Jörg Eichler

Relativistic Atomic Collisions

Introduction. Part I: Theoretical Methods. Relativistic Kinematics. Fields of Moving Charges. Relativistic Electron Motion. Ion-Atom Collisions. Part II: Elementary Atomic Processes. Excitation and Ionization. Ionization-Many Electrons. Charge Exchange. Radiative Electron Capture. Electron-Positron Pair Production. Part III: Experimental Methods. Charge-State Preparation. Target Arrangements. Cross Section Determination. Appendix. Bibliography. Index.

Theory of relativistic ion-atom collisions

Abstract Ion-atom collisions at relativistic beam energies constitute a new field of systematic experimental and theoretical studies. With the aid of sufficiently energetic heavy-ion beams, high stages of ionisation, including bare uranium nuclei, can be achieved, and these previously unavailable species can be used for further studies. Moreover, a wealth of collision phenomena can be studied either for their own theoretical interest, or as a way to produce highly stripped ions in specific states. In this review, we give a largely self-contained introduction to some general features of relativistic heavy-ion collisions and then proceed to a theoretical description of ionisation, of charge exchange, of a simultaneous treatment of excitation and charge transfer by the coupled-channel method, of radiative electron capture, and finally of electron-positron pair production. For all processes described, various theoretical approaches and their possible limitations are examined, comparison is made with existing experimental data, and attention is paid to the limit of extreme-relativistic collision energies.

QUADRUPLING AND PAIRING IN THE SHELL MODEL.

Abstract A system of Z protons and 4 N neutrons ( Z + N = even) moving in non-degenerate j -levels is treated for an isoscalar T = 1 pairing interaction and an effective four-body force. A classification scheme is introduced in which the basis states are explicitly classified with respect to the number of quadruples (systems of two pairs with J = 0, T = 1 coupled to T = 0) and the number of T = 1 pairs in each of the levels. For the particular case of two j -levels the system has been solved exactly. The two-particle transfer, the four-particle transfer and the four-particle scattering exhibit a phase transition between a normal and a superfluid phase. The superfluid phase is shown to consist mainly of quadruples, not pairs, even for a pure isoscalar pairing force. A quadrupling seniority scheme is discussed in close analogy to the pairing seniority scheme.

Asymptotic channels and gauge transformations of the time-dependent Dirac equation for extremely relativistic heavy-ion collisions

We discuss the two-center, time-dependent Dirac equation describing the dynamics of an electron during a peripheral, relativistic heavy-ion collision at extreme energies. We derive a factored form, which is exact in the high-energy limit, for the asymptotic channel solutions of the Dirac equation, and elucidate their close connection with gauge transformations which transform the dynamics into a representation in which the interaction between the electron and a distant ion is of short range. We describe the implications of this relationship for solving the time-dependent Dirac equation for extremely relativistic collisions. {copyright} {ital 1999} {ital The American Physical Society}

Photon angular distribution of Radiative Electron Capture into the M shell of He-like uranium ions at 110–140 MeV/u

Measurements of the photon angular distribution of Radiative Electron Capture into the M shell have been performed with He-like uranium ions in the range 110–140 MeV/u. In addition, L REC was studied at a projectile energy of 140 MeV/u. In both cases, the experimental data show an asymmetry around 90° and agree well with a fully relativistic theory.

QED in heavy few-electron ions

Abstract The influence of quantum electrodynamics in heavy ions is demonstrated. The contributions to the Lamb shift in hydrogen-like uranium are outlined, and quantum electrodynamical corrections to the radiative electron capture (REC) are investigated in the region of highly relativistic projectile energies by modifying the wave functions according to the Uehling potential. Exact relativistic calculations are employed for the radiative recombination. The deviation from non-QED calculations is found to amount to up to 2% in U 92+ for a projectile energy of 10 GeV/u and forward emission angles of the emitted photon.

REC investigations with the ESR storage ring at relativistic velocities

Using the experimental possibilities given by the ESR storage ring, it is possible to measure differential and total cross-sections for radiative electron capture by bare relativistic heavy ions. Exact relativistic calculations allow, e.g., for a unique identification of spin-flip processes and for an interpretation of two-step processes in terms of a strong alignment of the intermediate state.

Angular distribution of de-excitation X-rays from radiative electron capture in relativistic atomic collisions

Abstract In relativistic atomic collisions of high- Z ions with low- Z target atoms, radiative electron capture (REC) is one of the leading reaction channels. If the capture occurs into an excited state of the projectile, this state may decay by X-ray emission. The angular distribution of these decay X-rays with respect to the beam axis is calculated under the assumption that the REC photon escapes undetected. Angular distributions of REC-induced Lyman alpha lines are presently being measured.

Cross section determination

This chapter discusses experimental approaches to the determination of cross section in relativistic atomic collisions. Even though certain cross sections are related theoretically, such as excitation and ionization, quite different experimental methods may be used for their determination, such as projectile charge change for ionization and photon emission for excitation. It is found that ionization and capture cross sections, which are theoretically quite distinct, both can be measured by projectile charge change. Gaseous ionization detectors, scintillation detectors, and semiconductor detectors all have found application in relativistic atomic cross section determinations. For relativistic particles, two-dimensional position-sensitive particle detectors have a distinct advantage over simpler detectors because they allow online checking of beam focusing. A method has been developed to investigate collisions with scattering angles as small as 10 −8 rad, which is applicable to relativistic projectiles. The experimental techniques that have been used to obtain cross sections by photon detection are also elaborated.

Radiative electron capture in relativistic heavy-ion atom collisions

Abstract Based on systematic experimental studies and on exact relativistic calculations of the REC process in relativistic heavy-ion atom collisions, the limits of applicability of the nonrelativistic dipole approximation are discussed. In particular, direct comparison between a general REC scaling law and all available total electron-capture cross sections related to REC into bare and H-like ions is given. Similar to K-REC, a fortuitous agreement between the nonrelativistic approach and the experimental data is found. Moreover, the results of a dedicated L-REC experiment are presented, where this process was investigated for energy-resolved subshells. The measured angular distributions for REC into the j = 1 2 and j = 3 2 levels are in excellent agreement with exact relativistic calculations and manifest a complete breakdown of the nonrelativistic theory.