PHYSICAL REVIE% A VOLUME 2S, NUMBER S Comments Comments are short papers which comment on papers of other authors previously published in the Physical Review. Each Comment should followed, and page proofs are sent to authors. Electron-electron interaction in transition-metal X-rSQ CIIl1881011 8PCCtf 8 K. S. Srivastava, Shiv Singh, A. K. Srivastava, R. S. Nayal, Amita Chaubey, and Pratibha Gupta Theoretical Physics Division, Physics Department, Lucknow University, I. ucknow 226007 (U.P. ), India {Received 23 December 1980) An alternative explanation for the origin of the Kp' satellite of the Ep~ 3 x-ray emission line of the first transition elements Q1 &Z & 29) has been given using the Bohm and Pines theory of plasma oscillations in solids. The present calculated values for the energy separation (EE), and the relative intensity of the EP satellite with respect to the EP~ 3 x- ray emission line, agree better with the experimentally observed values than the values calculated by the exchange-interaction theory of Tsutsumi et al. , Salem et al. , and Ekstig et al. I. INTRODUCTION X-ray satelhtes are relatively weak lines often observed close to the main x-ray diagram lines. The energy of these lines cannot be expressed as the difFerence of two levels in the conventional energy-level diagram. For this reason these satel- lite lines are often called nondiagram lines. There exist a number of theories' which can satisfac- torily explain the origin of those x-ray satellites which are found on the high-energy side of the x- ray diagram lines, often abbreviated as high-energy satellites (HES). However, there is no theory which can account for the existence of the low-energy sa- tellites (I. ES) which are found on the low-energy side of the parent diagram line. In particular, the origin of the XP' satellite of the KPt 3 emission line, which have been observed by several work- ers ' in the elements (21 &Z &29) of the first transition series, lack proper explanation. Several researchers ' have proposed from time to time explanations for the origin of the XP' satel- lite. Tsutsumi, Parratt, 'o and Ekstig et ah. '3 have reviewed the various theories for the Kp' satellite; however, none of these theories can account satis- factorily for either the energy separation or the re- lative intensity. In this paper, we pmpose a theory based on plasrnon oscillations in solids and com- pare our results with earlier theoretical and experi- mental findings. II. PREVIOUS THEORIES Deodhar's theory based on double ionization and Sawada's theory invoking two-electron transi- tions were both rejected by Tsutsumi since the observed excitation voltage for the It. p' satellite is lower than what is predicted by both these theories. Parratt' proposed that the KP' satellite originated from 1s hole states with excited valence electron configuration (VEC) states but his hy- pothesis was disapproved by Schnopper, ' who stu- died the KP' satellite of ls hole states of Mn ori- ginating from E capture of Fe and found no difFerence to the emission from states produced with electron excitation. In the former case there would be little change in the efFective potential ex- perienced by the valence electrons and thus low probability for the production of VEC states com- pared with the electron excitation method. Coster and Druyvesteyns had proposed that the Ep' struc- ture originates from the interaction between a hole and the incomplete 3d shell. This hypothesis was extended by Tsutsumi and Tsutsumi et al. "' According to them the origin of the Ep' line is derived from the exchange interaction between the electrons in the incomplete 3d shell of elements in the first transition series and the hole in the incom- plete 3p shell, owing to the emission of the EP/ 3 line. Thus, the Xpt 3 and Ep' lines are emitted by transition to the states having the total spins equal $982 The Amcrjcan Physj~ Socjcty