Расчет коэффициента ассиметрии при рассеянии релятивистских частиц на кулоновском потенциале (стр. 6 из 7)
 ° |  0.2 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | |
| 15 |  S | 6.98*1062.97 *10-5 | 3.84*105-1.92*10-4 | 1.41*105-2.68*10-4 | 5.80*104-3.24*10-4 | 2.50*104-3.56*10-4 | 1.04*104-3.55*10-4 | 3.41*103-2.94*10-4 |
| 30 | S | 4.54*105-7.90*10-4 | 2.50*104-1.80*10-3 | 9.13*103-2.13*10-3 | 3.75*104-2.36*10-3 | 1.61*103-2.45*10-3 | 6.63*102-2.35*10-3 | 2.17*102-1.92*10-3 |
| 45 | S | 9.52*104-3.00*10-3 | 5.20*103-5.14*10-3 | 1.89*103-5.88*10-3 | 7.72*102-6.40*10-3 | 3.28*102-6.60*10-3 | 1.34*102-6.33*10-3 | 43.3-5.19*10-3 |
| 60 | S | 3.27*104-6.28*10-3 | 1.76*103-9.73*10-3 | 6.35*102-0.0110 | 2.56*102-0.0120 | 1.07*102-0.0125 | 43.0 -0.0121 | 13.6 -0.0101 |
| 75 | S | 1.48*104-9.90*10-3 | 7.87*102-0.0147 | 2.80*102-0.0167 | 1.11*102-0.0184 | 45.7 -0.0194 | 17.9 -0.0192 | 5.50 -0.0164 |
| 90 | S | 8.11*103-0.0130 | 4.22*102-0.0191 | 1.48*102-0.0220 | 57.7 -0.0244 | 23.1 -0.0263 | 8.76 -0.0269 | 2.58 -0.0240 |
| 105 | S | 5.09*103-0.0150 | 2.60*102-0.0220 | 89.6 -0.0256 | 34.2 -0.0290 | 13.3 -0.0321 | 4.83 -0.0341 | 1.34 -0.0324 |
| 120 | S | 3.56 -0.0152 | 1.78 -0.0226 | 6.04 -0.0266 | 2.25 -0.0309 | 8.47 -0.0353 | 2.93 -0.0394 | 0.748-0.0406 |
| 135 | S | 2.74*103-0.0136 | 1.34*102-0.0205 | 44.8 -0.0244 | 16.3 -0.0290 | 5.94 -0.0342 | 1.94 -0.0404 | 0.446-0.0461 |
| 150 | S | 2.28*103-0.0102 | 1.10*102-0.0155 | 36.4 -0.0187 | 13.0 -0.0226 | 4.58 -0.0276 | 1.42 -0.0343 | 0.288-0.0444 |
| 165 | S | 2.05*103-5.48*10-3 | 98.0 -8.38*10-3 | 32.1 -0.0102 | 11.3 -0.0125 | 3.90 -0.0156 | 1.16 -0.0202 | 0.211-0.0290 |
[3].
В данной работе мы рассчитали функцию Шермана S(θ) по формулам Мотта и сравнили ее с значениями приведенными Шерманом [3]. В ходе этого обнаружилось, что при малых углах и скоростях мы получаем расхождение с Шерманом, а при больших углах наблюдается хорошее согласие.
Z=80
| ° | 0.2 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | |
| 15 | S | -0.000418302 | -0.000756439 | 0.00145307 | 0.00329674 | 0.0039953 | 0.00373716 | 0.00274968 |
| 30 | S | -0.00187486 | 0.0152943 | 0.0195888 | 0.0166319 | 0.0114146 | 0.0063109 | 0.00229958 |
| 45 | S | -0.0096423 | 0.0392795 | 0.0201246 | 0.00200746 | -0.0106478 | -0.0173581 | -0.01755 |
| 60 | S | 0.0564524 | 0.00215459 | -0.0380525 | -0.061627 | -0.0722324 | -0.0717536 | -0.0585935 |
| 75 | S | 0.0819812 | -0.104404 | -0.143382 | -0.160522 | -0.16228 | -0.149558 | -0.117176 |
| 90 | S | -0.0359008 | -0.233591 | -0.261294 | -0.27086 | -0.265409 | -0.242333 | -0.190523 |
| 105 | S | -0.203417 | -0.33333 | -0.356412 | -0.367131 | -0.364091 | -0.340456 | -0.276848 |
| 120 | S | -0.283302 | -0.371493 | -0.400819 | -0.423479 | -0.435978 | -0.42863 | -0.372563 |
| 135 | S | -0.261868 | -0.341975 | -0.379889 | -0.41743 | -0.452872 | -0.478899 | -0.464095 |
| 150 | S | -0.187517 | -0.257346 | -0.294901 | -0.33715 | -0.386582 | -0.445469 | -0.504932 |
| 165 | S | -0.095583 | -0.137073 | -0.160618 | -0.189017 | -0.22625 | -0.281099 | -0.379501 |
Z=48
| ° | 0.2 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | |
| 15 | S | -0.000354003 | 0.00179185 | 0.00163194 | 0.00120204 | 0.000743085 | 0.000345745 | 0.0000581197 |
| 30 | S | 0.0043748 | 0.00230238 | -0.00115705 | -0.00367532 | -0.00523496 | -0.00581212 | -0.00513253 |
| 45 | S | 0.0122719 | -0.0119116 | -0.0187611 | -0.0226723 | -0.0241881 | -0.0232369 | -0.0188261 |
| 60 | S | -0.000775493 | -0.0427226 | -0.0510018 | -0.0550211 | -0.0553761 | -0.0515071 | -0.0410046 |
| 75 | S | -0.037162 | -0.0831498 | -0.0918924 | -0.0959215 | -0.0953098 | -0.0885493 | -0.0709926 |
| 90 | S | -0.0801096 | -0.12314 | -0.133128 | -0.138642 | -0.138991 | -0.13141 | -0.108084 |
| 105 | S | -0.111543 | -0.152591 | -0.165502 | -0.174899 | -0.179562 | -0.175566 | -0.151203 |
| 120 | S | -0.12179 | -0.16341 | -0.180143 | -0.195181 | -0.207542 | -0.21321 | -0.197411 |
| 135 | S | -0.110379 | -0.151191 | -0.17031 | -0.190084 | -0.210816 | -0.230797 | -0.237679 |
| 150 | S | -0.0822047 | -0.116163 | -0.133585 | -0.153371 | -0.177409 | -0.208322 | -0.24701 |
| 165 | S | -0.0435328 | -0.0630519 | -0.0735821 | -0.0862266 | -0.102987 | -0.128248 | -0.175791 |
Z=13
| ° | 0.2 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | |
| 15 | S | 0.0000289762 | -0.000193137 | -0.000269304 | -0.000324673 | -0.000355381 | -0.000352534 | -0.000294804 |
| 30 | S | -0.000789803 | -0.00179821 | -0.00212978 | -0.00235565 | -0.00244758 | -0.00234771 | -0.0019201 |
| 45 | S | -0.00300104 | -0.00513906 | -0.00588438 | -0.00639987 | -0.00660143 | -0.00632627 | -0.00519423 |
| 60 | S | -0.00627752 | -0.00972718 | -0.0110393 | -0.0120076 | -0.012464 | -0.0120817 | -0.0100823 |
| 75 | S | -0.00989484 | -0.0147189 | -0.0167393 | -0.0183716 | -0.0193562 | -0.01916 | -0.0164415 |
| 90 | S | -0.0130368 | -0.0191377 | -0.0219487 | -0.024452 | -0.0263322 | -0.0268673 | -0.0240351 |
| 105 | S | -0.0149871 | -0.0220317 | -0.0255784 | -0.0290456 | -0.0321584 | -0.0341475 | -0.0324057 |
| 120 | S | -0.015253 | -0.0226232 | -0.0266354 | -0.0308998 | -0.0353208 | -0.0393887 | -0.0405279 |
| 135 | S | -0.0136347 | -0.0204602 | -0.0244242 | -0.028945 | -0.0342038 | -0.0403082 | -0.0460698 |
| 150 | S | -0.0102474 | -0.0155458 | -0.0187767 | -0.0226657 | -0.0276005 | -0.0343413 | -0.0443492 |
| 165 | S | -0.00549471 | -0.00839936 | -0.0102252 | -0.0124995 | -0.0155491 | -0.0201658 | -0.029066 |
Также мы рассчитали функцию Шермана по формулам Вонга, которые он получил путем решения уравнений Дирака [5]. Они отличались от соотношений, полученных Моттом, значениями коэффициентов Dk. Вонг пришел к выводу, что асимптотическое аналитическое выражение для сечения рассеяния в приближении малых α совпадает с аналитическим выражением для сечения Мотта в том же приближении.