Measurement of helium-3 and deuterium stopping power ratio for negative muons

The measurement method and results measuring of the stopping power ratio of helium-3 and deuterium atoms for muons slowed down in the D/³He mixture are presented. Measurements were performed at four values of pure ³He gas target densities, ϕ_He = 0.0337, 0.0355, 0.0359, 0.0363 (normalized to the liquid hydrogen density) and at a density 0.0585 of the D/³He mixture. The experiment was carried out at PSI muon beam μE4 with the momentum Pμ= 34.0 MeV/c. The measured value of the mean stopping ratio S$_{3^He/D}$ is 1.66±0.04.     

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     

Diffusion radius of muonic hydrogen atoms in H-D gas

The diffusion radius of the 1S muonic hydrogen atoms in gaseous H₂ targets with various deuterium admixtures has been determined for temperatures T=30 and 300 K. The Monte Carlo calculations have been performed using the partial differential cross sections for pμ and dμ atom scattering from the molecules H₂, HD and D₂. These cross sections include hyperfine transitions in the muonic atoms, the muon exchange between the nuclei p and d, and rotational-vibrational transitions in the target molecules. The Monte Carlo results have been used for preparing the time-projection chamber for the high-precision measurement of the nuclear μ^- capture in the ground-state pμ atom, which is now underway at the Paul Scherrer Institute.     

Application of hyperspherical close-coupling method to antiproton collisions with muonic hydrogen

The cross sections for p^- + (Hμ^-)_1s (H = p, d, t) are calculated in the hyperspherical close-coupling method for collision energies below the (Hp^-)_n=4 threshold. The results show good convergence with respect to basis size. The formation cross section of (Hp^-)_n=2 is dominant and two orders of magnitude larger than that of (Hp^-)_n=1 below the (Hp^-)_n=3 threshold, while the (Hp^-)_n=3 formation cross-section exceeds that for (Hp^-)_n=2 formation above the (Hp^-)_n=3 threshold. Resonance parameters are also calculated below thresholds of (Hp^-)_n=2-4.     

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     

Semiclassical approach to the three-body muon-transfer collisions

Muon-transfer rates in collisions of hydrogen-like atoms or with light nuclei t, ³He, ⁴He, ⁶Li or ⁷Li, are calculated in a semiclassical approximation to the Faddeev-Hahn equations. The two nuclei involved are treated classically, while the motion of the muon in their Coulomb field is considered from the quantum mechanical point of view. The experimentally observed strong dependence on the charge of the nuclei is reproduced. Received: 1st November 1997 / Revised: 26 March 1998 / Accepted: 18 August 1998     

Three-body muon-transfer collisions from hydrogen isotope to He<Superscript>2+</Superscript> and Li<Superscript>3+</Superscript> ions

The muon transfer rates from hydrogen isotopes (p,d) to ^3,4He²⁺ and ^6,7Li³⁺ ions are calculated in the hyperspherical close coupling method. Well converged results are obtained. The present rates are comparable to those of existing calculations for He²⁺, but they are much larger for Li³⁺. The resonance parameters are also calculated for resonances near the (Hμ)_1s threshold.     

Nuclear fusion in charge-asymmetric muonic molecules

Nuclear fusion reactions in hydrogen-lithium muonic molecules, (where h=p,d,t) are considered and fusion rates from rotational states J=0 of the molecules are presented. Results obtained depend on the isotopic composition of the molecules and range between and . The upper limit for fusion rates from rotational states J=0 of hydrogen-helium muonic molecules, and , equal , is also found. Received: 4 December 1997 / Revised: 30 April 1998 / Accepted: 7 May 1998     

Scattering of muonic hydrogen atoms from a gold surface

Summary The scattering of μp atoms in the 1S state from gold atoms was calculated using semi-classical methods. The results were used to write a Monte Carlo program simulating backscattering from a gold surface. For isotropically incident μp of kinetic energy (0.035–10) eV it was found that approximately 5% escape from the surface. The fraction backscattered showed little dependence on the initial μp kinetic energy but increased greatly with incident angle from the normal to the surface.     

Exponential correlated basis in Schwinger variational principle for positronium formation in hydrogen

An exponential correlated basis set is tested within the framework of multi-channel Schwinger variational principle in the momentum space. It is found that inclusion of only the positron-electron correlation in the basis set is enough to obtain accurate results for all significant partial waves for ground state positronium formation in positron-hydrogen collisions at low and intermediate energies (6.856–75 eV). Results are in conformity with other accurate variational and non-variational calculations as well as observed data available in the literature.     

Neutralization of specularly reflecting ions on a clean (001) surface of SnTe

Neutral fractions of specularly reflected beams have been measured for the glancing-angle incidence of (0.2-0.5) MeV ions on a clean (001) surface of SnTe. The measured fractions have been compared with the results calculated by a classical model for charge exchanges and by a model based on the first-order perturbation theory. The experimental and calculated results have differed greatly. The disagreements are attributed to collisions with valence electrons on the surface. The electron capture cross-sections of (0.2-0.5) MeV ions for valence electrons have been derived, based on the measured neutral fraction and distribution of valence electrons for jellium background positive charges, and are found to be about ten times larger than those for the outermost electrons of Sn and Te atoms calculated by the classical model. Received: 23 October 1998     

Measurement of the Barkas effect in hydrogen

The stopping power of gaseous hydrogen for positive and negative muons at energies ranging from 3 to 100 keV has been measured by time-of-flight. A pronounced Barkas effect was observed: the energy loss in hydrogen for negative muons was found to be significantly smaller than that for positive muons. Received: 23 April 1998 / Accepted: 7 May 1998     

Corrections to the wave function and the hyperfine structure in exotic atoms

We present an analytical evaluation of radiative corrections in exotic atoms induced by the one-loop electronic vacuum polarization. We evaluate corrections to the energy levels, to the wave function (at the origin) and to the hyperfine structure. We treat all corrections analytically within a non-relativistic approximation. Agreement is found with a few available numerical results. The analytical treatment allows to determine the asymptotic forms of the corrections in the limit of a small atomic radius, which for the atomic systems considered corresponds to a large mass of the constituent particle as compared to the electron mass. The asymptotics can be verified using the effective charge approach. Received: 28 January 1998 / Accepted: 13 March 1998     

Time-evolution of cascade processes of muonic atoms in hydrogen-helium mixtures

The time-dependence of the population of muonic hydrogen states in hydrogen-helium mixtures is calculated for principal quantum number n. The number of muons transferred to helium nuclei is also determined. The dependence of the population of the ground state of muonic hydrogen on time and target density and the helium concentration is also considered. The results are in agreement with recent experimental data. The comparison of the calculated yield of K lines of X-ray in pure hydrogen and deuterium with experimental data indicates the essential role of the Coulomb deexcitation process. Possible Stark mixing is also analysed. Received 17 February 1999 and Received in final form 9 June 1999     

Positronium formation cross-sections in the ground and excited states ( levels) in an -He atom collision

The positronium formation cross-sections in the ground and excited n=2 levels have been studied in an -He atom collision in the framework of eikonal approximation. Both the differential and total formation cross-sections have been investigated in the intermediate- and high-energy regime. Present eikonal results are found to differ appreciably from the corresponding first Born values even at very high incident energies. The total cross-section results have been compared with available experiments due to different groups as well as with other existing theoretical results. Received: 20 July 1998 / Received in final form: 5 January 1999     

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     

Reciprocity in the electronic stopping of slow ions in matter

The principle of reciprocity, i.e., the invariance of the inelastic excitation in ion-atom collisions against interchange of projectile and target, has been applied to the electronic stopping cross section of low-velocity ions and tested empirically on ion-target combinations supported by a more or less adequate amount of experimental data. Reciprocity is well obeyed (within ~10%) for many systems studied, and deviations exceeding ~20% are exceptional. Systematic deviations such as gas-solid or metal-insulator differences have been looked for but not identified on the present basis. A direct consequence of reciprocity is the equivalence of Z₁ with Z₂ structure for random slowing down. This feature is reasonably well supported empirically for ion-target combinations involving carbon, nitrogen, aluminium and argon. Reciprocity may be utilized as a criterion to reject questionable experimental data. In cases where a certain stopping cross section has not been or cannot be measured, the stopping cross section for the inverted system may be available and serve as a first estimate. It is suggested to build in reciprocity as a fundamental requirement into empirical interpolation schemes directed at the stopping of low-velocity ions. Examination of the SRIM and MSTAR codes reveals cases where reciprocity is obeyed accurately, but deviations of up to a factor of two are common. In case of heavy ions such as gold, electronic stopping cross sections predicted by SRIM are asserted to be almost an order of magnitude too high.     

One and two-photon detachment cross-sections of Ps-

We present detailed calculations for one- and two-photon above-threshold detachment (ATD) cross-sections of the negative positronium ion Ps ^- ( e ⁺ e ^- e ^- ), below the threshold of Ps(n = 2), using a configuration interaction (CI) method on a B splines basis. Both the one- and two-photon detachment cross-sections have a form similar to the corresponding spectra of the H^- ion, scaled accordingly. The peak value of the one-photon cross-section agrees very well with the calculations by Bathia and Drachman [1], while it differs from those by Igarashi et al. [2], which give a value of 15% lower. Two-photon detachment cross-sections are also reported. Received 24 January 2002 / Received in final form 9 April 2002 Published online 19 July 2002     

Extracting generalized multiphoton ionization cross-sections from nonperturbative time-dependent calculations: An application in positronium

Ab initio time-dependent (TD) calculations of the behavior of positronium (Ps) under strong subpicosecond laser pulses are presented. The results are compared with results in H through scaling. It is found that a substantial amount of the population can be found in excited states after the pulse. In the perturbative regime, generalized multiphoton ionization cross-sections are extracted from the results of the time-dependent calculations. The generalized cross-sections are used to predict the response of Ps to nanosecond laser pulses at wavelengths of current experimental interest. Beyond the application to Ps, the generality of the method for extracting generalized cross-sections from TD nonperturbative calculations is discussed. Received 8 June 1999     

Quenching of molecular ions by He buffer loading at ultralow energies: rotational cooling of OH<Superscript>+</Superscript>(<Superscript>3</Superscript>Σ<Superscript>-</Superscript>) from quantum calculations

An ab initio computed potential energy surface is employed to evaluate the interaction of the OH⁺(³Σ ^-) molecule with ⁴He(¹S) atom and an analytic fitting of the raw points is directly employed in quantum scattering calculations at ultralow collision energies. The Hund's case (b) chosen to handle the spin-rotation coupling allows to extract from the numerous inelastic cross sections the relative importance of pure “spin flip" vis-à- vis rotational cooling cross sections. The final rates of all the above processes as a function of the initial |N〉 state are analysed in detail and possible propensity rules are discussed.