Thermalization of muonic hydrogen in hydrogen targets

The thermalization of pµ atoms in protium and dµ atoms in deuterium is considered. Monte Carlo calculations are performed for gaseous (300 K) and solid (3 K) protium and deuterium targets. Complete sets of the total and differential cross sections for the scattering of pµ on protium targets and dµ on deuterium targets are used as an input to the Monte Carlo simulations. At 300 K, muonic atom scattering from single molecules of H₂ and D₂ is considered. In the case of solid hydrogen the correlation effects from all molecules of the sample are taken into account. In particular, the Bragg and phonon scattering cross sections are calculated. The spin states and average energy of the muonic atoms are shown as functions of time. It is shown that at energies below about 0.01 eV the solid-state effects influence strongly the calculated cross sections, and therefore the deceleration processes in the solids are much slower than in the gaseous targets. It is shown that the neutron spectrum due to ddµ formation and subsequent dd fusion is significantly affected by slow dµ thermalization in solid deuterium.     

Ramsauer–Townsend Effect in Solid Hydrogen

The TRIUMF E742 experiment has measured the energy dependence of the scattering cross-sections of muonic deuterium and tritium on hydrogen molecules for collisions in the energy range 0.1–45 eV. The experimental setup permits the creation of muonic atom (μd or μt) beams. The multilayered target system gives the possibility to choose the type of interactions to study and to isolate a particular interaction. The scattering of μd or μt beams on H₂ is analyzed via the muon transfer reaction to neon. The time-of-flight method is used to measure the scattering cross section as a function of the energy of the muonic atom beam. The results are compared, using Monte Carlo simulations, with theoretical calculations which have been recently performed with high accuracy. This revised version was published online in August 2006 with corrections to the Cover Date.     

Vacuum polarization in muonic atoms: the Lamb shift at low and medium Z

In muonic atoms the Uehling potential (an effect of a free electronic vacuum polarization loop) is responsible for the leading contribution to the Lamb shift causing the splitting of states with Δn=0 and Δl≠0. Here we consider the Lamb shift in the leading nonrelativistic approximation, i.e., within an approach based on a certain Schr?dinger equation. That is valid for low and medium Z as long as (Zα)²≪1. The result is a function of a few parameters, including κ=Zαm_μ/m_e, n and l. We present various asymptotics and in particular we study a region of validity of asymptotics with large and small κ. Special attention is paid to circular states, which are considered in a limit of n≫1.     

Collisional deexcitation of exotic hydrogen atoms in highly excited states

The deexcitation of exotic hydrogen atoms in highly excited states in collisions with hydrogen molecules has been studied using the classical-trajectory Monte Carlo method. The Coulomb transitions with large change of principal quantum number n have been found to be the dominant collisional deexcitation mechanism at high n. The molecular structure of the hydrogen target is shown to be essential for the dominance of transitions with large Δn. The external Auger effect has been studied in the eikonal approximation. The resulting partial wave cross-sections are consistent with unitarity and provide a more reliable input for cascade calculations than the previously used Born approximation. Received 28 May 2002 Published online 15 October 2002 RID="a" ID="a"e-mail: thomas@physik.unizh.ch     

Calculation of decay widths of ppμ* ν,J ion in non-adiabatic approach

We calculate decay widths of the metastable ppμ^* _ν,J molecular ion in non-adiabatic approach. The muonic molecular ion can be formed in collision of the excited pμ(2s) atoms with H₂. Then, decay of the ppμ^* _ν,J system opens a path for the muon from pμ(2s) to pμ(1s). We employ trial wave function which includes non-adiabatic terms to calculate some radiationless decay widths. The present results of the widths do not good agree with those given in our previous work, while are more close to recent data of other researchers.     

Generation of the Ultracold Muonic Hydrogen Flux

We present the study of μp atom scattering in solid hydrogen. Anomalously large emission of E _pμ≤1.9 meV μp's from a solid H₂ layer was observed for the first time. This three times greater μp atom yield is due to non-elastic phonon scattering. As a result, it becomes possible to generate an ultracold flux of μp atoms. The recent calculations of the total and differential cross sections agree with all experimental results of μp atom scattering in solid H₂. This revised version was published online in August 2006 with corrections to the Cover Date.     

Charge exchange collisions of H<Superscript>+</Superscript>/D<Superscript>+</Superscript> ions with alkaline Earth atoms (Ca,Mg)

The Classical Trajectory Monte Carlo (CTMC) Method has been used to calculate the differential, partial and total single electron capture cross sections for the collision of H⁺/D⁺ with Ca and Mg atoms in the energy range of 1–100 keV. The differential cross sections at angles near the diffraction limit (<0.1^○) in both systems show a forward peak followed by an asymptotic fall at higher angles. Total and partial capture cross sections are found to be in good agreement with the experimental observations. Oscillations in the partial capture cross sections have been explained due to the swapping of the field electron. Isotope effect in the electron transfer is reported to be negligible.     

Cold collisions in strong laser fields: partial wave analysis of magnesium collisions

We have developed Monte Carlo wave function simulation schemes to study cold collisions between magnesium atoms in a strong red-detuned laser field. In order to address the strong-field problem, we extend the Monte Carlo wave function framework to include the partial wave structure of the three-dimensional system. The average heating rate due to radiative collisions is calculated with two different simulation schemes which are described in detail. We show that the results of the two methods agree and give estimates for the radiative collision heating rate for ²⁴Mg atoms in a magneto-optical trap based on the ¹S₀–¹P₁ atomic laser cooling transition.     

H<Superscript>+</Superscript><Emphasis Type="Bold">and He</Emphasis><Superscript>2+</Superscript> impact single and double ionization of lead

H⁺ and He²⁺ impact single and double ionization cross sections of ground state lead atoms have been calculated in the binary encounter approximation. Calculations of direct double ionization cross sections have been performed in the modified double binary encounter model. The accurate expressions of σ_ΔE (cross-section for energy transfer ΔE) and Hartree-Fock velocity distributions for the target electrons have been used throughout the calculations. Contributions to double ionization from Auger effect following ionization of inner shells have been considered in the present work. Our H⁺ impact single and double ionization cross sections are in good agreement with the experimental observations. In calculations of He²⁺ impact cross sections, the present theoretical approach shows limited success in the experimentally investigated region (50–350 keV amu^-1).     

Study of muonic hydrogen transport in TRIUMF experiment 742 by the Monte Carlo method

A technique of neutral muonic atom beams is proposed in the TRIUMF E742 experiment for measuring the scattering cross sections of muonic hydrogen isotopes in solid hydrogen. We present the results of Monte Carlo modeling of pµ and dµ atoms transport under the conditions of this experiment, taking into account the main physical as well as the geometrical aspects. The optimization of set-up parameters is performed in order to choose the most sensitive experimental conditions.     

Formation of fast exotic atoms by radiative Coulomb capture

Interesting surprises in some exotic atom kinetics have been reported recently. These involve muonic atom transfer cross sections, nuclear pion capture and theq 1s effect in CF. These can be explained if the exotic atom population contains a contributing fast component. Such fast atoms can be formed by radiative continuum to bound transitions of fast (keV) muons or pions. Cross sections for formation of such fast pionic and muonic atoms and their velocity distributions are reported. The possibility of these processes competing with the thermalisation channels and contributing effectively to the exotic atom population is discussed.     

Acceleration of cold Rb atoms by frequency modulated light pulses

The displacement of Rb atoms in a magneto-optical trap (MOT) caused by the force of a finite time series of counter-propagating frequency modulated light pulse pairs is measured as a function of the chirp of the pulses. The frequency modulated light pulses induced ⁸⁵Rb 5²S_1/2 F=3 ↔ ⁸⁵Rb 5²P_3/2 F'=2, 3, 4 excitation and de-excitation of the atoms. The result of this excitation de-excitation process is a force causing the acceleration and, consequently, the displacement of the maximum of the spatial distribution of the trap atoms. The time dependence of the populations of the levels of the atom are calculated — including also the ⁸⁵Rb 5²S_1/2 F=2 and F'=1 states — as the result of the interaction with the finite train of counter propagating frequency modulated light pulses by the solution of the Bloch equations. As the result of the measurement the interval of the chirp of the frequency modulated light of given intensity where the transitions take place, are determined. The results of the experiment and the expectation on the basis of model calculations are in qualitative agreement.     

Comparative study of rare gas-H<Subscript>2</Subscript> triatomic complexes

This paper presents a comparative analysis of complexes made of one rare gas (Rg) atom and molecular hydrogen, for five different Rg atoms. In particular, the vibrational band origins have been calculated, as well as the structural properties of the associated wavefunctions. The study is extended to ultra-cold Rg–H₂ collisions, object of a recent experiment aimed at producing ultra-cold H₂ [1]. The molecular systems are studied variationally using a simple, yet effective, isotropic trial wavefunction. A large number of potential energy surfaces available from the literature is considered. A comparative analysis shows that differences of up to two orders of magnitude exist for the zero-energy elastic cross sections of the five complexes. Corrections to the isotropic model have also been considered, showing no significant effect.     

Hyperfine structure effects in the collisions of the 2s metastable muonic hydrogen with hydrogen atoms

Cross sections for elastic and spin-flip scattering of metastable 2s muonic hydrogen on hydrogen atoms are calculated for the symmetric systems pμ+p, dμ+d and tμ+t. The calculations are performed in the two-level approximation of the adiabatic method with inclusion of the Lamb shift and electron screening. Due to the large polarizability of the 2s state, the obtained cross sections significantly exceed their counterparts for the ground-state muonic hydrogen.     

Cascade Processes in Muonic Hydrogen Atoms

The QCMC scheme created earlier for cascade calculations in heavy hadronic atoms of hydrogen isotopes has been modified and applied to the study of cascade processes in the μp muonic hydrogen atoms. The distribution of μp atoms over kinetic energies has been obtained and the yields of K-series X-rays per one stopped muon have been calculated. Comparison with experimental data indicated directly that for muonic and pionic atoms new types of non-radiative transitions are essential, while they are negligible for heavy (kaonic, antiprotonic, etc.) atoms. These processes have been considered and their probabilities have been estimated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Monte Carlo simulations of the <Emphasis Type="Italic">μ</Emphasis>CF processes kinetics in deuterium gas

The kinetics of muon-catalyzed-fusion processes (μCF) in pure D₂ gas have been studied by means of Monte Carlo simulations for various target temperatures and densities. In particular, the role of resonant and non-resonant ddμ formation in μCF has been investigated. It has been shown that non-resonant formation can be directly observed at very short times in the neutron time spectra from μCF for low-density D₂ targets. The time spectra of neutrons from the low-temperature ortho-D₂ and para-D₂ gas targets have been calculated. These spectra display a strong ortho-para effect, which agrees with experimental results for the dilute-gas D₂ targets.     

Interaction of frequency modulated light pulses with rubidium atoms in a magneto-optical trap

The spatial displacement of the ⁸⁵Rb atoms in a Magneto-Optical Trap (MOT) under the influence of series of frequency modulated light pulse pairs propagating opposite to each other is measured as a function of the time elapsed after the start of the pulse train, and compared with the results of simulations. Adiabatic excitation and consecutive de-excitation take place between the ground 5²S_1/2 (F=3) and the 5²P_3/2 (F'=2, 3, 4) excited levels as the result of the interaction. The displacement of the ⁸⁵Rb atoms is calculated as the solution of simple equation of motion where the expelling force is that arising from the action of the frequency modulated light pulses. The restoring and friction forces of the MOT are taken into account also. The system of Bloch equations for the density matrix elements is solved numerically for transitions between six working hyperfine levels of the atom interacting with the sequence of the frequency modulated laser pulses. According to these simulations, the momentum transferred by one pulse pair is always smaller than the expected 2ħk, (1) where ħ is the Plank constant and k=2π/λ where λ is the wavelength, (2) having a maximum value in a restricted region of variation of the laser pulse peak intensity and the chirp.     

Application of R-matrix method to electron-H<Subscript>2</Subscript>S collisions in the low energy range

Electron-H₂S collision process is studied using the R-matrix method. Nine low-lying states of H₂S molecule are considered in the R-matrix formalism to obtain elastic integral, differential, momentum transfer and excitation cross sections for this scattering system. We have represented our target states using configuration interaction (CI) wavefunctions. We obtained adequate representation of vertical spectrum of the target states included in the scattering calculations. The cross sections are compared with the experiment and other theoretical results. We have obtained good agreement for elastic and momentum transfer cross sections with experiment for entire energy range considered. The differential cross sections are in excellent agreement with experiment in the range 3–15 eV. A prominent feature of this calculation is the detection of a shape resonance in ²B₂ symmetry which decays via dissociative electron attachment (DEA). Born correction is applied for the elastic and dipole allowed transition to account for higher partial waves excluded in the R-matrix calculation. The electron energy range is 0.025–15 eV.     

Photoionization cross section and oscillator strength distribution in the near-threshold region of strontium

We present experimentally measured absolute values of the photoionization cross sections from the 5s5p ¹P₁ and 5s5p ³P₁ excited states of strontium at the first ionization threshold as 11.4±1.8 Mb and 10.7±1.7 Mb respectively using saturated absorption technique along with a thermionic diode ion detector in conjunction with a Nd:YAG pumped dye laser system. These threshold photoionization cross sections values have been utilized to determine the oscillator strengths of the 5s5p ¹P₁↦5snd ¹D₂ and 5s5p ³P₁↦5snd ³D₂ Rydberg transitions. The oscillator strength densities in the continuum corresponding to the 5s5p ³P₁ excited state have also been determined by measuring the photoionization cross sections at five ionizing wavelengths above the first ionization threshold. Smooth merging of the discrete f-values into the oscillator strength densities has been observed for the 5s5p ³P₁↦5snd ³D₂ series across the ionization threshold.     

Geometric shielding corrections for total cross section calculations of electron scattering by CH4, C2H6, C2H3F3, C2H4, C2F4, C2Cl4 and C2Cl2F2 from 30–5000?eV

To quantify the changes in the geometric shielding effect in a molecule as the incident electron energy varies, an empirical fraction, which represents the total cross section contributions of shielded atoms in a molecule at different energies, is presented. Using this empirical fraction, the total cross sections for electron scattering by CH₄, C₂H₆, C₂H₃F₃, C₂H₄, C₂F₄, C₂Cl₄ and C₂Cl₂F₂ are calculated over a wide energy range from 30 to 5000 eV by the additivity rule model at the Hartree-Fock level. The quantitative total cross sections are compared with those obtained by experiment and other theories where available. Good agreement is attained above 100 eV.