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This paper reports measurements of the temperature dependence of the rate constants for H-atom abstraction reactions from propane and n-butane by the light isotopic H-atom muonium (Mu), kMu(T), over temperatures in the range 300 K to 435 K. Simple Arrhenius fits to these data yield activation energies, EMua, that are some 2–4 times lower than EHa found from corresponding fits for the H + propane and H + n-butane reactions studied elsewhere, both experimentally and theoretically, and fit over a similar temperature range. These activation energies EMua are also much lower than estimated from zero-point-energy corrected vibrationally adiabatic potential barriers, both results suggesting that quantum tunneling plays an important role in determining kMu(T) and for the Mu + propane reaction in particular. The results are expected to pose a considerable challenge to reaction rate theory for isotopic H-atom reactions in alkane systems.

We report the reaction of muonium (Mu = [μ+e-]), a light isotopic analog of hydrogen, with uncapped gold nanoparticles embedded in mesoporous silica. Using the radio-frequency muon spin rotation (RF-μSR) technique, we directly observe and characterize the resulting final state on the nanoparticle surface, showing conclusively its diamagnetic nature. The magnetic environment experienced by the reacted muons is only weakly perturbed compared to that of muons in a silica reference, consistent with the surface of the gold nanoparticles being metallic and non-magnetic. We demonstrate the potential of RF-μSR for the investigation of the surface properties of nanoparticles and show the feasibility of Knight shift measurements of muons on metal surfaces.

The study of kinetic isotope effects for H-atom abstraction rates by incident H-atoms from the homologous series of lower mass alkanes (CH4, C2H6 and, here, C3H8) provides important tests of reaction rate theory on polyatomic systems. With a mass of only 0.114 amu, the most sensitive test is provided by the rates of the Mu atom. Abstraction of H by Mu can be highly endoergic, due to the large zero-point energy shift in the MuH bond formed, which also gives rise to high activation energies from similar zero-point energy corrections at the transition state. Rates are then far too slow near 300 K to be measured by conventional TF-μSR techniques that follow the disappearance of the spin-polarised Mu atom with time. Reported here is the first measurement of a slow Mu reaction rate in the gas phase by the technique of diamagnetic radio frequency (RF) resonance, where the amplitude of the MuH product formed in the Mu + C3H8 reaction is followed with time. The measured rate constant, kMu = (6.8 ± 0.5) × 10(-16) cm(3) s(-1) at 300 K, is surprisingly only about a factor of three slower than that expected for H + C3H8, indicating a dominant contribution from quantum tunneling in the Mu reaction, consistent with elementary transition state theory calculations of the kMu/kH kinetic isotope effect.

In order to provide an assessment of the “global” accuracy of the Liu–Siegbahn–Truhlar–Horowitz (LSTH) potential surface for H3, hot atom reaction yields, which are determined from collision processes over an energy range much wider than that of single-collision experiments, have been calculated for the Mu*+H2 and T*+H2 systems. The isotopic comparison of muonium (Mu=μ+e−), an ultralight isotope of hydrogen (mMu/mH≈1/9), with the heaviest H-atom isotope, tritium, is a novel approach in testing the global accuracy of the H3 surface. These reaction yields have been calculated using a formalism developed for (μ+) charge exchange, with input cross sections for elastic, inelastic (rovibrational excitation) and reactive collisions determined from quasi classical trajectories on the LSTH surface, in the center-of-mass energy range 0.5–11 eV. The rate of energy loss of the hot atom (Mu* or T*) due to elastic and inelastic collisions with the moderator (H2) drastically affects the hot atom reaction yield. In parti...

The recombination reaction Mu+NO+M⇌MuNO+M (M=He, N2, CH4) has been studied by the muon spin relaxation/rotation (μSR) technique up to 520 bar at room temperature. The reaction remains in the low pressure regime throughout. The measured termolecular addition rate constant in N2, 8.8±0.3×10−33 cm6 s−1, is essentially the same as that found in our earlier study at pressures below 60 bar [J. J. Pan et al., J. Phys. Chem., 1995, 99, 17160]. It is somewhat smaller in He, 7.7±1.0×10−33, but larger in CH4, 12.8±2.0×10−33. The Mu+NO reaction is about five times slower than the corresponding H+NO reaction. The strong collision limits of the rate constants for three H-isotopes (Mu, H, D) reacting with NO have been estimated with Troe's formalism for unimolecular dissociation in the low pressure regime, based on the ab initio potential energy surface of Guadagnini et al. [J. Chem. Phys., 1995, 102, 774]. The Troe calculations give less than satisfactory agreement with experiment with the corresponding weak collision factor, βc , higher than expected by a factor of ∽2 for H+NO. The calculated kinetic isotope effect in the strong collision limit for Mu/H is weaker than the measured effect by a factor of two giving an apparent large isotope effect in this factor, βcMu≈½βcH, possibly due to mode specific collisional stabilization.

The spin relaxation of the muonium‐substituted ethyl radical (MuCH2ĊH2) and its deuterated analog (MuCD2ĊD2) has been studied in the gas phase in both transverse and longitudinal magnetic fields spanning the range ∼0.5–35 kG, over a pressure range from ∼1–16 atm at ambient temperature. The Mu13CH213ĊH2 radical has also been investigated, at 2.7 atm. For comparison, some data is also reported for the MuCH2Ċ(CH3)2 (Mu‐t‐butyl) radical at a pressure of 2.6 atm. This experiment establishes the importance of the μSR technique in studying spin relaxation phenomena of polyatomic radicals in the gas phase, where equivalent ESR data is sparse or nonexistent. Both T1 (longitudinal) and T2 (transverse) μSR relaxation rates are reported and interpreted with a phenomenological model. Relaxation results from fluctuating terms in the spin Hamiltonian, inducing transitions between the eigenstates assumed from an isotropic hyperfine interaction. Low‐field relaxation is primarily due to the electron, via both the nuclear h...

Chemisorption of muonium onto the surface of gold nanoparticles has been observed. Muonium (μ+e−), a light hydrogen-like atom, reacts chemically with uncapped 7 nm gold nanoparticles embedded in mesoporous silica (SBA-15) with a strong temperature-dependent rate. The addition rate is fast enough to allow coherent spin transfer into a diamagnetic muon state on the nanoparticle surface. The muon is well established as a sensitive probe of static or slowly fluctuating magnetic fields in bulk matter. These results represent the first muon spin rotation signal on a nanoparticle surface or any metallic surface. Only weak magnetic effects are seen on the surface of these Au nanoparticles consistent with Pauli paramagnetism.

Rates for the gas‐phase thermal reaction Mu+CH4→MuH+CH3 (Mu=μ+e−), have been measured using the μSR (muon spin rotation) technique, over the temperature range 625–820 K. A good fit is obtained to the usual Arrhenius expression, k=A exp(−Ea/RT), giving an activation energy Ea=24.6±0.9 kcal/mol, ∼12 kcal/mol higher than that of the H‐atom isotopic variant of this reaction, H+CH4→H2+CH3. This Ea difference is the largest yet seen at high temperatures between H and Mu in the gas phase, and seems much too high to be explained in terms of [zero‐point‐energy (ZPE)] differences in their respective transition states, indicating instead a dramatic difference in reaction dynamics. The possible sources of this difference include differing reactivities from vibrationally excited states and/or a more favorable tunneling path for the H+CH4 reaction due to its suspected much earlier (and thinner) reaction barrier. In contrast, the similar H‐atom abstraction reactions with H2 and C2H6 gave Ea differences which matched expectations based on ZPE shifts, suggesting a qualitative difference in dynamics between these otherwise homologous reactions. It is suggested that reaction from vibrationally excited states may be relatively more important in the case of the Mu+CH4 reaction.

New evidence is presented for the observation of a muoniated radical in the Mu + Br(2) system, from μSR longitudinal field (LF) repolarisation studies in the gas phase, at Br(2) concentrations of 0.1 bar in a Br(2)/N(2) mixture at 300 K and at 10 bar total pressure. The LF repolarisation curve, up to a field of 4.5 kG, reveals two paramagnetic components, one for the Mu atom, formed promptly during the slowing-down process of the positive muon, with a known Mu hyperfine coupling constant (hfcc) of 4463 MHz, and one for a muoniated radical formed by fast Mu addition. From model fits to the Br(2)/N(2) data, the radical component is found to have an unusually high muon hfcc, assessed to be ∼3300 MHz with an overall error due to systematics expected to exceed 10%. This high muon hfcc is taken as evidence for the observation of either the Br-Mu-Br radical, and hence of vibrational bonding in this H[combining low line]-L[combining low line]-H[combining low line] system, or of a MuBr(2) van der Waals complex formed in the entrance channel. Preliminary ab initio electronic structure calculations suggest the latter is more likely but fully rigorous calculations of the effect of dynamics on the hfcc for either system have yet to be carried out.

Evidence for the formation of NeMu*, an isotopic analog of the Rydberg molecule NeH*, has been obtained from the observation of chemiluminescent emission in the near‐infrared region. This is the first spectroscopic detection of a muonium‐containing molecule. NeMu* was formed by stopping a 4 MeV muon (μ+) beam in a target vessel containing 1–6 atm of Ne and ∼1 Torr Ar. The wavelength spectrum of the emission, from ∼680–1000 nm, was measured using a variable‐wavelength filter, with a resolution of ±12.5 nm. Lower resolution spectra were also taken with a series of long pass filters. A complete histogram of photon events vs time was collected for each wavelength. Two strong transitions are observed, centered at 818 and 943 nm. Identification of NeMu* was made by a comparison of the experimental spectrum with a simulated spectrum based on detailed ab initio calculations, extended to higher excitation levels than had heretofore been reported. Both experimental and theoretical results are reported here. Althoug...

The reaction rates of the muonium (Mu) atom with HBr and HI in ∼1 atm N2 moderator have been measured over the temperature range 160–490 K using the μSR technique. While both abstraction and exchange reactions are possible, only the abstraction reaction should be observable, being moderately exothermic. Comparisons with the corresponding H(D) reactions reveal small kinetic isotope effects in both reactions, which do not vary strongly with temperature (kMu/kH≊3.5 near 300 K), consistent with the (classical) ratio of mean velocities. Surprisingly, quantum tunneling, normally facile for similarly exothermic reactions of the ultralight Mu atom (mMu/mH≊1/9), appears to be of little importance here. This despite the fact that the (temperature‐independent) experimental activation energies are much less than the expected vibrationally adiabatic barrier heights (estimated to be ≊1.5 kcal mol−1) and, particularly in the case of Mu+HI, much less than the corresponding H‐atom activation energy: 0.13±0.03 vs 0.70±0.3 ...

A new model is developed for the analysis of muon spin relaxation (μSR) measurements of muonium (Mu) reaction rates with other chemical species. The kinetics component of the model is specifically developed for addition reactions but can be extended to direct reactions. The polarization component of the model assumes that the adduct formed possesses a single, effective spin precession frequency. The complete model is solved to obtain an analytic expression for the μSR signal as a function of time. Both a time‐ordered sequence method and a Boltzmann spin equation method give equivalent solutions. These solutions are analyzed under various kinetic conditions. It is concluded that the coefficient controlling the decay of the μSR signal is closely related to the adduct formation rate constant, i.e., the high pressure limit of the apparent bimolecular addition rate constant. In the most favorable case, the decay constant gives the adduct formation rate constant directly at all pressures of buffer gas.

Muon polarizations are reported for nitrogen and ethane over a wide pressure range from below 1 to 200 atm for N2 and up to 245 atm for C2H6. The N2 measurements were made at ambient temperature, while those for C2H6 were made at temperatures both above and below the critical temperature (305.3 K). This is the first μSR study of muonium and diamagnetic muon formation to cover the entire range from a low pressure gas to densities typical of liquids. The data are discussed in terms of hot atom and spur models. In the lowest pressure range, below 1.5 atm for N2 and about 10 atm for C2H6, the muonium polarization increases with pressure. This is well understood in terms of epithermal charge exchange. In N2 there is a small diamagnetic fraction, which is ascribed to the N2Mu+ molecular ion. This fraction approaches zero as the pressure is increased to 200 atm, with a corresponding increase in the muonium fraction, consistent with charge neutralization of the molecular ion by electrons from the radiolysis track...

The reaction kinetics for the addition of the muonium (Mu=μ+e−) atom to C2H4 and C2D4 have been measured over the temperature range 150–500 K at (N2) moderator pressures near 1 atm. A factor of about 8 variation in moderator pressure was carried out for C2H4, with no significant change seen in the apparent rate constant kapp, which is therefore taken to be at the high pressure limit, yielding the bimolecular rate constant kMu for the addition step. This is also expected from the nature of the μSR technique employed, which, in favorable cases, gives kapp=kMu at any pressure. Comparisons with the H atom data of Lightfoot and Pilling, and Sugawara et al. and the D atom data of Sugawara et al. reveal large isotope effects. Only at the highest temperatures, near 500 K, is kMu/kH given by its classical value of 2.9, from the mean velocity dependence of the collision rate but at the lowest temperatures kMu/kH≳30/1 is seen, reflecting the pronounced tunneling of the much lighter Mu atom (mμ=1/9 mp). The present M...

The room-temperature termolecular rate constants, k0, for the Mu + CO + M==MuCO + M (M = He, N2, Ar) recombination reaction have been measured by the muSR technique, and are reported for moderator gas pressures of up to approximately 200 bar (densities less, similar 0.4 x 10(22) molec cm(-3)). The experimental relaxation rates reveal an unusual signature, in being dominated by the electron spin-rotation interaction in the MuCO radical that is formed in the addition step. In N2 moderator, k0 = 1.2+/-0.1 x 10(-34) cm(6) s(-1), only about 30% higher than found in Ar or He. The experimental results are compared with theoretical calculations carried out on the Werner-Keller-Schinke (WKS) surface [Keller et al., J. Chem. Phys. 105, 4983 (1996)], within the framework of the isolated resonance model (IRM). The positions and lifetimes of resonance states are obtained by solving the complex Hamiltonian for the nonrotating MuCO system, using an L2 method, with an absorbing potential in the asymptotic region. Accurate values of the vibrational bound and resonance states of MuCO reveal unprecedented isotope effects in comparisons with HCO, due to the remarkable effect of replacing H by the very light Mu atom (m(Mu) approximately (1/9)m(H)). Due to its pronounced zero-point energy shift, there are only two (J = 0) bound states in MuCO. Contributions from nonzero J states to the termolecular rate constants are evaluated through the J-shifting approximation, with rotational constants evaluated at the potential minimum. The value of the important A constant (181 cm(-1)) used in this approximation was supported by accurate J = K = 1 calculations, from which A = 180 cm(-1) was obtained by numerical evaluation. The calculations presented here, with a "weak collision factor" beta c = 0.001, indicative of the very sparse density of MuCO states, give a very good account of both the magnitude and pressure dependence of the experimental rates, but only when the fact that the two initially bound (J = 0) states become resonances for J0 is taken into account. This is the first time in IRM calculations of atom-molecule recombination reactions where J not equal to 0 states have proven to be so important, thus providing a truly unique test of quantum rate theory.

The neutral muonic helium atom 4Heμ, in which one of the electrons of He is replaced by a negative muon, may be effectively regarded as the heaviest isotope of the hydrogen atom, with a mass of 4.115 amu. We report details of the first muon spin rotation (μSR) measurements of the chemical reaction rate constant of 4Heμ with molecular hydrogen, 4Heμ + H2 → 4HeμH + H, at temperatures of 295.5, 405, and 500 K, as well as a μSR measurement of the hyperfine coupling constant of muonic He at high pressures. The experimental rate constants, kHeμ, are compared with the predictions of accurate quantum mechanical (QM) dynamics calculations carried out on a well converged Born–Huang (BH) potential energy surface, based on complete configuration interaction calculations and including a Born–Oppenheimer diagonal correction. At the two highest measured temperatures the agreement between the quantum theory and experiment is good to excellent, well within experimental uncertainties that include an estimate of possible sy...

The temperature dependence of the gas phase spin exchange reaction rates for muonium collisions with O2 and NO has been measured over the temperature range 295 to 478 K. In both cases the bimolecular rate constant k(T) was found to vary essentially as T1/2, leading to the following temperature independent spin exchange cross sections: σSE(Mu+NO) = (10.5±0.6)×10−16 cm2 and σSE(Mu+O2) = (9.1±0.7)×10−16 cm2. These results are in quantitative agreement with the H+O2 and H+NO results reported by Gordon et al., demonstrating that there is no isotope effect in spin exchange in this temperature range.

The bimolecular rate constants for the thermal chemical reactions of muonium (Mu): Mu + H 2 → MuH + H and Mu + D 2 → MuD + D, have been measured in the temperature range 610–850 K. For the hydrogen reaction, log A (cm 3 molecule −1 s −1 ) = −9.6 ± 0.4 and E a = 13.8 ± 1.5 kcal mole −1 , while for the deuterium reaction log A (cm 3 molecule −1 s −1 ) = −9.2 ± 1.2 and E a = 17.2 ± 4.2 kcal mole −1 . These results compare well with variational transition state theory calculations carried out on the Liu—Siegbahn—Truhlar—Horowitz potential surface.

In an experiment using the MSR (muonium spin rotation) technique, the rate of the chemical reaction Mu + Cl 2 → MuCl + Cl has been measured in Ar moderator gas at ≈ 1 atm and 22°C, yielding a bimolecular rate constant k = (5.2 ± 0.4) × 10 10 l mole −1 s −1 . This is 4.3 times faster than the most recent room temperature rate constant for the analogous II atom reaction.

The local magnetic fields at an interstitial µ + in single crystals Co and Gd have been measured by the µSR method in the temperature range from 4.2 K to 693 K, and from 4.2 K to 250 K, respectively. An anomalous variation is observed in the temperature range where the change of the direction of easy magnetization occurs, whose gross feature is explained by the change of the magnetic dipolar field from the moments of surrounding atoms. It is concluded that the µ + prefers to stay at an octahedral interstitial site and feels a nearly classical dipolar field. After the correction was made for dipolar field and Lorentz field, the contact hyperfine fields at T =0 are found to be –6.1 kOe for Co and –7.5 kOe for Gd, both decreasing with increasing temperature faster than the bulk magnetization. Comparison is made with µ + hyperfine fields in other ferromagnets, Ni and Fe.

The nuclear structure of the even and odd tin isotopes has been studied by 20 MeV (p,d) reactions. States strongly populated in the odd isotopes are due to the valence neutron shells and extend up to only 2 MeV of excitation energy; "deep hole" states were not identified. The occupation probabilities extracted from finite-range distorted-wavc-Born-approximation calculations generally agree well with the predictions of the BCS theory of superconducting nuclei, particularly with the calculations of Clement and Baranger. In the even tin isotopes, strongly populated states are characterized predominantly by L = 2 transfers extending up to 4 MeV excitation energy. The experimental spectroscopic factors for transitions populating even final states are compared with the BCS calculated values of Clement and Baranger, Alzetta and Sawicki, and Van Gunsteren; relatively good agreement is obtained for L = 2 transitions, but not for L = 0 transitions. A considerable fraction of the expected sum rule L = 2 strength in 118Sn is missing in the 119Sn(p,d)118Sn experimental spectrum; in like manner, no 4+ strength could be identified in either 114Sn or 118Sn.

Bimolecular rate constants for the thermal chemical reactions of muonium (Mu) with hydrogen and deuterium—Mu+H2→MuH+H and Mu+D2→MuD+D—over the temperature range 473–843 K are reported. The Arrhenius parameters and 1σ uncertainties for the H2 reaction are log A (cm3 molecule−1 s−1)=−9.605±0.074 and Ea =13.29±0.22 kcal mol−1, while for D2 the values are −9.67±0.12 and 14.73±0.40, respectively. These results are significantly more precise than those reported earlier by Garner et al. For the Mu reaction with H2 our results are in excellent agreement with the 3D quantum mechanical calculations of Schatz on the Liu–Siegbahn–Truhlar–Horowitz potential surface, but the data for both reactions compare less favorably with variational transition‐state theory, particularly at the lower temperatures.

Evidence for the formation and reactivity of the positive muon molecular ion NeMu + at room temperature in a low-pressure Ne moderator to which trace amounts of Xe, CH 4 , NH 3 or He have been added, is reported. A two-component relaxation of the diamagnetic muon spin rotation (μSR) signal is seen upon the addition of trace amounts of Xe to Ne: a fast relaxing component with bimolecular rate constant (3.6 ±) 0.6 × 10 −10 cm 3 atom −1 s −1 is thought to be due to thermal muonium formation in a charge-exchange process while the other slow relaxing component is attributed to a muon-transfer reaction, as in proton-transfer studies. With CH 4 or NH 3 added to Ne there is, at most, only a very slow relaxation seen, even though thermal muonium formation is expected, in analogy with Xe. These latter results may be due to very fast, possibly tunneling assisted, muon-transfer reactions, the first time that such processes have been at all characterized.

The MSR (muonium spin rotation) technique was used to measure the chemical reaction rate for Mu + F 2 → MuF + F in N 2 moderator at ≈ 1 atm from 295 to 383 K giving the Arrhenius expression: log 10 k (l/mole s) = (10.83 ± 0.20) - (200 ± 50)/ T , with k = (1.46 ± 0.11) × 10 10 l/mole s at 300 K. This is at least 6.8 times the room temperature rate constant for the analogous H atom reaction. The measured activation energy and enhancement over the H reaction rate are indicative of significant tunnelling in the Mu reaction, in agreement with the recent collinear quantum mechanical calculations of Connor et al.

We report a precise measurement of the rate of reaction of muonium atoms with bromine molecules in an argon moderator gas at a atm and 23 °C. The bimolecular rate constant is k= (2.4±0.3) ×1011 l/mole‐sec, ten times higher than that for the analogous reaction of hydrogen atoms. Since muonium can properly be treated as a light isotope of hydrogen, this comparison has potential significance for the theory of reaction rates. The technique is described and the results discussed.

Muonium atoms are found to undergo spin-conversion (triplet-to-singlet) with high probability in encounters with paramagnetic (but not diamagnetic) ions in aqueous solution. The spin-flip or spin-exchange process is compared in magnitude with electron-transfer reactions for eleven transition metal ions.

The spin‐exchange cross sections σSE for muonium collisions with O2 and NO have been measured in weak transverse magnetic fields in low pressure moderator at 300 K. Average values from runs at 1 and 2.5 atm are σSE(Mu+O2)?1.2)×10−16 cm2 and σSE(Mu+NO) ?1.2)×10−16 cm2. These numbers are in qualitative agreement with those determined earlier by Mobley et al. in ∼40 atm. moderator pressure using a longitudinal field technique. Comparison with recent measurements of the corresponding cross sections for H atom spin exchange at 300 K reveals no isotope effect, consistent with expectations based on a random‐phase approximation.

The interaction between Mu and O 2 in water, which could be a spin-conversion process, has a rate constant of (2.4 ± 0.5) × 10 10 M −1 s −1 and is compared with the diffusion-controlled limit and the corresponding gas phase reaction.

Muon spin rotation and level-crossing spectroscopy have been used to measure the muon, proton, deuteron and 13C hyperfine coupling constants for the isotopically substituted ethyl radicals CH2CH2Mu, CD2CD2Mu and 13CH213CH2Mu in the gas phase.

Bimolecular rate constants for the thermal chemical reactions of muonium (Mu) with the halogen gases—Mu+X2→MuX+X—are reported over the temperature ranges from 500 down to 100, 160, and 200 K for X2=F2,Cl2, and Br2, respectively. The Arrhenius plots for both the chlorine and fluorine reactions show positive activation energies Ea over the whole temperature ranges studied, but which decrease to near zero at low temperature, indicative of the dominant role played by quantum tunneling of the ultralight muonium atom. In the case of Mu+F2, the bimolecular rate constant k(T) is essentially independent of temperature below 150 K, likely the first observation of Wigner threshold tunneling in gas phase (H atom) kinetics. A similar trend is seen in the Mu+Cl2 reaction. The Br2 data exhibit an apparent negative activation energy [Ea=(−0.095±0.020) kcal mol−1], constant over the temperature range of ∼200–400 K, but which decreases at higher temperatures, indicative of a highly attractive potential energy surface. This...

A beam of surface muons (4.1 MeV) was used to generate thermalised muonium atoms (μ + e − ) in aqueous solutions. From measurements of the muonium atom relaxation time in the presence of various solutes, bimolecular rate constants were determined and compared with the corresponding reactions of the much heavier isotope, the hydrogen atom.

Plane-wave Born approximation calculations have been carried out for the (p,d) reaction at intermediate beam energies with the purpose of elucidating the manner in which the various physical parameters of the problem determine the behaviour of the cross-sections. Analytical formulae for the differential cross section are derived for three choices of the bound state wave function: square well, Woods–Saxon, and truncated harmonic oscillator. The formulae can essentially be factored into two parts, one which oscillates rapidly with momentum transfer q(and is not physically important) and the other which varies smoothly with q and describes the 'envelope' of the calculated angular distribution. For the square well and truncated harmonic oscillator form factors, this envelope function varies as q−8 and q−10 respectively, but in the Woods–Saxon case it is given predominantly by an exponential q-dependence. To illustrate our main points, calculations are presented for the 208Pb(p,d) reaction, primarily at 200 MeV, as well as normalized fits to presently available data at 185 MeV on light and intermediate mass nuclei and at 700 MeV on 12C. The envelope dependence of the square well and Woods–Saxon form factors gives a reasonably good account of these data.

A 43.7-MeV proton beam has been used to induce ($p, t$) and ($p$,$^{3}\mathrm{He}$) reactions on a $^{15}\mathrm{N}$ target. Transitions to mirror final states of $^{13}\mathrm{N}$ and $^{13}\mathrm{C}$ have been investigated over 15 MeV of excitation and several new spin and parity assignments have been made. The distorted-wave Born-approximation (DWBA) predictions of angular distributions for these $^{15}\mathrm{N}(p, t)^{13}\mathrm{N}$ and $^{15}\mathrm{N}(p, ^{3}\mathrm{He})^{13}\mathrm{C}$ reactions, using intermediate-coupling wave functions to obtain the two-nucleon structure factors, were generally found to reproduce experiment well; in addition, calculated cross sections for the $^{15}\mathrm{N}(p, t)^{13}\mathrm{N}$ reaction were in good agreement with the experimental values.

Author(s): Cosper, S.W.; McGrath, Robert L.; Cerny, Joseph; Maples, Creve C.; Goth, George W.; Fleming, Donald G.

We have studied precession of polarized positive muons in quartz and silicon in transverse magnetic fields, via the asymmetric decay. We observed free muon precession and two-frequency muonium precession, as well as two anomalous precession frequencies apparent only in silicon.

The spur model ofmuonium formation in water is further elucidated. The comments by percival5 on the authors experiments reported earlier, are answered. (AIP)

When spin-polarized positive muons are stopped in fine SiO 2 powder under vacuum, muonium precession is observed indicating 45% muonium formation. Depolarization by oxygen indicates that muonium, like positronium, emerges from the powder grains into the voids.

We report the first direct observation of radicals formed by formal addition of muonium to liquid organic compounds. They are characterized by muon precession frequencies in transverse magnetic fields of 0.3–5.0 kG. Comparison of the isotropic hyperfine coupling constants with those of hydrogen analogue reveals large isotope effects.