Ramsauer-Townsend effect

The Ramsauer-Townsend effect is a physical phenomenon involving the scattering of low-energy electrons by atoms of a noble gas. Since its explanation requires the wave theory of quantum mechanics, it demonstrates the need for physical theories more sophisticated than those of Newtonian physics.

Definitions

When an electron moves through a gas, its interactions with the gas atoms cause scattering to occur. These interactions are classified as "inelastic" if they cause excitation or ionization of the atom to occur and "elastic" if they do not.

The "probability of scattering" in such a system is defined as the number of electrons scattered, per unit electron current, per unit path length, per unit pressure at 0°C, per unit solid angle. The "number of collisions" equals the total number of electrons scattered elastically and inelastically in all angles, and the "probability of collision" is the total number of collisions, per unit electron current, per unit path length, per unit pressure at 0°C.

Because noble gas atoms have a relatively high first ionization energy and the electrons do not carry enough energy to cause excited electronic states, ionization and excitation of the atom are unlikely, and the probability of elastic scattering over all angles is approximately equal to the probability of collision.

Description

The effect, which is also sometimes called the Ramsauer effect or the Townsend effect, is named for Carl Ramsauer (1879-1955) and John Sealy Townsend (1868-1957), who each independently studied the collisions between atoms and low-energy electrons in the early 1920s.

If we try to predict the probability of collision with a classical model that treats the electron and atom as hard spheres, we find that the probability of collision should decrease monotonically with increasing electron energy. However, Ramsauer and Townsend observed that for slow-moving electrons in argon, krypton, or xenon, the probability of collision between the electrons and gas atoms obtains a minimum value for electrons with a certain amount of kinetic energy (about 0.7 electron volts for xenon gas). This is the Ramsauer-Townsend effect.

No good explanation for the phenomenon existed until the introduction of quantum mechanics, which explains that the effect results from the wave-like properties of the electron. A simple model of the collision that makes use of wave theory can predict the existence of the Ramsauer-Townsend minimum. Bohm presents one such model that considers the atom as a finite square potential well.

Predicting from theory the kinetic energy that will produce a Ramsauer-Townsend minimum is quite complicated since the problem involves relativistic, electron exchange, and spin polarisation effects. However, the problem has been extensively investigated both experimentally and theoretically and is well understood (see Johnson).

References

* Bailey, V. A. and Townsend, J. S., "The motion of electrons in gases", Philosophical Magazine, S.6, 42 (1921), pp. 873-891.
* Bailey, V. A., and Townsend, J. S., "The motion of electrons in argon", Philosophical Magazine, S.6, 43 (1922), pp. 593-600.
* Bailey, V. A., and Townsend, J. S., "The abnormally long free paths of electrons in argon", Philosophical Magazine, S.6, 43 (1922), pp. 1127-1128.
* Bailey, V. A., and Townsend, J. S., "The motion of electrons in argon and in hydrogen", Philosophical Magazine, S.6, 44 (1922), pp. 1033-1052.
* Bailey, V. A., and Townsend, J. S., "Motion of electrons in helium", Philosophical Magazine, S.6, 46 (1923), pp. 657-664.
* Ramsauer, C., "Über den Wirkungsquerschnitt der Gasmoleküle gegenüber langsamen Elektronen", Annalen der Physik, 4, 64 (1921), pp. 513–540.
* Bohm, D., "Quantum Theory". Prentice-Hall, Englewood Cliffs, New Jersey, 1951.
* Brode, R. B., "The Quantitative Study of the Collisions of Electrons with Atoms", Rev. Mod. Phys. 5, 257 (1933).
* Johnson, W. R., and Guet, C., "“Elastic scattering of electrons from Xe, Cs⁺, and Ba²⁺", Phys. Rev. A 49, 1041 (1994).
* Mott, N. F., "The Theory of Atomic Collisions", 3rd ed. Chapter 18. Oxford, Clarendon Press, 1965.