LOW-DEGREE POLYNOMIAL PHASE-FUNCTIONS WITH HIGH G-VALUE

In an attempt to construct an analytic theory of anisotropic random fl ight, the need has arisen to construct phase-functions for which the e xpansion in spherical harmonics has only a limited number of terms, bu t which have a high value for the asymmetry parameter g. We describe t he procedure to find the phase-function which has a maximum value of g for given N, where N is the number of spherical components of the pha se-function. It appears that in order to attain g = 0.9, one needs a p hase-function composed of at least nine spherical components, or equiv alently a polynomial of degree nine.