On the high spin expansion in the SYM theory

We study the form of the high spin expansion of the minimal anomalous dimension for long operators belonging to the sl(2) sector of SYM. Keeping fixed the ratio j between the twist and the logarithm of the spin, the minimal anomalous dimension expands as γ(g,j,s)=f(g,j)lns+f⁽⁰⁾(g,j)+O(1/lns). This particular double scaling limit is efficiently described, including the desired accuracy O((lns)⁰), in terms of a linear integral equation. By its use, we are able to evaluate both at weak and strong coupling the subleading scaling function f⁽⁰⁾(g,j) as a series in j, up to the order j⁵. Thanks to these results, the possible extension of the liaison with the O(6) non-linear sigma model may be tackled on a solid ground.     

Polarisierte Anregung der metastabilen 6s 5d-Terme im Ba I-Spektrum und Messung derg J-Faktoren

In an atomic beam experiment Ba-atoms were excited in the metastable levels of the 6s 5d-configuration by optical pumping and electron impact. The three states 6s 5d ¹ D ₂ and³ D _1,2 were populated by optical excitation of the 6s 6p ¹ P ₁- and³ P ₁-level resp., which decay partly into the metastable states. The¹ D ₂- and³ D ₃-level could be excited and aligned by impact of 50 eV-electrons. Radiofrequency transitions between Zeemansublevels were detected by resonance scattering of light and theg _J-values of the four 6s 5d-levels were measured:g _J(^1D ₂)=1.0032 (2),g _J(^3D ₁)=0.4986 (2),g _J(^3D ₂)=1.1638 (2) andg _J(^3D ₃)=1.3341 (2).     

Electronic absorption spectra of the 5d3 hexafluororhenate(IV) ion

The Γ₈(⁴A_2g) →Γ₇(²T_2g), Γ₈(²T_2g) electronic transitions for the 5d³ hexafluororhenate(IV) ion have been observed at liquid hydrogen temperature in a single Cs₂GeF₆ crystal and in a mixed crystal where the ReF^?2₆ ion is doped in the cubic Cs₂GeF₆ lattice. The electronic transitions have been assigned with a crystal field model to give information about the parameters B, C, Dq, and spin-orbit coupling. The vibrational structure in the mixed crystal system may be assigned to the ungerade modes of the ReF^?2₆ moiety. Comparison of the mixed and pure crystal vibrational structure shows that the pure crystal vibrational structure can be interpreted on the basis of K ≠ 0 lattice effects and a small distortion in the pure crystal.     

Effect of a heavy atom in the S 1(ππ*) ↝ T 1(ππ*) nonradiative transition. 9,10-Dichloroanthracene

The rate constant K _ST for the nonradiative intersystem crossing transition S ₁(¹ B _1u ) ? T ₁(³ B _1u ) (I) in 9,10-dichloroanthracene (DClA) is calculated in terms of the model of vibronic-induced spin-orbit (VISO) interactions. The magnitude fluorescence quantum yield ?_fl is estimated. Comparison of K _ST(I) and ?_fl for DClA with the corresponding values obtained earlier for anthracene (AC), where K _ST is governed by the conversion channels (I) and S ₁(¹ B _1u ) ? T ₂(³ B _3g ) (II), shows that the theoretical estimates reflect the anomalous heavyatom effect in these molecules in accordance with the experimental (literature) data. The cause for this effect is revealed. The influence of different factors on the K _ST(I) constant and on the ratio of its components K _ST ^s (where s denotes the z and y spin-sublevels) is established for DClA. These factors are the magnitude of the spin-orbit coupling parameter in a chlorine atom, the change, as compared to AC (in the same conversion channel (I)) of the distribution of electrons in the carbon core of the DClA molecule, and the change in the form of out-of-plane vibrational modes involved in VISO interactions.     

Multiple scattering and energy loss of fast heavy ions in thin solid targets

The hyperfine structure of the low-lying atomic levels 4d ² 5s ^{2 3} F _{2, 3, 4} and 4d ³ 5s ⁵ F _{2, 3, 4, 5} of⁹¹Zr has been studied using the atomic-beam magnetic-resonance method. Using intermediate coupling wave functions derived for the configurations (4d+5s)⁴ the experimental data are analysed with respect to the effective operator formalism. The effective radial parameters of the magnetic dipole and electric quadrupole interaction are determined for the two configurations 4d ² 5s ² and 4d ³ 5s and are compared with relativistic calculations. The value obtained for the electric quadrupole moment of the⁹¹Zr nuclear ground state isQ=? 0.21(2) barn (uncorrected for core polarization effects).     

Core polarization and 5/2+ states in91Nb

The energies and spectroscopic factors ofJ ^π=5/2⁺ states of nucleus⁹¹Nb excited via a reaction transferring a proton to the 2d _5/2 orbit of⁹⁰Zr target state have been calculated. Effective two-body interaction used has been extracted from the experimentally observed two-body energies of (1g ₉ ^2/?1 (n) 2d _5/2(n)), (1g ₉ ^2/?1 (n) 1g _9/2(p)) and (1g _9/2(p)-2d _9/2(n)) multiplets in⁹⁰Zr,⁹⁰Nb and⁹²Nb nuclei respectively. Most of the calculated energies and the strengths ofJ ^π=5/2⁺ levels have reasonably good counterparts in the experimental spectrum, however the calculation shows about 17% strength lying at 6.8 MeV, without having a confirmed counterpart in the observed level scheme. The reduced transition strengthsB(M1) forM l transitions from 5/2^? T>(11/2) state to the various components of 5/2⁺ T<(=9/2) state have also been reported; but the corresponding experimental values are not available. The main feature of the reduced transition strengths is that theM1 transition to the state at 3.69 MeV is inhibited whereas that to the state at 6.79 MeV is enhanced, the relevant core-configuration, interfering destructively in the former case and constructively in the latter.     

Coherence effects in low energy Na*(3p)+Na+ scattering: Experiment and semiclassical calculations

Pronounced polarization effects have been observed in inelastic collisions of laser state-prepared Na^*(3p,M _L) with Na⁺ leading to Na^*(3d) for the energy rangeE _CM=20–45 eV. Using linearly polarized light the dependence of the inelastic process on the alignment of the electronic charge cloud of the Na^*(3p) prior to the collision has been measured. In studies with left and right hand circularly polarized light the angular momentum transferred in the collision process has been determined. The results are compared with similar data for the 3p→3s deexitation process studied previously [6]. The density matrix of the Na^*(3p) state has been evaluated with respect to the collisional excitation to Na^*(3d). Semiclassical calculations based on the coupled channel impact parameter approximation using pseudopotentials [7] and nonadiabatic rotational coupling elements for the Na ₂ ^* system [12] have been performed. The agreement with the experimental results is good, in particular for the higher collision energies.     

Nuclear orientation study of97, 103, 105Ru in Fe

Angular distributions have been measured forγ-rays emitted following the decays of^{97, 103, 105}Ru oriented in an iron matrix at temperatures down to 2.8mK. From the temperature dependence of theγ-anisotropies the magnetic hyperfine splitting frequenciesν _M =|gμ _N B _HF/h| of^{97, 103, 105}RuFe were found to be 110(7), 57(15) and 80 _?50 ⁺¹⁷ MHz, respectively. With the known hyperfine fieldB _HF=?489.6(4.0) kG the nuclearg-factors are derived as ∣g(⁹⁷Ru;j ^π=5/2⁺)∣=0.29(2), ∣g(¹⁰³Ru;j ^π=3/2⁺)∣=0.15(4) and ∣g(¹⁰⁵Ru;j ^π=3/2⁺)∣=0.21 _-0.13 ^+0.05 . The analysis for¹⁰³RuFe has been performed with the assumption ofj ^π=3/2⁺ and 5/2⁺ for the ground state of¹⁰³Ru. Taking into account experimentally knowng-factors of 3/2⁺ and 5/2⁺ states in this mass region, our data strongly favour the assignmentj ^π=3/2⁺ for the¹⁰³Ru ground state.     

Radio-frequency spectroscopy in the states3 D 3,2 of platinum

The magnetic dipole hyperfine interaction constantsA of the atomic ground state³ D ₃ and of the first excited state³ D ₃ in¹⁹⁵Pt have been measured by atomic beam magnetic resonance. The electronicg _J factors of these states were determined from the Zeeman splitting in¹⁹⁴Pt. Using intermediate coupling wave functions derived for the configurations (5d+6s)¹⁰ effective hyperfine radial integrals are evaluated.     

Determination of hyperfine structures and Rydberg convergence limits of selected optical transitions in 93Nb using resonance ionization spectroscopy

Several two- and three-step schemes for resonance ionization of ⁹³Nb with field ionization of Rydberg levels were investigated in the context of feasibility studies of using ^93m Nb/⁹³Nb isomer ratio determination for fast neutron dosimetry. Hyperfine structures of the states 4d ⁴(a ⁵ D)5p ⁴ D ₁ ^2/0 , 4d ³5_s(a ⁵ P)5P ⁶ D ₁ ^2/0 , 4d ³5s(a ⁵ F)5p ⁶ F ₁ ^2/0 , and 4d ³5s(a ⁵ F)6s ⁶ F _1/2 of ⁹³Nb were measured. The Rydberg spectra of the excitation schemes were measured and corresponding ionization limits estimated.     

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.     

Blue laser cooling transitions in Tm I

We have studied possible candidates for laser cooling transitions in ¹⁶⁹Tm in the spectral region of 410–420 nm. By means of saturation absorption spectroscopy, we have measured the hyperfine structure and rates of two nearly closed cycling transitions from the ground state 4f¹³6s²(²F₀)(J_g=7/2) to upper states 4f¹²(³H₅)5d_3/26s²(J_e=9/2) at 410.6 nm and 4f¹²(³F₄)5d_5/26s²(J_e=9/2) at 420.4 nm and evaluated the life times of the excited levels as 15.9(8) ns and 48(6) ns, respectively. Decay rates from these levels to neighboring opposite-parity levels are evaluated by means of Hartree–Fock calculations. We conclude that the strong transition at 410.6 nm has an optical leak rate of less then 2×10^-5 and can be used for efficient laser cooling of ¹⁶⁹Tm from a thermal atomic beam. The hyperfine structure of two other even-parity levels, which can be excited from the ground state at 409.5 nm and 418.9 nm, is also measured by the same technique. In addition, we give a calculated value of 7(2) s^-1 for the rate of magnetic-dipole transition at 1.14 μm between the fine structure levels (J_g=7/2)↔(J’_g=5/2) of the ground state which can be considered as a candidate for applications in atomic clocks. PACS 32.70.Cs; 32.10.Fn; 32.80.Pj     

Laser-rf double-resonance hyperfine structure measurements of the metastable 3d 4s 1 D 2 state of43Ca

The hyperfine structure of the (3(d 4s)¹ D ₂metastable state of⁴³Ca has been measured using theABMR-LIRF method (atomic beam magnetic resonance, detected by laser induced resonance fluorescence). The measurements yielded for the magnetic dipole and electric quadrupole constantsA=?17.650(2) MHz andB=?4.642(12) MHz, respectively. From the measuredB factor the spectroscopic electric quadrupole moment (uncorrected for shielding effects) has been calculated to beQ(⁴³Ca)=?0.062(12) barn. In addition, isotope shifts in the lines (3d 4s)¹ D ₂(3d 4p)¹ F ₃ ⁰ and (3d 4s)¹ D ₂(4s 5p)¹ p ₁ ⁰ for the stable calcium isotopes have been obtained by high resolution laser spectroscopy.     

立方对称晶场中6S(3d5)态离子的磁相互作用及其自旋哈密顿参量的微观起源

基于完全对角化方法(complete diagonalization method, CDM), 研究了⁶S(3d⁵)态离子在立方对称晶场中的磁相互作用,分析了自旋哈密顿参量(a, g,Δg)的微观起源.研究中除了考虑研究者通常考虑的SO(spin-orbit)磁相互作用外,同时考虑了SS(spin-spin),SOO(spin-other-orbit),OO(orbit-orbit)磁相互作用.研究表明：⁶S(3d⁵)态离子在立方对称晶场中的自旋哈密顿参量起源于五种机理,即SO机理,SS机理,SOO机理,OO机理以及SO-SS-SOO-OO联合作用机理.文中研究了五种机理的相对重要性,结果表明：SO机理与SO-SS-SOO-OO联合作用机理在五种机理中最为重要.尽管SS,SOO,OO磁相互作用单独作用时对自旋哈密顿参量的贡献很小,但它们的联合作用SO-SS-SOO-OO机理对自旋哈密顿参量的贡献非常可观.此外研究表明：零场分裂参量a主要来自纯自旋四重态及自旋二重态与自旋四重态联合作用的贡献,而Zeemang(或者Δg)因子主要来自纯自旋四重态的贡献.纯自旋二重态对自旋哈密顿参量a与g(或者Δg)的贡献为零.在我们所选择的晶场区域,发现下列关系始终成立：a>0,a(-|Dq|)<a(|Dq|),g(-Dq)=g(Dq),a(-Dq,-ξ_d,B,C)=a(Dq,ξ_d, B,C),Δg(-Dq,-ξ_d, B, C)=Δg(Dq,ξ_d, B, C).作为本文理论的应用,研究了四种典型的Mn²⁺掺杂晶体材料,即Mn²⁺:KZnF₃,Mn²⁺: RbCdF₃,Mn²⁺: MgO,Mn²⁺: CaO,理论与实验测量符合很好. 关键词： 自旋哈密顿参量 6S(3d⁵)态离子')" href="#">⁶S(3d⁵)态离子 磁相互作用 完全对角化方法(CDM)     

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.     

Critical properties of high-spin Ising models on anisotropic lattices

The coordinates of the critical points of spin-S Ising models with coupling constants J and J′ are calculated for 1/2 ≤ S ≤ 13/2. The calculations are performed for several values of S and Δ ≡ J′/J independently by using the phenomenological renormalization-group method or (approximate) self-duality. Numerical results combined with a mean-field analysis show that the critical coupling strength for Δ ～ 1 (weakly anisotropic lattice) is K _c ^(S) (Δ) = K _c ^(S) (1)[1 + a(1 ? Δ)], where a = (d ? 1)/d is independent of S (d is the space dimension). Both free energy and internal energy are determined at the critical points. An extremum of the critical internal energy is found at Δ* ∈ (0, 1). The parameter Δ* can be used as a criterion that separates quasi-isotropic and quasi-one-dimensional regimes (Δ* < Δ ≤ 1 and Δ < Δ*, respectively). The finite-size scaling amplitudes A _s and A _e of the inverse spin-spin and energy-energy correlation lengths are estimated. Calculations show that the amplitudes A _s and A _e are independent of S within the accuracy of the adopted approximations. Moreover, their ratio A _e/A _s is independent of the anisotropy parameter Δ. These results support the Ising universality hypothesis.     

Level-crossing-Untersuchung der Hyperfeinstruktur des angeregten 32 P 3/2- und 42 P 3/2-Zustands von Na23

The hyperfine structure of the excited 3² P _3/2- and 4² P _3/2-state of Na²³ has been investigated in a level-crossing-experiment by means of a detailed analysis of the dependence of the scattered resonance light as a function of the magnetic field. From the experimental curves the following results for the hyperfine structure constantsA andB and for the lifetimesΤ were deduced 3² P _3/2-state: 4² P _3/2-state:A=18.65(10)Mc/sA=6.006(30)g _j/1.334Mc/sB=2.82(30)Mc/sB=0.86 (9)g _j/1.334Mc/sΤ=1.60 (3) · 10^?8sΤ=6.56 (25)1.334/g_j·10^?8 s. The nuclear electric quadrupolemoment of Na²³ derived from these values isQ=0,097 · 10^?24 cm², where the Sternheimer-correction has been applied.     

Properties of quark matter governed by quantum chromodynamics (II). Renormalization schemes in quark matter

Renormalization schemes are examined (in the Coulomb gauge) for quantum chromodynamics in the presence of quark matter. We demand that the effective coupling constant for all schemes become congruent with the vacuum QCD running coupling constant as the matter chemical potential, μ, goes to zero. Also, to enable us to standardize with the vacuum QCD running coupling constant at some asymptotic momentum transfer, $\text{|}\text{p}{}_0\text{|,}\text{we keep}\text{μ ? ¦}\text{p}{}_0\text{¦}$, to ensure that the matter contribution is negligible at this point. This means all schemes merge with vacuum QCD at $\text{|}\text{p}{}_0\text{|}$ and beyond. Two renormalization group invariants are shown to emerge: (i) the effective or invariant charge, g_inv², which is, however, scheme dependent and (ii) g²(M)/S(M), where S(M)^?1 is the Coulomb propagator, which is scheme independent. The only scheme in which g_inv² is scheme independent and identical to g²(M)/S(M) is the screened charged scheme (previous paper) characterised by the normalization of the entire Green function, S^?1, to unity. We conclude that this is the scheme to be used if one wants to identify with the experimental effective coupling in perturbation theory. However, if we do not restrict to perturbation theory all schemes should be allowed. Although we discuss matter QCD in the Coulomb gauge, the above considerations are quite general to gauge theories in the presence of matter.     

Determination of isotope shift crossed-second-order-effects and hyperfine-structure parameters in the Eu I configuration 4f 7 6s7s

In the Eu I configuration 4f ⁷(⁸ S)6s7s the isotope shift (IS) and hyperfine-structure (hfs) of the levelse ⁸ S _7/2 andf ⁸ S _7/2 were determined from the transitions 684.5 nm, 733.7 nm and 821.0 nm to 4f ⁷6s6p. Together with experimental results of our previous measurements a theoretical analysis of the IS and hfs for the complete configuration 4f ⁷ 6s7s can now be carried out. From the IS of the four 6s7s-levels we evaluated the two crossed-second-order-parametersg ₃(4f,6s)= ?l.l(l)mK andg ₃(4f, 7s)= ?0.1(l)mK. The ratiog ₃/G ₃ is determined for various Eu configurations and found to be equal to 5.6(3)·10^?6 in complete agreement with a theoretical value following from Hartree-Fock calculations. The single electron hfs splitting constantsa ¹⁰(4f)= ?1.9 (3) mK,a ¹⁰(6s)=396(3)mK, anda ¹⁰(7s)=65(3)mK are also determined and compared with those of other Eu configurations.     

Energy splitting betweenT > andT < single particle states in91Nb

The isobaric energy splitting ΔE(n, l, j) betweenT _>- andT _<-single particle states in the shell (2d _5/2, 2d _3/2, 1g _7/2, 3S _1/2) has been experimentally determined for⁹¹Nb from a study of the reaction⁹⁰Zr(³He,d)⁹¹Nb. The splitting of the 1g _7/2-states is found to be about 25% larger than that of the³ s _1/2-states. The observed dependence of the energy splitting ΔE(n, l, j) on the shell model quantum numbers (n, l, j) of the states is reproduced by the expression \(\Delta {\rm E}(n, l, j) = \frac{1}{2}(2T + 1) \left\langle {\phi _ > ^{n l j} | U_1 (r)|\phi _ > ^{n l j} } \right\rangle\) , which is based on approximate solutions of Lane's equations.φ _> ^nlj is the wave function of the parent state in the (nC) system. There is evidence, that only a Lane potentialU ₁(r) of surface type can reproduce the observed strong dependence of ΔE(n, l, j) on the quantum numbers. The depthū ₁ of Lane's potential is found to be 2.0 MeV.