Elementary processes with two quantum transitions

The first part of this work considers the coaction of two photons in an elementary process. With the help of Dirac’s dispersion theory, the probability of a process analogous to the Raman effect, namely the simultaneous emission of two photons, is calculated. It appears that a nonzero probability exists that an excited atom divides its excitation energy into two photons, whose energies in sum prove to be the excitation energy but are otherwise arbitrary. When light falls upon the atom with a frequency smaller than the corresponding atomic eigenfrequency, another stimulated double emission occurs during which the atom divides its energy into one incident and one frequency-difference photon. Kramers and Heisenberg have calculated the probability of this last process according to the correspondence principle. Additionally, the reversal of this process is considered, namely, where two photons whose frequencysum equals the excitation frequency of the atom co-act to excite the atom. Furthermore the behavior of an atom toward scattering particles when it simultaneously has the opportunity to spontaneously emit light is examined. Experimentally, Oldenberg finds a broadening of the resonance line of mercury when he lets the excited atoms collide repeatedly with slow particles. He interprets this through the assumption that a positive or negative part of the excitation energy can be transferred as kinetic energy to the colliding particle, and that the frequency-difference photon is emitted. For this process, a formula analogous to the Raman effect and the double-emission, respectively, is derived here. Finally, in connection with Franck’s work, an attempt is made to explain the excitation-intensity’s behavior of spectral lines through collisions with fast electrons via such a double-process. Franck discusses the behavior of the excitation function of a spectral line, i.e., the intensity as a function of the velocity of the incident electrons. This function is zero for small velocities, until the kinetic energy of the electrons becomes equal to the excitation energy of the respective initial state of the line. It then increases strongly, reaches a maximum at a velocity corresponding to just a few volts above this critical voltage, and then decreases again to zero. This part of the curve has repeatedly been calculated with the ordinary collision theory. One obtains a curve which represents the phenomena well, especially the sudden onset of the function at the critical voltage. For large velocities, the theoretical curve yields a monotonic