Word maps in finite simple groups

Elements of the free group define interesting maps, known as word maps, on groups. It was previously observed by Lubotzky that every subset of a finite simple group that is closed under endomorphisms occurs as the image of some word map. We improve upon this result by showing that the word in question can be chosen to be in $$v(\mathbf F _n),$$ the verbal subgroup of the free group generated by the word v, provided that v is not a law on the finite simple group in question. In addition, we provide an example of a word w that witnesses the chirality of the Mathieu group $$M_{11}$$. The paper concludes by demonstrating that not every subset of a group closed under endomorphisms occurs as the image of a word map.     

Fully differential cross sections for photo-double-ionization of D2

We report the first kinematically complete study of the four-body fragmentation of the D2 molecule following absorption of a single photon. For equal energy sharing of the two electrons and a photon energy of 75.5 eV, we observed the relaxation of one of the selection rules valid for He photo-double-ionization and a strong dependence of the electron angular distribution on the orientation of the molecular axis. This effect is reproduced by a model in which a pair of photoionization amplitudes is introduced for the light polarization parallel and perpendicular to the molecular axis.     

Routes to control of H2 Coulomb explosion in few-cycle laser pulses

We have measured coincident ion pairs produced in the Coulomb explosion of H2 by 8-30 fs laser pulses at different laser intensities. We show how the Coulomb explosion of H2 can be experimentally controlled by tuning the appropriate pulse duration and laser intensity. For laser pulses less than 15 fs, we found that the rescattering-induced Coulomb explosion is dominated by first-return recollisions, while for longer pulses and at the proper laser intensity, the third return can be made to be the major one. Additionally, by choosing suitable pulse duration and laser intensity, we show H2 Coulomb explosion proceeding through three distinct processes that are simultaneously observable, each exhibiting different characteristics and revealing distinctive time information about the H2 evolution in the laser pulse.