Search

The transfer reaction of negative muons from muonic protium to 3 and 4 in binary and triple gas mixtures was studied. In the binary mixtures the transfer rates to the two helium isotopes were determined from the time distribution of the 7-keV X-rays of the intermediate muonic molecule (pµHe)*. The experimental transfer rate to 4 is in good agreement with theoretical predictions, whereas the rate to 3 is a factor 2 to 3 smaller than the predicted ones. Radiative branching ratios of the (pµHe)8 molecular decay were obtained. Muon transfer from excited states of muonic protium gives the main contribution to the total intensity of the µHe Lyman series in the binary mixtures. Values of q 1s He are determined.

The energy and time distributions of the decay X-rays of excited, metastable, molecular (dµHe)*-resonances were measured. The comparison of the observed energy spectra with calculated ones suggests that decay from the rotational state J = 1 dominates at the investigated conditions. The muon transfer rates from ground state deuterium to the helium isotopes 3He and 4He at low temperatures were determined from the time distributions of these spectra. Additionally, the temperature dependence of the muon transfer rate was clearly established in deuterium / 4He mixtures.

The present status of research of muon transfer from the ground state of muonic protium to 4He is reviewed. The analysis of a recent measurement in a triple gas mixture of H2+4He+Ne at 15 bar and room temperature is presented and the result is compared to the existing experimental and theoretical rates. The average muon transfer rate from protium to 4He determined from all lifetime measurements is .

The charge exchange reaction of negative muons from the \((\mu {\text{p}})_{1{\text{s}}} \) atom to oxygen has been measured in gaseous mixtures of H2 + O2. The measurements were performed at three different relative oxygen concentrations ranging from 0.2% to 0.8% and total pressures 3.5–15 bar. A mean transfer rate of \(\lambda _{{\text{pO}}}^{\text{t}} = 0.85(2) \times 10^{11} {\text{s}}^{{\text{ - 1}}} \), describing the transfer from the ground state of thermalized \(\mu {\text{p}} \) atoms to oxygen, was determined. In order to investigate the energy dependence of the transfer rate, Monte Carlo simulations of the \((\mu {\text{p}})_{1{\text{s}}} \) thermalization and the muon transfer were carried out. The comparison of measured and simulated time spectra yielded an epithermal transfer rate \(\lambda _{{\text{pO}}}^{\text{e}} \)=3.9 \(\times \) 1011 s-1 in the energy interval 0.12–0.22 eV. The analysis with the model of “Two components” shows that all measured time spectra can be reproduced with the same set of parameters.

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}

The yields of muonic x rays of the Lyman series of nitrogen, neon and argon have been analysed to determine capture ratios A(Z1,Z2) in about thirty gaseous mixtures under different experimental conditions. In addition, capture ratios A(Z,H) have been determined in hydrogen mixtures by taking into account transfer processes from muonic hydrogen to elements Z. The influence of the spectral flux density of the muons on capture ratios has been analysed. Our per-atom ratios form a coherent set and confirm the value A(Ar,Ne) = 1. 262(10).

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}

Several experiments performed by our group in recent years have put into evidence the complex structure of the time distributions of the muonic X-rays following transfer from muonic hydrogen isotopes to heavier elements. Simulations have shown that a substantial fraction of the µp atoms in the ground state have epithermal energies. Therefore, an energy dependence of the transfer rate seems a reasonable assumption for the explanation of the complex time structure.

Muon transfer from hydrogen isotopes to helium is of importance in muon-catalyzed fusion and serves as a unique tool for the direct observation of the mesomolecular ion (pµHe)*. During two data-taking runs in 1994 and 1995 at PSI, measurements of the transfer from protium to helium were carried out using CCD's and Ge-diodes as independent X-ray detectors to obtain information on the time distribution and intensity of the 7 keV decay X-ray of the mesomolecular ion. Dual1H2 +4 He and triple1H2 + Ne +3,4He gas mixtures at low temperatures were investigated to extract transfer rates. Protium of high purity was available. For the first time a transfer rate from muonic protium to3He was measured. A general survey of our measurements and preliminary analysis is presented.

To investigate the energy dependence of muon transfer to oxygen, we performed measurements in gaseous mixtures of hydrogen and oxygen. The time distributions of the muonic oxygen X-rays showed the same structure as the one observed earlier in H2+SO2 mixtures. In the delayed part of these distributions, one can distinguish a short-time and a long-time component. From the latter, we deduced the transfer rates from thermalized muonic protium, respectively deuterium, to oxygen. The short-time component can be interpreted as being due to muon transfer from epithermal muonic hydrogen atoms. The time parameters are characteristic for the deceleration process as well as for energy-dependent transfer rates. With results of recent research on the formation and the thermalization of muonic hydrogen, we performed Monte Carlo simulations in order to test the hypothesis of an energy-dependent transfer rate.

The experimental muon transfer rates from muonic protium and deuterium to heavier elements show a complexZ dependence. Instead of the expected monotonicZ dependence considerable variations between neighboring elements are observed. Transfer to neon has a specially small rate. Furthermore, the time distribution of the muonic X-rays shows in a number of molecules a complex structure, and depends in the case of a H2 + CH4 gas mixture also on the total pressure.

A set of experiments is reviewed which makes use of the emission of muonic deuterium from the surface of a layer of solid hydrogen. The behaviour of muons in a solid target system has been studied via detection of muon decay electrons, muonic X-rays, and fusion products (neutrons and charged particles). The emission of muonic deuterium is understood to result from the Ramsauer-Townsend scattering minimum. The energy distribution of the emitted atoms ranges from tenths of eV to about 10 eV, and can be controlled to some extent. A proposal is described to use muonic tritium emission to measure the energy dependence of muonic molecular formation.

The ratios of prompt to delayed fission yields for the isotopes U-233, U-234, U-235, U-236, U-238, Np-237, Pu-242, and Pu-244 and the fission probabilities relative to each other have been investigated experimentally. Using the value of the total fission probability for Np-237 the absolute probabilities for prompt and delayed fission have been determined. The fission probabilities per muon capture P(fc) have been derived for all the isotopes and compared with an evaluation based on excitation functions from theory.

A study of muonic238U has been performed in a combined (μ−,γ f) and (μ−,γγ) coincidence experiment to investigate the role of non-radiative transitions and their fission probabilities. An augmentation of the outer fission barrier ofΔEb=(0.6±0.1) MeV due to the presence of the muon is deduced. A significant contribution to the prompt fission yield not only results from the (2p→1s) and (3d→1s) non-radiative transitions, but also from other radiationless transitions. Specifically, the measured fission probabilities of the transitions (2p→1s), (3d→1s), and (3p→1s) are (1.5±0.4)%, (5.7±1.7)%, and (5.3±1.9)%, respectively.

Fission fragments from the reaction237Np(μ−,γ,f) have been measured in coincidence with muonic X-rays. The efficiency of the fission fragment detector is determined from (μ−,γ,f)-data of the same experiment. The total fission probability perμ-stopPt has been measured as well as the fission probabilities Pf of the non-radiative muonic (3d→1s)- and (2p→1s)-transitions; the latter has been divided into two parts leading to different mean excitation energiesE:P t =(54±17)%,P f (3d→1s)=(41±21)%,P f (2p→1s,E=6.218 MeV)=(61±19)%, andP f (2p→1s,E=6.525 MeV)=(57±18)%. The influence of the muon on the fission barrier is discussed. The fission probability after muon capture is compared with a calculated value using a distribution of nuclear excitation energies following muon capture and the fission probability as measured in a238U(3He,αf)-reaction.

The time spectra for muon induced fission of233U,234U,235U,236U,238U, and237Np were measured simultaneously, detecting both fragments in coincidence in a fast multi parallel plate avalanche detector. The observed mean lifetimes τ are 68.9 ± 0.3 ns, 70.6 ± 0.2 ns, 72.2 ±0.2 ns, 74.3 ± 0.3 ns, 77.0 ±0.4 ns, and 69.8 ±0.2 ns for the above isotopes, respectively. No second time component, tentatively ascribed to a possible fission isomer, was observed. The deduced total capture rates are compared with theoretical predictions.

We report on an experiment at the Paul Scherrer Institute, Villigen, Switzerland measuring x rays from muon transfer from deuterium to helium. Both the ground state transfer via the exotic dmu3,4He* molecules and the excited state transfer from mud* were measured. The use of CCD detectors allowed x rays from 1.5 keV to 11 keV to be detected with sufficient energy resolution to separate the transitions to different final states in both deuterium and helium. The x-ray peaks of the dmu3He* and dmu4He* molecules were measured with good statistics. For the D2+3He mixture, the peak has its maximum at E_dmu3He = 6768 +- 12 eV with FWHM Gamma_dmu3He = 863 +- 10 eV. Furthermore the radiative branching ratio was found to be kappa_dmu3He = 0.301 +- 0.061. For the D_2+4He mixture, the maximum of the peak lies at E_dmu4He = 6831 +- 8 eV and the FWHM is Gamma_dmu4He = 856 +- 10 eV. The radiative branching ratio is kappa_dmu4He = 0.636 +- 0.097. The excited state transfer is limited by the probability to reach the deuterium ground state, q_1s. This coefficient was determined for both mixtures: q^3He_1s = 68.9 +- 2.7% and q^4He_1s = 90.1 +- 1.5., Comment: 9 pages, 11 figures

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 present situation of muon transfer to helium is summarized. A new gas target for a maximal pressure of 40 b with four thin beryllium windows for the detection of low energy photons is described. First results of an analysis of the time spectra of muonic carbon X-rays in a H2+CH4 gas mixture taken with the new target show a pressure dependent structure.

By analysing the time spectra of the muonic sulphur X-rays in seven different H2+SO2 gas mixtures, the muon transfer rates to the SO2 molecule, deduced from the lifetimes of the µp atoms, agree all well with each other. The muonic oxygen time spectra show an additional structure as if µp atoms of another kind were present. Reduced transfer rates Λ o ′ are reproducible if one uses the model of “ephemeral” µp atoms[1].

Experiments are described which use a solid hydrogen layer to form muonic hydrogen isotopes in vacuum. The method relies on transfer of the muon from protium to either a deuteron or a triton. The resulting muonic deuterium or muonic tritium will not immediately thermalize because of the very low elastic cross sections, and may be emitted from the surface of the layer. Measurements which detect decay electrons, muonic x-rays, and fusion products have been used to study the processes. A target has been constructed which exploits muonic atom emission in order to study the energy dependence of transfer and muon molecular formation.

The muonic atom 2${\mathit{p}}_{1/2}$-1${\mathit{s}}_{1/2}$ and 2${\mathit{p}}_{3/2}$-1${\mathit{s}}_{1/2}$ transition energies were measured with an experimental accuracy of better than 20 ppm for the isotope chain $^{112,114,116,117,118,119,120,122,124}\mathrm{Sn}$. Precise values for the Barrett equivalent nuclear radii ${\mathit{R}}_{\mathit{k}\mathrm{\ensuremath{\alpha}}}$ and their differences as well as root-mean-square radii were deduced. The \ensuremath{\Delta}N=2 isotope shifts between the even Sn isotopes show a subshell effect at the neutron number N=64. Otherwise, there is a nearly linear decrease with increasing N, in accordance with the general systematics of nuclear charge radii. Our muonic atom results are in a good agreement with recent optical data, including odd-even staggering. Hartree-Fock calculations reproduce the general trend but not the subshell effect. Regarding the nuclear polarization corrections, the problem in the 2p splitting found earlier in ${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$-Zr and ${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$-Pb seems also to persist in ${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$-Sn.

The muon transfer process in binary and ternary gas mixtures with hydrogen looks like a well known process. 1 From the ground state of the up atom, where the muon has a binding energy of about 2.6 keV, the muon is transferred to higher Z elements onto atomic orbits with much smaller radii than the outer electron shells of the atom Z, and where the muon has a comparable binding energy. The transfer process does therefore not depend on chemical structures and bonds in which the element, to which the muon is transferred, is involved.

A negative muon, captured in a mixture of natural hydrogen with a small amount of another gas of atomic number Z, forms a muonic hydrogen or a muonic Z atom in an excited state. In the deexcitation process, muonic X rays are emitted. Because the cascade time is very short (of the order of 10–12 s at 10 bar), they appear promptly with regard to the incoming muon. After deexcitation of the (μp)* system (in about 10–10s), which occurs essentially by collisions, 1 the (up) is atom can then disappear by muon decay with an associated rate λ0, by formation of a pup mesomolecule (λpp), or by transferring the muon to deuterium (λd) or to the Z element (λpz). The total disappearance rate of the up atom, λ is then: $$\lambda = {\lambda _{0}} + {\lambda _{{pp}}} + {\lambda _{d}} + {\lambda _{{pZ}}}$$ (1)

In the spectrum of muonic X-rays of238U measured in coincidence with prompt fission events a structure has been found which is attributed to 2p→1s transitions of the muon attached to heavy fragments. The intensityI s of this structure relative to the strengthI pf observed for prompt fission has been determined to beI s/I pf=(6.0± 2.1) %. Although the experimental significance for the appeareance of this phenomenon is weak, this is the first experimental indication for its occuxence.

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.

By analysing measured time distributions of the muonic oxygen and sulphur X-rays in a H2+SO2 gas mixture, one finds two different time constants. If these correspond to two lifetimes for the bound μp atom, two kinds of μp atoms exist: one kind transfers its muon only to oxygen, the other to both oxygen and sulphur. The difference in the two μp systems is presently unexplained.

The X-ray spectrum of muonic 237 Np has been investigated with stopped muons in a NpO 2 target, containing about 10 g of 237 Np. The probability of the radiationless muonic 3d→1s transition in 237 Np , (9±4)% , was obtained by comparing the relative intensities of the main muonic X-ray transitions in singles and coincidence spectra. The coincidences were gated by the 2p→1s transitions.

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 transfer rate of negative muons from the 1s state of hydrogen to argon has been measured in H2+Ar gas mixtures at total pressures of 100 and 140 bar and argon concentrations C (Ar/H2) of 6*10-4 and 20*10-4. The reduced transfer rates have been found to be independent of the total pressure and of the argon concentration. The mean reduced transfer rate obtained, Lambda pAr=(1.46+or-0.05)*1011 s-1, is compared with the rates measured by other authors.

Energies and intensities of muonic X-rays, nuclear γ-rays and μ-capture γ-rays were measured in natural muonic thallium with Ge(Li) detectors. The absolute intensities of higher μ X-rays were reproduced by a cascade calculation starting with a statistical population at n = 20 including K-, L- and M- conversion. The electron screening effect was deduced from energies of higher μ X-rays. Eight prompt nuclear μ-rays were found, due to an excitation of (4.1 ±1.0) % and (14.6 ± 3.0) % of the first 3 2 + level in μ 203 T1 and μ, 205 T1, respectively, and of (8.8 ± 0.9) % of the 5 2 − level at 2.63 MeV in 205 T1. This excitation explains the anomalous intensity ratios of the 2p-ls and 3d-2p fine structure components. From the nuclear y-rays of the first excited states were deduced: the magnetic h.f. splittings e 203 ( 1 2 ) = 2.57 ± 0.15 keV , e 205 ( 1 2 ) = 2.30 ± 0.02 keV, muonic isomer shifts ΔE is (203) = 0.26 ± 0.15 keV, ΔE is (205) = −(0.31 ± 0.11) keV; E2/M1 mixing ratios δ μ 2 (203) = 0.89 ± 0.27, δ μ 2 (205) = 1.00 ± 0.05, and the half-life in the presence of the muon T μ ( 3 2 ) = 1.4 ± 0.1 nsec in 205 T1. The values of e( 1 2 ) and ΔE ls were compared with shell-model calculations. From δ μ 2 and T gm ( 3 2 ) evidence for a magnetic nuclear polarization was found. From the 2p-ls, 3d-2p, 3p-2s and 2s-2p transitions the size and shape of the nuclear charge distribution and a nuclear polarization due to the 1s 1 2 muon of ΔE np = 8.3 ± 1.2 keV and 9.5 ± 1.2 keV for 203 Tl and 205 T1 respectively were determined in agreement with theoretical estimates. An isotope shift of ΔE = 10.35 ± 0.25 keV was measured for the 1s 1 2 state which is compared with data from optical spectroscopy. From an analysis of the time distribution of delayed γ-rays from μ-capture, an isotopic effect of (5.4 ± 2.5) % was found for the capture rates, in fair agreement with predictions from Primakoff's μ-capture formula.

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.

Measurements of relative Coulomb capture rates of muons in compounds of nitrogen, sulphur and selenium have been performed. The obtained results may be interpreted as showing a valence state dependence

The mean life times of negative muons bound to actinide nuclei have been measured by detecting the time difference between a stopped muon and the arrival of fragments from delayed fission after muon capture. The deduced capture rates c are 1.392(4)·107/s for237Np, 1.290(7)·107/s for242Pu and 1.240(7)·107/s for244Pu. The results are compared with published data for the fission and the neutron decay channels and for the electron decay of the bound muon. Including a former measurement of c for239Pu, an isotopic dependence of the muon capture rates in the Pu isotopes is clearly observed.

We report on muonic Lyman-series x-ray intensities measured in gaseous argon and in K/sup +/, Cl/sup -/, Na/sup +/, and F/sup -/ in the compounds KF and NaCl. The analysis of their structures, including neon, shows that both the spatial symmetry and the binding energy of the electrons of outer shells determine the angular momentum distribution of captured muons. The conclusions are in agreement with the modified model of ''large mesic molecules.''

Muon transfer from the ground state of muonic deuterium to a helium atom proceeds mainly via the formation of a muonic molecule in an excited state. A large number of decay X rays (∼ 6.8 keV) from these (dµHe)* molecules were observed for the4He as well as for the3He case. The time distributions of these X rays allow the determination of the ground state transfer rate. The simultaneous employment of Ge/Si-detectors and CCDs for the same target conditions allows the determination of the branching ratio of radiative to nonradiative decay for the first time.

Negative muons were trapped in gaseous mixtures of hydrogen and oxygen. The time distributions of the muonic oxygen X-rays showed a clear deviation from a single exponential structure. From these time distributions we evaluated the transfer rate from thermalized muonic hydrogen atoms to oxygen. In order to test the hypothesis of an energy-dependent transfer rate to oxygen we performed Monte Carlo simulations of the thermalization and the transfer process. We report on the present status of our investigations.