Table I. Kinematic set points for elastic electron-proton and electron-deuteron scattering at electron scattering angle 0 = 8 deg in the laboratory. The incident electron energy is E, the scattered electron energy is E', the recoil nuclear momentum and angle are pr and 0r, and Br is the recoil nuclear velocity divided by the velocity of light. ======================================================== Q2 E E' pr 0r B [(GeV/c)2] (GeV) (GeV) (GeV/c) (deg) ------------------------------------------------------- PROTON 0.8 6.628 6.201 0.989 60.58 0.726 1.0 7.439 6.906 1.131 58.02 0.770 1.5 9.187 8.388 1.461 52.96 0.841 1.75 9.960 9.027 1.617 50.92 0.865 2.0 10.684 9.618 1.769 49.10 0.883 2.5 12.019 10.687 2.066 46.00 0.911 3.0 13.240 11.641 2.356 43.42 0.929 4.0 15.441 13.309 2.922 39.32 0.952 6.0 19.229 16.031 4.026 33.64 0.974 DEUTERON 0.8 6.519 6.305 0.910 72.62 0.437 1.0 7.302 7.036 1.028 71.11 0.481 1.5 8.981 8.581 1.284 67.96 0.565 1.75 9.718 9.252 1.399 66.62 0.598 2.0 10.407 9.874 1.508 65.40 0.627 2.5 11.671 11.005 1.713 63.20 0.674 3.0 12.821 12.021 1.905 61.28 0.713 4.0 14.878 13.812 2.265 58.01 0.770 6.0 18.375 16.776 2.924 52.95 0.842 ======================================================== 1 Table IV. Double arm events and total Coulombs of incident electrons for electron-proton and electron-deuteron scattering at nine values of four-momentum transfer Q2. The numbers of events were obtained from our measured double arm time-of-flight distributions,as described in the text. The signal events were extracted from the ed coincidence peak in the TOF spectra by subtraction of the flat accidental background. The errors listed here are the statistical errors including the error from the background subtraction. At Q2 = 6 (GeV/c)2 for electron-deuteron scattering no elastic events were observed for 1.9533 Coulombs. We assign an upper limit on the cross section there assuming 3 events. ================================================== Q2 Coulombs Background Signal Events Events [(GeV/c)2] --------------------------------------------------- PROTON 0.8 1.9010x10-4 27 16405+-128 1.0 2.2740x10-4 10 9346+- 97 1.5 8.8880x10-4 18 11715+-108 1.75 1.5910x10-3 20 12356+-111 2.0 1.8492x10-3 10 9376+- 97 2.5 2.2040x10-3 4 4978+- 71 3.0 7.9410x10-3 12 9278+- 96 4.0 1.4330x10-2 5 5912+- 77 6.0 5.7230x10-3 1 440+- 20 DEUTERON 0.8 4.4757x10-3 180 640+- 32 1.0 1.9950x10-2 77 1019+- 34 1.5 9.8270x10-2 67 876+- 32 1.75 1.5715x10-1 43 516+- 24 2.0 8.1727x10-1 54 1258+- 36 2.5 0.9920 4 351+- 19 3.0 1.6228 0 173+- 13 4.0 2.7032 0 21+- 4.6 6.0 1.9533 0 0+- 3 =================================================== 1 Table V. Ratios of our measured elastic electron-proton cross sections to the world values at each of nine values of four-momentum transfer Q2. The world cross sections were obtained from the fit to the previously measured proton form factors labeled "Dipole([p=112 MeV)" in Ref . Our cross sections were determined by three different analysis methods, described in the text. At each point we formed the ratio Rp = dsigexpr/dsigworld. The sources of error on the points are given in Table IV. The ratio values for each analysis method were averaged to give the average ratios . The 2 was used to normalize the deuteron results for A(Q2) and the 3 was used to normalize the results for vW2. =================================================================== World Cross Ratios Section Q2 10+32 x ( ) (Rp)1 (Rp)2 (Rp)3 [(GeV/c)2] (cm2/sr) ------------------------------------------------------------------- 0.8 51.67 1.031+-0.032 1.130+-0.033 0.916+-0.033 1.0 27.75 1.008+-0.032 1.008+-0.034 0.900+-0.034 1.5 7.931 1.066+-0.032 1.115+-0.034 0.975+-0.033 1.75 4.719 1.088+-0.033 1.099+-0.034 0.986+-0.033 2.0 2.952 1.058+-0.033 1.088+-0.034 0.958+-0.034 2.5 1.295 1.040+-0.034 1.054+-0.036 0.942+-0.035 3.0 0.636 1.033+-0.035 1.090+-0.036 0.942+-0.035 4.0 0.194 1.041+-0.036 1.150+-0.038 0.969+-0.038 6.0 0.0317 0.988+-0.050 1.140+-0.064 0.877+-0.069 ---------------------------------------------- Averages = 1.046+-0.031 1.093+-0.033 0.950+-0.031 ================================================================== 1 Table VI. Sources of error on the proton calibration. ===================================================== Quantity +- error (%) ----------------------------------------------------- Ne - event statistics 0.8 - 5.0 Ni - incident charge 1.1 L - target length and density 3.0 Ceff - experimental efficiencies 0.2 - 3.0 ----------- Total added in quadrature 3.3 - 6.9 ===================================================== 1 Table VII. Final electron-deuteron elastic scattering cross sections and deuteron structure functions A(Q2) at nine values of four-momentum transfer Q2. The ed events were identified by measuring the scattered electrons in coincidence with the recoil nuclei. The ed cross sections were calculated using Eq. 3.1. They were normalized to the electron-proton cross sections using the average ratio 2, given in Table V, of our double arm ep cross sections to the world values. The errors on the results include the statistical errors given in column 4 added in quadrature to the systematic errors in column 5. The sources of systematic errors are listed in Table VIII. ================================================================= Q2 (do/d ) A(Q2) stat sys error error [(GeV/c)2] (cm2/sr) % % ----------------------------------------------------------------- 0.8 (1.14+-0.11)x10-33 (2.31+-0.22)x10-4 5.2 8.2 1.0 (3.52+-0.30)x10-34 (8.95+-0.77)x10-5 3.3 7.9 1.5 (5.26+-0.42)x10-35 (2.04+-0.16)x10-5 3.6 7.1 1.75 (1.99+-0.17)x10-35 (9.05+-0.78)x10-6 4.6 7.3 2.0 (9.04+-0.71)x10-36 (4.74+-0.37)x10-6 2.9 7.3 2.5 (2.15+-0.20)x10-36 (1.43+-0.14)x10-6 5.4 7.9 3.0 (6.24+-0.68)x10-36 (5.02+-0.55)x10-7 7.5 7.9 4.0 (4.68+-1.06)x10-38 (5.12+-1.16)x10-8 20.9 8.6 6.0 ( < 9.7 )x10-39 ( < 1.64 )x10-8 ================================================================= 1 Table VIII Sources of error on the results for A(Q2) ==================================================== Quantity +- error (%) ---------------------------------------------------- Ne - event statistics 2.9 - 21 Ni - incident charge 1.1 L - target length and density 3.0 Ceff - experimental efficiencies 0.7 - 4.0 2 - proton normalization 3.1 RMC - ratio of solid angles, 5.5 - 7.5 radiative corrections, and nuclear absorption for ep and ed scattering, from the Monte Carlo ----------- Total added in quadrature 8.0 - 22.6 ==================================================== 1 Table IX. Final results for the deuteron structure function vW2 at 0 = 8 deg versus the missing mass squared W2 at nine values of the incident electron energy E. The Q2 values shown are for elastic ed scattering at W2 = 3.519 GeV2. The numbers in parenthesis are the statistical errors followed by the systematic errors. The sources of systematic errors are given in Table X. ============================================================== E = 6.519 GEV (Q2 = 0.8 (GEV/C)2) ------------------------------------ W2 (GEV2) 10+4 NUW2 --------- --------- 3.471 2.81 +- ( 1.21, 0.38) 3.496 0.50 +- ( 7.33, 0.07) 3.520 9.75 +- ( 2.61, 1.34) 3.545 15.58 +- ( 2.76, 2.13) 3.569 20.45 +- ( 2.55, 2.80) 3.594 25.85 +- ( 1.67, 3.54) 3.618 34.14 +- ( 3.24, 4.68) 3.642 45.71 +- ( 2.73, 6.26) 3.667 53.94 +- ( 2.56, 7.39) 3.691 67.74 +- ( 5.19, 9.28) 3.716 85.80 +- ( 3.60,11.75) 3.740 103.27 +- ( 3.95,14.15) 3.765 120.62 +- ( 6.33,16.53) 3.789 134.01 +- ( 5.64,18.36) 3.814 184.12 +- ( 6.83,25.22) 3.838 211.98 +- ( 6.72,29.04) 3.863 254.50 +- ( 8.22,34.87) 3.887 313.5 +- (11.7 ,42.9 ) 3.911 362.9 +- (19.7 ,49.7 ) 3.936 434.8 +- (25.1 ,59.6 ) 3.960 497.2 +- (17.4 ,68.1 ) -------------------------------------- 1 E = 7.302 GEV (Q2 = 1.0 (GEV/C)2) ------------------------------------ W2 (GEV2) 10+4 NUW2 --------- --------- 3.492 0.85 +- ( 0.94, 0.08) 3.520 6.51 +- ( 0.54, 0.61) 3.547 8.82 +- ( 1.25, 0.82) 3.574 12.20 +- ( 1.19, 1.13) 3.602 16.08 +- ( 1.21, 1.50) 3.629 17.63 +- ( 0.88, 1.64) 3.657 23.81 +- ( 1.72, 2.21) 3.684 26.49 +- ( 2.34, 2.46) 3.711 31.50 +- ( 1.68, 2.93) 3.739 39.56 +- ( 1.70, 3.68) 3.766 46.42 +- ( 2.12, 4.32) 3.794 53.89 +- ( 2.41, 5.01) 3.821 66.87 +- ( 1.58, 6.22) 3.848 76.75 +- ( 2.80, 7.14) 3.876 97.38 +- ( 2.46, 9.06) 3.903 110.54 +- ( 4.20,10.28) 3.931 127.11 +- ( 5.15,11.82) 3.958 148.95 +- ( 4.58,13.85) 3.985 180.48 +- ( 8.17,16.78) 4.013 214.00 +- (10.54,19.90) -------------------------------------- 1 E = 8.981 GEV (Q2 = 1.5 (GEV/C)2) ------------------------------------ W2 (GEV2) 10+4 NUW2 --------- --------- 3.464 0.02 +- ( 0.22, 0.00) 3.498 1.17 +- ( 0.18, 0.09) 3.531 2.06 +- ( 0.28, 0.15) 3.565 2.92 +- ( 0.32, 0.22) 3.599 3.95 +- ( 0.28, 0.30) 3.632 4.77 +- ( 0.30, 0.36) 3.666 5.27 +- ( 0.38, 0.40) 3.700 7.07 +- ( 0.52, 0.53) 3.734 7.40 +- ( 0.42, 0.56) 3.767 8.86 +- ( 0.29, 0.66) 3.801 10.63 +- ( 0.63, 0.80) 3.835 11.93 +- ( 0.49, 0.89) 3.868 12.58 +- ( 0.60, 0.94) 3.902 14.43 +- ( 0.56, 1.08) 3.936 16.43 +- ( 0.81, 1.23) 3.969 20.47 +- ( 0.79, 1.54) 4.003 22.78 +- ( 0.47, 1.71) 4.037 26.24 +- ( 1.47, 1.97) 4.071 29.21 +- ( 1.59, 2.19) 4.104 33.93 +- ( 1.90, 2.54) 4.138 37.16 +- ( 1.93, 2.79) -------------------------------------- 1 E = 9.718 GEV (Q2 = 1.75 (GEV/C)2) ------------------------------------ W2 (GEV2) 10+4 NUW2 --------- --------- 3.424 0.14 +- ( 0.10, 0.01) 3.460 0.51 +- ( 0.17, 0.04) 3.497 1.26 +- ( 0.14, 0.10) 3.533 1.47 +- ( 0.18, 0.11) 3.569 2.05 +- ( 0.23, 0.16) 3.606 2.32 +- ( 0.23, 0.18) 3.642 2.98 +- ( 0.22, 0.23) 3.679 3.57 +- ( 0.20, 0.27) 3.715 4.27 +- ( 0.32, 0.33) 3.752 4.49 +- ( 0.29, 0.35) 3.788 5.11 +- ( 0.18, 0.39) 3.825 6.09 +- ( 0.43, 0.47) 3.861 7.33 +- ( 0.37, 0.56) 3.898 8.00 +- ( 0.46, 0.62) 3.934 8.35 +- ( 0.50, 0.64) 3.971 9.65 +- ( 0.54, 0.74) 4.007 10.91 +- ( 0.47, 0.84) 4.043 12.88 +- ( 0.60, 0.99) 4.080 14.17 +- ( 0.60, 1.09) 4.116 18.08 +- ( 0.51, 1.39) 4.153 17.80 +- ( 1.08, 1.37) 4.189 20.23 +- ( 1.12, 1.56) -------------------------------------- 1 E = 10.407 GEV (Q2 = 2.0 (GEV/C)2) ------------------------------------ W2 (GEV2) 10+5 NUW2 --------- --------- 3.421 0.83 +- ( 0.68, 0.06) 3.460 2.63 +- ( 0.81, 0.20) 3.499 6.26 +- ( 0.82, 0.48) 3.538 7.42 +- ( 0.77, 0.57) 3.577 10.82 +- ( 0.84, 0.83) 3.616 14.38 +- ( 0.93, 1.11) 3.655 15.34 +- ( 1.00, 1.18) 3.694 19.48 +- ( 1.28, 1.50) 3.733 24.03 +- ( 1.38, 1.85) 3.772 25.27 +- ( 1.95, 1.95) 3.811 28.37 +- ( 1.72, 2.18) 3.850 35.48 +- ( 1.97, 2.73) 3.889 35.65 +- ( 1.49, 2.75) 3.929 44.35 +- ( 1.94, 3.41) 3.968 47.65 +- ( 2.02, 3.67) 4.007 53.19 +- ( 2.19, 4.10) 4.046 64.80 +- ( 2.68, 4.99) 4.085 67.55 +- ( 3.81, 5.20) 4.124 75.79 +- ( 2.30, 5.84) 4.163 82.57 +- ( 5.83, 6.36) 4.202 92.43 +- ( 3.90, 7.12) 4.241 102.63 +- ( 6.20, 7.90) -------------------------------------- 1 E = 11.671 GEV (Q2 = 2.5 (GEV/C)2) ------------------------------------ W2 (GEV2) 10+5 NUW2 --------- --------- 3.456 0.23 +- ( 0.27, 0.02) 3.500 1.13 +- ( 0.34, 0.09) 3.544 2.46 +- ( 0.59, 0.20) 3.588 3.82 +- ( 0.40, 0.31) 3.632 4.26 +- ( 0.63, 0.34) 3.675 5.80 +- ( 0.60, 0.46) 3.719 6.43 +- ( 0.92, 0.51) 3.763 7.47 +- ( 0.61, 0.60) 3.807 7.88 +- ( 0.72, 0.63) 3.851 10.31 +- ( 0.93, 0.82) 3.894 11.49 +- ( 0.75, 0.92) 3.938 12.38 +- ( 1.15, 0.99) 3.982 16.50 +- ( 0.98, 1.32) 4.026 15.70 +- ( 1.28, 1.26) 4.070 17.29 +- ( 0.90, 1.38) 4.113 22.18 +- ( 1.34, 1.77) 4.157 22.73 +- ( 2.16, 1.82) 4.201 27.08 +- ( 1.60, 2.17) 4.245 32.45 +- ( 2.06, 2.60) 4.288 30.41 +- ( 2.39, 2.43) 4.332 33.92 +- ( 2.08, 2.71) -------------------------------------- 1 E = 12.821 GEV (Q2 = 3.0 (GEV/C)2) ------------------------------------ W2 (GEV2) 10+5 NUW2 --------- --------- 3.409 0.13 +- ( 0.20, 0.01) 3.457 0.46 +- ( 0.21, 0.04) 3.505 0.92 +- ( 0.23, 0.08) 3.553 1.60 +- ( 0.25, 0.14) 3.601 1.51 +- ( 0.28, 0.13) 3.649 1.84 +- ( 0.24, 0.16) 3.697 2.00 +- ( 0.36, 0.17) 3.746 2.96 +- ( 0.48, 0.26) 3.794 3.92 +- ( 0.31, 0.34) 3.842 3.79 +- ( 0.42, 0.33) 3.890 4.28 +- ( 0.40, 0.37) 3.938 5.25 +- ( 0.65, 0.46) 3.986 5.88 +- ( 0.59, 0.51) 4.034 6.06 +- ( 0.67, 0.53) 4.082 6.29 +- ( 0.66, 0.55) 4.130 8.67 +- ( 0.73, 0.75) 4.179 9.08 +- ( 1.06, 0.79) 4.227 10.11 +- ( 0.94, 0.88) 4.275 12.63 +- ( 0.99, 1.10) 4.323 13.42 +- ( 0.83, 1.17) 4.371 15.05 +- ( 1.21, 1.31) 4.419 18.04 +- ( 1.29, 1.57) -------------------------------------- 1 E = 14.878 GEV (Q2 = 4.0 (GEV/C)2) ------------------------------------ W2 (GEV2) 10+5 NUW2 --------- --------- 3.395 0.11 +- ( 0.13, 0.01) 3.451 0.10 +- ( 0.12, 0.01) 3.507 0.28 +- ( 0.10, 0.02) 3.562 0.25 +- ( 0.11, 0.02) 3.618 0.23 +- ( 0.22, 0.02) 3.674 0.45 +- ( 0.14, 0.04) 3.730 0.50 +- ( 0.19, 0.05) 3.786 0.53 +- ( 0.16, 0.05) 3.842 0.56 +- ( 0.15, 0.05) 3.897 0.85 +- ( 0.18, 0.08) 3.953 0.79 +- ( 0.20, 0.07) 4.009 0.74 +- ( 0.13, 0.07) 4.065 1.10 +- ( 0.39, 0.10) 4.121 1.12 +- ( 0.29, 0.10) 4.176 1.61 +- ( 0.32, 0.15) 4.232 1.47 +- ( 0.38, 0.13) 4.288 2.18 +- ( 0.25, 0.20) 4.344 2.05 +- ( 0.48, 0.18) 4.400 2.61 +- ( 0.52, 0.23) 4.456 3.26 +- ( 0.36, 0.29) 4.511 3.24 +- ( 0.61, 0.29) 4.567 3.25 +- ( 0.39, 0.29) -------------------------------------- 1 E = 18.375 GEV (Q2 = 6.0 (GEV/C)2) ------------------------------------ W2 (GEV2) 10+6 NUW2 --------- --------- 3.615 0.22 +- ( 0.20, 0.02) 3.753 0.56 +- ( 0.28, 0.05) 3.891 0.21 +- ( 0.20, 0.02) 4.029 0.65 +- ( 0.29, 0.06) 4.167 1.04 +- ( 0.38, 0.09) 4.305 1.78 +- ( 0.51, 0.16) 4.442 2.45 +- ( 0.62, 0.22) 4.580 2.37 +- ( 0.64, 0.22) 4.718 4.49 +- ( 0.88, 0.41) -------------------------------------- ============================================================ 1 Table X. Sources of systematic error on the results for vW2 ===================================================== Quantity +- error (%) ----------------------------------------------------- Ni - incident charge 1.1 L - target length and density 3.0 Cexp - experimental efficiencies 0.7 - 4.0 3 - proton normalization 3.1 energy calibration 6.0 - 13 ----------- Total added in quadrature 7.7 - 14 ===================================================== l