There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Annals of physics

Recoil-ion and electron momentum spectroscopy is a rapidly developing technique that allows one to measure the vector momenta of several ions and electrons resulting from atomic or molecular fragmentation. In a unique combination, large solid angles close to 4π and superior momentum resolutions around a few per cent of an atomic unit (a.u.) are typically reached in state-of-the art machines, so-called reaction-microscopes. Evolving from recoil-ion and cold target recoil-ion momentum spectroscopy (COLTRIMS), reaction-microscopes—the `bubble chambers of atomic physics'—mark the decisive step forward to investigate many-particle quantum-dynamics occurring when atomic and molecular systems or even surfaces and solids are exposed to time-dependent external electromagnetic fields. This paper concentrates on just these latest technical developments and on at least four new classes of fragmentation experiments that have emerged within about the last five years. First, multi-dimensional images in momentum space brought unprecedented information on the dynamics of single-photon induced fragmentation of fixed-in-space molecules and on their structure. Second, a break-through in the investigation of high-intensity short-pulse laser induced fragmentation of atoms and molecules has been achieved by using reaction-microscopes. Third, for electron and ion-impact, the investigation of two-electron reactions has matured to a state such that the first fully differential cross sections (FDCSs) are reported. Fourth, comprehensive sets of FDCSs for single ionization of atoms by ion-impact, the most basic atomic fragmentation reaction, brought new insight, a couple of surprises and unexpected challenges to theory at keV to GeV collision energies. In addition, a brief summary on the kinematics is provided at the beginning. Finally, the rich future potential of the method is briefly envisaged.

/pdf/recoil-ion-and-electron-momentum-spectroscopy-reaction-c7ai542e3l.pdf

Recoil-ion and electron momentum spectroscopy: reaction-microscopes

▪ Abstract Turbulence affects the structure and motions of nearly all temperature and density regimes in the interstellar gas. This two-part review summarizes the observations, theory, and simulations of interstellar turbulence and their implications for many fields of astrophysics. The first part begins with diagnostics for turbulence that have been applied to the cool interstellar medium and highlights their main results. The energy sources for interstellar turbulence are then summarized along with numerical estimates for their power input. Supernovae and superbubbles dominate the total power, but many other sources spanning a large range of scales, from swing-amplified gravitational instabilities to cosmic ray streaming, all contribute in some way. Turbulence theory is considered in detail, including the basic fluid equations, solenoidal and compressible modes, global inviscid quadratic invariants, scaling arguments for the power spectrum, phenomenological models for the scaling of higher-order structu...

http://www.ifa.hawaii.edu/%7Ereipurth/reviews/elmegreen1_araa.pdf

Interstellar Turbulence I: Observations and Processes

Cold Target Recoil Ion Momentum Spectroscopy: a &momentum microscope' to view atomic collision dynamics

We consider positron scattering on the alkali-metal atoms of Li, Na, and K at very low energies, where only the elastic scattering and positronium formation in the ground state are the two open channels. Utilizing the recently developed two-center convergent close-coupling method [Lugovskoy, Kadyrov, Bray, and Stelbovics, Phys. Rev. A 82, 062708 (2010)] we investigate the behavior of the cross sections as the impact energy goes to zero and demonstrate their convergence. The study sets quantitative benchmarks for any rigorous theoretical treatment of the collision problems.

/pdf/threshold-behavior-of-positronium-formation-in-positron-1s5f9bn6q1.pdf

Threshold behavior of positronium formation in positron-alkali-metal scattering

The R matrix with pseudostates and convergent close-coupling methods are applied to the calculation of excitation and ionization cross sections for the simplified S-wave model of e-He{sup +} scattering. Very good agreement is obtained between the results of the two methods. Furthermore, the problem of Rydberg series of pseudoresonances, converging to the unphysical positive-energy states in the continuum, is shown to be almost negligible if large basis sizes or simple averaging procedures are used. {copyright} {ital 1997} {ital The American Physical Society}

S-wave model for e-he+ scattering

We have extended the convergent close-coupling method to investigate electron scattering from the vibrationally excited molecular hydrogen ion H${{}_{2}}^{+}$, within the Born-Oppenheimer approximation. Results are presented for proton-production and dissociative-ionization cross sections. The comparison with experiment is excellent across the energy range from near threshold to 1 keV.

Calculations of electron scattering from H2

S-wave model for H-like ions

The close-coupling theory of electron-impact ionization of helium is studied. It is found that the ``raw'' convergent close-coupling equal-energy-sharing amplitudes converge to half the required amplitudes. As in the $e\ensuremath{-}\mathrm{H}$ case, solving the close-coupling equations yields amplitudes that behave as results of a finite Fourier expansion of a step function. We argue that the close-coupling formalism readily solves the $e\ensuremath{-}\mathrm{He}$ ionization problem with equal-energy outgoing electrons at all practical incident energies, and demonstrate it at the most difficult kinematic case of 2 eV above threshold.

/pdf/close-coupling-approach-to-electron-impact-ionization-of-2axannvtpq.pdf

Igor Bray

Papers

Threshold behavior of positronium formation in positron-alkali-metal scattering

S-wave model for e-he+ scattering

Calculations of electron scattering from H2

S-wave model for H-like ions

Close-coupling approach to electron-impact ionization of helium