction γ _⊥ ^* (Q ²)p→ρ _⊥ ⁰ p has been studied at large Q ² and W ²/Q ² and low momentum transfers to the nucleon, k _⊥ ² —that is, in the region where the Pomeron exchange mechanism is operative. At sufficiently large Q ², the Pomeron interacts with quarks occurring at small distances, whereby the hard component of the Pomeron is separated, so that the process is governed by the Pomeron of perturbative QCD (BFKL Pomeron). Our calculations indicate that, in vector-meson electroproduction at low k _⊥ ² , the perturbative regime cannot set in fast because, for Q ²≤100 GeV² and, accordingly, for W ²/Q ²≤10⁷, comparatively large distances of $\rho _{q\bar q} > 0.2$ fm are important.     

Hyperfeinstruktur des 82P3/2-Terms von Cäsium 134

The electric quadrupole interaction constantB of the 8p²P_3/2 state of Cs¹³⁴ has been determined by an optical double resonance measurement of the hyperfine structure transition v_F=11/2?F=9/2=47.84(12) Mc/s. The results are: B _8P ¹³⁴ =8.06(20) Mc/s and Q _8P ¹³⁴ =+ 0.427(8) · 10^?24cm². Comparison is made between the measurements in the 7p and 8p electronic states: Q _8P ¹³⁴ /Q _7P ¹³⁴ =0.977(20). The ratio of the corresponding Sternheimer correction factors yields the value C_7p/C_8P=0.982.     

Electronic color centers in SrF2-Na crystals

It was shown that optical bleaching of M _A ⁺ color centers at 80 K in SrF₂-Na crystals causes the core of an M _A ⁺ -center to transform into the V _a ⁺ Me ⁺ V _a ⁺ configuration, in which all three point defects are arranged diagnonally in the cube cell. Reirradiation of an optically bleached crystal by x-rays generates F _D centers in it: V _a ⁺ Me ⁺ V _a ⁺ + e ^? → V _a ⁰ Me ⁺ V _a ⁺ ≡ F _D. The F _D → M _A ⁺ transformation in SrF₂-Na crystals proceeds at T = 135 K, in contrast to the F _A → M _A ⁺ transformations, which take place at T > 200 K.     

Structural analysis of three-spin systems of photosystem II by PELDOR

The pulsed electron electron double resonance (PELDOR) pulse sequence is applied to a three-spin system consisting of three radicals (Y _D ^· , Y _Z ^· and Q _A ^? ) generated in spinach PS II. The distance between Y_Z and Q_A has been determined to be 3.4 nm with the previously derived distances of the other radical pairs, 2.9 nm for Y _D ^· -Y _Z ^· and 3.9 nm for Y _D ^· -Q _A ^? . This distance has been derived from the Y _Z ^· -Q _A ^? radical pair trapped in Y_D-less mutants ofChlamydomonas reinhardtii. Furthermore the method was applied to the Y _D ^· -Q _A ^? -Chl _Z ⁺ system to find the unknown distance between Q_A and Chl_Z. The derived distance was 3.4 nm. A triangular configuration was found in the membrane system that gives the relative positions of the electron transfer components.     

Hyperfeinstrukturaufspaltung und Lebensdauer des 72 P 3/2-Terms von Rb85 und Rb87

The hyperfine structure splitting of the 7² P _3/2 state of Rb⁸⁵ and Rb⁸⁷ has been measured with optical double resonance. The following hfs interaction constants have been obtained: Rb⁸⁵:A _7p ⁸⁵ =3.71(1) MHz;B _7p ⁸⁵ =3.68 (8)MHz. Rb⁸⁷:A _7p ⁸⁷ =12.57(1) MHz;B _7p ⁸⁷ =1.71 (3)MHz. These values yield quadrupole moments ofQ _7p,hfs ⁸⁵ =+0.316(7) barn andQ _7p,hfs ⁸⁷ =+0.147(2)barn which are reduced by application of the Sternheimer correction toQ _7p ⁸⁵ =+0.267(6) barn andQ _7p ⁸⁷ =+0.124(2) barn. The averaged ratio of the uncorrected values of Q_hfs in the 5p and 7p ² P _3/2 stake isQ _5p,hfs/Q _7p,hfs=1.07(3). This has to be compared with the correction factors for polarization of the core of electrons by the nuclear quadrupole moment (1?R)_5p/(1?R)_7p=1.07. The agreement between the measured and calculated ratio indicates a net antishielding of the nuclear quadrupole moments of rubidium by the core of electrons as has been predicted bySternheimer. The lifetime of the 7² P _3/2 state of the RbI-spectrum is:τ(7² P _3/2, Rb)=2.4(2)·10^?7 sec.     

The hadronic and point-like contributions to theF 2 photon structure function in perturbative QCD

A detailed discussion is given of the hadronic and point-like contributions to theF ₂ photon structure function (F ₂ ^γ ) in both the naive parton model and QCD. The non-singlet part of the leading order solution, first found by Witten, is re-derived using the QCD improved parton model, enabling the hadronic and point-like terms to be clearly identified and correlated with observed jet structure in the final state. When important non leading-log terms are included, the sensitivity of the solution to Λ is found to be weak for allQ ² values, and the all orders solution to be well approximated by theO(α _s ² solution. The approximations made in deriving the leading order solution are critically examined, and an approach enabling more quantitative tests of QCD to be made from measurements of the point-like (perturbative) component ofF ₂ ^γ is suggested.     

Lebensdauer- und Hyperfeinstrukturmessungen an einigen angeregten Zuständen der Konfiguration 4d 9 5p im Pd I-Spektrum mit der Level-crossing-Methode

Lifetimes and hfs coupling constants of some excited states of the 4d ⁹ 5p configuration of Pd I have been determined in a level crossing experiment by observing the field dependence of the polarization of the fluorescence radiation in a magnetic field. From the halfwidths of the measured zero field level crossing signals one obtains the mean lifetimes of the following fine structure states:τ(³P ₁ ⁰ )=(7.46±0.32)nsec;τ(³ P ₂ ⁰ )=(6.9±0.76)nsecτ(³P ₁ ⁰ )=(4.99±0.35)nsec;τ(³ D ₁ ⁰ )=(4.89±0.40)nsecτ((³D ₃ ⁰ )=(6.99±0.49)nsec;τ(³ F ₄ ⁰ )=(7.09±0.46)nsec.Δm=2 crossing signals were detected in the³ P ₁ ⁰ ,³D ₃ ⁰ and³F ₄ ⁰ -states of the odd isotope¹⁰⁵Pd. A detailed analysis of the experimental curves yields the hfs coupling constantsA andB of these states:A(³P ₁ ⁰ )=?(133±2) Mc/sec;B(³ P ₁ ⁰ )=(140±30) Mc/secA(³D ₃ ⁰ )=?(120±10) Mc/sec;B(³ D ₃ ⁰ )=?(660±100) Mc/secA(³F ₄ ⁰ )=?(87±2) Mc/sec;B(³ F ₄ ⁰ )=?(330±30) Mc/sec. A theoretical calculation of the hfs constants is given on the basis of reduced matrix elements. Within the limit of the errors these values agree with the experimental ones. The nuclear electric quadrupole moment deduced from the measuredB values isQ (¹⁰⁵Pd)=(0.8±0.3)·10^?24 cm² (without corrections).     

Spin effects in two-body hadronic decays of the B c mesons

Spin effects in the weak two-body hadronic decays of the B _c and B _c ^* mesons into J/ψ and ρ(π) mesons are considered within the model of hard one-gluon exchange between quarks at high momentum transfers. It is shown that the polarization of the J/ψ meson in the decays of the B _c ^* meson differs substantially from that in the decays of the B _c ^* meson. The decay widths of the B _c ^* meson differ significantly from the widths of the B _c ^* meson.     

Observation of perturbations in the rovibronic transition probabilities for the (4d)r 3Π g − , (4d) s 3 Δ g − → (2p) c 3Π u ± band systems of the H2 molecule

The ratios of the radiative transition probabilities for the lines of the P, Q, and R branches of the (4d)r ³Π _g ^? , (4d)s ³Δ _g ^? → (2p) c ³Π _u ^± band systems of the H₂ molecule have been measured for the first time. Significant (to two orders of magnitudes) differences are found between the experimental values and the adiabatic theory predictions. It is established that the results of the nonadiabatic calculation performed by us in the pure-precession approximation taking into account the electronic-rotational interaction of the 4d ³Π_g and 4d ³Δ_g states are in agreement with the experimental data. The optimal energies of rovibronic levels of the r ³Π _g ^? , s ³Δ _g ^? , c ³Π _u ^? , and c ³Π _u ⁺ states have been found and reidentification of 11 from 54 spectral lines, assigned previously to the (0-0) and (1-1) bands, was performed.     

Comparison of electron spin polarization of P 870 + Qa a − observed in Zn2+-containing and Fe2+-depleted bacterial reaction centers

Recently, a general model has been developed to explain electron spin polarized (ESP) electron paramagnetic resonance (EPR) signals found in systems where radical pairs are formed sequentially. The photosynthetic bacterial reaction center (RC) is such a system in which we can experimentally vary parameters (lifetime, structure, and magnetic interactions in the sequentially formed radical pairs) that affect ESP development in order to test this model. In Fe²⁺-depleted transfer step from intermediate radical pair, P ₈₇₀ ⁺ Q _a ^? which is produced in an electron transfer step from intermediate radical pair, P ₈₇₀ ⁺ I^?. (P ₈₇₀ ⁺ is the oxidized primary donor, a special pair of bacteriochlorophyll molecules, I^? is the reduced bacteriopheophytin acceptor, and Q _a ^? is the reduced primary quinone acceptor.) The lifetime of P ₈₇₀ ⁺ I^? can be shortened relative to the lifetime of P ₈₇₀ ⁺ I^? in Fe²⁺-depleted RCs by substitution of Zn²⁺. We report the first observation of X-band and Q-band ESP EPR signals due to P ₈₇₀ ⁺ Q^? from bacterial reaction centers that contain Zn²⁺. Comparison of these signals to those observed from Fe²⁺-depleted bacterial reaction centers shows intensity differences and g-factor shifts. The results are discussed in terms of the general sequential radical pair model.