Extension of the sum rule for the transition rates between multiplets to the multiphoton case D. Solovyev, L. Labzowsky, A. Volotka and G. Plunien Eur. Phys. J. D, 61 2 (2011) 297-304 Published online: 17 December 2010 DOI: 10.1140/epjd/e2010-10485-3