Retardation (Casimir) energy shifts for Rydberg helium-like low-Z ions

The development of storage rings and electromagnetic traps for heavy charged particles is opening up new regimes of atomic physics, including, in particular, spectroscopic studies of Rydberg helium-like ions — with nuclear chargeZ, one electron in the 1s state, and one electron in a near-hydrogenic state of highn andl <n, withn andl the principal and orbital quantum numbers, respectively. We consider the possibility of detecting energy shifts due to retardation, ΔE _ret (n,l), Casimir-like effects. These are quantum electrodynamic (QED) retardation effects associated with the finite speed of light. (As opposed to basically kinematic and dynamic QED effects for small quantum numbersn andl, the appropriate expansion parameter forn andl large for retardation QED corrections is notZ(e ²/?c) but [(Z ? 1)/n ² Z ²](?c/e ²).) We wish to provide some orientation to those planning experiments in the area, with regard to the choices ofn,l, andZ most likely to be able to generate a high-precision confirmation of a retarded interaction. To do so, we provide extensive tables of estimates, for 1s,nl states, of ΔE _ret(n,l), of radiative widths, and ofE, the spin-independent (“electric” fine structure) energy in the absence of retardation shifts, for (nuclear spin zero) ions withZ=2, 6, 8, 16 and 20. These ions might be experimentally accessible in storage rings, and theZ's are low enough that virtual pair production effects may not yet be significant. There is also a brief survey of possible experimental techniques.     

A mass formula for the energy of metal clusters

We obtain an analytic expression for the total energy of a metallic cluster formed by N atoms of valence v and with net charge Q, by solving variationally the extended Thomas–Fermi version of density functional theory within the spherical jellium model. The energy is expressed as an expansion (mass formula) in decreasing powers of the cluster radius R_I = r_sZ^1/3, with Z = _vN, and r_s, the one electron radius of the bulk, and the coefficients of this mass formula are functions of r_s. Contributions of volume (R_I³), surface (R_I²), curvature (R_I), constant (R_I⁰), (1/R_I), and (1/R_I²) are clearly separated in the formula. The Chemical potential, work function, electron affinity, and ionization potential are easily obtained for neutral and charged clusters of any electronic density in the metallic range. A general estimation of the critical size for stability against electron detachment of negatively charged clusters is also obtained. The stability of highly charged clusters against fragmentation is also studied. © John Wiley & Sons, Inc.     

Studies on thermo-acoustic parameters of poly(ethylene glycol)- 400 at different temperatures

The ultrasonic velocity and density have been measured at different temperatures between 299 and 363 K for the pure liquid sample, poly(ethylene glycol) with average molecular mass 400 g mol^?1 (PEG 400). From these, isentropic compressibility (β), intermolecular free length (L _f), acoustic impedance (Z), molar volume (V _m), Schaff’s available volume V _a(s), molar sound velocity (R _a), and molar compressibility (W) have been evaluated. The variations of these parameters with the temperature of the sample have been studied. Data so obtained are employed to compute other thermodynamic parameters. Variations in various parameters with respect to temperature are discussed in the light of the results obtained.     

Ultrasonic investigation on aqueous polysaccharide (starch) at 298.15 K

The ultrasonic velocity, density and viscosity at 298.15 K have been measured in the binary system of starch in aqueous medium. The acoustical parameters such as adiabatic compressibility (β), free length (L_f), free volume (V_f), internal pressure (π_i), acoustical impedance (Z), relative association (R_A), Rao’s constant (R), Wada’s constant (W), classical absorption coefficients (α/f²), relaxation time (τ) and relaxation strength (r) are calculated. The results are interpreted in terms of molecular interaction between the components of the mixtures.     

Acoustical studies of some derivatives of 4-amino antipyrene in 1,4-dioxane and dimethylformamide at 318.15 K

For three derivatives of 4-amino antipyrene, density, viscosity and ultrasonic velocity are measured at 318.15 K in 1,4-dioxane (DO) and dimethylformamide (DMF). From these experimental data, various acoustical properties such as specific impedance (Z), isentropic compressibility (κ_s), Rao’s molar sound function (R_m), the van der Waals constant (b), molar compressibility (W), intermolecular free length (L_f), relaxation strength (r), relative association (R_A), free volume (V_f), etc. and apparent molar volume and apparent molar compressibility were calculated. The results are interpreted in terms of molecular interactions occurring in the solutions. It is observed that in 1,4-dioxane solutions, solute–solute interactions exist whereas solvent–solute interactions predominant in DMF system.     

Systematics of the librational modes of water in the IR spectra of MSO4 · H2O (M = Mn,Co, Ni,Zn)

In the isomorphous hydrates MSO₄ · H₂O (M = Mn, Co, Ni, Zn), where M-O_W distance is the only variable, the frequencies of the wagging, rocking and bending modes of water and of metal-oxygen stretching have been shown to correlate smoothly with the distance r(M-O_W). Quantitative relations have been found for ν_W and ν(M-O_W) which vary linearly, while ν_R and ν^C₂ vary non-linearly with r(M-O_W).     

Further studies on the taumerization of the hydrido (alkynyl) cluster Ru3Pt(μ-H) {μ4-ν2-C ≡ C1Bu} (CO)9(L2) to the vinylidene cluster Ru3Pt{μ4-ν2-C ≡ C(H)tBu} (CO)9(L2): X-ray structures of Ru3Pt(μ-H){μ4-ν2-C = C(H)tBu} (CO)9(L2); L2 = dppet,dppp, andS,S-dppb

The first order rate constants for the tautomerization of the hydrio(alkynyl) clusters Ru₃Pt(μ-H){μ₄-ν²-C ≡ C¹Bu}(CO)₉(L₂);1a: L₂ = dppe,1b; L₂ = dppet,1c; L₂ = dppp and1d; L₂ =S,S-dppb to the corresponding vinylidene clusters Ru₃Pt{μ₄-ν²-C = C(H)^tBu}(CO)₉(L₂)2 have been measured, and they follow the orser1d <1a <1b ～1c. The reactions involving1a and1d exhibit an inverse kinetic deuterium isotope effect. The structures of1b, 2b, 2c, and2d were determined by X-ray crystallography, and are compared with those of1a and2a which have been previously reported. Crystal data for1b, space groupPbca,a = 13.338(4) Å,b = 17.771(6) Å,c = 36.092(8) Å,Z = 8,R(R _w) = 0.059(0.058) for 2342 absorption corrected, observed data; for2b, space group P2₁/n,a = 10.566(2) Å,b = 20.234(5) Å,c = 20.270(3) Å,β = 96.11(1)°,Z = 4,R(R _w) = 0.043(0.053) for 5865 absorption corrected, observed data; for2c, space group P2₁/n,a = 14.211(5) Å,b = 19.534(2) Å,c = 15.870(2) Å,β = 100.81(2)°,Z = 4,R(R _w) = 0.055(0.031) for 6566 absorption corrected, observed data: for2d, space group P2₁2₁2₁,a = 12.309(4) Å,b = 19.047(6) Å,c = 19.206(4) Å,Z = 4,R(R _w) = 0.055(0.053) fpr 2151 absorption corrected, observed data. The fluxional behavior of1d and1e (which consists of two interconverting isomers) has been examined by variable temperature¹³C NMR spectroscopy and by³¹P EXSY.     

Tungsten(V) dimeric complexes with heterocyclic dithiocarbamates

In this paper we report the syntheses and study of a number of oxo- and sulphido-bridged tungsten(V) complexes with morpholine dithiocarbamate and piperidine dithiocarbamate as ligands. We assign the following formulae to the complexes: W₂O₃(Rdtc)₄, W₂O₄(Rdtc)₂, W₂O₂S₂(Rdtc)₂ and W₂O₃S(Rdtc)₂ (where R = morpholine and piperidine), based on the analytical data. We have studied the complexes by IR and electronic spectra, and magnetic susceptibility measurements. We assign in the IR spectra the following bands: W=O (ν_s=939–948 cm^?1), W-O_b(ν_a=813–819 cm^?1, ν_s = 431–448 cm^?1), W-S_b (ν_a=470–476 cm^?1, ν_s = 368–370 cm^?1, C-N (β = 1511–1519 cm^?1) and C-S (ν = 1090–1113 cm^?1). The low values of the magnetic moments (0.03–0.60 B.M.) are in accordance with a dimeric species of tungsten(V).     

New alkaline earth equiatomic phases: SrAu and BaAu

The phases SrAu and BaAu were synthesized and characterized structurally. SrAu,mP40, space groupP/2₁m, a = 40.13(2), b = 4.697(1), c = 6.192(4)A?, β = 94.21(6)°,Z = 20, is a new stacking variant of the FeBCrB type, with Jagodzinski notationhch₂ch₂chc. The structure was refined from single crystal diffractometric data withR = 0.090. BaAu,oP8, space groupPnma,a = 8.338(5), b = 4.925(1), c = 6.390(4)A?,Z = 4, crystallizes in the FeB structure type. A general correlation among theAB equiatomic phases formed by the alkaline earths with VIII to IVB group elements is found by reporting theBB chain angle against the combinationR^AB_σ = |(r^A_s + r^A_p) ? (r^B_s + r^B_p)| with Zunger'sr orbital radii.     

The fission of197Au by protons of energies of 52–85 MeV

Data are shown for the absolute cross-sections of independently-formed⁹⁶Nb and⁹⁷Nb and the cumulatively-formed⁹⁷Zr and⁹⁸Nb in the fission of¹⁹⁷Au by protons of energy 52–85 MeV. Charge dispersion curves have been constructed and the variation of /Z_A–Z_p/ as a function of proton energy determined.     

Reactions of a hydrido(hydrosilylene)tungsten complex with oxiranes

Reactivity of a hydrido(hydrosilylene)tungsten complex, Cp¹(CO)₂(H)WSi(H)[C(SiMe₃)₃] (1), toward oxiranes was investigated. Treatment of 1 with racemic mono-substituted oxiranes with a substituent R (R = Ph, vinyl, ^tBu, or ⁿBu) at room temperature produced dihydrido(vinyloxysilyl)tungsten complexes, (E)- and/or (Z)-Cp¹(CO)₂(H)₂W{Si(H)(OCHCHR)[C(SiMe₃)₃]} [(E/Z)-2: R = Ph, (E)-3: R = vinyl, (E)-4: R = ^tBu, (E/Z)-5: R = ⁿBu] in high yields via regioselective ring-opening of oxiranes. When the substituent R on oxirane was relatively large, (E)-isomers (2, 3, and 4) were obtained predominantly (87–97%), while the substituent was a relatively small ⁿBu group, an approximately 1:1 mixture of (E)- and (Z)-isomers [(E/Z)-5] was obtained. Reaction of 1 with 2,2-dimethyloxirane afforded the corresponding complex, Cp¹(CO)₂(H)₂W{Si(H)(OCHCMe₂)[C(SiMe₃)₃]} (6), quantitatively. A reaction mechanism is also discussed.     

Triosmium clusters derived from the reactions of thioureas with dodecacarbonyltriosmium: Crystal structures of [Os3(CO)11{η 1-SC(NMe2)2}], [Os3(CO)9(μ-OH)(μ-OMeOCO){η 1-SC(NMe2)2}] and [(μ-H)Os3(CO)9{μ 3-NHC(S)NH2}]

The reaction of [Os₃(CO)₁₂] with tetramethylthiourea in the presence of a methanolic solution of Me₃NO·2H₂O at 60° yields the compounds [Os₃(CO)₁₁{η ¹-SC(NMe₂)₂}] (1) in 56% yield and [Os₃(CO)₉(μ-OH)(μ-MeOCO){η ¹-SC(NMe₂)₂}] (2) in 10% yield in which the tetramethylthiourea ligand is coordinatedvia the sulfur atom at an equatorial position. Compound2 is a 50 e^? cluster with two metal-metal bonds and the hydroxy and methoxycarbonyl ligands bridging the open metal-metal edge. In contrast, the analogous reaction of [Os₃(CO)₁₂] with thiourea gives the compounts [(μ-H)Os₃(CO)₁₀{μ-NHC(S)NH₂}] (3) in 8% yield and [(μ-H)Os₃(CO)₉{₃-NHC(S)NH₂}] (4) in 30% yield. In3, the thioureato ligand bridges two osmium atomsvia the sulfur atom, whereas in4 in addition to the sulfur bridge, one of the nitrogen atoms of thioureato moiety bonds to the remaining osmium atom. The decacarbonyl compounds 3 can also be obtained in 50% yield from the reaction of [Os₃(CO)₁₀(MeCN)₂] with thiourea at ambient temperature. Compound3 converts to4 (65%) photochemically. Compound1 reacts with PPh₃ and acetonitrile at ambient temperature to give the simple substitution products [Os₃(CO)₁₁(PPh₃)] and [Os₃(CO)₁₁(MeCN)], respectively, while with pyridine, the oxidative addition product [(μ-H)Os₃(CO)₁₀(μ-NC₅H₄] is formed at 80°C. All the new compounds are characterized by IR,¹-H-NMR and elemental analysis together with the X-ray crystal structures of1,2 and4. Compound1 crystallizes in the triclinic space group P $P\bar 1$ with unit cell parametersa = 8.626(3) Å,b = 11.639(3) Å,c = 12.568(3_ Å,α = 84.67(2)°,β = 75.36(2)°,γ = 79.49(3)°,V = 1199(1) ų, andZ = 2. Least-squares refinement of 4585 reflections gave a final agreement factor ofR = 0.0766 (R _w = 0.0823). Compound2 crystallizes in the monoclinic space group P2_1/n with unit cell parametersa = 9.149(5) Å,b = 17.483(5) Å,c = 15.094(4) Å,β = 91.75(2)°,V = 2413(2) ų, andZ = 4. Least-squares refinement of 3632 reflections gave a final agreement factor ofR = 0.0603 (R _w = 0.0802). Compound4 crystallizes in the monoclinic space group C2/c with unit cell parametersa = 13.915(7) Å,b = 14.718(6) Å,c = 17.109(6) Å,β = 100.44(3)°,V = 3446(5) ų, andZ = 8. Least-squares refinement of 2910 reflections gave a final agreement factor ofR = 0.0763 (R _w = 0.0863).     

Ultrasonic studies of polysaccharide (pectin) in aqueous media at 298.15 K

The ultrasonic velocity, density and viscosity of pectin in aqueous medium were measured at 298.15 K. The acoustical parameters such as adiabatic compressibility (β), free length (L _f), free volume (V _f), internal pressure (π_i), acoustical impedance (Z), and relative association (R _A), Rao’s constant (R) and Wada’s constant (W) are calculated. The results are interpreted in terms of molecular interaction between the components of the mixtures. Further, some more acoustical parameters such as relaxation time (τ), absorption coefficient (α/f ²) and relaxation strength (r) are calculated with various percentage of pectin has been studied which reveals interaction between the solvent and the polymer (pectin) at various concentration of the polymer. The observed values suggested the solute-solvent interaction is favored.     

Acoustical studies on fructose with enzyme amylase in aqueous media at 298.15 K

Ultrasonic velocity (U), density (ρ), and viscosity (η) measurements have been carried out in three ternary mixtures of fructose with amylase in aqueous medium at 298.15 K. The experimental data have been used to calculate some derived parameters such as acoustical impedance (Z), relative association (R _a ), Rao’s constant (R _R), Wada’s constant (W), relaxation time (τ), relaxation amplitude (α/f ²), relaxation strength (r), and some excess thermodynamical properties like excess adiabatic compressibility (β ^E ), excess free length (L _f ^E ) excess free volume (V _f ^E ), excess internal pressure (π _i ^E ), and excess acoustical impedance (Z ^E ). The above parameters have been evaluated and discussed in light of molecular interactions in the mixture.     

Crossed-second-order effects in the isotope shift for170–166Er and168–166Er in the configuration 4f 12 6s 2

High resolution interference and intermodulated optogalvanic saturation spectroscopy has been applied for isotope shift (IS) studies in the ground-configuration 4f ¹² 6s ² of ErI. For the isotope pairs^170–166Er and^168–166Er the results confirm a strongJ- and term dependence of the IS caused through crossed-second-order (CSO) effects. We performed a parametric analysis to evaluate the CSO-parametersz _4f for the interpretation of theJ-dependence andT(³ H),T(³ F),T(¹ G) to describe the term dependence. The following parameter values (in MHz) were determined, for^170–166Er:z _4f =40.1(0.6),T(³ F)=?153(5),T(³ H)=?220(6), andT(¹ G)=?79(4); for^168–166Er:z _4f =20.1(0.7),T(³ F)=?77(6),T(³ H)=?111(7), andT(¹ G) =?43(5). The normalization of these parameters with the corresponding nuclear parameters λ for both isotope pairs leads to almost identical parameter values indicating a dominant influence of the field shift effect in second-order for thez _4f parameter and in third-order for the parametersT(³ F),T(³ H), andT(¹ G).     

The crystal structures of α,ω-diaminoalkanecadmium(II) tetracyanonickelate(II)-aromatic molecule inclusion compounds. IV. (1,6-Diaminohexane)cadmium(II) tetracyanonickelate(II)-m-toluidine(1/1),-p-toluidine(1/1), and-2,4-xylidine(1/1) clathrates,and the coordination complex bis(p-toluidine) (1,6-diaminohexane)cadmium(II) tetracyanonickelate(II)

The crystal structures of the four title compounds have been analyzed by single crystal X-ray diffraction methods at room temperature. Three with a general formula Cd[NH₂(CH₂)₆NH₂]Ni(CN)₄·G (G=m-toluidine,Im;p-toluidine,Ip; and 2,4-xylidine,Ix) are the inclusion compounds of the respective aromatic molecules in the three-dimensional metal complex host (1,6-diaminohexane)cadmium(II) tetracyanonickelate(II). The remaining one is a coordination complex ofp-toluidine, bis(p-toluidine) (1,6-diaminohexane)cadmium(II) tetracyanonick-elate(II),II, Im, Ix, andII crystallize under similar experimental conditions;Ip is obtained using thep-toluidinemesitylene mixture at higher dilution than that used forII. Im crystallizes in the tri linic space group \(P\bar 1\) , witha=9.725(2),b=7.598(1),c=7.177(1) Å, α=90.44(1), β=98.80(1), γ=95.70(1)^o, andZ=1 (the final conventionalR=0.037 for 3526 reflections);Ip: monoclinic,P2/m,a=9.540(2),b=7.611(1),c=7.120(1) Å, β=100.95(1)^o, andZ=1 (R=0.027 for 1700 reflections);Ix: monoclinic,P2/m,a=9.628(2),b=7.613(1),c=7.122(1) Å, β=100.01(1)^o, andZ=1 (R=0.049 for 2704 reflections);II: monoclinic,P2₁/n,a=12.107(3),b=10.117(2),c=12.471(3) Å, β=113.67(2)^o, andZ=2 (R=0.037 for 2616 reflections). The structures ofIm, Ip andIx are similar to that of theo-toluidine inclusion compound of the same metal complex host. InII atrans pair of thep-toluidine molecules to the cadmium atom in the two-dimensional network formed by thecatena-μ-linkages of ?Cd?NH₂(CH₂)₆NH₂?Cd? and ?NC?Ni?CN?Cd?NC?Ni?CN?intersecting at each Cd atom; two cyanide groups of the tetracyanonickelate(II) moiety have free N-ends.     

The phenomenon of conglomerate crystallization. Part 40: The crystallization behavior oftrans- Co(III) amines (+)546-trans-[Co(3,2,3-tet)(NO2)2]Cl·3H2O (I), (−)589 -trans-[Co(3,2,3-tet)Cl2]NO3 (II), and of (+)546-trans-[Co(3,2,3-tet)(NO2)2]NO3 (III)

A racemic solution of (I) crystallizes as a conglomerate from which a crystal we selected was found to be (+)₅₄₆-trans-[Co(3,2,3-tet)(NO₂)₂]Cl·3H₂O (I), CoClO₇N₆C₈H₂₈. It crystallizes in the enantiomorphic space groupP2_l2_l2_l, with lattice constantsa=18.501(15) å,b=14.433(2) å, andc=6.441(3) å;V=1720.07 å³ andd(calc. M.W.=414.73,Z=4)=1.601 g cm^?3. A total of 2305 data were collected over the range of 4?≤2θ ≤55?; of these, 1724 (independent and withI > 3σ(I)) were used in the structural analysis. Data were corrected for absorption (Μ=11.920 cm^?1), and the relative transmission coefficients ranged from 0.8258 to 0.9565. Refinement was carried out for both lattice enantiomorphs, and at this stage theR(F) andR _w (F) residuals were, respectively, 0.0381 and 0.0479 for (+ + +) and 0.0448 and 0.0532 for (? ? ?). Thus, the former was selected as correct for our specimen, and the final cycle of refinement with the (+ + +) model converged toR(F) andR _w (F) of 0.0315 and 0.0365. A racemic solution of (II) crystallizes as a conglomerate from which a crystal we selected was found to be (?)₅₈₉-trans-[Co(3,2,3-tet)Cl₂]NO₃ (II), CoCl₂O₃N₅C₈H₂₂. It crystallizes in the enantiomorphic space groujp,P2_l with lattice constantsa=6.395(2) å,b=8.886(2) å,c=13.185(2) å, andΒ=99.24(2)?;V=739.59 å³ andd(calc. M.W.=366.14,Z=2)=1.646 g cm ^?3. A total of 2912 data were collected over the range of 4?<2θ<64?; of these, 2147 (independent and withI≥3σ(I)) were used in the structural analysis. Data were corrected for absorption (Μ =15.424 cm^?1), and the relative transmission coefficients ranged from 0.9632 to 0.9985. Refinement was carried out for both lattice enantiomorphs, and the finalR(F) andR _w (F) residuals were, respectively, 0.0326 and 0.0328 for (+ + +) and 0.0347 and 0.0348 for (? ? ?). Thus, the (+ + +) was selected as correct for our specimen. A racemic solution of (III) crystallizes as a conglomerate from which a crystal we selected was found to be (+)₅₈₉-trans-[Co(3,2,3-tet)(NO₂)₂]NO₃ (III), CoO₇N₇C₈H₂₂. It crystallizes in the enantiomorphic space group,P2_l with lattice constantsa=6.295(1) å, b=15.108(3) å,c=8.029(1) å, andΒ=100.28(2)?;V=751.35 å³ andd(calc. M.W.=387.24,Z=2)=1.712 g cm^?3. A total of 2393 data were collected over the range of 4?≤2θ≤60?; of these, 1869 (independent and withI≥3σ(I)) were used in the structural analysis. Data were corrected for absorption (Μ=11.859 cm^?1), and the relative transmission coefficients ranged from 0.8814 to 0.9976. Refinement was carried out for both lattice enantiomorphs and the finalR(F) andR _w (F) residuals were, respectively, 0.0463 and 0.0482 for (+ + +) and 0.0441 and 0.0442 for (? ? ?). Thus, the latter was selected as correct for our specimen, and the final cycle of refinement with the (? ? ?) model converged toR(F) andR _w (F) of 0.0436 and 0.0421. For all three compounds, the six-membered rings are chairs; the secondary nitrogens are chiral centers, and the five-membered rings are ordered and conformationally dissymmetric, as expected. Coincidentally, in (I), (II), and (III) the central rings are right-handed helices withδ(+50.0?),δ(+53.3?), andδ(+48.3?), respectively. Thus, the secondary nitrogens of all three cations are (R), rendering the cations chiral. The incidence of conglomerate crystallization intrans coordination compounds is rare, and those known are asymmetrically substituted (see Ref. 4 for the four known cases). Thus, the incidence of such crystallization mode in a new series of [trans- Co(amine ligands)X₂]⁺ cations bearing symmetrical pairs oftrans ligands was an unexpected and welcomed event. In all three cases, the counteranions are bonded to the hydrogens of the terminal -NH₂ moieties, thus forming an overall entity which resembles a macrocycle. In fact, parallels between the crystallization behavior of our compounds and that of macrocycles bearing related fragments is discussed. Finally, in the three compounds, homochiral cations are linked into infinite strings by hydrogen bonds between the axial ligands and amino hydrogens on adjacent cations of the string. In turn, strings are stitched together by the counteranions which form bonds with amino hydrogens on cations of adjacent strings.     

Electron affinities of the lanthanides

The electron affinities (EA's) of the lanthanides (La through Tm) have been determined from the expression EA = IP₁ ? C)r^?1)_n1, where IP₁ is the first ionization potential and (r^?1)_n1 is the relativistic radial integral of an electron in the unfilled shell, the constant C includes the quantum numbers n, 1 of the partly filled shells and the atomic number Z of each element. The EA's vary from +0.5 eV (La) to –0.2eV (Tm) which is consistent with other semi-empirical estimates for certain lanthanide elements.     

Quadrupole moments of radium isotopes from the 7p 2 P 3/2 hyperfine structure in Ra II

The hyperfine structure and isotope shift of^221–226Ra and^212,214Ra have been measured in the ionic (Ra II) transition 7s ² S _1/2–7p ² P _3/2 (λ=381.4 nm). The method of on-line collinear fast-beam laser spectroscopy has been applied using frequency-doubling of cw dye laser radiation in an external ring cavity. The magnetic hyperfine fields are compared with semi-empirical and ab initio calculations. The analysis of the quadrupole splitting by the same method yields the following, improved values of spectroscopic quadrupole moments:Q _s (²²¹Ra)=1.978(7)b,Q _s (²²³Ra)=1.254(3)b and the reanalyzed valuesQ _s (²⁰⁹Ra)=0.40(2)b,Q _s (²¹¹Ra)=0.48(2)b,Q _s (²²⁷Ra)=1.58(3)b,Q _s (²²⁹Ra)=3.09(4)b with an additional scaling uncertainty of ±5%. Furthermore, theJ-dependence of the isotope shift is analyzed in both Ra II transitions connecting the 7s ² S _1/2 ground state with the first excited doublet 7p ² P _1/2 and 7p ² P _3/2.     

On the evaluation of non-adiabatic coupling matrix elements for large scale CI wavefunctions

The implementation of a recently proposed technique for evaluating matrix elements of the form 〈Ψ_J(r;R)|∂Ψ_I(r;R)/t6R_α〉_r using analytic gradient techniques is described. The Ψ_K(r;R) are developed from state-averaged multiconfiguration self-consistent-field/configuration interaction (CI) wavefunctions. The CI wavefunctions are determined using the shape driven graphical unitary group approach. The method is shown to be considerably more efficient than presently existing approaches based on divided differences. As an illustration of the potentialities of this approach non-adiabatic coupling matrix elements are determined for the collinear charge transfer reaction: Mg(¹S) + FH(¹Σ⁺)→MgF(²Σ⁺)+H(²S).