Advanced adiabatic approach to superlow-energy inelastic collisions of mesic atoms in excited states

The advanced adiabatic approach previously proposed for describing collision problems in atomic physics is extended to the specific case of mesic-atom collisions in the excited states n≥2. The method and the algorithm of the calculations are described. The calculations of the charge-exchange and Coulomb deexcitation rates in collisions of (pμ)_n, (dμ)_n, and (tμ)_n muonic atoms in the excited states n=3, 4, 5 with the hydrogen isotopes p, d, t are presented in comparison with the conventional adiabatic approach.     

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.     

Muon transfer from protium to helium isotopes at low temperature

The transfer reaction of negative muons from muonic protium to ³ and ⁴ in binary and triple gas mixtures was studied. In the binary mixtures the transfer rates to the two helium isotopes were determined from the time distribution of the 7-keV X-rays of the intermediate muonic molecule (pμHe)*. The experimental transfer rate to ⁴ is in good agreement with theoretical predictions, whereas the rate to ³ is a factor 2 to 3 smaller than the predicted ones. Radiative branching ratios of the (pμHe)8 molecular decay were obtained. Muon transfer from excited states of muonic protium gives the main contribution to the total intensity of the μHe Lyman series in the binary mixtures. Values of q _1s ^He are determined. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Effects of vacuum polarization and of proton polarizability in the Lamb shift of muonic hydrogen

The contributions to the Lamb shift in muonic hydrogen from hadronic vacuum polarization and from the correction associated with electron vacuum polarization and with the proton polarizability are calculated by using present-day experimental data on the cross section for e ⁺ e ⁻ annihilation into hadrons and on structure functions for deep-inelastic ep scattering. The numerical value of the total contribution to the (2P-2S) shift in muonic hydrogen is found to be 10.95 μeV. __________ Translated from Yadernaya Fizika, Vol. 64, No. 7, 2001, pp. 1358–1363. Original Russian Text Copyright ? 2001 by Martynenko, Faustov.     

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.     

Deceleration of muonic hydrogen atoms in solid hydrogens

Results of recent calculations of cross-sections for muonic hydrogen atom scattering in solid hydrogen isotope targets are presented. The coherent parts of these cross-sections, namely, the elastic Bragg scattering and phonon coherent scattering, are calculated accurately for the first time. A fine structure of Bragg peaks is obtained in the case of Bravais fcc structure of hydrogen targets frozen rapidly at 3 K. The one-phonon coherent cross-section is estimated using the Debye approximation. The calculated differential cross-sections are used for Monte Carlo simulations of muonic atom diffusion and slowing down in solid hydrogens. Also is calculated the energy-dependent rate of resonant ddμ molecule formation in 3 K solid deuterium quantum crystal, using the Debye model and Van Hove's formalism of the response function. This rate is very different from that obtained for the 3 K gas model. The influence of dμ atom slowing down on the average ddμ formation rate is considered. It is shown that very slow dμ deceleration below 10 meV is important for explanation of experimental results. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Nonadiabatically Coupled Hyperspherical Equations Applied to the Collisional Spin Flip of Muonic Hydrogen

Nonadiabatically coupled equations in terms of hyperspherical coordinates are solved for the elastic and hyperfine transitions F→F′ of muonic hydrogen isotopes pμ, dμ, and tμ in collisions pμ(F)+p→p+μp(F′), dμ(F)+d→d+μd(F′), and tμ(F)+t→t+μt(F′), as an extension of our previous work on pμ [Igarashi et al., Phys. Rev. A 58 (1998), 1166]. Converged cross sections are obtained for collision energies 10^?3 to 10² eV and for the total orbital angular momentum L=0 and 1 including the spin–spin interactions V _S explicitly in the Hamiltonian, and for L≥2 neglecting V _S because of the large interparticle separations. The inclusion of V _S for L=0 and 1 reproduces the correct hyperfine-splitting energy Δ∈ in the separated-atom limit, and is found to be of vital importance for the calculation of the spin-flip cross sections for collision energies lower than Δ∈.     

The probability of prompt and delayed fission of muonic237Np

Fission fragments from the reaction²³⁷Np(μ ^?,γ,f) have been measured in coincidence with muonic X-rays. The efficiency of the fission fragment detector is determined from (μ ^?,γ,f)-data of the same experiment. The total fission probability perμ-stopP _t has been measured as well as the fission probabilities P_f of the non-radiative muonic (3d→1s)- and (2p→1s)-transitions; the latter has been divided into two parts leading to different mean excitation energiesE:P _t =(54±17)%,P _f (3d→1s)=(41±21)%,P _f (2p→1s,E=6.218 MeV)=(61±19)%, andP _f (2p→1s,E=6.525 MeV)=(57±18)%. The influence of the muon on the fission barrier is discussed. The fission probability after muon capture is compared with a calculated value using a distribution of nuclear excitation energies following muon capture and the fission probability as measured in a²³⁸U(³He,αf)-reaction.     

Long-range parity violating interaction in muonic atoms

Long-range parity violating forces are induced in muonic atoms by virtual γ?Z⁰ conversion between the muon and the nucleus. They are of order G_Fα with range (2m_e)^?1. The relevant diagrams in unified electroweak interactions are calculated and the effects of the corresponding potential on parity admixtures in muonic levels are studied. It is proved that they are negligible for n = 3 orbits, but they have overwhelmed the conventional short-range contribution for n = 5.     

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.     

Elastic cross sections of 1s-muonic atoms at low energies in non-adiabatic approach

The low-energy elastic cross-section in collisions of a muonic atom with the hydrogen isotope is investigated, employing a new wave function (trial) and using the coordinate-space Faddeev–Hahn model. The wave function includes non-adiabatic terms. Our results of s–wave cross-sections are given, at the tμ(1s) + d scattering. Calculated cross-sections are in good accord with the results published by Chiccoli et al., while having no good agreement with other recent reports.     

Relaxationserscheinungen im 63 P 2-Zustand des Quecksilber-Isotops199Hg bei Stößen mit Quecksilberatomen im Grundzustand

The decay ofrf resonance signals (Δm _F =± 1, ΔF=0) in the hfs-states (F=3/2, 5/2) of the 6³ P ₂-state of¹⁹⁹Hg has been observed by means of a sampling method. By comparing the relaxation times to those of the even isotopes, the cross section σ₂(F) for the destruction of an alignment in the hfs-states by collisions with ground state Hg-atoms could be measured. The following ratios were obtained: σ₂(F=3/2)/σ₂=1.04±0.06 and σ₂(F=5/2)/σ₂=0.90± 0.03. The cross section σ₂ for the even isotopes was found to be (2.620±0.265) 10^?14cm². Assuming total decoupling of nuclear spinI and electronic angular momentumJ during the collision, the cross sections for the destruction of an orientation (σ₁) and an “octupolarisation” (σ₃) could be calculated. For the even isotopes the following ratios were derived: σ₁/σ₂=0.76 ± 0.07 and σ₃/σ₂=1.08 ± 0.09.     

Experimental Search for μd 3He Fusion

The vast majority of muon catalyzed fusion research has been concerned with muonic molecules of hydrogen isotopes only, since the dynamics of higher-Z muonic atoms in general preclude the formation of molecular systems. In the specific case of hydrogen–helium mixtures, bound muonic molecular states can exist, and thus it is possible to search for the reaction μd ³He $$\xrightarrow{{\tilde \lambda f}}$$ μ+α(3.66 MeV)+p(14.64 MeV). Until recently, the theoretical predictions for the nuclear fusion rate in the μd ³He molecule, ${\tilde \lambda }$ _f , ranged over one order of magnitude, from 10⁵ to 10⁶ per second. An experimental upper limit has been measured for ${\tilde \lambda }$ _f in HD + ³He giving a value (<6×10⁴ s^?1 [1]). We report on the analysis of an experiment in D₂ + ³He which has shown a signal coming either from the muon catalyzed reaction, or from the fusion in flight of ³He's formed from dμd fusion.     

Constraints on the decay period of a free neutron from the characteristics of tritium beta decay

The reduced decay period of the triton, (ft _1/2)_T=(1129.6±3)s, and the free-neutron decay period, (t _1/2)_n=(616.7±;2.7±1.3) s, are determined from the experimental and theoretical values of the chemical shifts of atomic and molecular tritium.     

Isotopic fractionation between gaseous and dissolved carbon dioxide

The isotopic fractionation between gaseous carbon dioxide and an equilibrated aqueous solution of the gas has been measured at temperatures between 0° and 60 °C for the carbon isotopes and close to 0 °C for the oxygen isotopes. ¹³C¹⁶O₂ is slightly less, and¹²C¹⁶O¹⁸O slightly more soluble than¹²C¹⁶O₂, the actual values for the fractionation,?, being ?(1.18?0.0041 ·t)‰ (temperature,t, in °C) for the carbon isotopes and about 0.8‰ at 0°C for the oxygen isotopes. A theoretical expression is derived for the vapour-solute equilibrium system by treating it in a similar manner as the pure vapour-liquid system. The calculated isotopic fractionation for carbon dioxide, using data on the pure vapour-liquid system, is in satisfactory agreement with the experimental results.