Ulmeret al.Reply

Abstract

Ulmer et aL Reply:The authors of the Comment address variances in the occupation numbers and longitudinal-transverse (L/T) ratios quoted for our experiment 1 compared to theirs. 2,3 Regarding the occupation numbers, we claim there is no intrinsic discrepancy between our results and those of Ref. 2. By their nature, occupation numbers have meaning only in the context of a particular reaction model. We originally employed two methods of computing the distortions of the outgoing protons: a WKB approximation 4 and a distorted-wave impulse-approximation (DWIA) analysis. 5 We have since recalculated the occupation numbers based on the DWIA analysis of Boffi, Giusti, and Pacati 6 using the optical potential of Comfort and Karp 7 and have also estimated the effect of electron distortion. This allows a direct comparison of our data to those of Ref. 2 where the same procedure and models were used. Our new analysis gives /?-shell spectroscopic factors of 2.71 ±0.07±0.10 (2.76±0.07±0.10) at the forward-(backward-) angle kinematics. (Here, the systematic error does not include the uncertainty in the DWIA calculation but does include all kinematic uncertainties and so reflects our ability to determine which part of the momentum distribution was sampled.) This is to be compared with 2.26 ±0.17 ±0.23 obtained at NI-KHEF 2 and 2.5 from Mougey et a/. 8 Clearly, if similar DWIA models are used, both experiments 1 ' 2 are in reasonable agreement.Regarding the authors' second comment, we have also reanalyzed our L/T ratios with the same optical potential and bound-state wave function used in Ref. 2. Cuts were applied to the data to insure nearly identical sampling of the momentum distribution at both kinematics. Our new results, corrected for L/T differences in both the electron and proton distortions, give 0.95 ±0.10 ± 0.12 for the /?-shell L/T ratio. As in our initial Letter, our result is consistent with no (or equal) modifications of the proton electromagnetic form factors. The number 0.73 ±0.08 obtained at NIKHEF and quoted in the Comment is averaged over momentum transfer and includes no systematic errors. Because their most recent DWIA calculations show definite structure in the region measured at NIKHEF 9 we compared our results to the data point from Ref. 3 nearest in momentum transfer to ours. At q=420 MeV/c the NIKHEF measurement yields 0.69 ±0.20 (Ref. 10) which is consistent with our result.We emphasize that in our original paper the longitudinal strength vanishes at 6 m -50 MeV whereas the transverse remains constant out to e m~~ 65 MeV, the largest missing energy measured. This indicates that there is an additional current present in the transverse electromagnetic interaction. Its influence on p-shell occupation numbers and L/T ratios is unknown. Moreover, calcula-

Transparency of12Cfor protons

“…Experimental data for the cross section of the reaction 12 C(e, e ′ p) were obtained at Frascati [3], Tokyo [4], Saclay [5,6], NIKHEF [7,8,[16][17][18][19][20], MIT/Bates [21][22][23][24][25], Mainz [11], SLAC [15] and TJNAF [10]. In the re-analysis of these data we have only used data sets covering a large (> 100 MeV/c) range of missing momentum, as this gives a good indication of the internal consistency of each data set.…”

“…The square indicates the result from the combined analysis of NIKHEF, Saclay and Tokyo data (see sections III and IV), where the horizontal bar denotes the Q 2 range of these data. Other symbols, as indicated, represent the results from experiments at Bates [22,23], SLAC [15] and TJNAF [10].…”

“…at Bates [22,23], which covered a small p m acceptance and were therefore not included in the analysis of sections III and IV. All low Q 2 results, which were obtained with an optical-model treatment of the final-state interaction, are mutually consistent and lead to a total strength S 1p +S 1s =3.45±0.13.…”

“…Here, we plot the summed spectroscopic factors S 1p +S 1s for 1p and 1s knockout as a function of Q 2 in the range between 0.1 and 10 (GeV/c) 2 . At low Q 2 (< 0.6 (GeV/c) 2 ) the results of the combined analysis of the NIKHEF, Saclay and Tokyo data (see sections III and IV) are shown and those of two experiments performed [22,23], SLAC [15] and TJNAF [10].…”

Quasielastic reaction mechanism studied using the reactionC12(e,e’p)

“…Figure 2 shows the { p-and ^-shell spectroscopic factors from this experiment and from previous Bates measurements at #=400 MeV/c. 20 The vertical error bars include statistical and systematic experimental uncertainties and estimated model uncertainties. We observe 2.42 ±0.39, 1.87 ±0.40, and 2.53 ±0.38 ^-shell protons for g = 585, 775, and 827 MeV/c, respectively.…”