Dynamics of muonic atom cascade in hydrogen-helium mixtures

The deexcitation of excited muonic protium and deuterium in the mixture of hydrogen and helium isotopes is considered. Methods of experimental determination of the probability of direct atomic muon capture by hydrogen and muon transfer rates from excited muonic hydrogen to helium are proposed. Theoretical results for the population of the muonic atoms in the ground state, , are compared with the existing experimental data. Results obtained for mixtures are of interest for investigation of nuclear fusion in muonic molecules. Received: 6 August 1998 / Revised: 1st October 1998 / Accepted: 2 October 1998     

Statistical study of the muon catalyzed d-t fusion cycle

In this paper we discuss the statistics of the main branch species of the muon catalyzed d-t fusion. From a master equation we derive and numerically solve kinetic equations for the average density and the covariances of a system composed of muons, muonic deuterium and muonic tritium atoms, muon molecular d-t ions, muonic helium, helium and neutrons. The system consists of an initial fixed amount of muons in a 50–50% D₂ + T₂ mixture without any external muon source. It is known that the probability distribution function of the population species with the exception of the neutron and helium follow a multinomial distribution function.     

Challenge towards muonic atom formation with unstable nuclei

X-ray spectroscopy of muonic atoms is an important tool to obtain information on the nuclear charge distribution of nuclei. It has been successfully used for many years to study stable isotopes in condensed or gaseous states. A new method has been proposed to extend muonic atom X-ray spectroscopy to the use of radioactive isotope beams to form muonic atoms with unstable nuclei. This new method allows studies of the nuclear properties and nuclear sizes of unstable atoms by means of the muonic X-ray method at facilities where both negative muon and radioactive nuclear beams would be available. Progress of a feasibility study at RIKEN-RAL muon facility is also reported. Received: 1 May 2001 / Accepted: 4 December 2001     

Emission of muonic tritium into vacuum: An atomic beam for muon experiments

The emission of muonic tritium atoms from a thin film of hydrogen isotopes into vacuum was observed. The time and position of the muon decays were measured by tracking the decay electron trajectory. The observations are useful both for testing the theoretical cross sections for muonic atomic interactions, and producing an atomic beam of slow μ^-t with a controllable energy. This revised version was published online in August 2006 with corrections to the Cover Date.     

Ephemeral and/or coloured nuonic hydrogen atoms

The unexpected and, in conventional terms, yet unexplained experimental results, obtained in systematic measurements of muon transfer from muonic hydrogen to sulphur and oxygen of sulphur dioxide, seem to violate the principle of reproducibility of muon transfer data. With the hypothesis of ephemeral muonic hydrogen atoms, the number of different hydrogen atoms can be reduced from four to two. This hypothesis does, however, not help to interpret the transfer data to helium, neon and argon, where the muonic hydrogen atoms seem to wear colours.     

Measurement of the fusion rate in μd3He

Many atomic and molecular processes may occur after a muon has been stopped in a mixture of hydrogen and helium isotopes. In particular, the muonic molecule μd³He can be formed. This molecule either decays or undergoes muon catalyzed fusion. Theory predicts a fusion rate much lower than the decay rate; moreover, the various theoretical predictions differ from each other by several orders of magnitude. With the experiment presented here we intend to measure the effective fusion rate via the detection of the 14.7 MeV fusion proton. A new target and gas mixing system, designed at JINR, were used in a ten-day test run at PSI. The fusion protons and products from other transfer and background reactions were measured with several different detectors (plastic scintillators, BGO, Germanium, neutron, and Silicon detectors). The formation rate of the μd ³He molecule and an upper limit for the effective fusion rate have been measured and are presented here. This revised version was published online in August 2006 with corrections to the Cover Date.     

Correlation between muonic levels and nuclear structure in muonic atoms

A method that deals with the nucleons and the muon unitedly is employed to investigate the muonic lead, with which the correlation between the muon and nucleus can be studied distinctly. A “kink” appears in the muonic isotope shift at a neutron magic number where the nuclear shell structure plays a key role. This behavior may have very important implications for the experimentally probing the shell structure of the nuclei far away from the β-stable line. We investigate the variations of the nuclear structure due to the interaction with the muon in the muonic atom and find that the nuclear structure remains basically unaltered. Therefore, the muon is a clean and reliable probe for studying the nuclear structure. In addition, a correction that the muon-induced slight change in the proton density distribution in turn shifts the muonic levels is investigated. This correction to muonic level is as important as the Lamb shift and high order vacuum polarization correction, but is larger than anomalous magnetic moment and electron shielding correction.     

μ −SR-Spectroscopy on light neutral muonic atoms

In the past few years ^–SR-spectroscopy has been successfully applied to the simple muonic atoms, namely muonic helium: He ^–e^–. Here the theoretical and experimental progress in understanding this atomic system consisting of a nucleus, a muon and an electron is reviewed. The various effects contributing to the ground state hyperfine structure are explained. The experiments are described and are compared with the theoretical calculations.     

Temperature dependence of the formation rates of hydrogen-helium mesic molecules in collisions of slow hydrogen atoms with helium

The rates of molecular muon transfer from the ground-state muonic hydrogen to helium isotopes are calculated in an improved adiabatic approximation. The results obtained by us at various temperatures are compared with the available experimental data.     

The study of prompt and delayed muon induced fission

Mass yield and total kinetic energy release (TKE) distributions of fragments from prompt and delayed muon induced fission, separately, have been measured for the isotopes²³⁵U,²³⁸U,²³⁷Np and²⁴²Pu. The distributions from prompt muon induced fission are compared with the corresponding distributions from hadronic reactions and from spontaneous fission (s.f.). The distributions from the delayed muonic fission processes are compared to the distributions for neutron and proton-induced fission. No mass distributions measured in the prompt muonic fission process show any signature, which can be attributed to the presence of the muon. Differences observed between the TKE distributions of prompt muon induced and hadron induced fission can be explained by the screening effect of the negative charge of the muon bound in the orbit of one of the fission fragments. The observed yield of symmetric muon induced fission was found to be defined merely by the value of the excitation energy.     

Charge transfer from the ground state of muonic hydrogen to at room temperature

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 . Received: 22 January 1998 / Revised: 4 March 1998 / Accepted: 31 March 1998     

Muon Motion Induced by a Superintense Laser in Muon‐Catalyzed Fusion

Considering the mixture after muon‐catalyzed fusion (μ CF) reaction as overdense plasma, we study muon motion in the plasma produced by a superintense linearly polarized femtosecond laser pulse. Muon drift along the propagation of laser radiation remains after the end of the laser pulse. At the peak laser intensity of 10²¹W/cm², muon goes from the skin layer into field‐free matter at short time which is much less than the pulse duration, before the laser pulse reaches its maximum. Besides, the influence of the laser on other particles in the plasma is less. Hence, this work can avoid muon sticking to alpha (α) effectively and reduce muon‐loss probability in μ CF. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

X-ray studies on muon transfer reactions from hydrogen to helium

We have experimentally studied the muon transfer reactions from hydrogen to helium in liquid hydrogen with helium impurity concentration around 100–1000 ppm. The X-ray from the decay of (d⁴He) molecule was clearly observed in the D₂-⁴He system, whereas the corresponding X-ray was very weak in other systems such as D₂-³He and H₂-⁴He. This is well explained by the particle decay mode of the muonic molecule.     

Fission of muonic 232Th and 239Pu

The neutron emission is studied following the formation of muonic atoms of ²³²Th and ²³⁹Pu. Energy and time distributions are measured. Various processes which contribute to the measured spectra are considered. A collective resonance model of the muon capture is used to calculate the nuclear excitation function. The probability of the radiationless nuclear excitations and the influence of the presence of the bound atomic muon on the fission barrier are discussed. The existing data for the $\text{Γ}{}_{\mathrm{n}}\text{Γ}{}_{\mathrm{f}}$, are analysed. As a result of the analysis the rates of the prompt and delayed fission events (due to the radiationless mu-atomic transitions and the nuclear muon capture, respectively) are deduced from the experimental data to be 0.006/muon and 0.045/muon for ²³²Th and 0.10/muon and 0.49/muon for ²³⁹Pu, respectively. The increase of the fission barrier for muonic atoms is confirmed. The experimental neutron rates can be consistently explained only if it is assumed that in both nucleides the K_α radiationless transitions do not induce fission. The increase of the fission barrier for ²³⁹Pu is hence deduced to be not less than 1.2 MeV. The fate of the atomic muon after the nuclear fission is briefly discussed. Its influence on the interpretation of the present results is found to be small.     

Proposal for X-ray spectroscopy of muonic atoms formed from implanted ions in solid hydrogen films

A new method is proposed to extend muonic atom X-ray spectroscopy to the study of nuclear beams, including radioactive beams, by stopping both muon and nuclear beams in a solid hydrogen film. The muon transfer reaction to higher Z nuclei is used then to form muonic atoms. This method would allow studies of the nuclear charge distribution of unstable atoms. This revised version was published online in August 2006 with corrections to the Cover Date.     

Magnetic field stimulated transitions of excited states in fast μHe+ ions

It is shown that one can stimulate, by using the present-day laboratory magnetic fields, transitions between the lm sub-levels of fast μHe⁺ ions formed in muon catalyzed fusion. This gives a possibility to drive the population of the lm sub-levels by applying a field of a few Tesla, which affects the reactivation rate and is especially important to the Kα X-ray production. Strong fields also cause the self-ionization from highly excited states of the muonic helium. This revised version was published online in August 2006 with corrections to the Cover Date.     

Resonant scattering of an electron by a muon in the field of light wave

In the frame of the Born approximation we theoretically investigate resonant scattering of an electron by a muon in the field of elliptically polarized electromagnetic wave in the general relativistic case. It is studied kinematics of a scattering of an electron in resonant region. It is derived the expressions for the amplitude and the cross-section of the resonant scattering of an electron by a muon when the invariant intensity parameter of the laser field is small (η_e ≪1). It is demonstrated that the resonant cross-section of a scattering may be several orders of magnitude higher than the cross-section of a scattering in the absence of the external field.     

Nuclear polarization shifts in light muonic atoms

A consistent nonrelativistic expression for the energy shift in muonic atoms due to second-order processes is derived under the assumption that the muon is weakly bound. The transverse contribution is shown to be finite only if the two-photon (“seagull”) amplitude is taken into account as required by gauge invariance. Numerical results are presented for muonic ¹²C using a recently developed model for the nuclear response function. The total transverse contributions to the energy shift are found to be small although dependent to some extent on the detailed high-momentum behaviour of the seagull term.     

Development Towards Muonic Atom Formation with Unstable Nuclei

We report on the latest development of a new method for extending muonic atom X-ray spectroscopy to the use of radioactive isotope beams to form muonic atoms with unstable nuclei. This would allow studies of the nuclear properties and nuclear sizes of unstable atoms by means of the muonic X-ray method at facilities where both negative muon and radioactive nuclear beams would be available. Progress of a feasibility study at RIKEN-RAL muon facility is also reported. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mössbauer study of Fe3+/Fe2+ ratio in amphiboles to search correlation with hydrogen isotope fractionation

New intense muon beams with flux several orders of magnitude higher than at present muon facilities would allow many novel experimental studies that were until now statistically not feasible. The investigation of the nuclear properties of short-lived nuclei using muonic atom spectroscopy would become possible. A feasibility study at RIKEN-RAL muon facility using the cold hydrogen film method to produce radioactive muonic atoms is in progress. A new surface ionization type ion source was recently installed to expand the variety of available ions. Encouraging experimental results were obtained with stable alkaline-earth and rare-earth isotope ions implanted in solid deuterium films. The latest results are reported in this paper.