Formation of exotic atoms by direct capture and via transfer from hydrogen

Exotic atoms like muonic atoms can be formed either by direct capture, often called Coulomb capture, or by muon transfer from a muonic hydrogen atom. The first estimates for the formation predicted, for both mechanisms, probabilities approximately proportional to the charge numberZ. The experiments did not confirm such a simpleZ-dependence. In direct capture, it turned out that the chemical bond played a decisive role, at least for lighter elements. In the formation via transfer, surprising data were obtained not only for heteroatomic molecules but also for noble gases. Whereas for direct capture, a model is able to reproduce quite satisfactorily a great number of measured capture ratios, including those in hydrogen compounds, the formation via transfer seems to put completely different and more fundamental questions.     

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.     

Precision measurement of the (3p–1s) X-ray transition in muonic hydrogen

The (3p — 1s) X-ray transition to the muonic hydrogen ground state was measured with a highresolution crystal spectrometer. The assumption of a statistical population of the hyperfine levels of the muonic hydrogen ground state was directly confirmed by the experiment and measured values for the hyperfine splitting can be reported. The measurement supplements studies on line broadening effects induced by Coulomb de-excitation hindering the direct extraction of the pion-nucleon scattering lengths from pionic hydrogen and deuterium X-ray lines.     

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.     

Polarization of the vacuum in a relativistic hydrogenlike atom: The Lamb shift

This paper examines the shift of energy levels in a hydrogenlike atom induced by vacuum polarization effects. The contribution of free polarization is found for the ground state and several excited states in a closed analytical form. For the first time an expression is derived for the radiative correction to the energy in the form of an explicit function of the parameter Zα. The results are valid for states nl _j with the largest values of orbital and total angular momenta (l=n−1 and j=l+1/2). The final expression, found in terms of generalized hypergeometric functions, is a function of three variables, Zα, n, and the ratio of the particle masses on the orbit and in the vacuum loop, i.e., the result is valid for ordinary atoms and for muonic atoms. Several useful asymptotic expressions are also derived. Zh. éksp. Teor. Fiz. 116, 1575–1586 (November 1999)     

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.     

A search for colour van der Waals interaction

It is suggested that the strength of nuclear colour van der Waals interaction, if present, can be determined by measuring deviations from Rutherford scattering of charged hadrons from nuclei, at energies well below the Coulomb barrier. Experimental limit on the strength of such a potential is obtained asλ<50, when the colour van der Waals potential is given byV(r)=λ(hc/r ₀)(r ₀/r)⁷, withr ₀, the scaling length, taken as 1 fm. This limit is obtained from an analysis of existing experiments and by performing scattering experiments of 3–4.6 MeV protons from a²⁰⁸Pb target.     

μ + Knight shift and spin relaxation in indium single crystalKnight shift and spin relaxation in indium single crystal

μ ⁺ SR measurements have been performed in a single crystal indium sample between 12 K and 300 K with a stroboscopic μSR spectrometer. The muonic Knight shiftK _μ and the muonic depolarization rate σ were obtained for various angles θ between the tetragonal crystallinec-axis and the direction of the external field. The isotropic part ofK _μ is only weakly temperature dependent and is consistent with the estimated Pauli spin susceptibility value. At a temperature of 12 K the angular dependence ofM ₂ (the second moment of the field distribution at the muon, obtained from the measured σ(θ) values) allows a clear determination of the muon location — the symmetric tetrahedral site. The observed anisotropicK _μ cannot be explained by the dipoles at the In atoms responsible for the bulk magnetic susceptibility but probably originates from an anisotropic Pauli spin susceptibility.     

New results in the theory of muonic atom formation in molecular hydrogen

Muonic atom formation in molecular hydrogen proceeds in two stages. In the first stage, the mu-molecular complex (abµe)^* is formed due to Coulomb capture of a muon by a hydrogen molecule (abee), and, in the second stage, the decay of the complex leads to exotic-atom formation. We consider various channels for the decay of the complex. The main competition channels are direct dissociation and Auger decay. The primary distribution of muonic atoms over quantum states and kinetic energy has been obtained taking into account the competition of the decay channels.     

A generalized adiabatic approach to exotic three-body systems

A generalized adiabatic approach providing the asymptotic separation of the fast and slow variables for the three-body muonic scattering problem is considered. A uniform classification scheme of the different adiabatic bases for some typical three-body Coulomb systems is discussed. The estimations of the cross section of the elastic scattering process (t¯p) _n=1+d(t¯p)_n=1+d are presented.     

Comparison of the Seltzer Coefficient C 1 to Experimental Data

Experimental Coulomb isotope shifts δE _Coul from K _α transitions, and radius differences δ〈r ²〉 _eμ measured by electron scattering and muonic atom X-rays were used to derive ‘experimental’ coefficients C _1,exp for 54 isotope pairs of 18 elements from Mo to U. A χ²-analysis shows that these experimental coefficients are – on average – 3.5% lower than the theoretical C ₁ values calculated by Seltzer, or more precisely: C _1,exp=0.965(± 0.014)×C ₁. The need for more accurate theoretical calculations is stressed, and consequences of this deviation are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Observation of the Molecular Quenching of μp(2S) Atoms

Kinetic energy distributions of muonic hydrogen atoms μp(1S) have been obtained by means of a time-of-flight technique for hydrogen gas pressures between 4 and 64 hPa. A high energy component of ∼900 eV observed in the data is interpreted as the signature of long-lived μp(2S) atoms, which are quenched in a non-radiative process leading to the observed high energy: the collision of a thermalized μp(2S) atom with a hydrogen molecule H₂ results in the resonant formation of a {[(ppμ)⁺]^*pee}^* molecule. Then the (ppμ)⁺ complex undergoes Coulomb de-excitation and the ∼1.9 keV excitation energy is shared between a μp(1S) atom and one proton. The preliminary analysis of the time spectra gives a long-lived μp(2S) population of ∼1% of all stopped muons, and a quenching rate of ∼4⋅10¹¹ s⁻¹. This revised version was published online in August 2006 with corrections to the Cover Date.     

Observation of muonic HF molecule formation with TF μ− SR

Negative muon polarization has been measured in pure gaseous Ne (24 atm) and in Ne+H₂ mixtures (24 atm Ne+1.8 atm H₂, 8 atm H₂ and 16 atm H₂). The experiment was performed at JINR (Dubna) on aSR-spectrometer [1] with 200 G transverse magnetic field at room temperature. In pure Ne no polarization was observed (a ₀=0.09±0.1%) while in Ne+H₂ mixtures clear precession signals were detected at the free-muon frequency with asymmetries a_1.8=0.33±0.13%,a ₈=0.33±0.14% anda ₁₆=0.59±0.09%. The fact that polarization appears in the muonic HF molecule shows that at the moment of the molecule formation (t10^–10 s) the muon is not completely depolarized. The estimate of the reaction constantk=(2.3±1.6)×10^–11cm³ s^–1 agrees with the experimental values obtained by other methods. The result achieved demonstrates that ^– SR-method can be applied for studying fast kinetics processes in the gas phase and in particular for measuring chemical reaction rates of halogen atoms and ions.     

Muonic atoms testing the electron propagator of quantum electrodynamics and the Higgs boson contribution

In this work we consider the energy states of muonic atoms which are predominantly influenced by vacuum polarization. This fact is used for testing the electron propagator of QED with the modification \(S(p) = (\not p - me)^{ - 1} + f(\not p - M)^{ - 1}\) . The data of some well analyzed transitions in muonic He, Si, Ba, and Pb yield the limit M>29 MeV for f=1. Similarly the presence of a Higgs boson would cause a shift of the energy levels which can be measured easier in muonic atoms since the coupling grows with the fermion mass. The analysis of several transitions in heavy muonic atoms shows, that the mass of the Higgs boson is larger than 12.8 MeV. Further reductions of the present-day uncertainties concerning the experimental data and especially of the nuclear structure effects could improve these limits.     

Recent Advances in the Theoretical Methods and Computational Schemes for Investigations of Resonances in Few-Body Atomic Systems

This paper describes the research works performed in my group in recent years in the theoretical methods and computational schemes for investigations of resonances in few-body atomic systems. These methods include the complex absorbing potential method, the stabilization method, and the method of complex scaling. In addition to atomic resonances, this paper also describes some of our recent works on investigations of Borromean bindings in three-body atomic systems. By systematically changing the two-body interaction from the long range Coulomb potential to the short range screened Coulomb (Yukawa) potential, we have investigated the Borromean bindings for hydrogen molecule ion H ₂ ⁺ and the muonic molecular ions.     

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.     

Many-body study of van der Walls interaction involving lithium and rare-gas atoms and its contribution to hyperfine shifts

Using linked cluster many-body perturbation theory, the frequency-dependent dipole polarizabilitiesa(ω) has been calculated for the lithium atom. The value ofa(ω) at the static limit (169.04a ₀ ³ ) matches well with other available theoretical values and experimental results. These values have been used to calculate the van der Waals constants for interactions of lithium, helium and neon atoms. The values of the van der Waals constants for dipole-dipole interaction in atomic units are −22.9, −44.8, −1465.8, 184950.0, 2011.8, 3896.5, 30.3, 59.0 and 115.1 for Li-He, Li-Ne, Li-Li, Li-Li-Li, Li-Li-He, Li-Li-Ne, Li-He-He, Li-He-Ne and Li-Ne-Ne interactions respectively. Obtaining the suitable response functions for lithium and helium atoms, the long range contribution to Δa(r)/a ₀ in the study of fractional frequency shift in hyperfine pressure and temperature shift measurements is obtained as −541 atomic units.     

Lamb shift in muonic hydrogen—I. Verification and update of theoretical predictions

In view of the recently observed discrepancy of theory and experiment for muonic hydrogen [R. Pohl et al., Nature 466 (2010) 213], we reexamine the theory on which the quantum electrodynamic (QED) predictions are based. In particular, we update the theory of the 2P–2S Lamb shift, by calculating the self-energy of the bound muon in the full Coulomb + vacuum polarization (Uehling) potential. We also investigate the relativistic two-body corrections to the vacuum polarization shift, and we analyze the influence of the shape of the nuclear charge distribution on the proton radius determination. The uncertainty associated with the third Zemach moment 〈r³〉₂ in the determination of the proton radius from the measurement is estimated. An updated theoretical prediction for the 2S–2P transition is given.     

Hadronic vacuum polarization correction in muonic atoms

The contribution of hadronic vacuum polarization to the energy levels of muonic atoms is reevaluated using an improved parametrization of the total cross section for e⁺ e^?→hadrons. The numerical results can be simply related to the correction due to muonic vacuum polarization.