Muon Transfer Research Articles

Numerical study of the “two components” model and background effects in muonic hydrogen experiments

In this study, we explore the X-ray time spectra of muonic oxygen in various H 2 + O 2 gaseous mixtures by means of numerical simulations based on a sophisticated kineticrate equations model. Our primary focus is on the “two components” hypothesis, which was put forward to account for the experimentally observed two successive exponential behaviors in the radiation time-distribution. To ensure an accurate representation of the physical processes in the experiments, we incorporate precise transition rate coefficients for the elastic and inelastic scattering between the muonic hydrogen atoms and other gas constituents, in our simulation code. Specifically, a crucial aspect in our approach is the utilization of the energy dependence of the muon transfer rate to oxygen, recently extracted from experimental data by the FAMU collaboration. The accurate knowledge of such muonic oxygen X-ray time spectra is vital for cutting-edge experiments like FAMU, where the hyperfine splitting in muonic hydrogen atoms is to be determined with high accuracy, as this time spectra serves as a significant part of the background for the desired signal.

Experimental determination of the energy dependence of the rate of the muon transfer reaction from muonic hydrogen to oxygen for collision energies up to 0.1 eV

We report the experimental determination of the collision-energy dependence of the muon transfer rate from the ground state of muonic hydrogen to oxygen at near-thermal energies. A sharp increase by nearly an order of magnitude in the energy range 0--70 meV was found that is not observed in other gases. The results set a reliable reference for quantum-mechanical calculations of low-energy processes with exotic atoms and provide firm ground for the measurement of the hyperfine splitting in muonic hydrogen and the determination of the Zemach radius of the proton by the FAMU collaboration.

On the Energy Dependence of the Rate of Muon Transfer from Proton to Oxygen

The results of calculations of the muon transfer rate from the 1S state of muonic hydrogen to the nucleus of a free oxygen atom are presented in the interval of collision energies from 10^(-4) to 10 eV. The calculations were performed within a version of the perturbed stationary states method proposed earlier. The electron screening in the entrance channel of the transfer reaction was taken into account. A p-wave resonance in the transfer rate is predicted at collision energies of about 0.1 eV. This result is of interest in the context of the planned laser experiment on precise measurements of the hyperfine splitting energy of the 1S state of muonic hydrogen.

The muX project

The project is conducting a series of muonic X-ray measurements in medium- and high-Z nuclei at PSI, utilizing a high-purity germanium detector array, in-beam muon detectors, and a modern digital data-acquisition system. A novel hydrogen target for muon transfer was developed, enabling measurements with as little as a few micrograms of target material. First measurements with radioactive Cm and Ra targets were conducted, aimed at determining their nuclear charge radii. These serve as important input for upcoming atomic parity violation experiments. The apparatus is also used to perform a feasibility study of an atomic parity violation experiment with the 2s-1s2s−1s muonic X-ray transition. In addition, the setup has been made available for a wider range of nuclear, particle, and solid-state physics measurements.

Measurement of the muon transfer rate from muonic hydrogen to oxygen in the range 70-336 K

The first measurement of the temperature dependence of the muon transfer rate from muonic hydrogen to oxygen was performed by the FAMU collaboration in 2016. The results provide evidence that the transfer rate rises with the temperature in the range 104-300 K. This paper presents the results of the experiment done in 2018 to extend the measurements towards lower (70 K) and higher (336 K) temperatures. The 2018 results confirm the temperature dependence of ΛpO observed in 2016 and sets firm ground for comparison with the theoretical predictions.

Chemical effect on muonic atom formation through muon transfer reaction in benzene and cyclohexane samples

Abstract To investigate the chemical effect on the muon capture process through a muon transfer reaction from a muonic hydrogen atom, the formation rate of muonic carbon atoms is measured for benzene and cyclohexane molecules in liquid samples. The muon transfer rate to carbon atoms of the benzene molecule is higher than that to the carbon atoms of the cyclohexane molecule. Such a deviation has never been observed among those molecules for gas samples. This may be because the transfers occur from the excited states of muonic hydrogen atoms in the liquid system, whereas in the gas system, all the transfers occur from the 1s (ground) state of muon hydrogen atoms. The muonic hydrogen atoms in the excited states have a larger radius than those in the 1s state and are therefore considered to be affected by the steric hindrance of the molecular structure. This indicates that the excited states of muonic hydrogen atoms contribute significantly to the chemical effects on the muon transfer reaction.

Крос-верифікація Монте-Карло кодів Geant4 та MCNP6 для мюонної томографії

Muon tomography is a promising detection technology that uses natural radiation, the muons of cosmic rays. In the last decade, a significant number of scientific papers have appeared that investigate the possibility of using muon tomography in various fields of science and technology. Especially remarkable is the considerable potential of this technology for detecting the illegal transport of radioactive materials and for no-invasive testing of the integrity of spent nuclear fuel in dry storage facilities for such fuel. For the implementation of muon tomography technology, the process of preliminary modeling of the experimental detector facility is important, which also requires verification of the obtained calculation results. For this purpose, the well-known Monte Carlo codes MCNP and Geant4 are mainly used. This results of the first cross-verification studies of MCNP6 and Geant4 codes are demonstrated in the paper. The study was performed on simple models for different materials and for different energies of the muons bombarding the research object. The recommended QGSP_BERT physics library was used in the Geant4 code. In the MCNP6 code, the recommended settings for cosmic particle simulations were used. The calculations showed that for low-energy muons, both codes give results that agree well with each other. This can be explained by the fact that similar libraries of evaluated nuclear data are used in the low-energy range. Regarding the muons of intermediate energies, there is a significant difference between the two codes, which may indicate differences in physical models. The modeling of high-energy muon transfer has better agreement between MCNP6 and Geant4 codes than for intermediate-energy muons, but significant differences are still observed for heavy nuclei.

First measurement of the temperature dependence of muon transfer rate from muonic hydrogen atoms to oxygen

We report the first measurement of the temperature dependence of muon transfer rate from muonic hydrogen atoms to oxygen between 100 and 300 K. Data were obtained from the X-ray spectra of delayed events in a gaseous target, made of a H2/O2 mixture, exposed to a muon beam. This work sets constraints on theoretical models of muon transfer and is of fundamental importance for the measurement of the hyperfine splitting of muonic hydrogen ground state as proposed by the FAMU collaboration.

The FAMU experiment at RIKEN-RAL to study the muon transfer rate from hydrogen to other gases

The aim of the FAMU (Fisica degli Atomi Muonici) experiment is to realize the first measurement of the hyperfine splitting (hfs) in the 1S state of muonic hydrogen Δ Ehfs1S, by using the RIKEN-RAL intense pulsed muon beam and a high-energy mid-infrared tunable laser. This requires a detailed study of the muon transfer mechanism at different temperatures and hence at different epithermal states of the muonic system. The experimental setup involves a cryogenic pressurized gas target and a detection system based on silicon photomultipliers-fiber beam hodoscopes and high purity Germanium detectors and Cerium doped Lanthanium Bromide crystals, for X-rays detection at energies around 100 keV . Simulation, construction and detector performances of the FAMU apparatus at RAL are reported in this paper.

FAMU: study of the energy dependent transfer rate Λμp → μO

The main goal of the FAMU experiment is the measurement of the hyperfine splitting (hfs) in the 1S state of muonic hydrogen ΔEhfs (μ-p)1S. The physical process behind this experiment is the following: μp are formed in a mixture of hydrogen and a higher-Z gas. When absorbing a photon at resonance-energy ΔEhfs ≈ 0.182 eV, in subsequent collisions with the surrounding H2 molecules, the μp is quickly de-excited and accelerated by ∼ 2/3 of the excitation energy. The observable is the time distribution of the K-lines X-rays emitted from the μZ formed by muon transfer (μp) + Z → (μZ)* + p, a reaction whose rate depends on the μp kinetic energy. The maximal response, to the tuned laser wavelength, of the time distribution of X-ray from K-lines of the (μZ)* cascade indicate the resonance. During the preparatory phase of the FAMU experiment, several measurements have been performed both to validate the methodology and to prepare the best configuration of target and detectors for the spectroscopic measurement. We present here the crucial study of the energy dependence of the transfer rate from muonic hydrogen to oxygen (Λμp → μ0), precisely measured for the first time.

First FAMU observation of muon transfer from μp atoms to higher-Z elements

The FAMU experiment aims to accurately measure the hyperfine splitting of the ground state of the muonic hydrogen atom. A measurement of the transfer rate of muons from hydrogen to heavier gases is necessary for this purpose. In June 2014, within a preliminary experiment, a pressurized gas-target was exposed to the pulsed low-energy muon beam at the RIKEN RAL muon facility (Rutherford Appleton Laboratory, U.K.). The main goal of the test was the characterization of both the noise induced by the pulsed beam and the X-ray detectors. The apparatus, to some extent rudimental, has served admirably to this task. Technical results have been published that prove the validity of the choices made and pave the way for the next steps. This paper presents the results of physical relevance of measurements of the muon transfer rate to carbon dioxide, oxygen, and argon from non-thermalized excited μp atoms. The analysis methodology and the approach to the systematics errors are useful for the subsequent study of the transfer rate as function of the kinetic energy of the μp currently under way.

Muon Transfer Rates from Muonic Hydrogen Atoms to Gaseous Benzene and Cyclohexane

Muon Transfer Rates from Muonic Hydrogen Atoms to Gaseous Benzene and Cyclohexane

On the reaction of muon transfer from protium to neon at low collision energies

The direct muon transfer from protium to neon at low collision energies is considered. The question is discussed how the energy dependence of the transfer rate can be extracted from available experimental data. A model is suggested which is based on two assumptions. First, the muon transfer occurs within an interaction sphere out of which the entrance and transfer channels are not coupled. Secondly, for the s- and p-waves at low collision energies, the complex logarithmic derivatives of the radial wave functions of the entrance channel on the interaction sphere are energy-independent. With only the s-wave taken into account, two values of the logarithmic derivative were found, which agree with the transfer rates measured at the temperatures of 20 and 300 K. Within this temperature interval, the rates evaluated for these two values differ only slightly. Noticeable differences arise at temperatures of a few kelvins. The choice of the preferred value of the logarithmic derivative was made by the comparison of the energy dependence of the S-matrix with results of previous calculations. Thereby, the proposed procedure may be a way to correct calculations at low collision energies.

Toward the measurement of the hyperfine splitting in the ground state of muonic hydrogen

The recent Lamb shift experiment at PSI and the controversy about proton size revived the interest in measuring the hyperfine splitting in muonic hydrogen and extracting the proton Zemach radius. The efficiency of the experimental method depends on the energy dependence of the muon transfer rate to higher-Z gases in the near epithermal energy range. As long as the available experimental data only give the average transfer rate in the whole epithermal range, and the detailed theoretical calculations have not yet been verified, an experiment has been started for the measurement of the transfer rate in thermalized gas target at different temperatures and extracting from the data an estimate of the transfer rate for arbitrary energies. We outline the underlying mathematical method and estimate its accuracy.

Theoretical and computational study of the energy dependence of the muon transfer rate from hydrogen to higher-Z gases

The recent PSI Lamb shift experiment and the controversy about proton size revived the interest in measuring the hyperfine splitting in muonic hydrogen as an alternative possibility for comparing ordinary and muonic hydrogen spectroscopy data on proton electromagnetic structure. This measurement critically depends on the energy dependence of the muon transfer rate to heavier gases in the epithermal range. The available data provide only qualitative information, and the theoretical predictions have not been verified. We propose a new method by measurements of the transfer rate in thermalized target at different temperatures, estimate its accuracy and investigate the optimal experimental conditions.

Studies on the Kinetics of Muon Catalyzed Fusion in the HT Mixture with Very Low Tritium Concentration

A method for determination of optimum muon cycling coefficient and energy gain in the HT mixture with very low tritium concentration is proposed. The kinetics of the mu-atomic and mu-molecular processes preceding the pt reaction in the ptµ molecule is described. The time variations of γ quanta and conversion muons and the other particles formation in nuclear fusion reactions in ptµ molecules are studied. Our calculations show that, the optimum value of muon cycling coefficient at Ct=0.01 is equal to 106. In this paper our obtained results from theoretical calculations and experimental results are compared with together and we can receive that the obtained results are in good agreement with measured values. the rate of muon transfer from pµ atom to triton, the rate of transition between hyperfine levels of tµ atoms, the rate of formation of the ptµ molecule, the rate of nuclear synthesis in it and muon sticking) to interpret correctly the results of experiments in the triple mixture of hydrogen isotopes H-D-T and to describe the kinetics of all processes occurring in the mixture. From the theoretical point of view, the experiments investigating µCF processes in hydrogen -tritium mixture will allow one to test an algorithm describing a three-body system of particles interacting according to coulomb rule. It is necessary to emphasize the importance of the µCF study in HT mixture in order to obtain the information about characteristics of pt-reaction at ultra law energy range (≈KeV). The investigation of the reaction between light nuclei at ultra law energies (≈KeV) is very important for verification of fundamental symmetries in string interactions (3)-(5) the contribution of muon exchange currents and to solve some astrophysical problems. At present, there are few experiments that investigate characteristics of µCF in a H-T mixture. Only one was performed with a HT mixture and the references with triple mixture H-D-T. In this paper the authors survey the major areas of research: Section I describes the details of the kinetics of the µCF in HT mixture, while Sec. II describes the nonlinear point dynamics equations in HT mixture. Sec.III discusses on the numerical solution of these equations versus time in muon life time range. Sec.IV describes the optimum cycling coefficient and energy gain. The final section presents an overview of what is known, and outline some directions for future research.

Calculation of the rate of muon transfer from a proton to neon on the basis of the two-center coulomb basis

The results of an improved calculation of the rate of muon transfer from the 1s state of the muonic-hydrogen atom to neon at collision energies ranging between 10−4 and 15 eV are presented. The calculation in question is performed within the method of perturbed stationary states, where the wave function for the three-particle system formed by a muon, a proton, and a neon nucleus is constructed in the form of an expansion in eigenfunctions of the two-center Coulomb problem formulated in terms of Jacobi coordinates for the entrance reaction channel. This approach makes it possible to obtain an asymptotically correct description of the entrance channel at a low collision energy: one obtains a correct dissociation limit, spurious long-range potentials are absent, and a polarization attraction between a muonic-hydrogen atom and a neon atom appears in a natural way. Moreover, one can readily take into account electron screening, which is of importance at low collision energies. All flaws in the description come into play only in the muon-transfer channel, where one does not expect that their effect is significant because of high energies of divergence of reaction products. The calculation performed within this scheme previously permitted explaining special features observed experimentally in the behavior of the muon-transfer rate as a function of temperature of the hydrogen-neon mixture being considered. In the present study, a more refined algorithm for constructing basis functions in the two-center Coulomb problem was used, whereby agreement between the calculated values of the muon-transfer rate and experimental data was improved.

Muonic Anti-hydrogen $${(\bar{\rm H}_{\mu}})$$ Formation in Low-energy Three-body Reactions

A few-body type computation is performed for a three-charge-particle collision with participation of a slow antiproton \({\bar{\rm{p}}}\) and a muonic muonium atom (true muonium), i.e. a bound state of two muons \({(\mu^{+}\mu^{-})}\) in its ground state. The total cross section of the following reaction \({\bar{\rm p}+(\mu^{+}\mu^{-}) \rightarrow \bar{\rm{H}}_{\mu} + \mu^{-}}\), where muonic anti-hydrogen \({\bar{\rm{H}}_{\mu}=(\bar{\rm p}\mu^{+})}\) is a bound state of an antiproton and positive muon, is computed in the framework of a set of coupled two-component Faddeev-Hahn-type equation. A better known negative muon transfer low energy three-body reaction: \({{\rm t}^{+} + ({\rm d}^{+}\mu^{-})\rightarrow ({\rm t}^{+}\mu^{-}) + {\rm d}^{+}}\) is also computed as a test system. Here, t+ is triton and d+ is deuterium.

Investigation of the hydrogen multilayered target H/T−D2 and muonic X-ray yields in ion implantation

This paper extends applications of the multilayered solid target H/T−D2, which is kept at 3 K. The time evolutions of muonic tritium atoms (μt) are obtained, by taking into account μt production rate at different places of deuterium material. The apparatus H/T−D2 can be used for checking nuclear properties of implanted ions, which take part at muon transfer. Electromagnetic X-rays are generated by muon atomic transitions. The muonic X-ray transition energies are strongly affected by the size of nuclei. Here, a solid hydrogen–tritium (H/T) with a ≈1 mm thick is used for μt production. For ion implantation, the required amount of deuterium material is determined to be about 3.2 μm. Moreover, the muonic X-ray yields are estimated and compared with those of the arrangement H/T−D2. While the present target requires argon ion beam intensity nearly a factor of 2 times smaller; gives a relatively higher X-ray yield (15% enhancement per hour) at the energy 644 keV with the detection efficiency of ≈1%.

Resonant enhancement of the formation of hydrogen–helium muonic molecules

Formation of muonic molecules ( He 4 μ p ) J = 1 + + and ( He 3 μ d ) J = 0 , 1 , 2 + + , where J is rotational quantum number, in electron conversion process is investigated at collision energies between 0.004 eV and 50 eV. Corresponding reaction rates are calculated in adiabatic approximation for the three-body Coulomb problem. Significant enhancement of the rates for ( He 4 μ p ) 1 + + and ( He 3 μ d ) 2 + + is found near 7 eV and 30 eV, respectively. It is shown that the enhancement is due to resonances present in elastic ( p μ ) 1 s + He + + 4 and ( d μ ) 1 s + He + + 3 scattering at these energies. Acceleration of dμ atoms up to the resonant energy could be realized in triple H–D– 3He mixture due to the muon transfer from protium to deuterium. Experimental investigation of d – He + + 3 nuclear synthesis from ( He 3 μ d ) 0 + + molecular state directly formed in the mixture is suggested.