Fast Track Communication

Abstract Photoionization of Mg 3s is studied near the Cooper minimum in dipole channels using the relativistic-random-phase approximation. While the importance of first-order nondipole effects on photoelectron angular distributions at low energies is well known, it is reported here for the first time that in the energy region near the dipole Cooper minimum, quadrupole transitions are not just important, but actually dominate the total photoionization cross section. Studies of dipole-dipole, dipole-quadrupole and quadrupole-quadrupole interference terms in the photoelectron angular distribution show that in the region of dipole Cooper minimum even the calculation of the dipole angular distribution parameter, β, requires the inclusion of quadrupole channels. The significance of second-order [O(k 2 r 2 )] nondipole terms, primarily due to the contributions from electric quadrupole-quadrupole interference terms at photon energy as low as ∼11 eV, are shown to induce dramatic changes in the photoelectron angular distribution over a small energy range

Coexistence does not imply joint measurability

Abstract One of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously, in stark contrast to classical physics. In this context the notions of coexistence and joint measurability are employed to analyze the possibility of measuring together two general quantum observables, characterizing different degrees of compatibility between measurements. It is known that two jointly measurable observables are always coexistent, and that the converse holds for various classes of observables, including the case of observables with two outcomes. Here we resolve, in the negative, the open question of whether this equivalence holds in general. Our resolution strengthens the notions of coexistence and joint measurability by showing that both are robust against small imperfections in the measurement setups