Dramatic quadrupole effects in the low energy photoionization of the 4$s$ subshell of free and confined Ca

The importance of first-order nondipole effects in low-energy photoionization is well known [1], and, the significance of second-order [O($k^{2}r^{2})$, where $k$ is the photon wave number] nondipole terms has been stressed even at photon energies as low as $\sim $11 eV [2]. In the present work, valence dipole and quadrupole photoionization of free atomic Ca and @Ca (Ca atom trapped in a C$_{60}$ cage) are investigated using the relativistic random phase approximation (RRPA) [3]. In the vicinity of the 4$s$ Cooper minimum ($\sim $ 10 eV) [4], second-order nondipole terms are found to induce dramatic changes in the photoelectron angular distribution over a small energy range, primarily due to contributions from quadrupole-quadrupole interferences. Also, the calculation of the dipole angular distribution parameter $\beta $ in the vicinity of the dipole Cooper minimum requires the inclusion of the quadrupole terms, as was found earlier [2]. Finally, the results show that confinement of the Ca atom in the fullerene cage augments the quadrupole effects still further.\\[4pt] [1] W. R. Johnson \textit{et al}, Phys. Rev. A \textbf{59}, 3609 (1999). [2] G. B. Pradhan \textit{et al}, J. Phys. B \textbf{44}, 201001 (2011). [3] W. R. Johnson and C.D Lin, Phys. Rev. A \textbf{20}, 978 (1979). [4] J. W. Cooper, Phys. Rev. \textbf{128}, 681 (1962). Lett.\textbf{ 105}, 233002 (2010). [5] C. H. Zhang and U. Thumm, Phys. Rev. A \textbf{82}, 043405 (2010). [6] W. R. Johnson and C. D. Lin, Phys. Rev. A \textbf{20}, 964 (1979). [7] J. W. Cooper, Phys. Rev. \textbf{128}, 681 (1962).