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

In this work we show that in order to calculate spin asymmetries at projectile energies above the ionization threshold, the target continuum needs to be taken into account. However, we demonstrate that this does not imply that in the experiment intermediate excitation into the continuum plays a major role. Rather, any theory, such as the standard close-coupling method, that does not allow for electron flux to be in all open channels is likely to have difficulty in reproducing the measured spin asymmetries.

Calculations of spin asymmetries in electron-alkali scattering

The simplified model of electron-hydrogen atom scattering which has all orbital angular momenta set to zero is solved to convergence at a range of energies from 1 to 400 eV using a general coupled-channel approach. The results are in complete agreement with the solution of this problem by Poet using a method that is applicable to this model only. The corresponding singlet and triplet T-matrix elements for the transitions from the ground state to each one of 1s, 2s, and 3s states are presented in tabular form. The 1s, 2s, 3s, ionization, and total cross sections are also presented for each energy.

Simplified model of electron scattering on atomic hydrogen

The Laguerre-based convergent close coupling method is used to calculate the electron-impact excitation cross sections of the auto-ionizing states 2s2s1S, 2s3s1S and 2s3s3S, various ionization, as well as other cross sections for scattering from the 11S, 2 1S and 23S initial states of helium. The calculations are done within the S-wave model. Unlike the case of bound-state excitation, convergence studies need to take into account occasional mixing between the core manifolds which can severely affect the structure of the auto-ionizing states and those corresponding to ionization with excitation. A method to take this into account is given and it is shown that convergent results may be obtained, Comparison with the 'Z = 2' time-dependent calculations of Pindzola et al (1999 Phys. Rev. A 59 4390-8) is satisfactory.

Electron-impact helium double excitation within the S-wave model

We propose a model for the triple photoionization of Be in which a core 1s electron absorbs the photon γ + 1s22s2Be → 1p + 1s2s2Be+ and the valence 2s2 electrons are shaken off into continuum due to the sudden change of the core potential. We decompose the double shake-off amplitude into a single shake-off 2s2 → nss and a subsequent electron impact ionization of the doubly charged Be2+ ion s + 1sns Be2+ → 2l + 3l + 1s Be3+. The latter process is described by the T-matrix of inelastic electron scattering on the 'semi-hollow' 1sns Be2+ ion in the monopole singlet channel. The convergent close-coupling method is used to evaluate the T-matrix.

https://iopscience.iop.org/article/10.1088/0953-4075/36/13/103/pdf

Double shake-off model for the triple photoionization of beryllium

We compare the results obtained in a variety of numerical calculations for electron impact ionization of the 2s subshell in Ne and the 3s subshell in Ar. Comparison with the recent joint experimental and theoretical study by Kheifets et al (2009 J. Phys. B: At. Mol. Opt. Phys. 42 165204) shows good agreement with the calculations reported there, provided a similar theoretical model is used. The numerical results, however, become severely model dependent in certain cases, thus providing a major challenge to the theoretical treatment of such ionization processes.

Igor Bray

Papers

Calculations of spin asymmetries in electron-alkali scattering

Simplified model of electron scattering on atomic hydrogen

Electron-impact helium double excitation within the S-wave model

Double shake-off model for the triple photoionization of beryllium

A detailed study of electron impact ionization of Ne(2s) and Ar(3s)