Four-electron break-up geometries in beryllium

The two fixed points associated with the Coulomb singularity of a four-electron atom give rise to the highest symmetry four-electron escape geometries, i.e., a regular tetrahedron and a square. We analyze the non-linear properties of the fixed points and discuss how these properties allow for prevailing break-up patterns that are different than the generally expected ones of highest symmetry. Indeed, it was recently shown in Emmanouilidou and Price (2013) [1] that the prevailing break-up geometry in single photon quadruple ionization from the ground state of Be is a triangular pyramid. Moreover, using a previously introduced collision classification scheme we identify the collision sequences that are consistent with the regular tetrahedron and the square planar break-up geometries in single photon quadruple ionization from the ground state of Be. To illustrate the collision sequences contributing the most we plot the probability density of the inter-electronic angles.