Half-life measurements in59Co,141Pr and227Ac

The half-lives of the 1291.6 keV level in⁵⁹Co, 145.43 keV level in¹⁴¹Pr and 27.35 keV level in²²⁷Ac have been measured using leading edge and zero-crossover timing techniques. The decay curves analysed by moments, Laplace transform and slope methods gave the following half-life values: $$\begin{gathered} T_{\tfrac{1}{2}} (1291.6 keV level in {}^{59}Co) = (0.538 \pm 0.004) ns \hfill \\ T_{\tfrac{1}{2}} (145.43 keV level in {}^{141}\Pr ) = (1.82 \pm 0.04) ns \hfill \\ T_{\tfrac{1}{2}} (27.35 keV level in {}^{227}Ac) = (41.0 \pm 1.1) ns. \hfill \\ \end{gathered} $$ From the measured half-lives, the reduced transition probabilitiesB(M1)↓,B(E2)↓ for gamma transitions de-exciting the above mentioned levels in⁵⁹Co and¹⁴¹Pr are determined and compared with single particle, intermediate coupling and Sorensen estimates. In²²⁷Ac, absolute transition probability for the 27.35 keV transition is determined and compared with single particle and Nilsson estimates.     

Experimental determination of penetration parameter forM1 conversion,and theE2 admixtures for 77 and 191 keV transitions in197Au

TheL-subshell conversion for 77 keV transition andK,L ₁,L ₂-shell conversion for 191 keV transition in¹⁹⁷Au, as well asK-shell conversion transition of 158 keV in¹⁹⁹Hg were measured by means of Π√2-iron free electron spectrometer. Relative gamma-ray intensities have been determined by Ge(Li) spectrometer. From these measurements the α _K conversion coefficient value has been deduced for 191 keV transition as α_K(191 keV)=0.86±0.03. This value shows that the spin of the level at 268 keV in¹⁹⁷Au is 3/2⁺. For the penetration parameter (λ) and intensity ratio \(\left( {\delta ^2 = \frac{{\left\langle {E2} \right\rangle ^2 }}{{\left\langle {MI} \right\rangle ^2 }}} \right)\) the following values are obtained: $$\begin{gathered} \lambda = 3.4 \pm _{1.5}^{1.9} \delta ^2 = 0.11 \pm 0.03for 77 keV transition \hfill \\ \lambda = 3.2 \pm _{0.6}^{0.8} \delta ^2 = 0.17 \pm 0.04for 191 keV transition. \hfill \\ \end{gathered} $$ The agreement of these results with the predictions of De Shalit model is discussed.     

Alpha decay of neutron-deficient rhenium and osmium isotopes

Neutron-deficient osmium and rhenium isotopes were produced by bombarding an enriched¹⁴⁴Sm target with beams of²⁷Al and²⁸Si. Previously reported decay data concerning^168,169,170Os were confirmed. Three newα groups, observed in the¹⁴⁴Sm+²⁷Al reaction, were assigned to the decay of^166,167,168Re based on excitation functions,α-energy systematics and theoretical half-life predictions. Their decay properties are: $$\begin{gathered} {}^{166}\operatorname{Re} , E_\alpha = 5,372 (10) keV, T_{1/2} = 2.8 (3) s; \hfill \\ {}^{167}\operatorname{Re} , E_\alpha = 5,136 (8) keV, T_{1/2} = 6.1 (2) s and \hfill \\ {}^{168}\operatorname{Re} , E_\alpha = 4,894 (10) keV, T_{1/2} = 6.9 (8) s. \hfill \\ \end{gathered}$$ It is proposed that twoα groups, observed in the¹⁴⁴Sm+²⁸Si reaction, originate from isomeric states in^168,169Re. Our measured data for the isomeric states are: $$\begin{gathered} {}^{168m}\operatorname{Re} , E_\alpha = 5,250 (10) keV, T_{1/2} = 6.6 (15) s and \hfill \\ {}^{169m}\operatorname{Re} , E_\alpha = 5,050 (10) keV, T_{1/2} = 12.9 (11) s. \hfill \\ \end{gathered} $$      

Internal magnetic hyperfine fields at Hf nuclei in iron,cobalt and nickel hosts

Integral perturbed angular correlation technique has been used to measure the internal hyperfine magnetic fields at Hf nuclei in Fe, Co and Ni matrices. These represent a consistent set of measurements with diffused sources. The 9+/2 (208 keV) 9?/2 (113 keV) 7?/2 cascade in the decay of¹⁷⁷Lu→¹⁷⁷Hf was used for measurements. The results obtained are: $$\begin{gathered} H_{Fe}^{Hf} = - 266 \pm 47 kG, \hfill \\ H_{Co}^{Hf} = - 116 \pm 18 kG, \hfill \\ H_{Ni}^{Hf} = - 118 \pm 26 kG. \hfill \\ \end{gathered} $$ These measurements are compared with previous results and discussed in terms of methods of source preparation.     

Determination of hyperfine interactions from partly resolved moessbauer spectra

Moessbauer spectra with different sets of parameters were calculated. A fit with a superposition of Lorentzians to these theoretical spectra showed, that systematic errors must be expected if the hyperfine structure of the spectrum is only partly resolved. Correction factors for some simple cases are given. Experiments to test the calculations were performed with¹³³Cs (81 keV transition),¹⁶⁵Ho (94.7 keV transition) and¹⁷⁸Hf (93 keV transition). In all cases fits using the transmission integral and superpositions of Lorentzians showed the expected trends. We get the following results: $$\begin{gathered} ^{133} Cs:\frac{{g_{ex} }}{{g_{gr} }} = 1.90\left( 4 \right) \hfill \\ ^{165} Ho:\tau \left( {94.7keVlevel} \right) = 32\left( 1 \right)ps \hfill \\ \frac{{g_{ex} }}{{g_{gr} }} = 0.77\left( 3 \right) \hfill \\ ^{178} Hf:|H_{eff} \left( {4K,in iron} \right)| = 633\left( {40} \right)KG \hfill \\ |H_{eff} \left( {77K,in iron} \right)| = 630\left( {41} \right)KG. \hfill \\ \end{gathered}$$      

Hyperfeinstruktur- und Stark-Effekt-Untersuchungen der Terme 4d5s5p z 2 F 5/2 undz 2 F 7/2 im Yttrium I Spektrum

The hyperfine structure and the Stark effect shift of the 4d5s5p z ² F _5/2 states in the Y I spectrum were investigated by level-crossing technique. Between the Zeeman effect region and the Paschen-Back region of hyperfine structure states some of the levels cross. The resonance radiation of these coherently excited levels show an interference effect of the scattering amplitudes in the crossing region. The level-crossing signals give information about hfs splitting and lifetime of the excited states under investigation. The magnetic hfs splitting factorsA of the 4d5s5p z ² F _{5/2, 7/2} states and their lifetimes were deduced. $$\begin{gathered} |A (z^2 F_{5/2} )| = (23.8 \pm 0.04) MHz \frac{{g_J }}{{0.854}} \hfill \\ |A (z^2 F_{7/2} )| = (84.08 \pm 0.01) MHz \frac{{g_J }}{{1.148}} \hfill \\ \tau (z^2 F_{5/2} ) = (46 \pm 3) 10^{ - 9} s \frac{{0.854}}{{g_J }} \hfill \\ \tau (z^2 F_{7/2} ) = (44 \pm 4) 10^{ - 9} s \frac{{1.148}}{{g_J }}. \hfill \\ \end{gathered} $$ With an electric field parallel to the magnetic field a shift of the level-crossing signals of the 4d5s5p z ² F _{5/2, 7/2} states was observed, and the Stark constants β were deduced. $$\begin{gathered} |\beta (z^2 F_{5/2} )| = (0.0020 \pm 0.0002) MHz/(kV/cm)^2 \hfill \\ |\beta (z^2 F_{7/2} )| = (0.0025 \pm 0.0015) MHz/(kV/cm)^2 . \hfill \\ \end{gathered} $$      

Editorial

The production of charmed mesons ,D ^± , andD ^*± is studied in a sample of 478,000 hadronicZ decays. The production rates are measured to be

More corrections to the sixth-order anomalous magnetic moment of the muon

The contribution to the sixth-order muon anomaly from second-order electron vacuum polarization is determined analytically to orderm _e/m _μ. The result, including the contributions from graphs containing proper and improper fourth-order electron vacuum polarization subgraphs, is $$\begin{gathered} \left( {\frac{\alpha }{\pi }} \right)^3 \left\{ {\frac{2}{9}\log ^2 } \right.\frac{{m_\mu }}{{m_e }} + \left[ {\frac{{31}}{{27}}} \right. + \frac{{\pi ^2 }}{9} - \frac{2}{3}\pi ^2 \log 2 \hfill \\ \left. { + \zeta \left( 3 \right)} \right]\log \frac{{m_\mu }}{{m_e }} + \left[ {\frac{{1075}}{{216}}} \right. - \frac{{25}}{{18}}\pi ^2 + \frac{{5\pi ^2 }}{3}\log 2 \hfill \\ \left. { - 3\zeta \left( 3 \right) + \frac{{11}}{{216}}\pi ^4 - \frac{2}{9}\pi ^2 \log ^2 2 - \frac{1}{9}log^4 2 - \frac{8}{3}a_4 } \right] \hfill \\ + \left[ {\frac{{3199}}{{1080}}\pi ^2 - \frac{{16}}{9}\pi ^2 \log 2 - \frac{{13}}{8}\pi ^3 } \right]\left. {\frac{{m_e }}{{m_\mu }}} \right\} \hfill \\ \end{gathered} $$ . To obtain the total sixth-order contribution toa _μ?a _e, one must add the light-by-light contribution to the above expression.     

Some investigations on the decay of60Co

The⁶⁰Co decay has been reinvestigated using an electromagneticβ-spectrometer and a Ge(Li)γ-spectrometer. A new weakβ ^?-transition of characterΔJ=3, no parity change between the 5⁺ groundstate of⁶⁰Co and the second excited 2⁺ level atE=2.155 MeV in⁶⁰Ni could be established. The endpoint energies and intensities of the threeβ ^?-transitions are: $$\begin{gathered} E_{\beta \bar 1\max } = \left( {1.492 \pm 0.020} \right)MeV,I_{\beta \bar 1} = \left( {0.08 \pm 0.02} \right)\% ; \hfill \\ E_{\beta \bar 2\max } = \left( {0.670 \pm 0.020} \right)MeV,I_{\beta \bar 2} = \left( {0.18 \pm 0.03} \right)\% ; \hfill \\ E_{\beta \bar 3\max } = \left( {0.315 \pm 0.004} \right)MeV,I_{\beta \bar 3} = \left( {99.74 \pm 0.05} \right)\% ; \hfill \\ \end{gathered} $$ . The intensity ratio of the stopover and crossoverγ-transitions deexciting the 2.155 MeV level has been determined to be ≧120. Some conclusions for the theory are discussed.     

The g-factors of isomeric states in127, 128Xe

Excited states in^{127, 128}Xe were populated in the reaction⁹Be+¹²²Sn atE _lab=38 MeV. The de-excitation of the isomeric states 7/2⁺ in¹²⁷Xe and 8^? in¹²⁸Xe was studied using angular distribution and TDPAD methods on molten¹²²Sn targets. The results are $$\begin{gathered} T_{1/2} (7/2^ + ) = 37 \pm 1 ns, g(7/2^ + ) = + 0.241 \pm 0.009 \hfill \\ T_{1/2} (8^ - ) = 83 \pm 2 ns, g(8^ - ) = - 0.036 \pm 0.009. \hfill \\ \end{gathered}$$ The experimentalg-factors suggest the main configurationsvg _7/2 andvh _11/2 g _7/2 for the isomeric states. Detailed analysis of the combined information fromg-factors and transition rates set stringent limits on the admixtures of the wave functions. The quasirotational bands built on the two-quasiparticle 6^? and 10⁺ states are extended to higher spins, (14^?) and (16⁺), respectively, and their structures are analyzed within the framework of the Interacting Boson Model.     

Theg-factor of the 181 keV level of99Tc and hyperfine fields of Tc in Fe,Co, Ni

Theg-factor of the 181 keV-level of⁹⁹Tc has been redetermined by the spin rotation method. Measurements with polycrystalline sources of Tc in Fe, Co, and Ni yielded values of the hyperfine fields at the Tc nucleus. $$\begin{gathered} g = + 1.310(25) \hfill \\ H_{hf} (Tc{\mathbf{ }}in{\mathbf{ }}Fe) = ( - )290(15)kOe \hfill \\ H_{hf} (Tc{\mathbf{ }}in{\mathbf{ }}Co) = ( - )170(5)kOe \hfill \\ H_{hf} (Tc{\mathbf{ }}in{\mathbf{ }}Ni) = - 47.8(1.5)kOe. \hfill \\ \end{gathered} $$      

Paramagnetische Resonanz an Einkristallen einiger Selten-Erd-Oxide

The paramagnetic resonance of Nd³⁺ in Y₂O₃ has been measured at 4.2°K and 9.25 kMe/s. The values of theg-tensors are: ions onC _3i -sites:g _∥=2.434±0.007;g _⊥=0.702±0.005; ions onC ₂-sites:g _x =4.395±0.012;g _y =0.433±0.009;g _z =1.648±0.006. Further measurements have been performed on La₂O₃ crystals doped with Ce³⁺, Dy³⁺, and Er³⁺; the results are (C _3v -sites only): .      

An expansion of Hartree-Fock and correlation energies,relativistic corrections and the dipole matrix element in the powers of of 1/Z

Feynman diagrammatic technique was used for the calculation of Hartree-Fock and correlation energies, relativistic corrections, dipole matrix element. The whole energy of atomic system was defined as a polen-electron Green function. Breit operator was used for the calculation of relativistic corrections. The Feynman diagrammatic technique was developed for 〈H_B>. Analytical expressions for the contributions from diagrams were received. The calculations were carried out for the terms of such configurations as 1s² 2sⁿ¹ 2pⁿ² (2 ≧n₁≧ 0, 6≧ n₂ ≧ 0). Numerical results are presented for the energies of the terms in the form $$E = E_0 Z^2 + \Delta {\rm E}_2 + \frac{1}{Z}\Delta {\rm E}_3 + \frac{{\alpha ^2 }}{4}(E_0^r + \Delta {\rm E}_1^r Z^3 )$$ and for fine structure of the terms in the form $$\begin{gathered} \left\langle {1s^2 2s^{n_1 } 2p^{n_2 } LSJ|H_B |1s^2 2s^{n_1 \prime } 2p^{n_2 \prime } L\prime S\prime J} \right\rangle = \hfill \\ = ( - 1)^{\alpha + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 1} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 [E^{(0)} (Z - B) + \varepsilon _{co} ] + \hfill \\ + ( - 1)^{L + S\prime + J} \left\{ {\begin{array}{*{20}c} {L S J} \\ {S\prime L\prime 2} \\ \end{array} } \right\}\frac{{\alpha ^2 }}{4}(Z - A)^3 \varepsilon _{cc} . \hfill \\ \end{gathered} $$ Dipole matrix elements are necessary for calculations of oscillator strengths and transition probabilities. For dipole matrix elements two members of expansion by 1/Z have been obtained. Numerical results were presented in the form P(a,a′) = a/Z(1+τ/Z).     

Three-loop on-shell charge renormalization without integration:\Lambda _{QED}^{\overline {MS} } to four loops

Using algebraic methods, we find the three-loop relation between the bare and physical couplings of one-flavourD-dimensional QED, in terms of Γ functions and a singleF ₃₂ series, whose expansion nearD=4 is obtained, by wreath-product transformations, to the order required for five-loop calculations. Taking the limitD→4, we find that the \(\overline {MS} \) coupling \(\bar \alpha (\mu )\) satisfies the boundary condition $$\begin{gathered} \frac{{\bar \alpha (m)}}{\pi } = \frac{\alpha }{\pi } + \frac{{15}}{{16}}\frac{{\alpha ^3 }}{{\pi ^3 }} + \left\{ {\frac{{11}}{{96}}\zeta (3) - \frac{1}{3}\pi ^2 \log 2} \right. \hfill \\ \left. { + \frac{{23}}{{72}}\pi ^2 - \frac{{4867}}{{5184}}} \right\}\frac{{\alpha ^4 }}{{\pi ^4 }} + \mathcal{O}(\alpha ^5 ), \hfill \\ \end{gathered} $$ wherem is the physical lepton mass and α is the physical fine structure constant. Combining this new result for the finite part of three-loop on-shell charge renormalization with the recently revised four-loop term in the \(\overline {MS} \) β-function, we obtain $$\begin{gathered} \Lambda _{QED}^{\overline {MS} } \approx \frac{{me^{3\pi /2\alpha } }}{{(3\pi /\alpha )^{9/8} }}\left( {1 - \frac{{175}}{{64}}\frac{\alpha }{\pi } + \left\{ { - \frac{{63}}{{64}}\zeta (3)} \right.} \right. \hfill \\ \left. { + \frac{1}{2}\pi ^2 \log 2 - \frac{{23}}{{48}}\pi ^2 + \frac{{492473}}{{73728}}} \right\}\left. {\frac{{\alpha ^2 }}{{\pi ^2 }}} \right), \hfill \\ \end{gathered} $$ at the four-loop level of one-flavour QED.     

Determination of heavy quark non-perturbative parametersfrom spectral moments in semileptonic B decays

Moments of the hadronic invariant mass and of the lepton energy spectra in semileptonic B decays have been determined with the data recorded by the DELPHI detector at LEP. From measurements of the inclusive b-hadron semileptonic decays, and imposing constraints from other measurements on b- and c-quark masses, the first three moments of the lepton energy distribution and of the hadronic mass distribution, have been used to determine parameters which enter into the extraction of |V_cb| from the measurement of the inclusive b-hadron semileptonic decay width. The values obtained in the kinetic scheme are: and include corrections at order 1/m_b³. Using these results, and present measurements of the inclusive semileptonic decay partial width of b-hadrons at LEP, an accurate determination of |V_cb| is obtained: Received: 26 April 2005, Revised: 16 September 2005, Published online: 16 November 2005     

Gleichzeitige Messung von Hyperfeinstruktur,Starkeffekt und Zeemaneffekt des23Na19F mit einer Molekülstrahl-Resonanzapparatur

An electric molecular beam resonance spectrometer has been used to measure simultaneously the Zeeman- and Stark-effect splitting of the hyperfine structure of²³Na¹⁹F. Electric four pole lenses served as focusing and refocusing fields of the spectrometer. A homogenous magnetic field (Zeeman field) was superimposed to the electric field (Stark field) in the transition region of the apparatus. The observed (Δm _J=±1)-transitions were induced electrically. Completely resolved spectra of NaF in theJ=1 rotational state have been measured in several vibrational states. The obtained quantities are: The electric dipolmomentμ _el of the molecule forv=0, 1 and 2, the rotational magnetic dipolmomentμ _J forv=0, 1, the difference of the magnetic shielding (σ _⊥-σ _‖) by the electrons of both nuclei as well as the difference of the molecular susceptibility (ξ _⊥-ξ _‖), the spin rotational constantsc _F andc _Na, the scalar and the tensor part of the molecular spin-spin interaction, the quadrupol interactione q Q forv=0, 1 and 2. The numerical values are

$$\begin{gathered} \mu _{\mathfrak{e}1} = 8,152(6) deb \hfill \\ \frac{{\mu _{\mathfrak{e}1} (v = 1)}}{{\mu _{\mathfrak{e}1} (v = 0)}} = 1,007985 (7) \hfill \\ \frac{{\mu _{\mathfrak{e}1} (v = 2)}}{{\mu _{\mathfrak{e}1} (v = 1)}} = 1,00798 (5) \hfill \\ \mu _J = - 2,89(3)10^{ - 6} \mu _B \hfill \\ \frac{{\mu _J (v = 0)}}{{\mu _J (v = 1)}} = 1,020 (13) \hfill \\ (\sigma _ \bot - \sigma _\parallel )_{Na} = - 51(12) \cdot 10^{ - 5} \hfill \\ (\sigma _ \bot - \sigma _\parallel )_F = - 51(12) \cdot 10^{ - 6} \hfill \\ (\xi _ \bot - \xi _\parallel ) = - 1,59(120)10^{ - 30} erg/Gau\beta ^2 \hfill \\ {}^CNa/^h = 1,7 (2)kHz \hfill \\ {}^CF/^h = 2,2 (2)kHz \hfill \\ {}^dT/^h = 3,7 (2)kHz \hfill \\ {}^dS/^h = 0,2 (2)kHz \hfill \\ eq Q/h = - 8,4393 (19)MHz \hfill \\ \frac{{eq Q(v = 0)}}{{eq Q(v = 1)}} = 1,0134 (2) \hfill \\ \frac{{eq Q(v = 1)}}{{eq Q(v = 2)}} = 1,0135 (2) \hfill \\ \end{gathered} $$     

Fit of the parameters for Cabibbo's theory

All experimental data on leptonic decays of Baryons available after the Kiev Conference on High Energy Physics (Sept. 1970) are used to fit the parameters of the Cabibbo theory. Especially new results on σ^? and Λ leptonic decays and the values of the Σ^± lifetime are included. The data are consistent with the one angle Cabibbo theory. The results for the three parameters are: $$\begin{gathered} \theta = 0.239 \pm 0.005 \hfill \\ g_1^F = 0.451 \pm 0.019 \hfill \\ g_1^D = 0.777 \pm 0.021. \hfill \\ \end{gathered} $$      

A measurement of the forward-backward asymmetry of e+e?→bb by applying a jet charge algorithm to lifetime tagged events

The forward-backward asymmetry of has been measured using approximately 2.15 million hadronicZ ⁰ decays collected at the LEP e⁺e^– collider with the OPAL detector. A lifetime tag technique was used to select an enriched event sample. The measurement of the asymmetry was then performed using a jet charge algorithm to determine the direction of the primary quark. Values of:

On the Essential Spectrum of a Class of Singular Matrix Differential Operators. I: Quasiregularity Conditions and Essential Self-adjointness

The essential spectrum of singular matrix differential operator determined by the operator matrix