New recoil-effect-induced contributions to the fine shift of S levels in the muonium atom

A new α ⁶ μ ³/(m ₁ m ₂) ln (m ₁ m ₂) correction that arises in one-photon particle interaction in the muonium atom is found and calculated.     

The hyperfine quadrupole moment of muonium in the ground state

The quadrupole moment of the ground state of the μ⁺e^? atom is calculated to be (3m_em_μ)^?1; effects in a crystal are briefly discussed.     

Hyperfine splitting in positronium and muonium

We calculate corrections to the ground state hyperfine structure of relative order α² ln α^?1 in positronium and relative order $\text{(}\text{m}{}_{\mathrm{<mtext>e</mtext>}}\text{m}{}_{\mathrm{\mu }}\text{)α}{}^2\text{lnα}{}^{\mathrm{?1}}$ in muonium due to the exchange of virtual photons. Our results are in agreement with those of Lepage. Contributions arising from the Coulomb potential and from the exchange of one transverse photon along with any number of ladder Coulomb photons are discussed in detail. In treating the single transverse photon-multiple Coulomb photon exchanges, we sum the contributions involving different numbers of Coulomb photons and reexpand the resulting expression in terms of a quantity that is inherently smaller than the Coulomb potential in the non-relativistic region. The procedure enables us to take into account from the beginning important cancellations that occur between the various terms in an expansion in powers of the Coulomb potential. The techniques developed here may be useful in calculating higher order corrections.     

Effect of pressure on the distribution of hyperfine field about A Sn impurity in iron

The distribution of hyperfine field at the iron atoms in an FeSn alloy has been measured as a function of pressure to 15 kbar. The frequency of the main NMR line was found to change such that (? ln H_m/?P)_T = ? 1.7 × 10^?4 kbar^?1, which is close to the value in pure iron. The value for the satellite line, due to iron atoms which are third nearest neighbours of the impurity, was (? ln H₃/?P)_T = ? 2.4 × 10^?4 kbar^?1. The magnitude of the difference of the pressure derivatives of H_m and H₃ is not consistent with models in which the Sn atom is screened by conduction electrons but may be understood in terms of a perturbation of the 3d band of iron. The discrepancy between spin wave theory and the measured temperature dependence of the hyperfine fields at constant pressure is not removed by correction to constant volume.     

Radiative corrections to νμ + N → μ− + X and their effect on the determination of ϱ2 and sin2θW

We study the O(α) corrections to σ_T(ν_μ + N → μ^? + X). The coefficient of the leading O(αln m_Z) contribution is given by a general theorem as in the case of β decay, while the energy scale accompanying m_Z in the argument of the logarithm as well as mass singularities and non-logarithmic terms are obtained by a detailed quark-parton model calculation. The effect of muon mass singularities, when there is an experimental vut in the low range of the y distribution, is also investigated. Combining these new results with our previous analysis of σ_T(ν_μ + N → ν_μ + X), we calculate theSU(2)_L × U(1) parameter ?_(νμ;h)² and evaluate the effect of the O(α) corrections on the determination of sin²θ_W^exp from deep inelastic ν_μ scattering. Applying these corrections to existing data, we obtain the weigthed average sin²θ_W^exp = 0.216 ± 0.010 ± 0.004. This value when used in conjuction with our previous analysis of the W^± and Z⁰ masses provides the predictions m_W = 83.0_?2.8^+3.0 GeV and m_Z = 93.8_?2.4^+2.5 GeV. For the weak interaction angle defined by modified minimal subtraction we find sin²θ_W(m_W) = 0.215 ± 0.010 ± 0.004, which is in very good agreement with the SU(5) prediction we have recently given.     

Irreducible kernels and nonperturbative expansions in a theory with purem →m interaction

Recent results on the structure of theS matrix at them-particle threshold (m≧2) in a simplifiedm→m scattering theory with no subchannel interaction are extended to the Green functionF on the basis of off-shell unitarity, through an adequate mathematical extension of some results of Fredholm theory: local two-sheeted or infinite-sheeted structure ofF arounds=(mμ)² depending on the parity of (m?1)(ν?1) (where μ>0 is the mass and ν is the dimension of space-time), off-shell definition of the irreducible kernelU which is the analogue of theK matrix in the two different parity cases (m?1)(ν?1) odd or even, and related local expansion ofF, for (m?1)(ν?1) even, in powers of σ_β ln σ(σ=(mμ)²?s). It is shown that each term in this expansion is the dominant contribution to a Feynman-type integral in which each vertex is a kernelU. The links between the kernelU and Bethe-Salpeter type kernelsG of the theory are exhibited in both parity cases, as also the links between the above expansion ofF and local expansions, in the Bethe-Salpeter type framework, ofF _λ in terms of Feynman-type integrals in which each vertex is a kernelG and which include both dominant and subdominant contributions.     

Optical potential calculations for the 1s level in pionic atoms

The Ericson-Ericson optical potential for theπ-nucleuss-wave interaction was extended to be applicable also for light nuclei. In particular, terms of order A^?1 were evaluated and the (π2N) dispersion was considered. From comparison with experimental data we found that considerable improvement could be achieved by introducing terms of order A^?1. The (π2N) dispersion was found to be repulsive and of the same magnitude as the absorption. The (πN) scattering lengths were deduced to be α₃?α₁=0.258±0.008m _π ^?1 and α₁+2α₃=?0.018±0.008m _π ^?1 .     

Analysis of the 2ν3 band of 12CD3F at 5.06 μm recorded under high resolution

The 2ν₃(A₁) band of ¹²CD₃F near 5.06 μm has been recorded with a resolution of 20–24 × 10^?3 cm^?1. The value of the parameter (α^B ? α^A) for this band was found to be very small and, therefore, the K structure of the R(J) and P(J) manifolds was unresolved for J < 15 and only partially resolved for larger J values. The band was analyzed using standard techniques and values for the following constants determined: ν₀ = 1977.178(3) cm^?1, B″ = 0.68216(9) cm^?1, D″_J = 1.10(30) × 10^?6 cm^?1, α^B = (B″ ? B′) = 3.086(7) × 10^?3 cm^?1, and β^J = (D″_J ? D′_J) = ?3.24(11) × 10^?7 cm^?1. A value of α^A = (A″ ? A′) = 2.90(5) × 10^?3 cm^?1 has been obtained through band contour simulations of the R(J) and P(J) multiplets.     

Theory of the froissaron exchange

The results of the multi-pomeron exchange theory considered earlier, are shown to depend crucially on the threshold behaviour of the pomeron contribution at t = 4μ_π², under the condition α(0) ? 1 = Δ > α′(0) 4μ_π². The t-channel partial wave f(t) of the multi-pomeron exchange is calculated. In the limit ξ · Δ > 1, where ξ = ln s/4μ², it corresponds to the scattering on a black disk of expanding radius b₀ ≈ a · ξ where a = s/2μ_π ? α′2μ_π. Due to the threshold singularity influence, it does not violate the t-channel unitarity condition. At a sufficiently small value of the froissaron coupling constant g₀₀ ～ Δ³/a², the theory is shown to be simultaneously s-unitary.     

The πd scattering length from Kα X-rays

X-rays from the K_α transition (2P → 1S) of the π^?d mesic atom have been observed. Their energy, 2592.8 _?2.0^+1.6, has been measured by the critical absorber technique, using the M_V absorption edge in bismuth. The strong interaction shift in the 1S state is ?4.8 eV, corresponding to a scattering length a(πd) = ?(0.052_?0.017^+0.022)m_π^?1, in agreement with recent calculations. The intensity ratio K_α/K_total = 0.548 ± 0.015.     

Investigation of the electromagnetic structure of the η meson in the decay η → μ+μ−γ

600 events of the rare electromagnetic decay η → μ⁺μ^?γ have been detected. The branching ratio has been measured as BR(η → μ⁺μ^?γ) = (3.1 ± 0.4) × 10^?4. The electromagnetic form factor of the η meson, F(m_μμ²;0) = (1 ? m_μμ²/Λ²)^?1, has been determined. Λ = (0.72 ± 0.09) GeV/c² is in good agreement with the vector meson dominance model.     

Nuclear magnetic resonance on oriented 11/2− 129mXe and131mXe in Fe

The magnetic hyperfine splitting frequenciesν _M=¦gμ _NB_HF/h.¦ of the 11/2^? isomeric states^129m Xe (T_1/2=8.9d) and^131mXe (T_1/2=11.8d) in Fe were measured with nuclear magnetic resonance on oriented nuclei at temperatures of 10–15 mK as 188.0(1) MHz and 209.8(1) MHz, respectively, the samples being prepared with the technique of recoil implantation after (α, x n) reactions. The magnetic moments of^129m Xe and^131m Xe are deduced to be (?)0.8914(6)μ _N and (?)0.9943(6)μ _N, respectively. The missing γ-anisotropies for allγ-transitions following the decay of 36.4d ¹²⁷Xe indicateI=1/2 for the ground state spin of¹²⁷Xe.     

On the ground state energy of free excitons in group IV and III–V semiconductors

An approximate calculation of the ground state energy of direct and indirect free excitons for group IV and group III–V semiconductors is presented. The basic assumption in this treatment is that the anisotropy of the effective masses can be neglected, however, the degeneracy of the valence band cannot. The resulting exciton ground state energy has the usual form but with a reduced mass \(\overline \mu \) given by ( \(\overline \mu \) )^?1=(m _e)^?1+(m _lh)^?1+(m _hh)^?1. The agreement with experiments is considerably improved as compared to the conventional ground state energy comprising the reduced mass defined as (μ)^?1=(m _e)^?1+(m _hh)^?1. Anisotropy corrections are shown to be of minor importance in many cases. However, for the heavier III–V-compounds the neglect of linear terms inE(k) for the valence band results in more serious errors, which invalidate the present theoretical approach.     

Der Zerfall des Co60m und Zr90m

Co^60m was produced by the reaction Co⁵⁹ (n,γ) Co^60m ; its decay has been investigated by scintillation spectrometers. The half-period has been remeasured yielding a value ofT _1/2=(10·35 ±0·20) min. The isomeric decay mainly leads to the Co⁶⁰ ground state by a (58·6±0·6) keV transition. TheK-conversion coefficientα _K= 41±3 and the total conversion coefficientα=47±3 indicate the transition to beM3 and the spin of Co^60m to be 2⁺. Further Co^60m decays by beta transitions to Ni⁶⁰. The beta component (8·6±1·2)·10^?3%, log ft=7·32 leading to a (2·16±0·02) MeV level has been measured for the first time. A second component (0·24±0·03)%, log ft=7·23 leads to the 1·33 MeV level. The 2·16 MeV level decays to the Ni⁶⁰ ground state mainly by a 0·83–1·33 MeV cascade, in a few cases by a direct transition. The spin of the 2·16 MeV level is 2⁺. Zr^90m was produced by the reaction Zr⁹⁰ (n,n′) Zr^90m . The half-period was measured yielding a value ofT _1/2=(0·83±0·03) sec. Zr^90m decays in the following way: (77±5) % by a direct (2·31±0·02) MeV —E 5 transition to the Zr ground state and (23±5)% by a (132·5±1·5) keV-(2·18±0·03) MeV cascade detected for the first time in the isomeric decay. TheK-conversion coefficient of the 132·5 keV transition isα _k=(2·2±0·3) indicating this transition to beE3 and the spin of the 2·18 MeV level to be 2⁺. The Zr^90m -decay sheme is in accordance with the level sequence of Zr⁹⁰ as measured in the Nb⁹⁰ decay.     

Asymptotic restrictions and ππ scattering lengths in non-linear chiral SU(2) × SU(2) dynamics

The most general effective lagrangian for ππ scattering, that takes into account the exchange of scalar (0⁺), tensor (2⁺) and ? mesons, is constructed within the framework of non-linear chiral SU(2) × SU(2) dynamics. Asymptotic restrictions proposed by Weinberg are imposed on the amplitude of ππ scattering. These restrictions allow one to obtain four independent sum rules containing particle masses, coupling constants and the coefficient A₂ in an expansion of the symmetry-breaking term in a power series of π². The use of only the f⁰ meson in the obtained sum rules leads to the following values of the ππ scattering lengths, the width of ?(700) → 2π decay, and the parameter A₂: α₀⁰ = 0.92m_π^?1, α₀² = 0.27 m_π^?1, α₁¹ = 0.033 m_π^?3, Γ[ε(700) → 2π] = 390 MeV, A₂ = + 1.6. It is shown that the inclusion of heavier mesons results in some increase of the ππ scattering lengths and the parameter A₂, but a decrease of the value of Γ(? → 2π). The field-algebra requirements lead to negligible changes in the results. Analysis of the sum rules shows the incompatability of the asymptotic restrictions with a symmetry breaking which has the transformation properties of the fourth component of a chiral vector.     

Die isomeren Atomkerne: Yb169m,Yb175m,Yb177m

Short lived isomers of Yb were produced by neutron irradiation of enriched isotopes and have been investigated with the aid of scintillation spectrometers. Yb^169m decays with a half-life ofT _1/2=(46±2) sec emitting only L-radiation. This decay is assumed to be the same as the E 3-transition of 24 keV following the electron capture of Lu¹⁶⁹. Yb^175m [T _1/2=(0,072±0,005) sec] emitsγ-rays of (495±15) keV. The measured K-conversion coefficientα _{K 495}=0,24±0,04 and the total conversion coefficientα _{4 5}=0,6±0,3 indicate the transition to be M3. Yb^177m [T _1/2=(6,4±0,1) sec] decays by a cascade of twoγ-rays. The isomeric (228±3) keV-transition is followed by a (104±1,5) keV-radiation. The measured conversion coefficients areα _{K 228}=4,1±0,4 andα _{K 228}=6,5±0,5 for the first transition andα _{K 104}=0,39±0,05 andα ₁₀₄=0,51±0,05 for the second, indicating a M3-E1-cascade. For the M 3-transition the measured coefficients agree well with those calculated for a nucleus of finite size, but they differ by a factor of 1,5 for the E1-transition.     

On the origin of ferromagnetism in semiconducting TiO2−δ:Co oxide

In Co-doped TiO_2?δ oxide films deposited on SrTiO₃(100) substrates, a room-temperature ferromagnetism is found to occur only in a limited charge-carrier concentration interval from 2×10¹⁸? 5×10²² cm^?3. This indirectly testifies that ferromagnetism in the aforementioned n-type semiconductor is associated with the exchange interaction of magnetic ions via conduction electrons rather than with the formation of Co clusters in the material. The magnetic moment per Co atom is 0.8μ_B in the TiO cubic phase and 0.5μ_B in the anatase tetragonal phase of TiO₂.     

Der Zerfall des125m Xe,des127m Xe und des127g Xe

The decay of^125m Xe produced by the reaction¹²²Te(α, n)^125m Xe using a target enriched in¹²²Te (95.4%) and the decay of^127m Xe produced by the reaction¹²⁷J(d, 2n)^127m Xe have been investigated: ^125m Xe decays with a half-life ofT _1/2=(56±3) sec by ayy- cascade withE _γ1=(140.4 ±0.5) keV andE _γ2=(110.5 ±0.5) keV. The experimental conversion coefficients yield multipolarities ofE3 for the 140.4 keV isomeric transition and predominantlyM1 for the 110.5 keV-transition. ^127m Xe decays with a half-life ofT _1/2=(71±2) sec. The decay also proceeds by aγγ-cascade with an isomeric E3 transition ofE _γ1=(172.5±0.3) keV and a predominantlyM1 transition ofE _γ2=(124.6±0.3) keV. In the decay of^127g Xe an additional branching of the electron capture to a level at (618.1±0.3) keV was observed. The relative probability forK-captureP _K618/P_K375=0.40 ±0.07 yields a total transition energyQ _EC=(664 ±4)keV. A spin of 1/2⁺ was assigned to the ground state.     

Gamma and Alpha decay from the 2.1-msec isomer213m Ra

The isomer^213mRa was produced by the reaction²⁰⁹Bi(¹⁰B, 6n), as well as by bombardments of¹²C on Pb isotopes,¹⁴N on Bi, and¹⁶O on natural Hg, with projectile energies in the range 60–100 MeV. The isomer decays with a halflife of 2.1 ms both via gamma internal transitions and via alpha branching to levels in²⁰⁹Rn. A level scheme is proposed in which the isomeric state is assigned as either 17/2^? or 13/2⁺ with shell-model configurations either of theh _9/2 protons coupled to ap _1/2 neutron hole, or of an uncoupledi _13/2 neutron hole. On the basis of alpha decay rate predictions from the new Fliessbach theory, the 17/2^? isomeric assignment is to be preferred. Phys. Abstracts classifications 4.200–4.375 E [Radioactivity^213m Ra [from²⁰⁹Bi(¹⁰B, 6n),^204-6Pb(¹²C, 3n–5n) etc.,E=60–100 MeV]; measuredE _α ,E _γ ,I _α ,I _γ ,I _x ,γγ-coin,xγ-coin,α _K,T _1/2.²¹³Ra,²⁰⁹Rn deduced levels,J, π,γ-multipolarity.]