Calculations of the cascade characteristics for hadronic hydrogen atoms based on a quantum-classical approach

The quantum–classical Monte Carlo cascade calculation model for the muonic (non-hadronic) hydrogen atom has been modified for exotic pK ^??? and $p\bar p$ atoms with strong interaction. The radiative and collision transitions were taken into account only because in such a case of “heavy” atoms the effects of exotic molecule formation are not essential. The radiative cascade was considered within the framework of quantum mechanics whereas the collisions of exotic atoms in excited states with hydrogen were described by methods of classical mechanics. The yields for the K-series X-rays in pK ^??? and $p\bar p$ atoms have been calculated and compared with the experimental data.     

On the formation of exotic atoms

A general disagreement exists between theory and experiment in the field of formation and decay of muonic and pionic atoms. Allowing for collisional processes in the deexcitation of heavy exotic atoms can substantially change the interpretation of experimental Coulomb-capture ratios, particularly of those measured by the muonic X-ray method.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.The author is grateful to Prof. F. Measday (Univ. of British Columbia, Vancouver, Canada) and Dr. J. Révai (C. R. I. P., Budapest) for illuminating discussions.     

μ −SR-Spectroscopy on light neutral muonic atoms

In the past few years ^–SR-spectroscopy has been successfully applied to the simple muonic atoms, namely muonic helium: He ^–e^–. Here the theoretical and experimental progress in understanding this atomic system consisting of a nucleus, a muon and an electron is reviewed. The various effects contributing to the ground state hyperfine structure are explained. The experiments are described and are compared with the theoretical calculations.     

应用光核反应计算μ原子中的核极化效应

近年来,瑞士保罗谢勒研究所的CREMA合作组通过测量$\mu$氢原子兰姆位移显著提升了质子半径的测量精确度。然而这一新实验结果与已知质子半径标准值(CODATA)相差5.6个标准差,被称为质子半径之谜,受到众多物理学家的关注。受此启发,CREMA合作组在不同的$\mu$原子中展开了一系列兰姆位移光谱的测量实验。他们计划从这些$\mu$原子的测量中得到轻核(包括$^{2,3}{\rm{H}}$,$^{3,4}{\rm{He}}$)的电荷半径。除了对光谱测量精度的要求外,轻核半径的实验精度当前仍被一项理论输入量限制:核极化效应对$\mu$原子光谱的修正。核极化效应体现了$\mu$子与原子核进行双光子交换中对核的虚激发,进而对$\mu$原子能谱产生高阶修正。因此,这一效应与光核反应以及康普顿散射直接相关。核极化效应对兰姆位移的修正可通过计算光核吸收截面以及虚光子康普顿振幅的求和规则而得到。本工作运用第一性原理的核结构计算方法,研究了$\mu$原子中的核极化效应。通过结合现代核力模型与超球简谐基展开多体方法,计算了一系列与核极化相关的光核反应及康普顿散射求和规则。这一理论研究为从$\mu$原子光谱测量中对核半径的精确提取提供了关键性的理论输入。     

Collisional problems in the μCF cycle before muonic molecule formation

Important processes in the muon-catalyzed fusion cycle preceding muonic molecule formation are discussed. These include muonic atom formation as well as the subsequent elastic, isotopic-exchange, and hyperfine-state quenching collisions of the muonic atoms. Modern methods for atomic capture of the negative muon are reviewed. Elastic and inelastic cross sections obtained in the improved adiabatic representation are given, and rates at liquidhydrogen density are tabulated for easy reference and comparison.     

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.     

Challenge towards muonic atom formation with unstable nuclei

X-ray spectroscopy of muonic atoms is an important tool to obtain information on the nuclear charge distribution of nuclei. It has been successfully used for many years to study stable isotopes in condensed or gaseous states. A new method has been proposed to extend muonic atom X-ray spectroscopy to the use of radioactive isotope beams to form muonic atoms with unstable nuclei. This new method allows studies of the nuclear properties and nuclear sizes of unstable atoms by means of the muonic X-ray method at facilities where both negative muon and radioactive nuclear beams would be available. Progress of a feasibility study at RIKEN-RAL muon facility is also reported. Received: 1 May 2001 / Accepted: 4 December 2001     

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.     

Development Towards Muonic Atom Formation with Unstable Nuclei

We report on the latest development of a new method for extending muonic atom X-ray spectroscopy to the use of radioactive isotope beams to form muonic atoms with unstable nuclei. This would allow studies of the nuclear properties and nuclear sizes of unstable atoms by means of the muonic X-ray method at facilities where both negative muon and radioactive nuclear beams would be available. Progress of a feasibility study at RIKEN-RAL muon facility is also reported. This revised version was published online in August 2006 with corrections to the Cover Date.     

High precision X-ray spectroscopy in hydrogen-like fermionic and bosonic atomic systems

Some time after its formation an exotic atom may be considered a hydrogen-like system consisting of a nucleus and an exotic particle in a bound state. In this situation it is an ideal tool to study cascade properties, while for the innermost orbits it can be used to probe the interaction with the nucleus. From an extended series of experiments using high resolution X-ray spectroscopy for both aspects typical examples are reported and preliminary results are given: 1. To determine the complex scattering length in H the hyperfine transitions have been measured. 2. To determine the pion mass the 5 4 transitions in N have been studied. In all cases a major contribution to the uncertainty originates from the calibration. Therefore a new method is proposed that will establish a universal set of high precision calibration lines for pionic, muonic and electronic systems. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Study of muonic hydrogen transport in TRIUMF experiment 742 by the Monte Carlo method

A technique of neutral muonic atom beams is proposed in the TRIUMF E742 experiment for measuring the scattering cross sections of muonic hydrogen isotopes in solid hydrogen. We present the results of Monte Carlo modeling of pµ and dµ atoms transport under the conditions of this experiment, taking into account the main physical as well as the geometrical aspects. The optimization of set-up parameters is performed in order to choose the most sensitive experimental conditions.     

Classification scheme for resonant states of muonic molecules

We have performed a hyperradial-adiabatic one-state calculation of resonant states of (dd)⁺ and (dt)⁺ below then=2 level of the muonic atoms. The results are used for a new classification scheme of these states. Comparing our calculation with a recent full variational calculation by Hara and Ishihara and opposing our findings to the analysis of Shimamura we demonstrate that the classical Born-Oppenheimer classification scheme can be misleading. The symmetry-adapted hyperradial-adiabatic potential curves provide better grounds for the classification procedure.     

The effect of alignment of the exotic atom orbital angular momentum on depolarization of negative muons

The theory of cascade depolarization of negative muons is generalized to the case where the orbital angular momentum of a meson becomes aligned as a result of its atomic capture. An explanation of the experimental data on the residual polarization of ^– in helium is proposed on the basis of the developed theory and available arguments in favour of the possible existence of alignment of the orbital angular momentum in the lightes exotic atoms. An angular distribution and linear polarization of muonic X-rays is considered. The connection between these characteristics and the depolarization factor due to the alignment of the orbital angular momentum enables one to make a direct experimental test of the proposed explanation of the residual polarization of muons in helium.     

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.     

Hyperfine structure of light exotic atoms

Recoil corrections to the hyperfine structure of light exotic atoms, including the effect of the anomalous magnetic moment are calculated for light muonic and baryonic atoms. In the case of muonic atoms, the effects of recoil and finite nuclear size are significant in view of the presently attainable experimental precision.     

Time-of-flight measurement of resonant molecular formation in muon-catalyzed dt fusion

Preliminary results are reported for an experiment at TRIUMF where a time-of-flight technique was tested for measuring the energy dependence of the rate for muon-catalyzed dt fusion. Muonic tritium atoms were created following transfer of negative muons from muonic protium in a layer of solid hydrogen (protium) containing a small fraction of tritium. The atoms escaped from the solid layer via the Ramsauer-Townsend mechanism, traversed a drift region of 18 mm, and then struck an adjacent layer of deuterium, where the muonic atom could form a molecular system. The time of detection of a fusion product (neutron or alpha) following muon arrival is dependent upon the energy of the muonic tritium atom as it traverses the drift region. By comparison of the time distribution of fusion events with a prediction based on the theoretical energy dependence of the rate, the strength of resonant formation can in principle be determined. The results extracted so far are discussed and the limitations of the method are examined.     

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.     

Exotic hyperons: Theoretical status and search perspectives in hyperon beam facilities

The theoretical models that predict the existence of exotic hyperons made of more than three quarks are reviewed. We present the properties of exotic hyperons with strangenessS=–1 (quark contents ),S=–2 ( ) andS=–3 ( ) predicted by the sum rules for reggeon-particle scattering amplitudes. The inclusive cross sections for the production of these hyperons in hyperon-proton interactions are calculated. The cross sections turn out to be of the order of millibarns, thus opening a good perspective to encounter such exotic hyperons in the available hyperon beam facilities at CERN and FNAL.We also propose to study the Regge trajectories corresponding to the exotic hyperons, analyzing the inclusive spectra of andK mesons produced in hyperon-proton collisions.     

Control of Non-Neutral Plasmas and Generation of Ultra-Slow Antiproton Beam

The Antiproton Decelerator (AD) devoted primarily to atomic physics experiments has been stably operated since 2000. Until now, three proposals have been approved, two of which are on the production and spectroscopy of antihydrogen, and the third one is on atomic collisions and precision spectroscopy of antiprotonic atoms, ASACUSA collaboration. One of the unique features of the ASACUSA collaboration is to develop intense slow and ultra slow antiproton beams of high quality, which will open a new multidisciplinary field involving atomic physics, nuclear physics and elementary particle physics. The ultra slow antiprotons will be prepared by combining the AD (down to 5.3 MeV), the RFQD (Radio Frequency Quadrupole Decelerator) (down to several tens keV), and an electron cooling device which will be called “MUSASHI” (Monoenergetic Ultra Slow Antiproton Source for High-precision Investigations) (down to several eV). MUSASHI produces the eV antiproton beam through an electron cooling of trapped antiprotons and a radial compression followed by an extraction through a transport beam line. The transport beam line is specially designed so that the pressure at the trap region can be maintained more than six orders of magnitude better than the collision region and at the same time the transport efficiency is kept at almost 100%. The ultra slow antiproton beam allows for the first time to study collision dynamics such as antiprotonic atom formation and ionization processes under single collision conditions, and also to study spectroscopic nature of various metastable antiprotonic atoms such as p, He⁺, He⁺⁺, etc. Metastable p are particularly interesting because they allow to make high precision spectroscopy of two body exotic atoms. Production and spectroscopy of antiprotonic atoms consisting of unstable exotic nuclei will also be discussed. This revised version was published online in August 2006 with corrections to the Cover Date.