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Calculation of anistropic glories for atom—molecule collisions
Physica 77 (1974) 203-204 ©North.Holland Publishing Co.
ERRATUM Calculation of anisotropic glories for a t o m - m o l e c u l e collisions W. FRANSSEN and J. REUSS [Physica 63 (1973) 313]
Recently, A. S. Dickinson and D. Richards have recalculated the integrals S (n, l-l', E, b) occurring in our article ref. 1 ; they used an advanced method observing that the S-integrals represent the solution o f a relatively simple differential equation (ref. 2). The numerical results o f this recent calculation deviate from the values tabulated in ref. 1 by as m u c h as 13%, in the worst case, ref. 3. L. Zande6 of our group has reanalyzed our integration routine; he discovered an error in the program. After correction o f this error and with a finer mesh of integration steps he was able to produce results in agreement with the calculations of Dickinson and Richards up to the third figure after the decimal point. Because the results o f ref. 3 are more accurate and because that way o f calculation is less expensive we are grateful for the permission to produce the following more accurate table of S-integrals based on the results communicated to us by Dickinson and Richards. TABLE I S-integrals. The column belonging to one set of
E,b values corresponds to S(6,0,E,b); S(6,2,E,b); S(12,0,E,b ), and S(12,2,E,b). 1
2
3
5
7.5
1.10
0.48833 0.42325 0.25034 0.24068
0.61868 0.50222 0.31912 0.29817
0.69273 0.53662 0.35334 0.32269
0.76634 0.55837 0.37715 0.33340
0.79737 0.55753 0.37531 0.32398
1.15
0.49431 0.41910
0.62511 0.48809
0.69258 0.50941
0.73862 0.50524
0.73220 0.48312
203
204
W. FRANSSEN AND J. REUSS TABLE I (cont.) 1
2
3
5
7.5
1.15
0.24626 0.23521
0.30509 0.28092
0.32524 0.29054
0.31808 0.27280
0.28791 0.24127
1.20
0.50118 0.41403 0.24185 0.22918
0.63191 0.46991 0.28891 0.26097
0.68801 0.47372 0.29153 0.25284
0.69010 0.44019 0.25028 0.20715
0.64138 0.40318 0.20214 0.16497
1.25
0.50914 0.40774 0.23708 0.22249
0.63864 0.44590 0.26981 0.23747
0.67373 0.42648 0.25000 0.20830
0.61228 0.36685 0.17811 0.14246
0.53439 0.32705 0.13026 0.10463
1.30
0.51848 0.39983 0.23188 0.21500
0.64399 0.41322 0.24643 0.20905
0.63833 0.36538 0.19795 0.15663
0.50913 0.29498 0.11329 0.088746
0.43026 0.26212 0.079695 0.063732
REFERENCES 1) 2) 3)
Franssen, W. and Reuss, J., Physica 63 (1973) 313. Dickinson, A. S. and Richards, D., J. Phys. B, to be published. Dickinson, A. S. and Richards, D., private communication.
ERRATUM Calculation of anisotropic glories for a t o m - m o l e c u l e collisions W. FRANSSEN and J. REUSS [Physica 63 (1973) 313]
Recently, A. S. Dickinson and D. Richards have recalculated the integrals S (n, l-l', E, b) occurring in our article ref. 1 ; they used an advanced method observing that the S-integrals represent the solution o f a relatively simple differential equation (ref. 2). The numerical results o f this recent calculation deviate from the values tabulated in ref. 1 by as m u c h as 13%, in the worst case, ref. 3. L. Zande6 of our group has reanalyzed our integration routine; he discovered an error in the program. After correction o f this error and with a finer mesh of integration steps he was able to produce results in agreement with the calculations of Dickinson and Richards up to the third figure after the decimal point. Because the results o f ref. 3 are more accurate and because that way o f calculation is less expensive we are grateful for the permission to produce the following more accurate table of S-integrals based on the results communicated to us by Dickinson and Richards. TABLE I S-integrals. The column belonging to one set of
E,b values corresponds to S(6,0,E,b); S(6,2,E,b); S(12,0,E,b ), and S(12,2,E,b). 1
2
3
5
7.5
1.10
0.48833 0.42325 0.25034 0.24068
0.61868 0.50222 0.31912 0.29817
0.69273 0.53662 0.35334 0.32269
0.76634 0.55837 0.37715 0.33340
0.79737 0.55753 0.37531 0.32398
1.15
0.49431 0.41910
0.62511 0.48809
0.69258 0.50941
0.73862 0.50524
0.73220 0.48312
203
204
W. FRANSSEN AND J. REUSS TABLE I (cont.) 1
2
3
5
7.5
1.15
0.24626 0.23521
0.30509 0.28092
0.32524 0.29054
0.31808 0.27280
0.28791 0.24127
1.20
0.50118 0.41403 0.24185 0.22918
0.63191 0.46991 0.28891 0.26097
0.68801 0.47372 0.29153 0.25284
0.69010 0.44019 0.25028 0.20715
0.64138 0.40318 0.20214 0.16497
1.25
0.50914 0.40774 0.23708 0.22249
0.63864 0.44590 0.26981 0.23747
0.67373 0.42648 0.25000 0.20830
0.61228 0.36685 0.17811 0.14246
0.53439 0.32705 0.13026 0.10463
1.30
0.51848 0.39983 0.23188 0.21500
0.64399 0.41322 0.24643 0.20905
0.63833 0.36538 0.19795 0.15663
0.50913 0.29498 0.11329 0.088746
0.43026 0.26212 0.079695 0.063732
REFERENCES 1) 2) 3)
Franssen, W. and Reuss, J., Physica 63 (1973) 313. Dickinson, A. S. and Richards, D., J. Phys. B, to be published. Dickinson, A. S. and Richards, D., private communication.