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.     

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: $$\begin{gathered} ^{133} Cs:\frac{{g_{ex} }}{{g_{gr} }} = 1.90\left( 4 \right) \hfill \\ ^{165} Ho:\tau \left( {94.7keVlevel} \right) = 32\left( 1 \right)ps \hfill \\ \frac{{g_{ex} }}{{g_{gr} }} = 0.77\left( 3 \right) \hfill \\ ^{178} Hf:|H_{eff} \left( {4K,in iron} \right)| = 633\left( {40} \right)KG \hfill \\ |H_{eff} \left( {77K,in iron} \right)| = 630\left( {41} \right)KG. \hfill \\ \end{gathered}$$      

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. $$\begin{gathered} g = + 1.310(25) \hfill \\ H_{hf} (Tc{\mathbf{ }}in{\mathbf{ }}Fe) = ( - )290(15)kOe \hfill \\ H_{hf} (Tc{\mathbf{ }}in{\mathbf{ }}Co) = ( - )170(5)kOe \hfill \\ H_{hf} (Tc{\mathbf{ }}in{\mathbf{ }}Ni) = - 47.8(1.5)kOe. \hfill \\ \end{gathered} $$      

Laser-Rf double-resonance studies of the hyperfine structure of metastable atomic states of55Mn

The hyperfine structure (hfs) of the metastable atomic states 3d⁶4s⁶ D _{1/2, 3/2, 5/2, 7/2, 9/2} of⁵⁵Mn was measured using theABMR- LIRF method (atomicbeammagneticresonance, detected bylaserinducedresonancefluorescence). The hfs constantsA andB, corrected for second order hfs perturbations, could be derived from these measurements. The theoretical interpretation of these correctedA- andB-factors was performed in the intermediate coupling scheme taking into account the configurations 3d ⁵4s ², 3d ⁶4s and 3d ⁷. Examining the influence of the composition of the eigenvectors on the hfs parameters \(\left\langle {r^{ - 3} } \right\rangle ^{k_s k_l } \) it was found, that for the configuration 3d ⁶4s the two-body magnetic interaction should be considered in the calculation of the eigenvectors. Investigating second order electrostatic configuration interactions and relativistic effects and using calculated relativistic correction factors we obtained for the nuclear quadrupole moment of the nucleus⁵⁵Mn a value ofQ=0.33(1) barn, which is not perturbed by a shielding or antishielding Sternheimer factor. The following hfs constants have been obtained: $$\begin{gathered} A\left( {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 882.056\left( {12} \right)MHz \hfill \\ A\left( {{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 469.391\left( 7 \right)MHzB\left( {{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = - 65.091\left( {50} \right)MHz \hfill \\ A\left( {{5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 436.715\left( 3 \right)MHzB\left( {{5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = - 46.769\left( {30} \right)MHz \hfill \\ A\left( {{7 \mathord{\left/ {\vphantom {7 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 458.930\left( 3 \right)MHzB\left( {{7 \mathord{\left/ {\vphantom {7 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 21.701\left( {40} \right)MHz \hfill \\ A\left( {{9 \mathord{\left/ {\vphantom {9 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 510.308\left( 8 \right)MHzB\left( {{9 \mathord{\left/ {\vphantom {9 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 132.200\left( {120} \right)MHz \hfill \\ \end{gathered} $$      

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

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.     

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. $$\begin{gathered} |\beta (z^2 F_{5/2} )| = (0.0020 \pm 0.0002) MHz/(kV/cm)^2 \hfill \\ |\beta (z^2 F_{7/2} )| = (0.0025 \pm 0.0015) MHz/(kV/cm)^2 . \hfill \\ \end{gathered} $$      

Gleichzeitige Messung von Hyperfeinstruktur,Starkeffekt und Zeemaneffekt des133Cs19F 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 of¹³³Cs¹⁹F. 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. Electrically induced (Δ m _J =±1)-transitions have been measured in theJ=1 rotational state, υ=0, 1 vibrational state. The obtained quantities are: The electric dipolmomentμ _el of the molecule for υ=0, 1; the rotational magnetic dipolmomentμ _J for υ=0, 1; the anisotropy of the magnetic shielding (σ _⊥-σ‖) by the electrons of both nuclei as well as the anisotropy of the molecular susceptibility (ξ _⊥-ξ‖), the spin rotational interaction constantsc _Cs andc _F, the scalar and the tensor part of the nuclear dipol-dipol interaction, the quadrupol interactioneqQ for υ=0, 1. The numerical values are:

$$\begin{gathered} \mu _{el} \left( {\upsilon = 0} \right) = 73878\left( 3 \right)deb \hfill \\ \mu _{el} \left( {\upsilon = 1} \right) - \mu _{el} \left( {\upsilon = 0} \right) = 0.07229\left( {12} \right)deb \hfill \\ \mu _J /J\left( {\upsilon = 0} \right) = - 34.966\left( {13} \right) \cdot 10^{ - 6} \mu _B \hfill \\ \mu _J /J\left( {\upsilon = 1} \right) = - 34.823\left( {26} \right) \cdot 10^{ - 6} \mu _B \hfill \\ \left( {\sigma _ \bot - \sigma _\parallel } \right)_{Cs} = - 1.71\left( {21} \right) \cdot 10^{ - 4} \hfill \\ \left( {\sigma _ \bot - \sigma _\parallel } \right)_F = - 5.016\left( {15} \right) \cdot 10^{ - 4} \hfill \\ \left( {\xi _ \bot - \xi _\parallel } \right) = 14.7\left( {60} \right) \cdot 10^{ - 30} erg/Gau\beta ^2 \hfill \\ c_{cs} /h = 0.638\left( {20} \right)kHz \hfill \\ c_F /h = 14.94\left( 6 \right)kHz \hfill \\ d_T /h = 0.94\left( 4 \right)kHz \hfill \\ \left| {d_s /h} \right|< 5kHz \hfill \\ eqQ/h\left( {\upsilon = 0} \right) = 1238.3\left( 6 \right) kHz \hfill \\ eqQ/h\left( {\upsilon = 1} \right) = 1224\left( 5 \right) kHz \hfill \\ \end{gathered} $$     

QCD perturbation theory in the temporal gauge

In this paper we present a non-trivial check of the consistency of the quantization of a gauge theory with fermions (QCD) in the temporal gauge. We use the approach based on the finite time Feynman propagation kernel, in which the Gauss law is imposed as a constraint on the states by means of a functional integration over all the time independent gauge transformations acting on the boundary values of the fields. We spell out in detail the “Feynman rules” when fermions are present and we compute, as an example, the gauge invariant correlation function $$\begin{gathered} G(t) = \left\langle {\bar \psi (0,t)(\gamma _5 \gamma _0 )\frac{{1 - \gamma _0 }}{2}P} \right. \hfill \\ \left. { \cdot \exp \left( {ig\int\limits_0^t {A_0 (0,t')dt'} } \right)(\gamma _5 \gamma _0 )^ + (0,0)} \right\rangle \hfill \\ \end{gathered} $$ up to orderg ², obtaining the expected result.     

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.     

The band spectrum of SbO: A new doublet system

The band spectrum of SbO was excited in a heavy current discharge from a 2000 volt D. C. generator. A new doublet system of bands occurring in the region λ 2800 toλ 3600 arising from a transition of the type²Δ_r?² Π _r was identified. The lower² Π _r state is found to be common to those of the three band systems reported earlier, which is in all probability the ground state of the SbO molecule. The band heads of the high frequency and low frequency components could be represented by the following quantum formulae:

$$\begin{gathered} ^2 \Delta _{\tfrac{3}{2}} - ^2 \Pi _{\tfrac{1}{2}} : \hfill \\ v = 29754 \cdot 6 + 570 \cdot 6 (v' + \tfrac{1}{2}) - 3 \cdot 52 (v' + \tfrac{1}{2})^2 - 820 \cdot 5 (v'' + \tfrac{1}{2}) + 4 \cdot 62 (v'' + \tfrac{1}{2})^2 \hfill \\ ^2 \Delta _{\tfrac{5}{2}} - ^2 \Pi _{\tfrac{3}{2}} : \hfill \\ v = 28044 \cdot 8 + 568 \cdot 1 (v' + \tfrac{1}{2}) - 3 \cdot 28 (v' + \tfrac{1}{2})^2 - 819 \cdot 2 (v'' + \tfrac{1}{2}) + 4 \cdot 62 (v'' + \tfrac{1}{2})^2 . \hfill \\ \end{gathered} $$     

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     

Nuclear quadrupole moments of radioactive83Rb,84Rb and86Rb

Excited atomic² P _3/2-states of radioactive Rb isotopes have been investigated by level crossing and optical double resonance spectroscopy. The measured hyperfine structure constants yielded the nuclear moments $$\begin{gathered} \mu _I (^{84} Rb) = - 1.296(11)\mu _K Q(^{83} Rb) = + 0.27(5) \cdot 10^{ - 24} cm^2 \hfill \\ Q(^{84} Rb) = + 0.005(13) \cdot 10^{ - 24} cm^2 \hfill \\ Q(^{86} Rb) = + 0.20(3) \cdot 10^{ - 24} cm^2 \hfill \\ \end{gathered} $$ and the hyperfine anomaly₈₄Δ₈₅=+1.7(1.0) · 10^?2. The quadrupole moments of⁸³Rb to⁸⁷Rb can be explained with the unified model of vibrations.     

On the upper critical dimension of Bernoulli percolation

We derive a set of inequalities for thed-dimensional independent percolation problem. Assuming the existence of critical exponents, these inequalities imply: $$\begin{gathered} f + v \geqq 1 + \beta _Q , \hfill \\ \mu + v \geqq 1 + \beta _Q , \hfill \\ \zeta \geqq \min \left\{ {1,\frac{{v^, }}{v}} \right\}, \hfill \\ \end{gathered} $$ where the above exponents aref: the flow constant exponent, ν(ν′): the correlation length exponent below (above) threshold, μ: the surface tension exponent, β _Q : the backbone density exponent and ζ: the chemical distance exponent. Note that all of these inequalities are mean-field bounds, and that they relate the exponentv defined from below the percolation threshold to exponents defined from above threshold. Furthermore, we combine the strategy of the proofs of these inequalities with notions of finite-size scaling to derive: $$\max \{ dv,dv^, \} \geqq 1 + \beta _Q ,$$ whered is the lattice dimension. Since β _Q ≧2β, where β is the percolation density exponent, the final bound implies that, below six dimensions, the standard order parameter and correlation length exponents cannot simultaneously assume their mean-field values; hence an implicit bound on the upper critical dimension:d _c ≧6.     

Gauge-invariant on-shellZ 2 in QED,QCD and the effective field theory of a static quark

We calculate theon-shell fermion wave-function renormalization constantZ ₂ of a general gauge theory, to two loops, inD dimensions and in an arbitrary covariant gauge, and find it to be gauge-invariant. In QED this is consistent with the dimensionally regularized version of the Johnson-Zumino relation: d logZ ₂/da ₀=i(2)^–D e ₀ ² d ^D k/k ⁴=0. In QCD it is, we believe, a new result, strongly suggestive of the cancellation of the gauge-dependent parts of non-abelian UV and IR anomalous dimensions to all orders. At the two-loop level, we find that the anomalous dimension _F of the fermion field in minimally subtracted QCD, withN _L light-quark flavours, differs from the corresponding anomalous dimension of the effective field theory of a static quark by the gauge-invariant amount

Detection of a hexadecapole interaction in the atomic ground state3 H 6 of167Er

Using the atomic beam magnetic resonance method, precision measurements of the hyperfine structure and Zeeman interactions have been performed in the ground state 4f ¹²6s ^{2 3} H ₆ of¹⁶⁷Er. The experimental data were analyzed using an effective operator parametrized in the space of states of the ground state multiplet. It yielded eight effective hyperfine structure and Zeeman interaction constants which served to calculate the seven hyperfine separations of the ground state. The results are: $$\begin{gathered} 2F 2F' v_{FF'} (MHz) \hfill \\ 5 7 - 354.371 9409 (27) \hfill \\ 7 9 - 2{\text{78}}{\text{.231}} {\text{8263(14)}} \hfill \\ {\text{9}} 11 - 69.050 7785 (4) \hfill \\ 11 13 + 302.735 3731(12) \hfill \\ 13 15 + 866.691 3871(10) \hfill \\ 15 17 + 1,652.383 5154 (6) \hfill \\ 17 19 + 2,689.380 8050(10) \hfill \\ \end{gathered}$$ From the effective Zeeman interaction constants it was possible to determine an improvedg _I -value, uncorrected for atomic diamagnetism: $$ g_I = + 0.086 775 (19) \cdot 10^{ - 3}$$ Furthermore a hexadecapole interaction corresponding to a diagonal hexadecapole interaction constant $$A_4 = - 16 (10) Hz$$ could be established which is of the order of magnitude expected from Coulomb excitation experiments as well as theoretical calculations.     

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).     

Hyperfine structure,g j factors and lifetimes of excited2 P 1/2 states of Rb

The hyperfine structure of the 6² P _1/2 and 7² P _1/2 state of⁸⁵Rb and⁸⁷Rb and of the 6² P _3/2 state of⁸⁷Rb has been investigated with optical double resonance at intermediate magnetic fields. The magnetic interaction constants,g _j factors and lifetimes are: $$\begin{gathered} 6^2 P_{1/2} state: A\left( {^{85} Rb} \right) = 39.11\left( 3 \right) MHz,A\left( {^{87} Rb} \right) = 132.56 \left( 3 \right)MHz, \hfill \\ g_j = 0.6659\left( 3 \right), \tau = 1.14\left( {13} \right) \cdot 10^{ - 7} \sec , \hfill \\ 7^2 P_{1/2} state: A\left( {^{85} Rb} \right) = 17.68\left( 8 \right)MHz,A\left( {^{87} Rb} \right) = 59.92\left( 9 \right)MHz, \hfill \\ g_j = 0.6655\left( 5 \right), \hfill \\ 6^2 P_{3/2} state: g_j = 1.3337\left( {10} \right), \tau = 1.12\left( 8 \right) \cdot 10^{ - 7} \sec for ^{87} Rb. \hfill \\ \end{gathered} $$ From the hfs coupling constants of then ² P multiplets a 11.5% core polarization contribution to the magnetic hfs of then ² P _3/2 states is obtained, which is found to be independent from the main quantum numbern. The expectation values <r ^?3> _j for thenp valence electrons corrected for core polarization are compared with those derived from the² P fine structure separation. Good agreement is achieved for allnp levels with the choice ofZ _i =Z?3=34 for the effective nuclear charge number. The nuclear quadrupole moments of⁸⁵Rb and⁸⁷Rb are rederived on the basis of this more improved treatment for thep-electron-nucleus interaction yielding $$\begin{gathered} Q_N \left( {^{85} Rb} \right) = + 0.274\left( 2 \right) \cdot 10^{ - 24} cm^2 \hfill \\ Q_N \left( {^{85} Rb} \right) = + 0.132\left( 1 \right) \cdot 10^{ - 24} cm^2 \hfill \\ \end{gathered} $$ where the error does not include the remaining theoretical uncertainty of about 10%.