Hyperfine structure measurements in the ground states4 F 3/2,4 F 5/2 and4 F 7/2 of Ta181 with the atomic beam magnetic resonance method

Applying a recently developed evaporation technique for refractory elements the following results have been obtained for Ta¹⁸¹ in an atomic beam magnetic resonance experiment studying the hyperfine structure of 3 levels of the ground state multiplet⁴ F: $$\begin{gathered} g_J (^4 F_{3/2} ) = 0.45024 (4) \hfill \\ \Delta v (^4 F_{3/2} ;F = 5 \leftrightarrow F = 4) = 1822.389 (6) MHz \hfill \\ \Delta v (^4 F_{3/2} ;F = 4 \leftrightarrow F = 3) = 2325.537 (2) MHz \hfill \\ \Delta v (^4 F_{5/2} ;F = 6 \leftrightarrow F = 5) = 1451.476 (7) MHz \hfill \\ \Delta v (^4 F_{5/2} ;F = 5 \leftrightarrow F = 4) = 1537.530 (8) MHz \hfill \\ \Delta v (^4 F_{5/2} ;F = 4 \leftrightarrow F = 3) = 1444.685 (2) MHz \hfill \\ \Delta v (^4 F_{7/2} ;F = 4 \leftrightarrow F = 3) = 1218.372 (2) MHz. \hfill \\ \end{gathered}$$ From these measurements the following constants of the magnetic dipole interaction (A) and the electric quadrupole interaction (B) have been derived: $$\begin{gathered} A (^4 F_{3/2} ) = 509.0801 (8) MHz \hfill \\ B (^4 F_{3/2} ) = - 1012.251 (8) MHz \hfill \\ A (^4 F_{5/2} ) = 313.4681 (8) MHz \hfill \\ B (^4 F_{5/2} ) = - 834.820 (12) MHz. \hfill \\ \end{gathered}$$      

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.     

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

Lifetimes andg J factors of 6s7p and 5d6p levels of Ba I

Excited states of Ba have been investigated with optical double resonance and Hanle effect. The followingg _J factors and natural lifetimes (in 10^?9 sec) have been measured $$\begin{gathered} 6s7p\left\{ {\begin{array}{*{20}c} {^1 P_1 :g_J = 1.003(2)\tau = 13.5(6)} \\ {^3 P_1 :g_J = 1.4971(8)\tau = 85.0(8.0)} \\ \end{array} } \right. \hfill \\ 5d6p\left\{ {\begin{array}{*{20}c} {^1 P_1 :g_J = 1.004(2)\tau = 12.4(9)} \\ {^3 P_1 :g_J = 1.4847(15)\tau = 11.7(9)} \\ {^3 D_1 :g_J = 0.5064(3)\tau = 17.0(5).} \\ \end{array} } \right. \hfill \\ \end{gathered}$$ g _J is utilized to test the mixing coefficients of the wave functions in the intermediate coupling model. The lifetimes are converted into absolute transition probabilities for all the decays originating from the states investigated under the assumption that their branching ratios obtained elsewhere are correct. This assumption is not unquestionable, however.     

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

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

Nuclear orientation and NMR/ON of205,207Po

^205,207Po have keen implanted with an isotope separator on-line into cold host matrices of Fe, Ni, Zn and Be. Nuclear magnetic resonance of oriented²⁰⁷Po has been observed in Fe and Ni, of²⁰⁵Po in Fe. The resonance frequencies for zero external field are $$\begin{gathered} v_L (^{207} Po\underline {Fe} ) = 575.08(20)MHz \hfill \\ v_L (^{207} Po\underline {Ni} ) = 160.1(8)MHz \hfill \\ v_L (^{205} Po\underline {Fe} ) = 551.7(8)MHz. \hfill \\ \end{gathered} $$ From the dependence of the resonance frequency on external magnetic field theg-factor of²⁰⁷Po was derived as $$g(^{207} Po) = + 0.31(22).$$ Using this value the magnetic hyperfine fields of Po in Fe and Ni were obtained as $$\begin{gathered} B_{hf} (Po\underline {Fe} ) = + 238(16)T \hfill \\ B_{hf} (Po\underline {Ni} ) = 66.3(4.6)T. \hfill \\ \end{gathered}$$ Theg-factor of²⁰⁵Po follows as $$g(^{205} Po) = + 0.304(22).$$ From the temperature dependence of the anisotropies ofγ-lines in the decay of^205,207Po the multipole mixing of several transitions was derived. The electric interaction frequenciesv _Q=eQV_zz/h in the hosts Zn and Be were measured as $$\begin{gathered} v_Q (^{207} Po\underline {Zn} ) = + 42(3)MHz \hfill \\ v_Q (^{207} Po\underline {Be} ) = - 70(20)MHz \hfill \\ v_Q (^{205} Po\underline {Be} ) = - 42(17)MHz. \hfill \\ \end{gathered}$$      

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%.     

A new determination of the capture ratior_c = \frac{{\sum ^ - p \to \sum ^0 n}}{{(\sum ^ - p \to \sum ^0 n) + (\sum ^ - p \to \Lambda ^0 n)}}, the Λ0-lifetime and the ∑−-Λ0 mass difference

The two∑ ^? reactions at rest∑ ^? p→Λ ⁰ n and∑ ^? p→Λ ⁰ n have been studied in order to determine the capture ratio $$r_c = \frac{{\sum ^ - p \to \sum ^0 n}}{{(\sum ^ - p \to \sum ^0 n) + (\sum ^ - p \to \Lambda ^0 n)}}$$ , theΛ ⁰-lifetime and the∑ ^?-Λ ⁰ mass difference. The following results were obtained: $$\begin{gathered} rc = 0.474 \pm 0.016 \hfill \\ \tau _{\Lambda ^0 } = (2.47 \pm 0.08) \times 10^{ - 10} \sec \hfill \\ M_{\sum ^ - } - M_{\sum ^0 } = 81.64 \pm 0.09{{MeV} \mathord{\left/ {\vphantom {{MeV} {c^2 }}} \right. \kern-\nulldelimiterspace} {c^2 }} \hfill \\ \end{gathered} $$ The∑ ^?-mass was determined from the range of the stopping∑ ^?-hyperons,M _∑} =1197.19±0.32 MeV/c ².     

Zeeman-Effekt im Grundzustand von atomarem Kohlenstoff

The Landé factors of the ground state levels³ P ₁ and³ P ₂ of atomic carbon are calculated. The Hamilton operator proposed by Abragam and Van Vleck takes account of relativistic effects up to the second order. Additionally, corrections to the orbital and spin moments of the electrons are applied. The deviation from Russell-Saunders coupling is treated in perturbation theory. The results $$\begin{gathered} g_J ({}^3P_1 ) = 1.501069 \hfill \\ g_J ({}^3P_2 ) = 1.501056 \hfill \\ \end{gathered} $$ differ from the experimental values by about 10^?5.     

Centrifugal distortion constants of pentafluorobenzene from its pure rotation spectrum

The centrifugal distortion analysis of the pure rotational spectrum of pentafluorobenzene in the frequency region of 8 to 18 GHz involvingJ upto 54 has yielded the following rotational and quartic centrifugal distortion constants: $$\begin{gathered} A'' = 1480 \cdot 8665 \pm 0 \cdot 0026 MHz, \tau = - 1 \cdot 751 \pm 0 \cdot 20 kHz, \hfill \\ B'' = 1030 \cdot 0782 \pm 0 \cdot 0025 MHz, \tau _2 = - 0 \cdot 567 \pm 0 \cdot 066 kHz, \hfill \\ C'' = 607 \cdot 5152 \pm 0 \cdot 0026 MHz, \tau _{aaaa} = - 0 \cdot 765 \pm 0 \cdot 068 kHz, \hfill \\ \tau _{bbbb} = - 0 \cdot 612 \pm 0 \cdot 065 kHz, \hfill \\ \tau _{cccc} = - 0 \cdot 547 \pm 0 \cdot 068 kHz. \hfill \\ \end{gathered} $$      

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.     

Branching ratios and properties ofD-meson decays

Properties ofD mesons produced in the photo-production experiment NA 14/2 at CERN are reported. The following ratios of branching fractions were measured:

Ground state hyperfine structure and nuclear magnetic dipole moments of177Hf and179Hf

Using the atomic beam magnetic resonance method the experimental hyperfine structure data of the 5d ²6s ^{2 3} F ₂ ground state of¹⁷⁷Hf and¹⁷⁹Hf described in a previous paper [1] have been completed. After applying corrections due to perturbations by other fine structure levels of the configuration 5d ²6s ² we got the following multipole interaction constants: $$\begin{gathered} ^{177} Hf:A = 113.43314 (7) MHz B = 624.3293 (13) MHz \hfill \\ C = 0.27 (18) KHz D = 0.045 (40) KHz \hfill \\ ^{179} Hf: A = - 71.42891 (9) MHz B = 705.5181 (24) MHz \hfill \\ C = - 0.43 (20) MHz D = 0.07 (6) KHz. \hfill \\ \end{gathered} $$ By measuring rf transitions at magnetic fields between 1100 and 1550 Gauss the nuclear ground state magnetic dipole moments were determined. The results are: $$\mu _I (^{177} Hf) = 0.7836 (6) \mu _N , \mu _I (^{179} Hf) = - 0.6329 (13) \mu _N $$ (uncorrected for diamagnetic shielding).     

Total cross sections of charged-current neutrino and antineutrino interactions on isoscalar nuclei

New measurements of the total crosssections of charged-current interactions of muonneutrinos and antineutrinos on isoscalar nuclei have been performed. Data were recorded in an exposure of the CHARM detector in an 160 GeV narrow-band beam. The antineutrino flux was determined from the measurements of the pion and kaon flux, and independently from the muon flux measured in the shield; the two methods are found to agree. The neutrino flux was determined from the muon flux ratio forv _μ and \(\bar v_\mu \) runs which was normalized to the antineutrino flux. The cross-section slopes thus determined are $$\begin{gathered} \sigma _T^{\bar v} /E = (0.335 \pm 0.004(stat) \hfill \\ \pm 0.010(syst)).10^{ - 38} cm^2 /(GeV \cdot nucleon) \hfill \\ \sigma _T^v /E = (0.686 \pm 0.002(stat) \hfill \\ \pm 0.020(syst)).10^{ - 38} cm^2 /(GeV \cdot nucleon) \hfill \\ \end{gathered} $$ The momentum sum of the quarks in the nucleon and the ratio of sea quark to total quark momentum are derived from the measurements.     

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: $$\begin{gathered} {}^{168m}\operatorname{Re} , E_\alpha = 5,250 (10) keV, T_{1/2} = 6.6 (15) s and \hfill \\ {}^{169m}\operatorname{Re} , E_\alpha = 5,050 (10) keV, T_{1/2} = 12.9 (11) s. \hfill \\ \end{gathered} $$      

Gyromagnetic ratios of collective states of166Er

The static hyperfine field ofB _hf ^4.2k (ErHo) = 739(18)T of a ferromagnetic holmium single crystal polarized in an external magnetic field of ± 0.48T at ～4.2K was used for integral perturbed γ-γ angular correlation (IPAQ measurements of the g-factors of collective states of¹⁶⁶Er. The 1,200y ^166m Ho activity was used which populates the ground state band and the γ vibrational band up to high spins. The results: $$\begin{gathered} g(4_g^ + ) = + 0.315(16) \hfill \\ g(6_g^ + ) = + 0.258(11) \hfill \\ g(8_g^ + ) = + 0.262(47)and \hfill \\ g(6_\gamma ^ + ) = + 0.254(32) \hfill \\ \end{gathered}$$ exhibit a significant reduction of the g-factors with increasing rotational angular momentum. The followingE2/M1 mixing ratios of interband transitions were derived from the angular correlation coefficients: $$\begin{gathered} 5_\gamma ^ + \Rightarrow 4_g^ + :\delta (810keV) = - (36_{ - 7}^{ + 11} ) \hfill \\ 7_\gamma ^ + \Rightarrow 6_g^ + :\delta (831keV) = - (18_{ - 2}^{ + 3} )and \hfill \\ 7_\gamma ^ + \Rightarrow 8_g^ + :\delta (465keV) = - (63_{ - 12}^{ + 19} ). \hfill \\ \end{gathered}$$ The results are discussed and compared with theoretical predictions.     

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).     

Measurement of the ∑± lifetimes

From about 2 × 10⁶ measured ∑^± decay's produced by stoppingK ^? mesons in the 81 cm Saclay hydrogen bubble chamber about 140,000 ∑^? →n π^? and 20,000 ∑⁺ →nπ⁺ decays were selected for a lifetime measurement. We obtained: $$\begin{gathered} \tau _{\Sigma ^ + } = (0.795 \pm 0.010) \times 10^{ - 10} \sec \hfill \\ \tau _{\Sigma ^ - } = (1.485 \pm 0.022) \times 10^{ - 10} \sec . \hfill \\ \end{gathered} $$