Observation of zeros and amplification of quadrupole-matrix-element contributions to photoelectron angular distributions

Abstract

We point out several possible observable features of quadrupole contributions to intermediate- and low-energy photoelectron angular distributions $\frac{d\sigma }{d\Omega }$, including zeros (Cooper minima) in the quadrupole-matrix elements. These features result in deviations from the dipole symmetry of $\frac{d\sigma }{d\Omega }$ about 90° (under $\theta \to \pi -\theta$) and include an oscillation with energy in distributions which vary from peaking forward and backward of 90°. The quadrupole contribution to photoelectron angular distributions can remain significant even for outer shells in the low-energy region, particularly when there are zeros (Cooper minima) in the dominant dipole-matrix elements. As an example we discuss the photoelectron angular distribution from the $5s$ subshell of tin and estimate the magnitudes of the deviations from symmetry which would be the experimental signatures of these features.