We report experimental differential cross sections for the scattering of electrons by calcium-40 and by calcium-48 at 750 MeV. We have thereby examined the possible energy dependence of the phenomenological charge distribution in terms of which previous data at 250 MeV have been analyzed, 1 and also have explored larger values of the recoil momentum q than was possible at that energy. We find that while there is good agreement over the range of q measured at 250 MeV, the larger q results are significantly different from those predicted by the phenomeno logical charge distribution. A method is presented and used for determining directly, from the experimental data at large q, the modification needed by the charge distribution so that it gives agreement at large q while preserving the good fit at smaller q values. What emerges is an oscillating modulation in the charge distribution which resembles qualitatively an effect obtained using the shell model. The effects are surprisingly similar for the two isotopes.Experimental results are given in Fig. 1 for both Ca 40 and Ca 48 . They are compared with the cross sections predicted from the charge distribution p 0 (r) whose parameters were obr tained from the 2 50-MeV data. (Details are given in the caption to Fig. 1.) An adjustment of +1% has been made in the incident energy, consistent with the possible uncertainty in energy selection that the steering magnets had at the time the data were taken. With no further adjustment except this one, which makes the incident energy 757.5 MeV, the agreement of the 250-MeV prediction with the experimental results is remarkably good out to 35°, the angle at which the recoil momentum q = 2E 0 sini 6 is the same as at the largest measured angle _i i i i i i i \ i i 20 30 40 50 60 SCATTERING ANGLE IN DEGREES FIG. 1. Experimental and theoretical differential cross sections at 757.5 MeV. The nominal energy was 750 MeV, and a 1% adjustment was made to improve the fit at low q. The dashed curves are the best fits to earlier 250-MeV data. The charge distributions which yield them are parabolic Fermi (three-parameter) shapes [see Eq. (3) of Ref. 1] with the following parameter values; Ca 40 , c = 3.6685 F, 2 = 0.5839 F, w = ~0.1017; Ca 48 , c = 3.7369 F, 2 = 0.5245 F, w = -0.0300.The solid curves, obtained by the method described in this Letter, come from charge distributions with an added Ap(r), and parameter values p = 0.5 F^" 1 , q 0 = 3.0 F-1 , andA(Ca 40 ) = 0.5xlO~3, A(Ca 48 ) = 0.8xio-3 . The cross section for Ca 40 has been multiplied by 10 and that for Ca 48 by 10" 1 . 527

The first- and second-order matrix equations for the magnetic optics of the midplane of uniform-field wedge magnets have been derived. The calculations include rotated input and output wedges and curved surfaces on the input and output faces. A second-order matrix algebra has been developed to handle beam transport optics for multiple element systems in a manner similar to that which has been used in the past for the first-order beam transport optics.

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