IEEE Transactions on Nuclear Science, Vol. NS-28, No. 2, April 1981 Z139 Z14 CORRECTIONS TO HEAVY ION ENERGY LOSS J. M. Anthony, P.D. Parker Wright Nuclear Structure Laboratory Yale University, New Haven, Connecticut 06511 and W.A. Lanford Department of Physics S. U. N. Y. at Albany, Albany, New York 12222 We have measured the energy loss of several heavy ions (Zl = 6, 14, 17, 22, 26, 28, 32, 35, 41 and 53) in elemental targets (Z2 = 6, 13, 29, 47 and 79) at energies near the stopping power maximum. The results are not well described by current compilations,which are based on a Z12 stopping power dependence. Use of higher order Z1 corrections to the stopping power, however, in conjunction with simple effective charge expressions, allows reasonable fits to the data to be made. Introduction Although the energy loss of heavy charged particles in matter has been studied by many workers, some aspects of this process are still not well described theoretically. The behavior of heavy ions near the maximum (peak) of the stopping power vs. energy curve is especially complicated by insufficient knowledge of the effective charge of the ion as it passes through the target material. Current stopping power compilations that deal with this energy range include those of Northcliffe and Schilling (NS)1 and Ziegler. 2 The energy loss in this velocity region, for a pro- jectile of charge Zle and velocity v = ,c passing through a target material of charge Z2e, is usually written as Z1 2 -dE/dx = C fl2 L where C = 2 07x 0-4 2 MeV-cm2/mg, inc2 A2 A2 and the stopping number L depends on the particular theory used to describe the energy loss. Both Ziegler and NS assume L = Lo(v, Z2), i. e. it depends only on target ma- Fig. 1. Electronic s si in Cu gE 4 ~~~----- ZIEGLER_ 2_ 0 20 40 60 80 100 120 ENERGY (MeV) Fig. 1. Electronic stopping power of Si in Cu vs. energy. Also shown are the predictions of Ziegler (---) and NS (-. -) as well as the calculations of the present study (-). terial and projectile velocity, which results in a simple z12 stopping power dependence. Recent measurements3 on TT+ and ir ranges are not consistent with this scaling, however. Ashley, et al.4 and Jackson and McCarthy5 have calculated Z 3 corrections to the stopping power, while Lindhard6 suggested a Z13 term approximately twice that of Jackson and McCarthy, as well as a Z14 correction originally pro- posed by Bloch, 7 i. e. L = Lo (v, Z2) + Z1L1 (v, Z2) + Zl2L2(v) The Lindhard corrections provide the best fit to the pion data. Moreover, Andersen, et al. 8 have made precision measurements with proton, alpha, and Li projectiles in Al, Cu, Ag and Au which allow them to separate out higher order contributions to the stopping power. They have found Z13 and Z14 corrections which are well described by the Lind- hard predictions. These corrections all vanish at high velocities. Recently we reportedll on an extension of these ideas to heavy ion stopping powers and ranges. For Si and Ni projectiles in Cu and Ag targets, the peak in the stopping power vs. energy curve shows systematic deviations from the predictions of Ziegler and NS. We investigated the effect of higher order Z1 corrections on this data. Values of LO(v, Z2) were taken from the experimental measure- ments of Andersen, et al., while the higher order correc- tions were based on the Lindhard formalism. Some assumption about the projectile effective charge, Z1* was also necessary, and we used the expression Z1* -1 -v exp VQZ12/3 where VO = e2/h and X is a free parameter. This functional Fig. 2. Electronic stopping power of Si in Ag vs. energy. Also shown are the predictions of Ziegler (---) and NS (- -) as well as the calculations of the present study (-). 0018-9499/81/0400-1227$00.75© 1981 IEEE 1227