Experimental Evidence for the Collective Nature of the Characteristic Energy Loss of Electrons in Solids–Studies on the Dispersion Relation of Plasma Frequency–

The energy loss of 25 kv electrons was studied by a modified velocity analyzer of Möllenstedt type. By means of the analyzer we obtained the diagram which shows the variation of energy loss with the scattering angle. The specimens studied were Be, Mg, Al, Ge and C (graphite). In the diagram we classified six types of patterns in which two are of the fundamental importance: (1) The first type is the sharp energy loss lines such as first discovered for Al and Be by Ruthemann. In the present experiment it was found that the value of energy loss of these lines increases with the scattering angle. To represent this relation an empirical formula was established. On the other hand, a theoretical formula was derived from the dispersion relation in Bohm-Pines' plasma oscillation theory. These two formulas are in good agreement for the lines of Be (19 ev), Mg (10.3 ev) and Al (14.8 ev). This agreement proves most decisively that the sharp lines are caused by the excitation of the collective plasma oscillation. For Ge (16.4 ev) and C (7.3 ev) the agreement is less perfect. (2) The lines of second type are observed at 23 ev for Al and 25 ev for C. They are rather diffuse and their energy losses do not vary with the scattering angle. The author attributes them to the excitation of individual electrons in energy bands. The value 23 ev for Al is in agreement with the energy difference between the large peaks in the fine structure of L-absorption edge. According to the theory the curving and the position of the patterns in the first type are insensitive to the temperature of the specimen, being in agreement with the experiment.