A note on Δn ≠ 0 Stark transitions in hydrogenlike atoms

In a gaseous helium or hydrogen target slow muons or antiprotons are captured into orbits with a high principal quantum number (n = 15 to 50) to form (μ^? α)⁺ ions, (p α)⁺ ions, or (p p) atoms respectively. In the subsequent deexcitation process Stark mixing of the intermediary states plays an important role. The successful Mainz Cascade Model assumed Δn = 0 for the Stark transitions, although formally no such selection rule exists. This note examines the reasons why Δn ≠ 0 Stark transitions play only a negligible role in the deexcitation cascade.     

Coulomb deexcitation of muonic hydrogen within the quantum close-coupling method

The Coulomb deexcitation of muonic hydrogen in collisions with the hydrogen atom has been studied in the framework of the fully quantum-mechanical close-coupling method for the first time. The calculations of the l-averaged cross sections of the Coulomb deexcitation are performed for (μp)_n and (μd)_n atoms in the initial states with the principal quantum number n = 3–9 and at relative energies E = 0.1–100 eV. The obtained results for the n and E dependences of the Coulomb deexcitation cross sections drastically differ from the semiclassical results. An important contribution of the transitions with Δn > 1 to the total Coulomb deexcitation cross sections (up to ～37%) is predicted.     

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.     

Nuclear size correction to the hyperfine splitting in low- hydrogen-like atoms

The finite nuclear size effect on the hyperfine splitting of low-Z hydrogen-like atoms is studied in the external field approximation. A simple non-relativistic formula is proposed which expresses the nuclear size correction to the hyperfine splitting in terms of moments of the nuclear charge and magnetization distribution. The numerical results obtained via this formula are compared with corresponding results derived by means of the Zemach formula. A relativistic formula for the nuclear size correction to the hyperfine splitting is also derived. Received 18 March 2002 / Received in final form 14 November 2002 Published online 28 January 2003 RID="a" ID="a"e-mail: plunien@physik.tu-dresden.de     

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     

Collisions of fast electrons with positronium atoms

Summary Elastic and inelastic collisions of fast non-relativistic electrons with positronium atoms have been studies in the Born-Ochkur approximation. It has been shown that exchange plays an important role for transitions between states with the same parity as in this case the direct scattering amplitude vanishes. Numerical results for the total and ortho-para conversion cross-sections for the 1s→1s, 1s→2s and 1s→2p transitions have been presented for projectile energies varying from 0.1 to 10 keV. According to charge symmetry, presented results apply also to positron projectiles.     

Scattering of light exotic atoms in excited states

The differential and total cross-sections for the scattering of muonic, pionic, kaonic and antiprotonic hydrogen in excited states from atomic hydrogen have been calculated for the purpose of atomic cascade calculations. The scattering problem is treated in a fully quantum mechanical framework which takes the energy shifts and, in the case of the hadronic atoms, the widths of the ns states into account. The validity of semiclassical approximations is critically examined. Received 4 December 2001 and Received in final form 4 February 2002     

Exactly solvable models through the generalized empty interval method,for multi-species interactions

Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for E _n(t)'s, the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time t. The constraints are solved for the single-species left-right-symmetric systems. Also, examples of multi-species system for which the evolution equations of E _n(t)'s are closed, are given. Received 25 September 2002 / Received in final form 3 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: mamwad@iasbs.ac.ir     

Interaction of coupled higher order nonlinear Schrödinger equation solitons

The novel inelastic collision properties of two-soliton interaction for an n-component coupled higher order nonlinear Schr?dinger equation are studied. Some interesting features of three soliton interactions, related to the integrability of the n-component coupled higher order nonlinear Schr?dinger equation are also discussed. Received 17 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: abhijit@iitg.ernet.in RID="b" ID="b"e-mail: sasanka@iitg.ernet.in RID="c" ID="c"e-mail: sudipta@iitg.ernet.in     

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.     

Hyperthermal surface-collisions of water cluster cations

Size-selected, protonated water cluster cations (H₂O)_nH⁺, 4 n 32, are scattered at normal incidence from the surface of a diamond-coated silicon wafer at collision energies 0 E _coll 500 eV. The size distribution of collision-induced fragment-ions and the ion yield of scattered particles are analyzed, using a secondary time-of-flight mass spectrometer, as a function of the cluster size, n, and the collision energy, E _coll. Even at low impact energies only very small fragment-ions can be detected, with a maximum fragment size of 35% of the colliding parent cluster ions. For clusters consisting of more than 10 molecules, the protonated water dimer (H₂O)₂H⁺ becomes the predominant fragment-ion. The total charge survival yield obeys a nonlinear increase with cluster size; for the largest clusters investigated, more than 35% of the impacting ions survive the surface collision in the cationic charge state.     

Angular distributions of scattered excited muonic hydrogen atoms

Coulomb deexcitation differential cross sections of excited muonic hydrogen in collisions with the hydrogen atom are studied for the first time. In the fully quantum-mechanical close-coupling approach, both the differential cross sections for the nl → n′l′ transitions and l-averaged differential cross sections have been calculated for the initial exotic atom states with n = 2–6 at kinetic energies of E _cm = 0.01–15 eV and for scattering angles of ϑ_cm = 0°–180°. The vacuum polarization shifts of the ns states are taken into account. The differential cross sections of the elastic and Stark scattering obtained in the same approach are also presented. The main features of the calculated differential cross sections are discussed, and a strong anisotropy of Coulomb deexcitation cross sections is predicted. The text was submitted by the authors in English.     

Quasi-free Compton scattering and the polarizabilities of the neutron

Differential cross-sections for quasi-free Compton scattering from the proton and neutron bound in the deuteron have been measured using the Glasgow/Mainz photon tagging spectrometer at the Mainz MAMI accelerator together with the Mainz [48]cm ;SPMOslash; × [64]cm NaI(Tl) photon detector and the G?ttingen SENECA recoil detector. The data cover photon energies ranging from [200]MeV to [400]MeV at θ^LAB _γ = 136.2^°. Liquid deuterium and hydrogen targets allowed direct comparison of free and quasi-free scattering from the proton. The neutron detection efficiency of the SENECA detector was measured via the reaction p(γ,π⁺ n). The “free” proton Compton scattering cross-sections extracted from the bound proton data are in reasonable agreement with those for the free proton which gives confidence in the method to extract the differential cross-section for free scattering from quasi-free data. Differential cross-sections on the free neutron have been extracted and the difference of the electromagnetic polarizabilities of the neutron has been determined to be α_n - β_n = 9.8±3.6(stat)^+2.1 _-1.1(syst)±2.2(model) in units of [10^-4]fm ³. In combination with the polarizability sum α_n + β_n = 15.2±0.5 deduced from photoabsorption data, the neutron electric and magnetic polarizabilities, α_n = 12.5±1.8(stat)^+1.1 _-0.6(syst)±1.1(model) and β_n = 2.7±1.8(stat)^+0.6 _-1.1(syst)±1.1(model) are obtained. The backward spin polarizability of the neutron was determined to be γ⁽ⁿ⁾ _π = (58.6±4.0)×10^-4 fm ⁴. Received: 21 August 2002 / Accepted: 16 October 2002 / Published online: 11 February 2003 RID="a" ID="a"Part of the Doctoral Thesis. RID="b" ID="b"Present address: Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig. RID="a" ID="a"Part of the Doctoral Thesis. RID="b" ID="b"Present address: Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig. RID="c" ID="c"Part of the Habilitation Thesis. RID="d" ID="d"e-mail: schumacher@physik2.uni-goettingen.de Communicated by Th. Walcher     

Thermal undulations of quasi-spherical vesicles stabilized by gravity

The classical treatment of quasi-spherical vesicle undulations has, in the present work, been reviewed and extended to systems, which are affected by a gravitational field caused by a density difference across the membrane. The effects have been studied by the use of perturbation theory leading to corrections to the mean shape and the fluctuation correlation matrix. These corrections have been included in an analytical expression for the flicker spectrum to probe how the experimentally accessible spectrum changes with gravity. The results are represented in terms of the gravitational parameter, g ₀ = ΔρgR ⁴/κ. The contributions from gravity are in most experimental situations small and thus negligible, but for values of g₀ above a certain limit, the perturbational corrections must be included. Expressions for the relative error on the flicker spectrum have been worked out, so that it is possible to define the regime where gravity is negligible. An upper limit of g₀ has also been identified, where the error in all modes of the flicker spectrum is significant due to distortion of the mean shape. Received 9 July 2002 and Received in final form 15 November 2002 RID="a" ID="a"e-mail: jonas@kemi.dtu.dk RID="b" ID="b"e-mail: ipsen@memphys.sdu.dk     

Vibrational Structure of the Absorption Spectra and a Model of the HNO and DNO Molecules in the Excited State

The vibrational structure of the absorption spectra of the first n–^*–electron transitions of the HNO and DNO molecules is calculated in the Franck–Condon approximation. A structural model of the molecules in the excited electronic state is constructed on the basis of correlations and with the aid of a method of hybrid atomic orbitals. Evaluation of the influence of deuterium substitution on the intensities of the vibrational components upon electronic excitation is made. A comparison of the experimental and theoretical absorption spectra calculated for different models of the molecules is carried out.     

Radiative lifetime and oscillator strength determination in Mg-like potassium (K VIII)

Theoretical transition probabilities have been obtained for 54 n = 3 transitions depopulating the 3s3p ¹P^o, 3p^{2 3}P, ¹D, ¹S, 3s3d ¹D, ³D and 3p3d ³P^o, ³D^o, ³F^o, ¹F^o, ¹D^o, ¹P^o levels, including 14 transitions not yet observed. Some of these predictions have been compared with experimental lifetimes obtained by beam-foil spectroscopy for four n = 3 levels of K⁷⁺. An excellent agreement is observed between theory and experiment for all the levels. Received 23 January 2002 / Received in final form 23 April 2002 Published online 19 July 2002     

Quenching of metastable antiprotonic helium atoms in collisions with deuterium molecules

Quenching of metastable antiprotonic helium atoms in collisions with deuterium molecules has been studied using laser spectroscopy at CERN's new Antiproton Decelerator facility. The quenching cross-sections of the states (n, l )= (39, 36), (39, 37), and (39, 38) were determined from the decay rates of the states which were observed using the “deuterium-assisted inverse resonance” (DAIR) method. The results revealed a similar (n, l )-dependence of the quenching cross-sections as in the case of hydrogen but the values were smaller by a factor of ∼1.5. Received 6 July 2001     

Structure of water-in-oil microemulsions of AOT by infrared spectroscopy

Summary The structure of water in water/AOT/n-heptane reverse micelles has been studied as a function of the [H₂O]/[AOT] ratio (W) by using the absorption IR due to O−H stretching modes in the 3800–3000 cm⁻¹ range. The results show that the IR spectra can be expressed as a sum of contributions from bound- and bulk-like water. The fraction of water in the two ?regions? within the water pool was evaluated as a function ofW. The ?bound? water region seems to hold 3.5 water molecules (corresponding to 7 O−H oscillators) per AOT molecule and its formation is nearly complete atW>6. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Spin glass and ferromagnetism in Kondo lattice compounds

The Kondo lattice model has been analyzed in the presence of a random inter-site interaction among localized spins with non zero mean J₀ and standard deviation J. Following the same framework previously introduced by us, the problem is formulated in the path integral formalism where the spin operators are expressed as bilinear combinations of Grassmann fields. The static approximation and the replica symmetry ansatz have allowed us to solve the problem at a mean field level. The resulting phase diagram displays several phase transitions among a ferromagnetically ordered region,a spin glass one, a mixed phase and a Kondo state depending on J₀, J and its relation with the Kondo interaction coupling J_K. These results could be used to address part of the experimental data for the CeNi _{1 - x} Cu _x compound, when x ⩽ 0.8. Received 24 June 2002 Published online 31 December 2002     

Static anisotropic and isotropic electric dipole polarizabilities of Na n F n-1 clusters

Recently, electric susceptibilities of Na_nF_n-1 clusters have been measured by deflecting a molecular beam in an inhomogeneous electric field. The analysis of the deflection of a cluster by the electric field needs the calculation of the electric properties. We present the calculation of the static anisotropic and average dipolar polarizabilities within a model in which the Na_nF_n-1 clusters ( 2 n 23) are treated as one electron embedded in the field of n ions Na⁺ and of n - 1 ions F^-. The accuracy of the results is evaluated and discussed on small clusters (n 5) in comparison with ab initio calculations. The relationship between the polarizabilities, the electronic localization and the geometric structure is discussed. Received 10 September 2002 Published online 3 July 2003