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A method is proposed for investigating muon transfer from excited muonic hydrogen atoms to an element Z{gt}2, and is applied to argon measurements. It makes use of a comparison between the muonic x-ray intensity patterns of the Lyman series of this element measured in mixtures with and without hydrogen. The analysis of the data taken in two gas mixtures H{sub 2} + Ar at 15 bar with argon concentrations of 2{percent} (0.3{percent}), yields consistent results. In both mixtures, two thirds of the prompt argon x rays proceed from transfer from excited {mu}p{sup {asterisk}} states. The Coulomb capture ratio determined in both mixtures yields a mean value of A(H{sub 2},Ar) = 0.21(2), and agrees with the corresponding pionic ratio. {copyright} {ital 1997} {ital The American Physical Society}

Recent experimental results on the muon exchange from muonic hydrogen to argon show that the reaction rate is energy dependent near 0.1 eV. A muonic hydrogen atom, formed by muon capture in H{sub 2} gas at 15 bars, is thermalized in a few hundreds of nanoseconds. If the muon transfer reaction occurs before that time, the rate is shown to be slightly lower compared to thermalized muonic atoms [{lambda}{sub pAr}=(1.63{plus_minus}0.09){times}10{sup 11} s{sup {minus}1}]. As an indirect consequence, the muon transfer rate from {mu}p to helium, determined by our group [R. Jacot-Guillarmod and co-workers, Phys. Rev. A {bold 38}, 6151 (1988)] is lowered by about 40{percent}. The present value {lambda}{sub pHe}=(0.51{plus_minus}0.19){times}10{sup 8} s{sup {minus}1} is in good agreement with other experiments. The transfer rate from muonic deuterium to argon shows also an energy dependence. The muon transfer rate to argon from the deuteron is {lambda}{sub dAr}=(0.86{plus_minus}0.04){times}10{sup 11} s{sup {minus}1} at room temperature. The intensity patterns of the muonic Lyman series of argon obtained by muon transfer from both hydrogen isotopes are determined and compared with theoretical predictions. {copyright} {ital 1997} {ital The American Physical Society}

The present work extends the systematics of nuclear charge radii obtained by the method of muonic atoms to nuclei with 8\ensuremath{\le}Z,N\ensuremath{\le}20. The accuracy of the measured muonic Lyman transition energies of generally \ensuremath{\le}10 eV leads to a precision in the model-independent nuclear charge radii differences of 2--3 am for the isotope shifts and 4--9 am for isotone shifts. Both isotope and isotone shifts within the s-d shell behave ``anomalously'' with respect to the systematics of heavier nuclei. However, such behavior is predicted on theoretical grounds, if mixing in the s-d shells and the strong deformation of some of the nuclei in this region are considered. We compare charge radii from elastic electron scattering data with muonic atom rms radii and suggest that observed deviations are possibly due to incomplete dispersion corrections.

We have observed the deexcitation x-ray spectra of the exotic molecules $(d{\ensuremath{\mu}}^{4}\mathrm{He}{)}^{*}$ and $(d{\ensuremath{\mu}}^{3}\mathrm{He}{)}^{*}$ with good statistics and low background. From the time distributions of these x rays, we have directly determined the muon transfer rates from ground-state muonic deuterium atoms to helium nuclei. The obtained transfer rates in gaseous mixtures at $\ensuremath{\sim}30$ K are ${\ensuremath{\lambda}}_{{d}^{3}\mathrm{He}}=(1.856\ifmmode\pm\else\textpm\fi{}0.077)\ifmmode\times\else\texttimes\fi{}{10}^{8} {\mathrm{s}}^{\ensuremath{-}1}$ to ${}^{3}\mathrm{He},$ and ${\ensuremath{\lambda}}_{{d}^{4}\mathrm{He}}=(10.50\ifmmode\pm\else\textpm\fi{}0.21)\ifmmode\times\else\texttimes\fi{}{10}^{8} {\mathrm{s}}^{\ensuremath{-}1}$ to ${}^{4}\mathrm{He}.$ In liquid mixtures, we measured the muon transfer rates ${\ensuremath{\lambda}}_{{d}^{3}\mathrm{He}}=(2.77\ifmmode\pm\else\textpm\fi{}0.73)\ifmmode\times\else\texttimes\fi{}{10}^{8} {\mathrm{s}}^{\ensuremath{-}1}$ and ${\ensuremath{\lambda}}_{{d}^{4}\mathrm{He}}=(14.2\ifmmode\pm\else\textpm\fi{}1.4)\ifmmode\times\else\texttimes\fi{}{10}^{8} {\mathrm{s}}^{\ensuremath{-}1}.$ These transfer rates have to be multiplied with the target density and the atomic helium concentration to obtain the ``effective transfer rates'' for a specific target composition. The expected isotopic effect between mixtures containing ${}^{3}\mathrm{He}$ and mixtures containing ${}^{4}\mathrm{He},$ as well as with respect to the hydrogen-helium case, is clearly confirmed. A density effect was observed for both isotopic compositions. We investigated the widths and the energies of the intensity maxima of the observed energy spectra of the molecular x rays. From the comparison of the measured energy spectra with calculated ones, we conclude that decay from the rotational state $J=1$ of the muonic molecule dominates over decay from $J=0$ at the investigated experimental conditions.

The muonic Coulomb capture ratio A(${\mathrm{H}}_{2}$,Ar) has been measured in two different ${\mathrm{H}}_{2}$-Ar gas mixtures using two different methods of evaluation based on the muon transfer from hydrogen. The measured ratios agree with each other, but disagree with the corresponding pionic capture ratio and also with the ratios calculated from muonic and pionic A(He,Ar) and A(He,${\mathrm{H}}_{2}$) capture ratios. The large discrepancies might be related to unsolved problems in muon transfer.

The transfer of negative muons from the ground state of muonic hydrogen to argon and helium has been measured in gaseous mixtures at pressures between 10 and 15 bars and at different relative concentrations. The transfer rate to argon, reduced to liquid-hydrogen density [${\ensuremath{\Lambda}}_{p\mathrm{Ar}}$ =1.42(4)\ifmmode\times\else\texttimes\fi{}${10}^{11}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$], agrees well with those obtained at ten times higher pressures. The transfer rate to helium [${\ensuremath{\Lambda}}_{p\mathrm{He}=0.88(9)\ifmmode\times\else\texttimes\fi{}{10}^{8}}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$], measured in a triple gas mixture, disagrees with the only other experimental value and is about two times higher than recent theoretical predictions. In addition, the muonic x-ray intensities of the Lyman series of argon resulting from muon transfer have been determined. They are well reproduced by a cascade calculation assuming a theoretical initial distribution over n and l states.

The energies of muonic x-ray transitions sensitive to the nuclear charge parameters have been measured with a precision up to 9 ppm in muonic /sup 90/Zr. Combining our muonic-atom results for the equivalent nuclear charge radii R/sub k/,..cap alpha.. with recent elastic electron scattering data, the rms radius of /sup 90/Zr could be determined as /sup 1/2/ = 4.2726(9) fm. In addition to the nuclear monopole charge distribution, nuclear polarization correlations between the muonic 1s and 2s and the 1s and the two 2p states could be determined. With additional constraints from elastic electron scattering and theory, the nuclear polarization corrections of the four lowest-lying states could be evaluated with precisions of the order of 15%. Of particular significance is the result for the two 2p states, because the experimentally determined 2p/sub 1/2/ correction is smaller than the nuclear polarization correction in the 2p/sub 3/2/ state, in contrast to current theoretical models.

Energies of muonic x rays of the Lyman series of the even sulphur isotopes /sup 32/S, /sup 34/S, and /sup 36/S and of natural phosphorus have been determined with absolute precisions up to 23 parts/10/sup 6/. Equivalent Barrett charge radii R/sub k/,..cap alpha.. have been deduced. Their differences between the sulphur isotopes amount to ..delta..R/sub k/,..cap alpha..( /sup 34/S- /sup 32/ S) = 29.7(1.4) am and ..delta..R/sub k/,..cap alpha..( /sup 36/S- /sup 34/ S) = 18.7(1.5) am. Combining these results with recent elastic electron scattering data, we obtain in a model-independent way ..delta../sup 1/2/( /sup 34/S- /sup 3/ 2S) = 23.1(1.2) am and ..delta../sup 1/2/( /sup 36/S- /sup 3/ 4S) = 13.0(1.2) am.

Muonic x-ray intensities of the Lyman series have been measured in carbon (diamond, graphite, and soot) and in boron and nitrogen in the cubic (diamond) and hexagonal (graphite) structures of boron nitride. By means of muon cascade calculations which reproduce the measured intensities, angular momentum distributions of the captured muons have been determined for carbon and nitrogen in the $\ensuremath{\mu}$-atomic level $n=13$. The boron-to-nitrogen capture ratios have been found to be 0.233\ifmmode\pm\else\textpm\fi{}0.011 in the cubic structure and 0.275\ifmmode\pm\else\textpm\fi{}0.012 in the hexagonal structure. The difference of 18\ifmmode\pm\else\textpm\fi{}3% has to be attributed to the difference in the solid-state structures.

Muonic transition energies between low-lying states in ${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{-}}}^{208}$Pb have been measured in a precision experiment using a Compton suppression spectrometer. Nuclear charge parameters and nuclear polarization corrections have been adjusted to the data. In particular, experimental correlations between the nuclear polarization corrections of the lower muonic levels have been established. A set of nuclear charge parameters reproducing all the experimental transition energies can only be obtained by assuming an inversion in magnitude of the nuclear polarization corrections not only for the 2p states, but also for the two 3p states. Such a result is unexplained by present theoretical models, but corroborates the findings of a recent experiment concerning the 2p states in ${\ensuremath{\mu}}^{\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{-}}}^{90}$Zr. Using our best-fit parameters, a $^{208}\mathrm{Pb}$ rms radius of 〈${r}^{2}$${〉}^{1/2}$=5.5031(11) fm has been obtained.

The muonic x-ray intensities of the Lyman series in pure silicon are investigated. The fitted data are compatible with a statistical initial angular momentum distribution of the captured muons. From a comparison with data measured in diamond, cubic boron nitride and in the two isoelectronic series F/sup -/,Ne,Na/sup +/ and Cl/sup -/,Ar,K/sup +/, we conclude that the calculated muon distribution reflects the symmetry of the electrons through which muon capture proceeds.