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THE EMPIRICAL ANALYSIS
σ q,q+1 | Emax,L1 | σ max,L1 | αL1 | βL1 |
σ q,q-1 | σ max,c1 | αc1 | ||
σ q,q+1 | Z | Emax,L1 , MeV/amu | |||||||
H2 | He | N2 | Ne | Ar | Kr | Xe | Recom. data | ||
σ -1,0 | 1 | 0.020 | 0.020 | 0.020 | 0.020 | 0.020 | 0.020 | 0.020 | 0.020 |
6 | 0.020 | 0.020 | 0.020 | 0.020 | 0.020 | 0.020 | 0.020 | ||
8 | 0.020 | 0.020 | 0.020 | 0.020 | 0.020 | 0.020 | 0.020 |
σ 0,1 | 1 | 0.070 | 0.030 | 0.070 | 0.070 | 0.070 | 0.070 | 0.070 | 0.050 |
2 | 0.070 | 0.070 | 0.070 | 0.070 | 0.070 | 0.070 | 0.070 |
6 | 0.050 | 0.050 | 0.050 | 0.050 | 0.050 | 0.050 | 0.050 |
7 | 0.050 | 0.050 | 0.050 | 0.050 | 0.050 | 0.050 | 0.050 |
8 | 0.050 | 0.050 | 0.050 | 0.050 | 0.050 | 0.050 | 0.050 |
σ 1,2 | 2 | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 | 0.100 |
6 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 |
7 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 |
8 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 | 0.100 |
σ 2,3 | 6 | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 |
7 | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 |
8 | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 |
σ 3,4 | 6 | 0.300 | 0.300 | 0.300 | 0.300 | 0.300 | 0.300 | 0.300 | 0.300 |
7 | 0.300 | 0.300 | 0.300 | 0.300 | 0.300 | 0.300 | 0.300 |
8 | 0.300 | 0.300 | 0.300 | 0.300 | 0.300 | 0.300 | 0.300 |
σ 4,5 | 6 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 |
7 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 |
8 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 | 0.500 |
σ 5,6 | 6 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 |
7 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 |
8 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 |
σ 6,7 | 7 | 1.0 | 1.0 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.3 |
8 | 1.0 | 1.0 | 1.0 | 1.5 | 1.5 | 1.5 | 1.5 |
σ 7,8 | 8 | 1.5 | 1.5 | 2.0 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 |
σ q,q+1 | Z | σ max,L1 , 10 -16 , cm 2 /atom | ||||||
H2 | He | N2 | Ne | Ar | Kr | Xe | ||
σ -1,0 | 1 | 4.60 | 6.20 | 11.3 | 4.90 | 18.0 | 24.4 | 30.0 |
6 | 3.80 | 5.20 | 9.50 | 11.3 | 15.0 | 20.7 | 25.4 | |
8 | 3.40 | 4.70 | 8.50 | 10.0 | 13.0 | 17.9 | 22.0 |
σ 0,1 | 1 | 0.88 | 1.42 | 2.45 | 2.02 | 4.80 | 4.55 | 5.50 |
2 | 0.73 | 1.05 | 2.40 | 2.50 | 3.80 | 4.80 | 6.00 |
6 | 2.30 | 3.05 | 4.70 | 5.30 | 6.60 | 8.40 | 9.80 |
7 | 2.00 | 2.70 | 4.70 | 5.40 | 6.80 | 9.30 | 11.1 |
8 | 1.85 | 2.60 | 4.70 | 5.50 | 7.50 | 10.2 | 12.4 |
σ 1,2 | 2 | 0.15 | 0.24 | 0.56 | 0.73 | 1.16 | 1.73 | 2.20 |
6 | 0.90 | 1.24 | 2.20 | 2.60 | 3.48 | 4.80 | 5.70 |
7 | 0.95 | 1.38 | 2.60 | 3.10 | 4.10 | 5.70 | 7.05 |
8 | 1.00 | 1.50 | 2.70 | 3.20 | 4.40 | 6.20 | 7.70 |
σ 2,3 | 6 | 0.27 | 0.42 | 0.94 | 1.19 | 1.78 | 2.80 | 3.60 |
7 | 0.40 | 0.60 | 1.30 | 1.60 | 2.30 | 3.55 | 4.45 |
8 | 0.50 | 0.77 | 1.57 | 1.90 | 2.74 | 4.10 | 5.30 |
σ 3,4 | 6 | 0.095 | 0.155 | 0.38 | 0.51 | 0.78 | 1.26 | 1.70 |
7 | 0.150 | 0.245 | 0.67 | 0.83 | 1.27 | 2.20 | 2.90 |
8 | 0.23 | 0.37 | 0.92 | 1.21 | 1.82 | 3.00 | 4.10 |
σ 4,5 | 6 | 0.0090 | 0.022 | 0.105 | 0.160 | 0.320 | 0.720 | 1.100 |
7 | 0.025 | 0.071 | 0.330 | 0.400 | 0.770 | 1.340 | 2.300 |
8 | 0.042 | 0.100 | 0.386 | 0.570 | 0.850 | 2.050 | 3.200 |
σ 5,6 | 6 | 0.0030 | 0.0069 | 0.0320 | 0.0530 | 0.105 | 0.234 | 0.400 |
7 | 0.0084 | 0.0180 | 0.0730 | 0.125 | 0.200 | 0.450 | 0.700 |
8 | 0.015 | 0.031 | 0.120 | 0.180 | 0.340 | 0.670 | 1.120 |
σ 6,7 | 7 | 0.0028 | 0.0063 | 0.0300 | 0.0473 | 0.0995 | 0.220 | 0.314 |
8 | 0.0035 | 0.0081 | 0.0370 | 0.0620 | 0.124 | 0.260 | 0.340 |
σ 7,8 | 8 | 8.6e-4 | 0.0020 | 0.0082 | 0.0125 | 0.0247 | 0.0530 | 0.0870 |
E/Emax,l1 | α l1 |
6.7 | -0.520 |
10.0 | -0.524 |
20.0 | -0.536 |
33.3 | -0.555 |
50.0 | -0.573 |
100.0 | -0.600 |
200.0 | -0.632 |
500.0 | -0.670 |
σ q,q+1 | Z | βL1 | ||||||
H2 | He | N2 | Ne | Ar | Kr | Xe | ||
σ -1,0 | 1 | 0.07 | 0.135 | 0.255 | 0.285 | 0.340 | 0.404 | 0.444 |
6 | 0.20 | 0.255 | 0.349 | 0.377 | 0.425 | 0.477 | 0.511 | |
8 | 0.20 | 0.255 | 0.349 | 0.377 | 0.425 | 0.477 | 0.514 | |
Recom. | 0.20 | 0.255 | 0.349 | 0.377 | 0.425 | 0.477 | 0.514 |
σ 0,1 | 1 | 0.42 | 0.55 | 0.80 | 0.87 | 1.00 | 1.15 | 1.25 |
2 | 0.78 | 1.06 | 1.56 | 1.47 | 1.94 | 2.22 | 2.38 |
6 | 0.42 | 0.55 | 0.80 | 0.87 | 1.00 | 1.15 | 1.25 |
7 | 0.42 | 0.54 | 0.80 | 0.87 | 1.00 | 1.15 | 1.25 |
8 | 0.42 | 0.55 | 0.80 | 0.87 | 1.00 | 1.15 | 1.25 |
Recom. | 0.42 | 0.55 | 0.80 | 0.87 | 1.00 | 1.15 | 1.25 |
σ 1,2 | 2 | 1.30 | 1.54 | 2.00 | 2.14 | 2.35 | 2.64 | 2.77 |
6 | 0.90 | 1.06 | 1.38 | 1.47 | 1.61 | 1.80 | 1.90 |
7 | 0.90 | 0.75 | 1.38 | 1.51 | 1.60 | 1.80 | 1.90 |
8 | 0.90 | 1.06 | 1.38 | 1.48 | 1.61 | 1.80 | 1.90 |
Recom. | 0.90 | 1.03 | 1.38 | 1.47 | 1.61 | 1.80 | 1.90 |
σ 2,3 | 6 | 1.00 | 1.20 | 1.58 | 1.70 | 1.86 | 2.08 | 2.20 |
7 | 1.00 | 1.20 | 1.58 | 1.70 | 1.86 | 2.08 | 2.20 |
8 | 1.00 | 1.20 | 1.58 | 1.70 | 1.86 | 2.08 | 2.20 |
Recom. | 1.00 | 1.20 | 1.58 | 1.70 | 1.86 | 2.07 | 2.20 |
σ 3,4 | 6 | 1.20 | 1.42 | 1.83 | 1.95 | 2.14 | 2.35 | 2.50 |
7 | 1.20 | 1.42 | 1.83 | 1.95 | 2.13 | 2.35 | 2.50 |
8 | 1.20 | 1.42 | 1.83 | 1.95 | 2.13 | 2.36 | 2.50 |
Recom. | 1.20 | 1.42 | 1.83 | 1.95 | 2.13 | 2.35 | 2.50 |
σ 4,5 | 6 | 1.30 | 1.60 | 2.13 | 2.28 | 2.53 | 2.83 | 3.01 |
7 | 1.30 | 1.60 | 2.13 | 2.28 | 2.53 | 2.83 | 3.00 |
8 | 1.30 | 1.60 | 2.13 | 2.28 | 2.53 | 2.83 | 3.00 |
Recom. | 1.30 | 1.60 | 2.13 | 2.28 | 2.53 | 2.83 | 3.00 |
σ 5,6 | 6 | 1.40 | 1.80 | 2.51 | 2.75 | 3.06 | 3.46 | 3.70 |
7 | 1.40 | 1.80 | 2.51 | 2.74 | 3.05 | 3.46 | 3.71 |
8 | 1.40 | 1.80 | 2.51 | 2.74 | 3.06 | 3.46 | 3.70 |
Recom. | 1.40 | 1.80 | 2.51 | 2.74 | 3.06 | 3.46 | 3.70 |
σ 6,7 | 7 | 1.45 | 1.90 | 2.75 | 2.96 | 3.35 | 3.83 | 4.11 |
8 | 1.45 | 1.90 | 2.75 | 2.97 | 3.35 | 3.82 | 4.11 |
Recom. | 1.45 | 1.90 | 2.75 | 2.97 | 3.35 | 3.83 | 4.10 |
σ 7,8 | 8 | 1.50 | 2.00 | 2.95 | 3.25 | 3.65 | 4.20 | 4.50 |
Recom. | 1.50 | 2.00 | 2.95 | 3.25 | 3.65 | 4.20 | 4.50 |
σ q,q-1 | Z | σ max,c1 , 10 -16 , cm 2 /atom | ||||||
H2 | He | N2 | Ne | Ar | Kr | Xe | ||
σ 0,-1 | 1 | 0.116 | 0.065 | 0.156 | 0.129 | 0.341 | 0.460 | 0.728 |
6 | 0.335 | 0.235 | 0.327 | 0.447 | 0.920 | 1.50 | 2.11 | |
8 | 0.500 | 0.257 | 0.450 | 0.800 | 1.76 | 3.39 | 5.39 |
σ 1,0 | 1 | 4.84 | 1.75 | 5.80 | 2.94 | 14.5 | 26.0 | 34.3 |
2 | 1.34 | 7.11 | 3.60 | 6.60 | 7.59 | 10.2 | 13.5 |
6 | 4.29 | 1.47 | 4.54 | 5.29 | 9.99 | 21.7 | 48.5 |
7 | 4.99 | 3.28 | 5.80 | 4.85 | 17.9 | 23.6 | 33.1 |
8 | 6.20 | 1.81 | 6.50 | 4.39 | 14.9 | 10.9 | 20.7 |
σ 2,1 | 2 | 5.99 | 2.60 | 6.28 | 5.34 | 12.1 | 20.9 | 28.0 |
6 | 5.44 | 5.83 | 6.86 | 10.4 | 13.4 | 27.6 | 77.8 |
7 | 4.00 | 5.76 | 9.00 | 18.8 | 10.1 | 21.7 | 41.2 |
8 | 2.76 | 6.92 | 3.49 | 5.30 | 6.33 | 15.6 | 24.8 |
σ 3,2 | 6 | 7.38 | 16.9 | 9.49 | 13.7 | 16.2 | 35.7 | 78.1 |
7 | 7.83 | 6.86 | 8.15 | 10.3 | 20.7 | 32.8 | 55.5 |
8 | 7.29 | 4.54 | 9.33 | 11.5 | 16.5 | 28.6 | 35.0 |
σ 4,3 | 6 | 13.9 | 5.15 | 12.5 | 17.8 | 38.0 | 44.9 | 86.8 |
7 | 16.5 | 8.07 | 14.0 | 18.0 | 32.0 | 42.7 | 64.7 |
8 | 15.4 | 8.99 | 12.8 | 16.5 | 28.0 | 34.5 | 48.5 |
σ 5,4 | 6 | 14.4 | 16.7 | 20.2 | 29.8 | 48.8 | 60.0 | 97.2 |
7 | 13.7 | 15.5 | 18.8 | 25.8 | 38.0 | 48.6 | 80.8 |
8 | 16.4 | 21.2 | 16.5 | 18.2 | 34.1 | 43.8 | 59.1 |
σ 6,5 | 6 | 22.3 | 14.8 | 41.0 | 52.0 | 77.2 | 89.8 | 111.1 |
7 | 22.0 | 15.1 | 30.7 | 37.1 | 62.8 | 76.4 | 103.2 |
8 | 21.4 | 14.0 | 19.5 | 25.0 | 55.3 | 66.0 | 95.0 |
σ 7,6 | 7 | 24.5 | 28.0 | 45.2 | 69.3 | 83.1 | 124.3 | 148.7 |
8 | 22.9 | 18.1 | 24.8 | 33.0 | 73.7 | 95.0 | 124.0 |
σ 8,7 | 8 | 26.3 | 30.8 | 45.2 | 62.2 | 87.9 | 114.0 | 147.7 |
σ q,q-1 | Z | αc1 | ||||||
H2 | He | N2 | Ne | Ar | Kr | Xe | ||
σ 0,-1 | 1 | 5.35 | 5.35 | 4.19 | 3.89 | 3.63 | 3.45 | 3.45 |
6 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.84 | 2.85 | |
8 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
σ 1,0 | 1 | 5.35 | 5.35 | 4.19 | 3.90 | 3.62 | 3.45 | 3.45 |
2 | 5.35 | 5.35 | 3.50 | 3.25 | 3.00 | 2.84 | 2.85 |
6 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
7 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
8 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
σ 2,1 | 2 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.86 | 2.85 |
6 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
7 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
8 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
σ 3,2 | 6 | 4.56 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
7 | 4.50 | 4.51 | 3.50 | 3.25 | 3.00 | 2.86 | 2.85 |
8 | 4.50 | 4.50 | 3.50 | 3.23 | 2.98 | 2.85 | 2.85 |
σ 4,3 | 6 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
7 | 4.51 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
8 | 4.50 | 4.50 | 3.49 | 3.25 | 2.99 | 2.85 | 2.82 |
σ 5,4 | 6 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
7 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
8 | 4.53 | 4.51 | 3.50 | 3.26 | 3.00 | 2.85 | 2.84 |
σ 6,5 | 6 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
7 | 4.50 | 4.51 | 3.51 | 3.25 | 3.00 | 2.85 | 2.85 |
8 | 4.50 | 4.51 | 3.52 | 3.25 | 2.99 | 2.84 | 2.85 |
σ 7,6 | 7 | 4.50 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
8 | 4.51 | 4.50 | 3.50 | 3.25 | 3.00 | 2.85 | 2.85 |
σ 8,7 | 8 | 4.51 | 4.47 | 3.51 | 3.25 | 3.01 | 2.86 | 2.87 |
σ q,q-1 | Recom. | 4.51 | 4.47 | 3.51 | 3.25 | 3.01 | 2.86 | 2.87 |