“…From multiple scattering theory the nonchanneled yield is given by min ϭP(˜c ,m), with the reduced critical angle ˜c given by ˜c ϭaE 1/2 /8 ⑀ 0 Z 1 Z 2 e 2 , where E is the energy of the beam and 1/2 is given by Barrett's critical half-width c B . 10 The fraction P(˜c ,m) of particles scattered outside the reduced critical angle ˜c is given by P(˜c ,m)ϭ͐ ˜c ϱ f 1 (m,˜)˜d˜, which can be determined from numerical integration of the f 1 tables in Sigmund and Winterbon. 11 With c B ϭ7.5 and 5.7 mrad for 2 and 3.5 MeV He ϩ ions in Si, respectively, the values of P(˜c ,m) are about 0.04 and 0.02 for 2 and 3.5 MeV, respectively.…”