Rc he aan nmcak anlers o cae ae Es mallee ME de ee dea te 207 INELASTIC-SCATTERING CROSS SECTIONS OF FAST CHARGED PARTICLES BY Li * Y.-K. Kim and Mitio Tnokutt TABLE 70. Paramerers ror tir BETHE Cross SECTIONS oF Lit The eross sections for some important discrete excitations and for the total inelastic scattering of fast charged particles by Lit are evaluated directly from correlated wave functions and other data in the literature according to the Bethe procedure and related sum rules. Cross sections for other discrete excitations are determined by extrapolating their dependence on the effective quantum numbers, The ionization cross section is then obiained by subtracting the sum ofall discrete excitation cross sections from the total inelastic scattering cross section, thus avoiding the direct use of any continuum wave functions. The resulting ionization cross section is reliable, and agrees very well with the experiment by Peart and Dolder. The total inelastic-scattering cross section ot for sufficiently fast charged particles of charge ze and . se 1, 2) velocity v is given by‘ _ a| 4 Cos) a) Stor = Sais (Mn jin (#,) where dp is the Bohr radius, m the electron mass, R the Rydberg energy, and 8 = v/c, c being the speed oflight. The constants Mio. and Ciot can be evaluated from the ground-state wave function and the optical (dipole) oscillator strength distribution of the target system.” The ground-state wave function of Li” computed by Weiss” leads to Jfj.1 = 0.2860, in complete agreement with a more accurate result of Pekeris.“’ The value ZT, — I, = 0.6280 (in the notation of Reference 2) obtained from the Weiss wave function should, therefore, be very reliable. Furthermore, a value of £(--1) 0.526 + 0.015 [see Reference 2 for the definition of L(~1)] was adopted on the basis of the oscillatorstrength distribution in the literature.” The value of Cor = —2L(-1) th -ht+ Mice In (2me"/R) is given in Table 70. The Bethe cross sections for discrete excitations are also given by” In = Cc Total 0.2860 2.787 Discrete excitation 0.1414 1.224 Tonization 0. 1446 1.563 ean be calculated from wave functions directly (sce Sec. 5 of Reference 8). Weiss” calculated for Lit very accurate wave func- tions not only for the ground state but also for the 2’S, 2'P, 3'S, 3'P and 3'D states, and Perkins” computed correlated wave functions for the 4.5, 5S, 64S and 7148 states with similar accuracy. From these wave functions one can evaluate accurate Bethe cross sections for the excitations to the above-mentioned discrete states and eventually to higher discrete states by extrapola- tion. The values of Jf;,, C,, and b, are listed in Table 71. The sum ofall discrete (single) excitation cross sections Sexe CaN be expressed in the form similar to Eq. (1) with two constants M2,, and Coxe. These constants are defined as (4) IM. = > (discrete) AZ%, , and (5) Coxe => (diserete) [Ci + 5,], respectively. The results thus obtained are given in Table 70. Once the values of Af’ and C are knownfor oto: and Fexe, Ole can evaluate the “‘counting” ionization cross section gion by subtraction: Fion = Ttot — Tex G _ Srapz" a 2 | “+ mv/R {Ata In (43) — 8 Srazz" mit/R iat |s (*,) — | ++ Cs) (2) for an (optically) allowed transition, and 22 CG, = Sraoz mv/R Dn (3) for a forbidden transition. The constants 177,,C,, and 6, * Principal results of this work presented at the VIth International Conference on the Physies of Electronic and Atomic Collisions (VI ICPEAC), Cambridge, Massachusetts, July 28-Aug. 2, 1969. MW , Cu . (6) This method leads to an accurate ionization cross section without calculating the continuum wave functions directly. The same method was applied successfully to Heas explained elsewhere in this report."” The values of Mion and Cion are listed in Table 70. The uncertainty in gexe is about the same as that in Stot-| When appropriate values of the constants are substituted, one gets t The generalized oscillator strengths of Lit computed from the Weiss and Perkins wave functions in the length andvelocity formulas agree with each other within 1%or better. hea be, vale ae