Quadrupole effects in the photoionization of sodium 3s in the vicinity of dipole Cooper minimum

We present a study on the impact of quadrupole transitions on the asymmetry parameter for the 3s photoionization of Na atom. The nondipole parameters are derived from the general formulation of angular distribution of photoelectrons developed by Keh-Ning Huang (KH) [1], which is based on Jacob and Wick's helicity formulation [2]. The required transition amplitudes for these calculations are obtained from RATIP [3], which is based on KH formulation. The wavefunctions of the initial and ionized state of the system are obtained from GRASP [4]. We compare and contrast Johnson, Lin [5] and Derevianko et.al’s [6] formulation with that of KH formulation and show that for closed shell atoms the two formulations are equivalent. [1] Huang, K. N. Phys. Rev. A 1980, 22, 223. [2] Jacob, M., Wick, G. C. Ann. Physics 1959, 7, 404. [3] S. Fritzsche, Comput. Phy.s Commun. 2012, 183, 525. [4] Parpia F. A., Fischer C. Froese, and Grant I. P., Comput. Phy.s Commun. 1996, 94, 249. [5] Johnson W. R. and Lin C. D. Phys. Rev. A 1979, 20, 964. [6] Derevianko A., Johnson W. R. and Cheng K. T., ADND, 1999, 73, 153.