24 



There is one case, other than the interaction of electrons with isolated mol- 

 ecules, that is known quite well. That is the loss of energy of a moving electron 

 to lattice oscillations in penetrating a polar solid such as an ionic crystal. This 

 case is not entirely dissimilar to those that I mentioned previously and is, in- 

 deed, in some respects closer to the case of an electron in water than either of 

 them. For this problem, which is of the greatest importance in many aspects 

 of the physics of solids, there is a quite adequate theory developed by Frohlich 

 (4). 



ONSAGER: There is some recent work on dielectric breakdown. 



PLATZMAN: We shall not be concerned with dielectric breakdown. The 

 over-all picture of dielectric breakdown involves a great deal more than what 

 we require here and it is still not a little obscure. Fortunately, it is one of the 

 things we don't have to worry about. _ 



If we consider our single electron to have kinetic energy W, then Frohlich 

 has derived an expression for the rate of energy loss, - dW/dt. When I refer 

 to the rate of energy loss I mean, literally, rate of energy loss and not -dW/dx. 

 This theory applies immediately, of course, to polar solids, but has to be mod- 

 ified drastically if one wishes to apply it to the case of an electron penetrating 

 water. This I have tried to do in a crude way. I think the result is probably 

 correct to within an order of magnitude, and it gives the following: 



13 

 (-dW/dt) ^-,10 ev/sec 



at an energy of several ev. For lower energies -dw/dt increases as l/v. 

 This will be the contribution to the rate of energy loss of the electron arising 

 from the loss of oscillational quanta to the medium. This means excitation of 

 molecular vibrations. It is evaluated numerically for the case of liquid water. 



ONSAGER: Could that be rather closely correlated with the infrared ab- 

 sorption of water? 



PLATZMAN: Yes. 



ALLEN: Has this result something to do with the size of the permanent 

 dipole moment? 



PLATZMAN: Yes. I am, in effect, assuming that each molecular vibra- 

 tion corresponds to a certain component of the spectrum of lattice vibrations of 

 a crystal. 



ONSAGER: This order of magnitude involves the motions which can take up 

 energy here, the motions of hydrogen atoms relative to the oxygens, and pri- 

 marily the vibrations. I think the hydrogen atoms here could be very nearly 

 free atoms. 



PLATZMAN: A further point about this result is that it applies only down 

 to a certain minimum velocity. When the electron's energy goes below that of 

 the first oscillational level of the water molecule it cannot lose any more en- 

 ergy in this manner. The quantity dW/dt goes to zero. Indeed, it in fact be- 

 comes positive -- about 10 11 ev/sec. That is to say, there will be a certain 

 tendency for electrons to acquire energy from the oscillations. In somewhat 



