A new high precision measurement of the muonium hyperfine structure interval Δv1

At LAMPF we have observed muonium resonance curves in low pressure argon and krypton at very weak magnetic field using two line narrowing techniques, and have obtained Δv = 4 463 302.2 (1.4) kHz (0.3 ppm). This is the most precise value of Δν yet quoted, and from it we obtain improved values for the muon magnetic moment and mass: $\text{μ}{}_{\mathrm{\mu }}{}_{\mathrm{<mtext>p</mtext>}}\text{= 3.183 329 9 (25) (0.8}\text{ppm}\text{);}\text{m}{}_{\mathrm{\mu }}\text{m}{}_{\mathrm{<mtext>e</mtext>}}\text{= 206.769 27 (17) (0.8}\text{ppm}\text{)}$.     

New value of m(mu)/m(e) from muonium hyperfine splitting

The complete contribution to the muonium hyperfine splitting of relative order alpha(3)(m(e)/m(mu))lnalpha is calculated. The result is much smaller than suggested by a previous estimate and leads to a 2sigma upward shift of the most precise value for the muon-electron mass ratio. Analogous contributions are calculated for the positronium hyperfine splitting, where a discrepancy with experiment remains.     

Quadrupole moment of muonium and hyperfine structure of muonium levels in silicon

It is shown that experimental data on Mu¹ in silicon are most satisfactorily described by the uniaxial symmetric spin hamiltonian which means muonium displacement from the octa-cell center.     

O(alpha(3) lnalpha) corrections to muonium and positronium hyperfine splitting

We compute O(alpha(3)lnalpha) relative corrections to the ground-state hyperfine splitting of a QED two-body bound state with different masses of constituents. The general result is then applied to muonium and positronium. In particular, a new value of the muon-to-electron mass ratio is derived from the muonium ground-state hyperfine splitting.     

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.     

Calculations of the hyperfine parameters of bond-centered muonium in diamond

The electronic structure of hydrogen and muonium at the bond-centered site in diamond is investigated using ab initio cluster calculations. Correlation effects are accounted for by a configuration interaction expansion and by the local density approximation in the density functional approach. The hyperfine and superhyperfine parameters for anomalous muonium are determined by averaging over the spread of the muon wave function. Good agreement with experimental hyperfine parameters is found.This work has partially been supported by the Swiss National Science Foundation.     

A non-perturbative approach to hyperfine splitting

A hyperfine energy splitting for atomic hydrogen is calculated in a non-perturbative manner for a finite width contact interaction. A close agreement between this result and first order perturbation theory is obtained.     

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.     

Precise determination of the ground state hyperfine splitting of135Ba+

A microwave-optical double resonance experiment has been performed on¹³⁵Ba⁺ ions, confined in a r.f. quadrupole trap. Linewidths as narrow as 0.9 Hz have been obtained on the 7.18 GHz,F=1,m=0 toF=2,m=0 transition. Shifts of the resonance frequency due to magnetic stray fields and the electric trapping field have been observed. The final result, extrapolated to zero field strengths, isΔ υ _HFS=7183340234.90(0.57) Hz.     

Electronic structure and hyperfine interaction of muonium in semi-conductors

The Unrestricted Hartree-Fock self-consistent field cluster procedure is being utilized for first-principle investigations of the electronic structures and hyperfine interactions in normal and anomalous muonium states in semi-conductors. Our results for the total energy for the normal muonium state for a twenty-seven atom cluster in diamond, including the muonium and its neighboring atoms, show a minimum at the tetrahedral site and a maximum at the hexagonal site indicating that normal muonium is located in the tetrahedral region and avoids the hexagonal region. Using the calculated spin-density as a function of the position of muonium and carrying out averaging over the vibrational motion of the muon governed by the total energy curve obtained from our work, we have derived a muon hyperfine constant which is about 75% of that in free muonium, in good agreement with experiment. The natures of the total energy and spindensity curves permit us to draw conclusions regarding the origin of the observed trend in the hyperfine constants for normal muonium in diamond, silicon and germanium. The UHF cluster procedure is also applied to study a model of a muon in a positively charged environment for the anomalous muonium center in diamond. This model leads to a hyperfine interaction tensor with the observed feature of strong anisotropy but significantly weaker than experiment. The results obtained for this model indicate the importance for the anomalous muonium state with its relatively weak hyperfine interaction, of exchange polarization effects inherent in the UHF procedure.     

Temperature dependence of the hyperfine parameters of anomalous muonium in germanium

The temperature variation of the anomalous muonium hyperfine interaction in germanium has been measured between 5 and 100 K. The results show that the component perpendicular to the defect axis decreases, while the parallel component increases with increasing temperature. These effects are a result of the interaction of anomalous muonium with the germanium host phonons.Work supported by National Science Foundation Grant DMR-79-09223.     

Hyperfine splitting of muonium in SiO2 powder

The hyperfine splitting of Mu in evacuated SiO₂ powder has been measured over the temperature range 17–300 K using the two frequency method. Above 100 K it is consistent with the vacuum value (4463.3 MHz) indicating the Mu atoms are moving freely between the particle grains. At lower temperatures it drops rapidly to 4437±4 MHz at 17 K. The effect is attributed to thermal adsorption on the SiO₂ surface. Measurements were also made on an Ar coated powder between 7–62 K. The hyperfine splitting is consistent with the vacuum value over this range.