The Fokker-Planck equation for quantum noise of theN-level system

The hyperfine structure of the ReI-lines λκ 4889 å (5d⁵ 6s 6pz ⁸P_7/2?5d⁵ 6s² a ⁶S_5/2) and 5275 å (5d⁵ 6s 6p z⁸P_5/2?5d⁵ 6s² a⁶S_5/2) was measured by a photoelectric recording double Fabry Perot spectrometer using enriched isotopes of Re¹⁸⁵ and Re¹⁸⁷, which have been excited in liquid air cooled hollow cathodes. Besides the usual recording the signal was also measured by a digital voltmeter and punched into paper tape making it possible to evaluate the measurements by a computer. The linewidth obtained in the experiments was small enough that besides the splitting of the⁸P states also the splitting of the ground state could be detected in asymmetries of the hyperfine structure components. By the mathematical analysis of the components it was possible to derive the quadrupole coupling constantB of the 5d⁵ 6s² a ⁶S_5/2 ground state: 5=1.6(8)· 10^?3cm^?1 for Re¹⁸⁵ and Re¹⁸⁷. The quadrupole moments of Re¹⁸⁵ and Re¹⁸⁷ have been estimated fromB (z⁸P_{7/2, 5/2}) with LS coupling eigenfunctions considering relativistic effects: Q(Re¹⁸⁵)=2.30 (4) [90] · 10^?24 cm² Q (Re¹⁸⁷)=2.20 (4) [90] · 10^?24 cm². (Figures in round brackets are experimental errors, those in square brackets are estimated uncertainties introduced by the theoretical evaluation.) Using these results and the knownB (a ⁶S_5/2) of Re¹⁸⁶ and Re¹⁸⁸ also the nuclear quadrupole moments of these isotopes were derived. Q(Re¹⁸⁶)≈Q(Re¹⁸⁸)≈0.4 · 10^?24 cm².     

Eine Hyperfeinstruktur-Analyse der Grundkonfigurationen 5d 8 6s 2 und 5d 9 6s des Pt-I Spektrums

The hyperfine structure of the ground configurations 5d ⁸ 6s ² and 5d ⁹ 6s of the stable Platin isotopes 194, 195, 196, 198 was analyzed. For the isotope 195 a complete set of the magnetic splitting constantsA is given. TheA constants of the levels 5d ⁸ 6s ^{2 3} P ₁ and¹ D ₂ were determined for the first time. From these data the electronic splitting constants a_{6 s}=l010(10) mK, a_{d 3/2}=57 (6) and a_{d 5/2}=27 (2) mK could be evaluated. The effect of core polarization is discussed and a fieldκ _cp=?5.6(1.0) a.u. per 5d-electron spin is found. Also the isotopic shift is determined and for the mean quadratic nuclear charge radius the valueΒδ <r ²>=0.095 (10) fm² is derived.     

Hyperfine-structure investigation in the 6s5d configuration of135Ba and137Ba

The hyperfine structure of the metastable states of the 6s5d configuration of¹³⁵Ba and¹³⁷Ba has been studied by the atomic-beam magnetic resonance (ABMR) method. The metastable barium states were populated in a plasma-discharge inside the atomic-beam oven. The atoms emerging from the ABMR-apparatus were detected by the use of a dyelaser. Compared to conventional methods this technique has the advantage of being state selective. The following magnetic dipole and electric quadrupole interaction constantsa andb have been obtained:¹³⁷Ba:a(³ D ₁)=?520.536 (3) MHzb(³ D ₁)=17.890 (3) MHza(³D₂=415.928 (3) MHzb(³D₂)=25.899 (13) MHza(³D₃)=456.559 (4) MHzb ³D₃=47.390 (16) MHz¹³⁵Ba:a ³ D ₁=?465.166 (4) MHzb(³D₁)=11.642 (4) MHza(³D₂)=371.736(4) MHzb ³ D ₂=16.745 (14) MHza(³D₃)=408.038 (6) MHzb(³D₃)=30.801 (24) MHz Using these constants and the earlier known ones for the¹ D ₂ state the hyperfine structure for the 6s5d configuration has been analyzed with an effective hyperfine hamiltonian. Hyperfine parameters obtained from the analysis have been compared with theoretical values calculated with relativistic self-consistent-field (SCF) wavefunctions. The quadrupole moments have been evaluated with the following result Q(¹³⁵Ba) =0.20(3)b and Q(¹³⁷Ba) = 0.34(4)b uncorrected for the quadrupole shielding.     

Observation of E2-fission decay for232Th from electro- and photoinduced reactions

The hyperfine structure constants of⁹⁵Mo and⁹⁷Mo and the g_J-factors have been measured in the metastable multiplets 4d⁴5s² a⁵D, 4d⁵5s a⁵S, a⁵P, and 4d⁶ c⁵D by atomic beam magnetic resonance combined with state-selective laser-induced detection of the rf-resonant atoms. Line isotope shifts and the A- and B-factors of further metastable levels and of high-lying odd-parity states were obtained from high-resolution Doppler-free laser spectroscopy.     

Hyperfine structure in the atomic spectrum of niobium

A parametric analysis of the fine and the hyperfine structure for the three even configurations 4d^45s, 4d ⁴5s ² and 4d⁵ has been performed. Effective one-electron parameters a _nl ^kskl(k _s k _l = 01, 12 and 10) and b _nl ⁰² were determined for these three configurations. Extremely large ratios a _4d ¹⁰/a _4d ⁰¹ were found. Theoretical predictions for the hyperfine structure constants A and B for all levels of the configurations 4d^45s, 4d ⁴5s ² and 4d⁵ have been determined from experimental data. Additionally, the fine and hyperfine structure for the two energetically high lying even configurations 4d^46s and 4d^35s6s are discussed. The results presented here call into doubt the existence of the fine structure levels 4d ³5s6s ⁶ F _11/2 at an energy of 39 408.88 cm^-1 and 4d ³5s5p ⁶ G _13/2 at 18 876.46 cm^-1 given in the Moore tables.     

Determination of transition probabilities for singly ionized vanadium

Transition probabilities of 211 spectral lines of VII, in the wavelength range 2340–4200 Å, have been determined by emission spectroscopy using a wall-stabilized arc as source. The lines studied belong to the transition arrays 3d⁴, 3d³4s-3d³4p (199 lines) and 3d³4p-3d³4d, 3d³5s (12 lines). Vanadium was introduced into the helium-arc discharge as the liquid VOCl₃. An important feature of this work is the determination of transition probabilities for many lines from a wide spectral range with a uniform absolute scale. The absolute A_ki values were obtained by normalizing relative A_ki values to an absolute scale set by ionic lifetime for the level y³H⁰₄. These results are compared with other experimental as well as theoretical results.     

Hyperfine anomaly in the spectrum of the osmium atom. effect of the spatial distribution of nuclear charge

Contributions of the superposition of configurations ns ²5d ⁸+ns5d ⁸ n′s (n=1–5, n′=6–10) and ns ²5d ⁶+ns5d ⁶ n′s (n=1–6, n′=7–10) to parameters a _5d ⁰¹ , a _5d ¹² , and a _5d ¹⁰ of the hyperfine structure in the spectrum of the osmium atom OsI are calculated. It is shown that the nonzero contribution is made only to a _5d ¹⁰ . The effect of the spatial distribution of nuclear charge on the parameters of the hyperfine structure in the spectra of ¹⁸⁷Os and ¹⁸⁹Os isotopes and on the hyperfine anomaly for the 5d ⁷6s levels in the spectrum of these isotopes is estimated.     

Optical determination of the nuclear moments of137La

Using the reactor-produced lanthanum isotope ₅₇ ¹³⁷ La, the hyperfine structure (hfs) of the transition La I, 5d ² 6p z ⁴ G ₁₁ ^2/0 ?5d ² 6s a ⁴ F _9/2, λ=6250 Å and La I, 5d ² 6p z ² H ₁₁ ^2/0 ? 5d ² 6s a ²G_9/2, λ=6266 Å were measured by means of a Fabry-Pérot interferometer. The nuclear spin I (¹³⁷La)=7/2, already theoretically estimated by earlier authors, was confirmed. The nuclear magnetic dipole moment μ_I(¹³⁷La)=+ 2.690 (6) n.m. and the electric quadrupole momentQ(¹³⁷La)=+ 0.26 (8) · 10^?24 cm² were determined from the ratios of the hfs interaction constantsA andB of¹³⁷La and the natural¹³⁹La.     

Lifetime measurements in the Fe I spectrum using tunable dye laser excitation

Radiative lifetimes of single fine structure levels of the multiplets 3d⁶ 4s(a⁶ D)4p z⁵ D ⁰ and 3d⁷ (a⁴ F)4py ⁵F⁰ of the FeI spectrum were measured. The different levels were excited by a tunable dye laser which was pumped by a pulsed nitrogen laser. The exponential decay of the fluorescence was measured directly.     

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).     

Gas phase high temperature photoelectron spectroscopy: an investigation of the transition metals scandium and vanadium

The He(I) photoelectron spectra of atomic scandium and vanadium have been recorded in the gas-phase. For scandium two bands associated with a (4s)^?1 ionization and one band associated with a (3d)^?1 ionization of the neutral atom have been observed. Measurement of their relative intensities allows the σ_3d:σ_4s photoionization cross-section ratio in atomic scandium to be estimated as 57.1 ± 9.0. In the atomic vanadium spectrum, six bands were seen. Four of these correspond to (3d)^?1 and (4s)^?1 ionizations of the ground state of the neutral atom, the V a⁴F state, whereas two bands correspond to (3d)^?1 ionizations of an excited state, the V a₆D state, which is approximately 2100 cm^?1 above the ground state. Measurement of the intensities of bands arising from the V a₄F state allows σ_3d:σ_4s to be estimated as 29.8 ± 2.5 for vanadium. Spectra of vanadium have been recorded with both single- and multi-detector photoelectron spectrometers. Comparison of the data acquisition rates obtained with both spectrometers demonstrates the advantage of using a multidetector instrument in high temperature photoelectron spectroscopy.     

Analysis of the lattice,strong coupling series for g0φ4 field theory in d dimensions

We analyze the renormalized strong coupling series for lattice g₀φ⁴ field theory which is a double series in x = M⁴a⁴/g₀a_4?dandy = 1/M²a², where M is the renormalized mass, a the lattice spacing, g₀ the bare coupling constant and d the dimension of space-time. We extrapolate to large y for fixed x by using a Padé-like extrapolation technique. We study the dimensionless renormalized coupling constant G/M^4?d and find that as we approach the continuum(x → 0, y → ∞) the entire spectrum of g₀ from zero to infinity can be studied. Our results for d = 1,2,3,4 based on a series in y up to y⁵ and in x up to x³ show that for fixed lattice spacing a, G/M^4?d is a monotonic function of g₀ ranging from zero at g₀ = 0 to a maximum at g₀ = ∞. Using the high temperature expansion results, we have also derived 9 terms in y on 8 lattices of dimension 1,2,3 and 4 for the linear term in x, and studied this series to see if one can see a breakdown in this monotonic behavior of G for large y. The analysis of this latter series is inconclusive.     

New neutron deficient isotopes with mass numbersA=136 and 145

High resolution laser-atomic-beam spectroscopy was applied to study crossed-second-order effects in the isotope shift of the terms 4f⁷5d6s a¹⁰D and a⁸D for¹⁵¹Eu-¹⁵³Eu. The term dependent effects lead to a difference in the isotope shift of the terms a¹⁰D and a⁸D of 415(20) MHz. The J dependent effects are interpreted through the use of one parameter z_5d for each term; z_5d(a¹⁰D)=41(7)MHz, z_5d(a⁸D)=50(26)MHz.     

New Identification of the Visible Bands of the C2 Swan System

The well known Swan system (d³Π_g-a³Π_u) of C₂ has been observed in absorption in a hollow cathode discharge in a mixture of C₂H₂ and helium. Three bands, (v′, v″)=(5, 7), (6, 8), and (7, 9), of the Swan system have been identified and rotationally analyzed. However, the transition wavenumbers are found not to be quite consistent with the literature values compiled by Phillips and Davis. The (7, 9) band has been observed and identified for the first time. New identifications of the (5, 7) and (6, 8) bands are presented. The observed wavenumbers are fit to the effective Hamiltonian derived by Brown and Merer for ³Π states. The molecular constants for both the upper and lower electronic states have been determined from the least squares fitting.     

Dissociative multiple photoionization of Br2, IBr,and I2 in the VUV and X-ray regions: a comparative study of the inner-shell processes involving Br(3d,3p,3s) and I(4d,4p,4s,3d,3p)

Dissociative multiple photoionization of the bromine, the iodine monobromide, and the iodine molecules in the Br(3d,3p,3s) and I(4d,4p,4s,3d,3p) inner-shell regions has been studied by using time-of-flight (TOF) mass spectrometry coupled to synchrotron radiation in the ranges of 90∼978 eV for Br₂, 60∼133 eV for IBr, and 86∼998 eV for I₂. Total photoion and photoion–photoion coincidence (PIPICO) yields have been recorded as functions of the photon energy. Here, giant shape resonances have been observed beyond the thresholds of the inner-shells owing to the Br(3d¹⁰)→Br(3d⁹ϵf), I(4d¹⁰)→I(4d⁹ϵf), and I(3d¹⁰)→I(3d⁹ϵf) transitions. The dissociation processes of the multiply charged parent ions have also been evaluated from variations of photoelectron–photoion coincidence (PEPICO) and PIPICO spectra with the photon energy. From each Br(3p_3/2) (189.9 eV) and I(4p_3/2) threshold (129.9 eV), quintuple ionization of the molecules begins to play important roles in the photoionization, subsequently yielding ion pairs of X³⁺–X²⁺ (X=Br, I). From the I(3d_5/2) threshold (627.3 eV), loss of six electrons from iodine molecule additionally begins to play a minor role in the multiple photoionization, giving rise to the formation of ion pairs of either I³⁺–I³⁺ or I⁴⁺–I²⁺. A direct comparison of the strengths and the ranges of the I(4d) and Br(3d) giant resonances was successfully made from dissociative photoionization of IBr. Over the entire energy range examined, 60<E<133 eV, biased charge spread relevant to the specific core-hole states of IBr is observed, presumably reflecting the fact that charge localizes mostly in the excited atoms, which can be accounted for mainly by a two step decay via a fast dissociation followed by autoionization upon the VUV absorption.     

Doppler-limited dye laser excitation spectrum of the C2 Swan band (v′ − v″ = 1 − 0)

The dye laser excitation spectrum of the Swan band (v′ ? v″ = 1 ? 0) has been observed with Doppler-limited resolution. The C₂ molecule was generated by the reaction of microwave discharge products of CF₄ with CH₄. The high sensitivity of laser excitation spectroscopy has enabled us to observe not only $\text{ΔΩ}\text{= 0}$ transitions, but also $\text{ΔΩ}\text{= ± 1}$ transitions and to determine molecular constants including the spin-orbit coupling constant for both the d³Π_g and a³Π_u states. The parameters thus obtained for a³Π_u were favorably compared with those previously obtained from the Ballik-Ramsay band. The present results on the d³Π_gv = 1 state were combined with those of an earlier Fourier spectroscopic study on the Swan band (v′ ? v″ = 0 ? 0) to derive equilibrium molecular constants for the d³Π_g state. The contributions of the spin-rotation interaction and the centrifugal correction for the spin-orbit coupling to the energy levels in a ³Π state have been discussed in detail.     

Hyperfine structure of the atomic osmium spectrum: Superposition of configurations and the effect of nucleus volume

The contributions of the superposition of configurations ns ²5d ⁷6s+ns5d ⁷6sn′s+ns5d ⁷6s ² (n=1–5, n′=7–10) to the parameters of the hyperfine structure a _5d ⁰¹ , a _5d ¹² , a _5d ¹⁰ , a _6s ¹⁰ in the spectrum of the osmium atom Os I are calculated. Nonzero contributions are shown to be made only to the parameters a _5d ¹⁰ and a _6s ¹⁰ . This fact justifies the inclusion of the parameter a _5d ¹⁰ in the semiempirical analysis of experimental values of magnetic dipole constants of the hyperfine structure of the 5d ⁷ s configuration in the spectrum of the osmium atom. The effect of nucleus volume on the parameters of the hyperfine structure in the spectra of osmium isotopes ¹⁸⁷Os and ¹⁸⁹Os is estimated.     

Discharged generator of singlet oxygen for oxygen-iodine laser. Transport kinetics of O2(a 1δg) and O2(b 1σ g + ) molecules and O(3 P) atoms in Ar:O2 and He:O2 flows excited by a 13.56-MHz discharge

To understand and reveal the basic physical factors providing the possibility of scaling of a discharged singlet oxygen generator (DSOG) in an oxygen-iodine laser, the production, and transport kinetics of metastable O₂(a ¹δ_g) and O₂(b ¹σ _g ⁺ ) molecules, as well as O(³ P) atoms, were investigated in Ar:O₂ and He:O₂ gas flows excited by a 13.56-MHz discharge in a wide range of pressures (4–40 Torr) and oxygen percentages. It is shown that the densities and transport kinetics of O₂(a ¹δ_g), O₂(b ¹σ _g ⁺ ), and O(³ P) appear similar for oxygen mixtures with argon and helium in the same conditions independent of discharge mode. Compared to pure O₂, the dilution of oxygen with an inert gas allows higher energy inputs per an oxygen molecule to achieved, especially under conditions of the homogeneous discharge mode (α-mode), which gives a higher efficiency of O₂(a ¹δ_g) excitation in Ar:O₂ and He:O₂ mixtures. But the maximum attainable yield of singlet oxygen in Ar:O₂ and He:O₂ at fixed partial O₂ pressure is found to be comparable with the O₂(a ¹δ_g) yield in pure oxygen at the same pressure. The reason for this is the increased three-body deactivation of O₂(a ¹δ_g) by atomic oxygen in the mixtures because of the greater total pressure. The estimation of the rate constant of O₂(a ¹δ_g) three-body quenching by O(³ P) in Ar:O₂ and He:O₂ mixtures as (1.5 ± 0.5) × 10^?32 cm⁶/s was carried out from the analysis of transport kinetics of singlet and atomic oxygen in the discharge afterglow at high pressures exceeding ～10 Torr. A similar analysis for the lower pressures has revealed that losses both of metastable O₂(a ¹δ_g) and O₂(b ¹σ _g ⁺ ) molecules, and of O(³ P) atoms on the surface of the discharge tube, are determined by the density of each of the components. The obtained loss probabilities of O₂(a ¹δ_g), O₂(b ¹σ _g ⁺ ), and O(³ P) on the silica surface show that the surface loss probabilities of all the species can increase noticeably under the discharge exposure. Thus, the key parameters determining the maximal O₂(a ¹δ_g) yield in the DSOG are a homogeneous volumetric mode of the discharge, energy input per oxygen molecule in this mode, and a low rate of O₂(a ¹δ_g) quenching. Just three-body quenching of O₂(a ¹δ_g) by O(³ P) limits the singlet oxygen yield with increasing pressure. The fast removal of atomic oxygen both in discharge and in the earlier afterglow could provide DSOG scaling with pressure.     

High-temperature VUV spectroscopy of KYF4 crystals doped with Nd3+, Er3+ and Tm3+ ions

Thermal quenching of 5d-4f luminescence from Nd³⁺, Er³⁺ and Tm³⁺ ions doped into KYF₄ crystals has been investigated in the temperature range up to ∼750 K where this luminescence is completely quenched. The obtained temperatures of thermal quenching (T_q) are ∼270, 495, 450 K for Nd³⁺, Er³⁺, Tm³⁺, respectively. At high temperatures, thermal quenching of 5d-4f luminescence from Nd³⁺ and Er³⁺ is accompanied by the appearance of 4f-4f luminescence from the lower-energy 4f levels. It has been shown that the dominating mechanism of thermal quenching for Nd³⁺ and Er³⁺ ions is thermally stimulated non-radiative transitions (intersystem crossing) from the 5d states to lower-energy 4f levels, namely ²G(2)_9/2 and ²F(2)_7/2, respectively, whereas for the Tm³⁺ ion, thermally stimulated ionization of 5d electrons to the conduction band states is responsible for thermal quenching of 5d-4f luminescence. The energy gap between the lowest Tm³⁺ 5d level and the bottom of the KYF₄ conduction band has been estimated to be 0.66 eV.     

Studies of R.F. discharges at moderate pressures and chemical applications—II. Nitrogen-hydrogen,nitrogen-methane and nitrogen-methane-hydrogen mixtures

Simultaneous vibro-rotational analyses have been carried out for the second positive system (SPS) of N₂ (C³П_u ? B³П_g), for the violet system (VS) of CN (B²Σ ? X²Σ) and for the Swan system (SS) of C₂ (d³П_g ? a³П_u), emitted by 35 MHz electrical discharges, containing N₂, H₂ and CH₄ flowing mixture s, in the 5–40 torr pressure range and at 1–10 Wcm^-3 power densities. The results are consistent with a Boltzman distribution for the rotational levels, but they show a deviation from this law for upper vibrational levels of CN and C₂.