Scattering Processes of Excited Muonic Atoms by Molecular Hydrogen

The coupled-channel approach of an excited exotic atom scattering from a hydrogen molecule in the rigid-rotator approximation is developed. The K-matrix method is used to solve the set of coupled collisional equations in the space-fixed (SF) framework for the systems pμ+H₂, dμ+D₂, pμ+D₂, and dμ+H₂. The elastic and Stark mixing cross-sections for scattering on molecular ortho- and para-states are calculated for the principle quantum number n = 2 and collisional energies E≥0.1 eV.     

Theory of the muonic hydrogen-muonic deuterium isotope shift

Corrections of the α³, α⁴, and α⁵ orders are calculated for the Lamb shift of the 1S and 2S energy levels of muonic hydrogen μp and muonic deuterium μd. The nuclear structure effects are taken into account in terms of the charge radii of the proton r _p and deuteron r _d for one-photon interaction, as well as in terms of the electromagnetic form factors of the proton and deuteron for the case of one-loop amplitudes. The μd-μp isotope shift for the 1S-2S splitting is found to be equal to 101003.3495 meV, which can be treated as a reliable estimate when conducting the corresponding experiment with an accuracy of 10^?6. The fine-structure intervals E(1S)-8E(2S) in muonic hydrogen and muonic deuteron are calculated.     

Optical characterization of the deep Cr level in GaAs

Comparison between the excitation spectra of luminescence (ESL) of the 0.57 eV band (typical of p or SI materials) and of the 0.62 eV band (typical of n samples) with the photoionization cross-sections σ⁰_n(hv) and σ⁰_p(hv) of the chronium level leads us to attribute unambiguously these luminescence transitions to the (Cr³⁺?Cr²⁺) center in chromium doped GaAs.     

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.     

Absolute cross sections of electron attachment to molecular clusters: Part I. Formation of (CO2) N −

A procedure of determining absolute cross section σ^? of electron attachment to (CO₂)_N clusters at pair collisions in crossed beams is suggested. The cross section is measured as a function of energy (E = 0.1–50 eV) and of cluster mean size N in a beam $(\bar N = 2 - 4000 molecules)$ . It is found that, even at $\bar N > 200$ and E ≤ 3 eV, σ^? is equal to, or larger than, 7 × 10^?13 cm², i.e., by more than one order of magnitude exceeds the maximal cross section of CO₂ ionization by electron impact. The dependences σ^? $(\bar N,E)$ have two wide continua at E ≤ 5.2 eV and E ≥ 6.9 eV, which correlate well with known functions of CO₂ electron-impact-induced excitation. These continua are attributed largely to formation of (CO₂) _N ^? ions during electron thermalization and solvation in the clusters. At E → 0, the polarization capture of an incident electron by the cluster leads to a sharp increase in cross section σ^?(E). From the dependences σ^? $(\bar N,E)$ measured, the thermalization and sovation probabilities for electrons with E ≤ 0.8 eV and the rate of electron energy loss in the cluster are found.     

Hyperfine splitting in muonic hydrogen: QED corrections of the α2 order

The α² order corrections to the hyperfine splitting of the 1 s and 2 s states in muonic hydrogen have been determined. The specially normalized difference 8E _hfs(2s) ? E _hfs(1s), as well as the general situation with the theoretical calculations of hyperfine splitting in muonic hydrogen, is considered.     

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.     

Nitrogen lasers, optical devices of variable gain coefficient: Theoretical considerations

Based on our previous measurements on the gain values by employing an oscillator amplifier (OSC-AMP) N₂-laser system of variable AMP electrode lengths, a calculation has been made for evaluation of the gain coefficient using rate equations. It is shown both numerically and analytically that small signal gain, g₀, is following our experimental observations of g₀=m+n/l_AMP, where m and n are some constants, and l_AMP is the length of the amplifier. For simplifying the calculation in the OCS-AMP circuit, an experimental condition of imposing the OSC-open-circuit operation has been applied, where the voltage waveforms from the relevant sections of the Blumlein circuit have been used for evaluation of the circuit parameters. Due to the fact that during the past years different cross-sections for the electron-impact excitations from the ground to the upper, N₂(C), and lower, N₂(B), have been introduced, our experimental observations have also been applied to examine the effect of introduced electron impact-excitation cross-sections on the g₀(l_AMP) behavior.     

Kotani theory for one dimensional stochastic Jacobi matrices

We consider families of operators,H _ω, on ?₂ given by (H _ω u)(n)=u(n+1)+u(n?1)+V _ω(n)u(n), whereV _ω is a stationary bounded ergodic sequence. We prove analogs of Kotani's results, including that for a.e. ω,σ_ac(H _ω) is the essential closure of the set ofE where γ(E) the Lyaponov index, vanishes and the result that ifV _ω is non-deterministic, then σ_ac is empty.     

Charge exchange and Coulomb de-excitation of muonic atoms in low energy collisions

The muon transfer and Coulomb de-excitation rates at the collisions of (pμ) _n , (dμ) _n and (tμ) _n muonic atoms in excited states n = 3, 4, 5 with hydrogen isotopes p, d, t are calculated for all possible combinations of hydrogen isotopes. The advanced adiabatic approach (AAA) [1–3] is adapted and used to the specific case of muonic atom collisions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Magnetic hyperfine interaction in muonic indium,osmium and mercury

The magnetic hyperfine interaction in several muonic atoms has been measured. The magnetic splittings of the 1s _1/2, 2s _1/2 and 2p _1/2 muon states in the 9/2⁺ ground state of¹¹⁵In, determined by measuring muonic X rays areΔE _mag(1s _1/2,¹¹⁵In 9/2⁺)=3580±70 eVΔE _mag(2s _1/2,¹¹⁵In 9/2⁺)=525±120 eVΔE _mag(2p _1/2,¹¹⁵In 9/2⁺)=850±180 eV. The magnetic splitting of nuclearγ rays in the presence of a muon in the 1s _1/2 state yields for the 1/2^? ground state in¹⁹⁹HgΔE _mag(1s _1/2,¹⁹⁹Hg 1/2^?)=468±115 eV and the following values for the first excited 2⁺ states in the nuclei^190,192Os and²⁰⁰Hg:ΔE _mag(1s _1/2,¹⁹⁰Os 2⁺)=665± ₄₀ ⁸⁰ eVΔE _mag(1s _1/2,¹⁹²Os 2⁺)=800±80 eVΔE _mag(1s _1/2,²⁰⁰Hg 2⁺)=655± ₇₅ ¹⁰⁵ eV. These data are compared with calculations using different nuclear models.     

Direkte Messung des (n, 2n)-Wirkungsquerschnitts von Niob 93

Using the watertank-method for natural niobium σ _n ,2 _n =1.35±0.25 barn was found. This value agrees with statistical model calculations and fits the systematics of the (n, 2n) cross-sections.     

Eigenvalue comparisons for quantum systems in a box

Comparison theorems are obtained for the first even and odd solutions of Schrödinger's equation −v″ + Q(t)v = λv, −l ≤ t ≤ l with boundary conditions v(−l) = v(l) = 0. The comparison functions Q_i(t), i = 1, 2, may intersect at a finite number of points within [−l,l]. Immediate extensions are possible for a more general class of Sturm-Liouville problems, and for problems in unbounded regions.     

The determination of hopping rates and carrier concentrations in ionic conductors by a new analysis of ac conductivity

The a.c. conductivity σ(ω) of ionic materials takes the form, σ(ω) = σ(0) + Aωⁿ. The carrier hopping rate, ω_p, is obtained from the new expression σ(0) = A ω_pⁿ and the carrier concentration is estimated from σ(0). The contribution of creation and migration terms to the activation energy for conduction may be determined from the thermal activation of σ(0) and ω_p and the corresponding entropy terms quantified. Data have been analyzed for four widely different ionic materials: single crystal Na β-alumina, polycrystalline Li₄SiO₄, Ag₇l₄AsO₄ glass and Ca(NO₃)₂/KNO₃ glass and melt. For each, the carrier concentration and hopping rates have been obtained.     

Band structure and optical transitions in semiconducting double-wall carbon nanotubes

The electronic structure of semiconducting double-wall carbon nanotubes (CNTs) is calculated using the linearized augmented cylindrical wave method. The consideration is performed in the framework of the local density functional theory and the muffin-tin (MT) approximation for the one-electron Hamiltonian. The electronic spectrum of a double-wall CNT is determined by the free motion of electrons in the interatomic space of the two cylindrical layers, scattering by the MT spheres, and tunneling through the classically impenetrable region. Calculated results for double-wall CNTs of the (n, 0)@(n′, 0) zigzag type indicate that the shift of the band-gap width depends on whether n and n′ are divided by 3 with a remainder of 1 or 2. It is found that, regardless of the type of the inner tube, the energy gap E _g of the outer tube decreases by 0.15–0.22 eV if the tube belongs to the sequence n = 2 (mod 3). For the outer tubes of the sequence n = 1 (mod 3), the shifts of the band gap ΔE _g are always negative ?0.15 ≤ ΔE _g ≤ ?0.05 eV. In both cases, the shifts ΔE _g weakly oscillate rather than decrease in going to tubes of a larger diameter d. For the inner tubes, the changes in the band gap ΔE _g are more sensitive to the diameter. At 10 ≤ n ≤ 16, the shifts ΔE _g are positive and the maximum value of ΔE _g equals 0.39 and 0.32 for the sequences n = 2 (mod 3) and n = 1 (mod 3), respectively. In going to the inner tubes of a larger diameter, ΔE _g rapidly drops and then oscillates in the range from ?0.05 to 0.06 eV. The calculated results indicate that the shifts of the optical band gaps in core and shell tubes upon the formation of double-wall CNTs are significant, which must hinder the identification of double-wall CNTs by optical methods. On the other hand, the obtained results open up possibilities for a more detailed classification of double-wall nanotubes.     

Fine and hyperfine structure of <Emphasis Type="Italic">P</Emphasis>-wave levels in muonic hydrogen

Corrections of order α ⁵ and α ⁶ are calculated for muonic hydrogen in the fine-structure interval ΔE ^fs = E(2P _3/2) − E(2P _1/2) and in the hyperfine structure of the 2P _1/2-and 2P _3/2-wave energy levels. The resulting values of ΔE ^fs = 8352.08 μeV, ΔẼ ^hfs(2P _1/2) = 7819.80 μeV, and ΔẼ ^hfs(2P _3/2) = 3248.03 μeV provide reliable guidelines in performing a comparison with relevant experimental data and in more precisely extracting the experimental value of the (2P–2S) Lamb shift in the muonic-hydrogen atom. Original Russian Text ? A.P. Martynenko, 2008, published in Yadernaya Fizika, 2008, Vol. 71, No. 1, pp. 126–136.     

Local density valence band offset in GaAs/AlAs: Role of interface dipole

The valence band offset, ΔE_V ,at the lattice-matched GaAs/AlAs(001) interface is derived from highly precise self- consistent all-electron local density band structure calculations of the (GaAs)_n(AlAs)_n(001) superlattices (with n ⩽ 3). Using the core levels as reference energies, we find that ΔE_V = 0.50 ± 0.05 eV, in very good agreement with recent experimental results (ΔE_V = 0.45 − 0.55 eV). The dependence of ΔE_V on the superlattice thickness is studied and related to the interface charge redistribution which produces an interface dipole potential estimated to be ∼ 0.14 eV.     

Electroabsorption in TlInS2

Electroabsorption spectra of single crystals have been studied near the fundamental absorption edge at 77 and 300 K. At 300 K two positive peaks (2.34 and 2.42 eV) and a negative peak (2.38 eV) are observed in the electroabsorption spectrum. At liquid-nitrogen temperature a fine structure corresponding to the formation of a parabolic exciton (2.503 eV) is observed.Values of the width of the forbidden gap E_g, the n = 1 exciton positions, the exciton activation energy ΔE_b, the effective Bohr radius a_exc, the reduced effective mass of an electron-hole pair μ, and the exciton ionization field F(E_g = 2.535 eV, E_exc = 2.503 eV, E_b = 32 meV, $\text{a}{}_{\mathrm{<mtext>exc</mtext>}}\text{=}\text{28}\text{A}\text{A;}\text{;}$;, μ = 0.15 m₀, and F = 1.2 × 10⁵ V cm^-1) have been determined from the electroabsorption spectrum.     

Scattering of muonic hydrogen atoms

Our measurement compares 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. A time-of-flight method was used to measure the scattering cross-section as a function of the muonic atom beam energy and shows clearly the Ramsauer–Townsend effect. The results are compared with theoretical calculations by using Monte Carlo simulations. The molecular pdμ and ptμ formation creates background processes. We measure the formation rates in solid hydrogen by detecting the 5.5 MeV (pdμ) and 19.8 MeV (ptμ) γ-rays emitted during the subsequent nuclear fusion processes. This revised version was published online in August 2006 with corrections to the Cover Date.