Production of slow muonic hydrogen isotopes in vacuum

Muonic hydrogen isotopes (μ⁻ p, μ⁻ d, and μ⁻t) are simple quantum mechanical systems ideally suited for studies of numerous fundamental phenomena in electroweak and strong interactions as well as in applied areas such as muon chemistry or muon catalyzed fusion. Emission of muonic hydrogen isotopes into vacuum helps to overcome the limitations which are normally imposed on conventional investigations with gaseous and liquid targets. A proof of principle experiment for this new technique was performed at TRIUMF last year. Negative muons with 30 MeV/c momentum were stopped in a thin film of solid hydrogen and produced very low energy μ⁻d in vacuum. The distribution center of the normal velocity components of emitted μ⁻d atoms was measured to be ∼1 cm/μs. The yield of μ⁻d in vacuum is an increasing function of H₂ film thickness δ up to a value of δ≥1 mm.     

The capture of slow antiprotons in helium, neon and argon

We consider the capture of antiprotons with energies less than roughly 27 eV by helium, neon and argon atoms. We use the adiabatic ‘hidden-crossing’ theory to calculate both the capture cross-sections and the angular distribution of the antiprotons. We find that important differences between helium and the other noble gases can be attributed to the properties of the ‘hidden’ crossings appropriate to each system. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Resonant enhancement of the formation of hydrogen-helium muonic molecules

Formation of muonic molecules and , where J is rotational quantum number, in electron conversion process is investigated at collision energies between 0.004 eV and 50 eV. Corresponding reaction rates are calculated in adiabatic approximation for the three-body Coulomb problem. Significant enhancement of the rates for and is found near 7 eV and 30 eV, respectively. It is shown that the enhancement is due to resonances present in elastic and scattering at these energies. Acceleration of dμ atoms up to the resonant energy could be realized in triple H-D-³He mixture due to the muon transfer from protium to deuterium. Experimental investigation of nuclear synthesis from molecular state directly formed in the mixture is suggested.     

The lifetime of the dimuon atom

Summary The weak decay of a muon in the ground state of a dimuon atom is analysed. Although the two muons are correlated by Fermi-Dirac statistics, it is shown that, in marked contrast to the seemingly analogous case of neutron beta-decay in³H, statistics have no effect on the muon decay rate. The distinction between the two cases is discussed. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

State-specified protonium formation in low-energy antiproton-hydrogen-atom collisions

We calculate state-specified protonium-formation cross sections in low-energy antiproton-hydrogen-atom collisions by solving the Chew-Goldberger-type integral equation directly instead of integrating the traditional differential scattering equation. Separating the incident wave from the total wave function, we calculate only the scattered outgoing wave propagated by the Green function. The scattering boundary condition is hence automatically satisfied without the tedious procedure of adjusting the wave function at the asymptotic region. The formed protonium atoms tend to be distributed in higher angular momentum l and higher principle quantum number n states as the collision energy increases. The present method has the advantage over the traditional ones in the sense that the required memory size and the computational time are much smaller, and accordingly the problem can be solved with higher accuracy.     

Evidence for the production of slow antiprotonic hydrogen in vacuum

We present evidence showing how antiprotonic hydrogen, the quasistable antiproton (p)-proton bound system, has been synthesized following the interaction of antiprotons with the molecular ion H2+ in a nested Penning trap environment. From a careful analysis of the spatial distributions of antiproton annihilation events, evidence is presented for antiprotonic hydrogen production with sub-eV kinetic energies in states around n=70, and with low angular momenta. The slow antiprotonic hydrogen may be studied using laser spectroscopic techniques.     

Renormalization of the two-photon vacuum polarization and the self energy vacuum polarization for a tightly bound electron

The renormalization method of Bogoljubov-Parasiuk-Hepp-Zimmermann (BPHZ) is used in order to derive the renormalized energy shift due to the gauge invariant K?llén-Sabry diagram of the two-photon vacuum polarization (VPVP) as well as the self energy vacuum polarization S(VP)E beyond the Uehling approximation. It is outlined, that no outer renormalization is required for the two-photon vacuum polarization and that only the inner renormalization has to be accomplished. It is shown that the so-called nongauge invariant spurious term is absent for a wide class of vacuum polarization (VP) diagrams if one applies the widely used spherical expansion of bound and free-electron propagator. This simplifies significantly calculations in bound state quantum electrodynamics. As one result of our paper the use of the BPHZ-approach in bound state QED is established. Received 28 September 2001     

Radiative Coulomb sum rules from a continuum-spectrum initial state

Summary Considering as the initial state a positive-energy wave function belonging to the continuum spectrum of a Coulomb field, we derive, using completeness for the discrete plus the continuum states, the total sum rule and, using other techniques, the radiative capture and the bremsstrahlung sum rules, which are of interest in exotic atoms, cooling processes and plasma physics. As a consequence, the inverse-bremsstrahlung sum rule, of interest in astrophysics, is also deduced. Introducing an average energy, we deduce the energy emitted by negative particles of densityN _e and statistical distributionf(V) after radiative atomic recombination with positive particles belonging to a system of densityN _i . The energy that is eventually absorbed in the inverse-bremsstrahlung process is likewise deduced.

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Riassunto Usando la completezza degli stati del discreto piú quelli del continuo e considerando come stato iniziale una funzione d'onda a energia positiva appartenente allo spettro continuo di un campo coulombiano, si calcola una regola di somma totale per i processi radiativi. Usando altri metodi, si calcola la regola di somma parziale di cattura radiativa e quella di bremsstrahlung, che sono di particolare interesse nel campo degli atomi esotici, nei processi di raffreddamento in acceleratori, in fisica del plasma. Si deduce come conseguenza anche la regola di somma di bremsstrahlung inversa, utile in astrofisica. Inoltre, introducendo un'energia media, si deduce l'energia emessa da particelle negative di densitàN _e aventi distribuzione statisticaf(V), dopo che si sono ricombinate radiativamente con particelle positive di densitàN _i . L'energia eventualmente assorbita nel processo di bremsstrahlung inversa è anche dedotta.

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Резюме Считая, что волновая функция начального состояния с положительной энергией прнадлежит непрерывному спектру Кулоновского поля, мы выводим, используя полноту дискретных плюс непрерывных состояний, полные правила сумм, используя другие методы, правила сумм для радиационного захвата и тормозного излучения, которые представляют интерес для экзотических атомов, процессов охлаждения и физики плазмы. Также выводится правило сумм для обратного тормпзного излучения, представляющее интерес в астрофизике. Вводя среднюю энергию, мы выводим энергию, излученную отрицательными частицами с плотностью и статистическое распредениеf(V) после радиационной атомной рекомбинации с положительными частицами, принадлежащими системе с плотностьюN _i . Также определяется энергия, которая поглощается в процессе обратного тормозного излучения.

     

Reciprocity in the electronic stopping of slow ions in matter

The principle of reciprocity, i.e., the invariance of the inelastic excitation in ion-atom collisions against interchange of projectile and target, has been applied to the electronic stopping cross section of low-velocity ions and tested empirically on ion-target combinations supported by a more or less adequate amount of experimental data. Reciprocity is well obeyed (within ~10%) for many systems studied, and deviations exceeding ~20% are exceptional. Systematic deviations such as gas-solid or metal-insulator differences have been looked for but not identified on the present basis. A direct consequence of reciprocity is the equivalence of Z₁ with Z₂ structure for random slowing down. This feature is reasonably well supported empirically for ion-target combinations involving carbon, nitrogen, aluminium and argon. Reciprocity may be utilized as a criterion to reject questionable experimental data. In cases where a certain stopping cross section has not been or cannot be measured, the stopping cross section for the inverted system may be available and serve as a first estimate. It is suggested to build in reciprocity as a fundamental requirement into empirical interpolation schemes directed at the stopping of low-velocity ions. Examination of the SRIM and MSTAR codes reveals cases where reciprocity is obeyed accurately, but deviations of up to a factor of two are common. In case of heavy ions such as gold, electronic stopping cross sections predicted by SRIM are asserted to be almost an order of magnitude too high.     

ATRAP antihydrogen experiments and update

Antihydrogen (Hbar) was first produced at CERN in 1995. Over the past decade our ATRAP collaboration has made massive progress toward our goal of producing large numbers of cold Hbar atoms that will be captured in a magnetic gradient trap for precise comparison between the atomic spectra of matter and antimatter. The AD at CERN provides bunches of 3 × 10⁷ low energy antiprotons approximately every 90 s. We capture and cool to 4 K, 0.1% of these in a cryogenic Penning trap. By stacking many bunches we are able to do experiments with 3 × 10⁵ Antiprotons. Approximately 100 positrons (e+)/s from a 22 Na radioactive source are captured and cooled in the trap, with 5 × 10⁶ available experiments. We have developed two ways to make Hbar from these cold ingredients, namely three-body collisions, and two-stage Rydberg charge exchange. We have also developed techniques to measure the excited-state distribution of the Hbar and measure their velocity. A new apparatus is being used this year that includes a e+ accumulator built at York University providing many more e+. The new antiproton annihilation detector provides spatial information of annihilations. Windows allow lasers to enter the trap for spectroscopic measurements and for laser cooling of the Hbar. Possibly the most exciting inclusion in this new apparatus is the inclusion of a neutral particle trap which may, for the first time, capture the Hbar and lead to the first atomic spectrum from antimatter.     

A moving magnetic mirror to slow down a bunch of atoms

A fast packet of cold atoms is coupled into a magnetic guide and subsequently slowed down by reflection on a magnetic potential barrier (`mirror') moving along the guide. A detailed characterization of the resulting decelerated packet is performed. We show also how this technique can be used to generate a continuous and intense flux of slow, magnetically guided atoms.     

Production of Entanglement of Multiple Three-Level Atoms with a Two-Mode Cavity

A scheme is proposed for generating maximally entangled states for two or more three-level atoms. In the scheme the atoms are sent through a two-mode cavity one by one and interact with the two-cavity modes sequentially. The required experimental techniques are within the scope of what can be obtained in the microwave cavity QED setup.     

Production of 87Rb Bose-Einstein condensates in a hybrid trap

We report a rapid evaporative cooling method using a hybrid trap which is composed of a quadrupole magnetic trap and a one-beam optical dipole trap. It contains two kinds of evaporative coolings to reach the quantum degeneracy: initial radio-frequency (RF) enforced evaporative cooling in the quadrupole magnetic trap and further runaway evaporative cooling in the optical dipole trap. The hybrid trap does not require a very high power laser such as that in the traditional pure optical trap, but still has a deep trap depth and a large trap volume, and has better optical access than the normal magnetic trap like the quadrupole-Ioffe-configuration (QUIC) cloverleaf trap. A high trap frequency can be easily realized in the hybrid trap to enhance the elastic collision rate and shorten the evaporative cooling time. In our experiment, pure Bose-Einstein condensates (BECs) with about 1 × 105 atoms can be realized in 6 s evaporative cooling in the optical dipole trap.     

压缩真空场与耦合双原子Raman相互作用过程中光场的相位演化特性

采用Pegg-Barnett相位理论，研究了压缩真空场与耦合双原子Raman相互作用过程中光场的相位演化特性.具体计算了场的相位概率分布函数及相位涨落，给出了在极坐标中概率分布变化曲线.讨论了原子与场相互作用、两原子间偶极-偶极相互作用以及原子初始状态对光场相位性质的影响. 关键词： 相位特性 压缩真空场 耦合双原子 Raman相互作用     

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     

Dynamics of antiproton cooling in a positron plasma during antihydrogen formation

We demonstrate cooling of 10⁴ antiprotons in a dense, cold plasma of 10⁸ positrons, confined in a nested cylindrical Penning trap at about 15 K. The time evolution of the cooling process has been studied in detail, and several distinct types of behavior identified. We propose explanations for these observations and discuss the consequences for antihydrogen production. We contrast these results with observations of interactions between antiprotons and “hot” positrons at about 3000 K, where antihydrogen production is strongly suppressed.     

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