Differential cross sections for muonic atom scattering from hydrogenic molecules

The differential cross sections for low-energy muonic hydrogen atom scattering from hydrogenic molecules are directly expressed by the corresponding amplitudes for muonic atom scattering from hydrogen-isotope nuclei. The energy and angular dependence of these three-body amplitudes is thus taken naturally into account in scattering from molecules, without involving any pseudopotentials. Effects of the internal motion of nuclei inside the target molecules are included for every initial rotational-vibrational state. These effects are very significant as the considered three-body amplitudes often vary strongly within the energy interval $\lesssim{}0.1$ eV. The differential cross sections, calculated using the presented method, have been successfully used for planning and interpreting many experiments in low-energy muon physics. Studies of $\mu^{-}$ nuclear capture in $p\mu$ and the measurement of the Lamb shift in $p\mu$ atoms created in H$_2$ gaseous targets are recent examples.Comment: 21 pages, 13 figures, submitted to Phys. Rev.

The LIL for UU-statistics in Hilbert spaces

We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for $U$-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued $U$-statistics of arbitrary order, which are of independent interest

Transition Analysis for the HIFiRE-1 Flight Experiment

The HIFiRE-1 flight experiment provided a valuable database pertaining to boundary layer transition over a 7-degree half-angle, circular cone model from supersonic to hypersonic Mach numbers, and a range of Reynolds numbers and angles of incidence. This paper reports the initial findings from the ongoing computational analysis pertaining to the measured in-flight transition behavior. Transition during the ascent phase at nearly zero degree angle of attack is dominated by second mode instabilities except in the vicinity of the cone meridian where a roughness element was placed midway along the length of the cone. The first mode instabilities were found to be weak at all trajectory points analyzed from the ascent phase. For times less than approximately 18.5 seconds into the flight, the peak amplification ratio for second mode disturbances is sufficiently small because of the lower Mach numbers at earlier times, so that the transition behavior inferred from the measurements is attributed to an unknown physical mechanism, potentially related to step discontinuities in surface height near the locations of a change in the surface material. Based on the time histories of temperature and/or heat flux at transducer locations within the aft portion of the cone, the onset of transition correlated with a linear PSE N-factor of approximately 14

Stability Analysis for HIFiRE Experiments

The HIFiRE-1 flight experiment provided a valuable database pertaining to boundary layer transition over a 7-degree half-angle, circular cone model from supersonic to hypersonic Mach numbers, and a range of Reynolds numbers and angles of attack. This paper reports selected findings from the ongoing computational analysis of the measured in-flight transition behavior. Transition during the ascent phase at nearly zero degree angle of attack is dominated by second mode instabilities except in the vicinity of the cone meridian where a roughness element was placed midway along the length of the cone. The growth of first mode instabilities is found to be weak at all trajectory points analyzed from the ascent phase. For times less than approximately 18.5 seconds into the flight, the peak amplification ratio for second mode disturbances is sufficiently small because of the lower Mach numbers at earlier times, so that the transition behavior inferred from the measurements is attributed to an unknown physical mechanism, potentially related to step discontinuities in surface height near the locations of a change in the surface material. Based on the time histories of temperature and/or heat flux at transducer locations within the aft portion of the cone, the onset of transition correlated with a linear N-factor, based on parabolized stability equations, of approximately 13.5. Due to the large angles of attack during the re-entry phase, crossflow instability may play a significant role in transition. Computations also indicate the presence of pronounced crossflow separation over a significant portion of the trajectory segment that is relevant to transition analysis. The transition behavior during this re-entry segment of HIFiRE-1 flight shares some common features with the predicted transition front along the elliptic cone shaped HIFiRE-5 flight article, which was designed to provide hypersonic transition data for a fully 3D geometric configuration. To compare and contrast the crossflow dominated transition over the HIFiRE-1 and HIFiRE-5 configurations, this paper also analyzes boundary layer instabilities over a subscale model of the HIFiRE-5 flight configuration that was tested in the Mach 6 quiet tunnel facility at Purdue University

Muon Catalyzed Fusion in 3 K Solid Deuterium

Muon catalyzed fusion in deuterium has traditionally been studied in gaseous and liquid targets. The TRIUMF solid-hydrogen-layer target system has been used to study the fusion reaction rates in the solid phase of D_2 at a target temperature of 3 K. Products of two distinct branches of the reaction were observed; neutrons by a liquid organic scintillator, and protons by a silicon detector located inside the target system. The effective molecular formation rate from the upper hyperfine state of $\mu d$ and the hyperfine transition rate have been measured: $\tilde{\lambda}_(3/2)=2.71(7)_{stat.}(32)_{syst.} \mu/s$, and $\tilde{\lambda}_{(3/2)(1/2)} =34.2(8)_{stat.}(1)_{syst.} \mu /s$. The molecular formation rate is consistent with other recent measurements, but not with the theory for isolated molecules. The discrepancy may be due to incomplete thermalization, an effect which was investigated by Monte Carlo calculations. Information on branching ratio parameters for the s and p wave d+d nuclear interaction has been extracted.Comment: 19 pages, 11 figures, submitted to PRA Feb 20, 199

Measurement of the Resonant dμtd\mu t Molecular Formation Rate in Solid HD

Measurements of muon-catalyzed dt fusion ($d\mu t \to ^4He+n+\mu^-$) in solid HD have been performed. The theory describing the energy dependent resonant molecular formation rate for the reaction $\mu t$ + HD $\to [(d\mu t)pee]^*$ is compared to experimental results in a pure solid HD target. Constraints on the rates are inferred through the use of a Monte Carlo model developed specifically for the experiment. From the time-of- flight analysis of fusion events in 16 and 37 $\mu g\cdot cm^{-2}$ targets, an average formation rate consistent with 0.897$\pm$(0.046)$_{stat}\pm$ (0.166)$_{syst}$ times the theoretical prediction was obtained.Comment: 4 pages, 5 figure