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

Abstract The two-centre wave-packet convergent close-coupling approach to ion–atom collisions is extended to study proton collisions with molecular hydrogen including electron-capture channels. We use a model potential to represent the molecular target as an effective one-electron spherically symmetric system. This greatly simplifies the target structure, allowing us to use already existing code developed for ion collisions with single-electron targets. Calculated total cross sections for electron capture, single ionisation, and excitation processes generally agree well with experimental data and other theoretical calculations where available. However, the total electron capture cross section is found to overestimate the experimental data at low energies, while the total ionisation cross section is slightly underestimated. Additionally, we present state-resolved cross sections for capture into the 1s, 2 $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> , and 3 $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> states of the projectile where deviation between various previous calculations is substantial. Our results lead to overall improvement over previous theoretical studies although discrepancies with experiment are observed for 3p and 3d capture. We conclude that treating molecular hydrogen as an effective one-electron system within the two-centre coupled-channel approach to one-electron targets can give reasonably accurate total cross sections at intermediate and high energies, without the need for a complex and computationally demanding two-electron target representation. 

/pdf/effective-one-electron-approach-to-proton-collisions-with-3tllw2ax.pdf

Effective one-electron approach to proton collisions with molecular hydrogen

The convergent close-coupling (CCC) method is applied to the calculation of electron–helium ionization doubly differential cross sections (DDCSs) at low to intermediate incident energies We re-examine the CCC calculations and measurements of Roder et al (1997 J Phys B: At Mol Opt Phys 30 1309–22) by making allowance for the step-function behaviour of the underlying CCC-calculated amplitudes As done previously, the experimental DDCS were normalized at energies below 100 eV using the 100 eV CCC calculation to determine analyser properties at several secondary energies In addition, substantially larger calculations are presented, to check the convergence The agreement between the experiment and the calculations as a whole is much improved on the situation reported earlier

Electron-impact ionization doubly differential cross sections of helium

The measurements of Bartsch et al (1992 J. Phys. B: At. Mol. Opt. Phys. 25 1511) of the left‐right spin asymmetry for elastic and inelastic scattering of polarized electrons from unpolarized indium atoms are compared with corresponding relativistic convergent close-coupling (RCCC) calculations over the full range of energies (1‐14 eV) and 5p 2 P o/2 → 5p 2 P o/2 ,5 p 2 P o/2 → 5p 2 P o/2 ,5 p 2 P o/2 → 6s 2 S1/2 and 5p 2 P o/2 → 6s 2 S1/2 transitions. There is very good agreement between theory and experiment for elastic scattering spin asymmetries. Some discrepancies still exist between the RCCC results and experiment for excited state spin asymmetries.

Relativistic convergent close-coupling calculation of spin asymmetries for electron-thallium scattering

/pdf/effective-one-electron-approach-to-proton-collisions-with-2zwmurzj.pdf

Triple-differential cross sections (TDCSs) for electron-impact ionization of He(1s{sup 2}){sup 1}S leading to He{sup +}(1s) are calculated using the highly accurate convergent close-coupling (CCC) method for incident projectile energies of 268.6 and 112.6 eV, with at least one of the outgoing electrons having an energy of 44 eV. These results are used to obtain absolute TDCSs from the recent experimental data [Bellm et al., Phys. Rev. A 75, 042704 (2007)] for TDCS ratios of ionization with no excitation to ionization with excitation resulting in He{sup +}(n=2,3,4). The TDCSs can be used as comparison benchmarks in future studies, and already allow us to test the accuracy of the TDCSs obtained from the hybrid distorted-wave+R-matrix (close-coupling) model, which was fairly successful in predicting the ratios, using CCC for n=1 and experimental results for n=2,3,4.

Igor Bray

Papers

Effective one-electron approach to proton collisions with molecular hydrogen

Electron-impact ionization doubly differential cross sections of helium

Relativistic convergent close-coupling calculation of spin asymmetries for electron-thallium scattering

Effective one-electron approach to proton collisions with molecular hydrogen

Absolute triple-differential cross sections for ionization-excitation of helium