ANGULAR-MOMENTUM AND HEISENBERG CORRESPONDENCE PRINCIPLE .3. ROTATIONMATRIX-ELEMENTS

Heisenberg's correspondence principle is applied to the matrix element s of the rotation operator, in this way, an approximation for the redu ced rotation matrix elements d(M'M)J(theta) in terms of Bessel functio ns is obtained. It is shown that two distinct approximate forms are ne cessary to give sufficient accuracy over the entire range 0 to pi of t he angle theta if the approximation is to be of value. The two forms a re most accurate for theta near 0 and pi respectively, deteriorating a s theta = pi/2 is approached; however, they retain a surprising degree of accuracy over the full range, particularly when (M'-M) is small an d J large, the case for which the exact expression is most complex. Ta ken in conjunction with the results of the previous papers in this ser ies, the present work allows Bessel function approximations to be obta ined for both Clebsch-Gordan and Racah coefficients; indications as to the likely accuracy of such approximations are given.