Remarks On The Average Chord Length

A volume averaged chord length < R >, is suggested and some results concerning < R > and < R³ > are demonstrated. Usually when reference is made to the average chord length < t > we mean < l > = J J l(x_g, Ω)(n. Ω) ds dΩ / tts (1) S a-n>0 where (x. Ω) is the distance from ds on the surface to the surface S in the direction of Ω. This average chord length corresponds physically to the average path length traversed by particles current impinging homogeneously and isotropically on the surface of a vacuum volume. It is a well known⁽¹⁾ result that < l > = 4v/S, V being the volume and S the surface. Recently it has been shown that the same result holds if the vacuum is replaced by a pure scatterer. Another type of average chord length is also of interest in many cases in radiation physics. This is the average path length traversed by particles emitted from a homogeneous isotropic source in the volume. Such averages are considered in self absorption of nuclear sources. Let x be a point in the connected volume V and let R(x, Ω) be the distance from that point to the surface S in the direction Ω then < B > = f f R(x, dO n) g (2) kit V ^4lrV.