экстраполяция экспериментальных функций отклика ядер 2н и

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À.Þ. Áóêè, È.À. Íåíüêî, Í.Ã. Øåâ÷åíêî ...
Ýêñòðàïîëÿöèÿ ýêñïåðèìåíòàëüíûõ ôóíêöèé ...
«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 664, 2005
ñåð³ÿ ô³çè÷íà «ßäðà, ÷àñòèíêè, ïîëÿ», âèï. 2 /27/
ɍȾɄ 539.171
ɗɄɋɌɊȺɉɈɅəɐɂə ɗɄɋɉȿɊɂɆȿɇɌȺɅɖɇɕɏ ɎɍɇɄɐɂɃ ɈɌɄɅɂɄȺ əȾȿɊ 2ɇ ɂ
4
ɇȿ ɋɌȿɉȿɇɇɈɃ ɎɍɇɄɐɂȿɃ
Ⱥ.ɘ. Ȼɭɤɢ, ɂ.Ⱥ. ɇɟɧɶɤɨ, ɇ.Ƚ. ɒɟɜɱɟɧɤɨ, ɂ.ɋ. Ɍɢɦɱɟɧɤɨ
ɇɇɐ “ɏɚɪɶɤɨɜɫɤɢɣ ɮɢɡɢɤɨ-ɬɟɯɧɢɱɟɫɤɢɣ ɢɧɫɬɢɬɭɬ”, 61108, ɍɤɪɚɢɧɚ, ɝ. ɏɚɪɶɤɨɜ, ɭɥ. Ⱥɤɚɞɟɦɢɱɟɫɤɚɹ 1
E-mail:[email protected]
ɉɨɫɬɭɩɢɥɚ ɜ ɪɟɞɚɤɰɢɸ 10 ɢɸɧɹ 2005 ɝ.
Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ ɨɩɪɟɞɟɥɟɧɢɹ ɦɨɦɟɧɬɨɜ ɮɭɧɤɰɢɣ ɨɬɤɥɢɤɚ ɹɞɟɪ ɧɟɨɛɯɨɞɢɦɨ ɷɤɫɬɪɚɩɨɥɢɪɨɜɚɬɶ
ɮɭɧɤɰɢɸ ɨɬɤɥɢɤɚ ɜ ɨɛɥɚɫɬɶ ɛɨɥɶɲɢɯ ɩɟɪɟɞɚɧɧɵɯ ɷɧɟɪɝɢɣ, ɝɞɟ ɧɟɜɨɡɦɨɠɧɨ ɩɪɨɜɟɞɟɧɢɟ ɢɡɦɟɪɟɧɢɣ. ɇɚɫɬɨɹɳɚɹ ɪɚɛɨɬɚ ɩɨɫɜɹɳɟɧɚ ɢɫɫɥɟɞɨɜɚɧɢɸ ɜɨɩɪɨɫɚ ɷɤɫɬɪɚɩɨɥɹɰɢɢ ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ ɩɨɫɪɟɞɫɬɜɨɦ ɫɬɟɩɟɧɧɨɣ ɮɭɧɤɰɢɢ. Ⱦɥɹ ɷɬɨɝɨ ɢɫɩɨɥɶɡɨɜɚɧɵ
ɞɚɧɧɵɟ ɢɡɦɟɪɟɧɢɣ ɧɚ ɹɞɪɚɯ 2ɇ ɢ 4ɇɟ ɩɪɢ ɩɟɪɟɞɚɧɧɵɯ ɢɦɩɭɥɶɫɚɯ 0,9 y 1,5 ɮɦ1. ɇɚɣɞɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɩɨɤɚɡɚɬɟɥɹ ɫɬɟɩɟɧɢ
ɷɤɫɬɪɚɩɨɥɹɰɢɨɧɧɨɣ ɮɭɧɤɰɢɢ ɫɪɚɜɧɢɜɚɸɬɫɹ ɫ ɪɟɡɭɥɶɬɚɬɚɦɢ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɪɚɫɱɺɬɨɜ.
ɄɅɘɑȿȼɕȿ ɋɅɈȼȺ: ɚɬɨɦɧɵɟ ɹɞɪɚ, ɪɚɫɫɟɹɧɢɟ ɷɥɟɤɬɪɨɧɨɜ, ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ, ɷɤɫɬɪɚɩɨɥɹɰɢɹ, ɫɬɟɩɟɧɧɚɹ ɮɭɧɤɰɢɹ.
ȼɚɠɧɵɦ ɧɚɩɪɚɜɥɟɧɢɟɦ ɹɞɟɪɧɨ-ɮɢɡɢɱɟɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɹɜɥɹɟɬɫɹ ɢɡɭɱɟɧɢɟ ɦɨɦɟɧɬɨɜ ɮɭɧɤɰɢɣ ɨɬɤɥɢɤɚ
(ɫɦ. ɧɚɩɪɢɦɟɪ ɨɛɡɨɪ [1]), ɤɨɬɨɪɵɟ ɢɦɟɸɬ ɜɢɞ
(k )
S T/L (q)
f
³ RT/L (q,Ȧ)Ȧ
k
dȦ ,
(1)
0
ɝɞɟ k ɧɨɦɟɪ ɦɨɦɟɧɬɚ, q ɢ Z ɩɟɪɟɞɚɧɧɵɟ ɹɞɪɭ 3-ɢɦɩɭɥɶɫ ɢ ɷɧɟɪɝɢɹ ɜ ɫɢɫɬɟɦɟ ɰɟɧɬɪɚ ɢɧɟɪɰɢɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ,
RT/L(q,Z) ɩɨɩɟɪɟɱɧɚɹ (T) ɢɥɢ ɩɪɨɞɨɥɶɧɚɹ (L) ɮɭɧɤɰɢɹ ɨɬɤɥɢɤɚ (ɡɞɟɫɶ R-ɮɭɧɤɰɢɢ ɜ ɩɪɟɞɫɬɚɜɥɟɧɢɢ ɪɚɛɨɬɵ [1]). ȼ
ɫɥɭɱɚɟ q = const, ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ ɩɨ ɩɟɪɟɦɟɧɧɨɣ Z ɢɦɟɸɬ ɜɢɞ ɤɚɤ ɧɚ ɪɢɫ.1ɚ ɚɫɢɦɦɟɬɪɢɱɧɨɝɨ ɩɢɤɚ ɫ ɦɨɧɨɬɨɧɧɨ ɭɛɵɜɚɸɳɢɦ ɜ ɫɬɨɪɨɧɭ ɛɨɥɶɲɢɯ ɩɟɪɟɞɚɧɧɵɯ ɷɧɟɪɝɢɣ “ɯɜɨɫɬɨɦ” (ɞɚɥɟɟ ɛɟɡ ɤɚɜɵɱɟɤ).
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɩɨɩɟɪɟɱɧɨɣ ɢ ɩɪɨɞɨɥɶɧɨɣ ɮɭɧɤɰɢɣ ɨɬɤɥɢɤɚ ɨɛɵɱɧɨ ɨɯɜɚɬɵɜɚɸɬ (80 y 90)%
ɩɥɨɳɚɞɢ ɩɨɞ ɷɬɢɦɢ ɮɭɧɤɰɢɹɦɢ, ɚ ɜɟɪɯɧɹɹ ɝɪɚɧɢɰɚ ɢɯ ɢɡɦɟɪɟɧɢɣ ɩɨ ɩɟɪɟɞɚɧɧɨɣ ɷɧɟɪɝɢɢ ɨɤɨɥɨ Z = 0,5·q. ɂɡ ɷɬɨɝɨ ɫɥɟɞɭɟɬ, ɱɬɨ ɞɥɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɩɪɨɜɟɪɤɢ ɪɚɫɱɺɬɨɜ S(k)T/L(q) ɬɪɟɛɭɸɬɫɹ ɷɤɫɬɪɚɩɨɥɹɰɢɢ ɮɭɧɤɰɢɣ RT/L(q,Z) ɜ
ɨɛɥɚɫɬɶ ɛɨɥɶɲɢɯ ɩɟɪɟɞɚɧɧɵɯ ɷɧɟɪɝɢɣ, ɝɞɟ ɧɟɜɨɡɦɨɠɧɵ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɵɟ ɢɡɦɟɪɟɧɢɹ. Ɉɬ ɷɬɨɣ ɷɤɫɬɪɚɩɨɥɹɰɢɢ
ɡɚɜɢɫɢɬ ɤɚɤ ɬɨɱɧɨɫɬɶ ɩɨɥɭɱɚɟɦɵɯ ɢɡ ɷɤɫɩɟɪɢɦɟɧɬɚ ɦɨɦɟɧɬɨɜ S(k)T/L(q), ɬɚɤ ɢ ɡɧɚɱɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɧɨɦɟɪɚ
ɦɨɦɟɧɬɚ kmax, ɩɪɢ ɤɨɬɨɪɨɦ ɢɧɬɟɝɪɚɥ (1) ɢɦɟɟɬ ɤɨɧɟɱɧɨɟ ɡɧɚɱɟɧɢɟ. Ɂɧɚɱɢɦɨɫɬɶ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɷɤɫɬɪɚɩɨɥɹɰɢɢ
ɨɩɪɟɞɟɥɟɧɚ ɜ ɪɚɛɨɬɟ [1] (ɫɬɪ. 275) ɤɚɤ ɜɨɩɪɨɫ, ɛɟɡ ɨɬɜɟɬɚ ɧɚ ɤɨɬɨɪɵɣ ɩɪɚɜɢɥɚ ɫɭɦɦ ɪɢɫɤɭɸɬ ɨɫɬɚɬɶɫɹ ɩɪɟɞɫɬɚɜɥɹɸɳɢɦɢ ɬɨɥɶɤɨ ɚɤɚɞɟɦɢɱɟɫɤɢɣ ɢɧɬɟɪɟɫ.
ȼ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɪɚɛɨɬɚɯ ɩɨ ɢɫɫɥɟɞɨɜɚɧɢɸ ɦɨɦɟɧɬɨɜ S(k)T/L(q) (ɫɦ. [2, 3, 4]), ɤɚɤ ɩɪɚɜɢɥɨ, ɢɫɩɨɥɶɡɭɸɬɫɹ ɮɭɧɤɰɢɢ ɷɤɫɬɪɚɩɨɥɹɰɢɢ ɜɢɞɚ
R t, E(q,Z) = CE(q) eE Z,
(2)
R t,D(q,Z) = CD(q) Z D.
(3)
E
D
ɜɟɥɢɱɢɧɵ C (q), C (q), D ɢ E ɦɨȼ ɫɥɭɱɚɟ q = const, ɱɬɨ ɹɜɥɹɟɬɫɹ ɭɫɥɨɜɢɟɦ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɦɨɦɟɧɬɨɜ
ɝɭɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶɫɹ ɤɚɤ ɩɚɪɚɦɟɬɪɵ ɩɨɞɝɨɧɤɢ R t-ɮɭɧɤɰɢɢ ɤ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ.
Ɏɭɧɤɰɢɹ (2), ɧɚɫɤɨɥɶɤɨ ɧɚɦ ɢɡɜɟɫɬɧɨ, ɹɜɥɹɟɬɫɹ ɷɦɩɢɪɢɱɟɫɤɨɣ. Ɏɭɧɤɰɢɹ (3), ɤɨɬɨɪɚɹ ɛɭɞɟɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶɫɹ ɜ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɟ, ɩɪɟɞɥɨɠɟɧɚ ɜ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɪɚɛɨɬɚɯ [1, 5]. ȿɺ ɪɚɫɱɺɬ ɜɵɩɨɥɧɟɧ ɧɚ ɨɫɧɨɜɟ ɩɨɬɟɧɰɢɚɥɚ Ɋɟɣɞɚ ɫ ɦɹɝɤɢɦ ɤɨɪɨɦ ɞɥɹ 2ɇ (D = 3 y 4) [1] ɢ ɞɥɹ ɛɨɥɟɟ ɬɹɠɟɥɵɯ ɹɞɟɪ (D = 2,5) [5]. ɋɨɝɥɚɫɧɨ ɷɬɢɦ ɪɚɛɨɬɚɦ ɡɧɚɱɟɧɢɟ
ɩɚɪɚɦɟɬɪɚ D ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɜɟɥɢɱɢɧɵ ɩɟɪɟɞɚɧɧɨɝɨ ɢɦɩɭɥɶɫɚ.
ȼ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɪɚɛɨɬɚɯ ɩɨ ɮɭɧɤɰɢɹɦ ɨɬɤɥɢɤɚ ɩɪɨɛɥɟɦɚ R t-ɮɭɧɤɰɢɣ ɨɫɜɟɳɟɧɚ ɦɚɥɨ. Ɍɚɤ, ɢɡ ɨɩɭɛɥɢɤɨɜɚɧɧɵɯ ɞɚɧɧɵɯ ɢɡɜɟɫɬɧɨ ɬɨɥɶɤɨ ɞɜɚ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɚ D, ɤɨɬɨɪɵɟ ɩɨɥɭɱɟɧɵ ɢɡ ɷɤɫɩɟɪɢɦɟɧɬɚ: ɧɚɣɞɟɧɧɨɟ
ȼ.Ⱦ. ɗɮɪɨɫɨɦ [6] ɩɨ ɢɡɦɟɪɟɧɢɹɦ ɪɚɛɨɬɵ [7] ɞɥɹ ɹɞɪɚ 3He ɩɪɢ q = 1,5 ɮɦ1 (DL = 3,9 y 4,1) ɢ ɜ ɪɚɛɨɬɟ [8] ɞɥɹ ɹɞɪɚ
2
ɇ ɩɪɢ q = 1,05 ɮɦ1 (DT/L = 2,9).
ȼ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɟ ɦɵ ɢɫɫɥɟɞɭɟɦ ɩɪɨɛɥɟɦɭ ɚɞɟɤɜɚɬɧɨɫɬɢ ɫɬɟɩɟɧɧɨɣ ɮɭɧɤɰɢɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ ɜ ɪɚɣɨɧɟ ɯɜɨɫɬɚ R-ɮɭɧɤɰɢɣ ɹɞɟɪ 2ɇ ɢ 4He, ɧɚɯɨɞɢɦ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɚ D, ɪɚɫɫɦɚɬɪɢɜɚɟɦ ɩɪɢɦɟɧɟɧɢɟ ɩɨɥɭɱɟɧɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɤ ɩɪɨɛɥɟɦɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɦɨɦɟɧɬɨɜ ɮɭɧɤɰɢɣ ɨɬɤɥɢɤɚ ɹɞɟɪ.
S(k)T/L(q),
ɆȿɌɈȾɂɄȺ ɂɋɋɅȿȾɈȼȺɇɂə ɎɍɇɄɐɂɃ ɗɄɋɌɊȺɉɈɅəɐɂɂ
Ɂɚɞɚɱɚ ɨɩɪɟɞɟɥɟɧɢɹ ɚɞɟɤɜɚɬɧɨɫɬɢ R t-ɮɭɧɤɰɢɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɡɧɚɱɟɧɢɹɦ RT/L(q,Z) ɨɫɧɨɜɵɜɚɟɬɫɹ ɧɚ
ɩɨɞɝɨɧɤɟ ɟɺ ɤ ɷɬɢɦ ɞɚɧɧɵɦ ɜ ɬɨɦ ɞɢɚɩɚɡɨɧɟ Z, ɤɨɬɨɪɵɣ ɨɬɧɨɫɢɬɫɹ ɤ ɢɡɦɟɪɟɧɧɨɣ ɱɚɫɬɢ ɯɜɨɫɬɚ ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ
46
À.Þ. Áóêè, È.À. Íåíüêî, Í.Ã. Øåâ÷åíêî ...
«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 664, 2005
Ɋɢɫ. 1. Ɇɟɬɨɞɢɤɚ ɨɩɪɟɞɟɥɟɧɢɹ ɚɞɟɤɜɚɬɧɨɫɬɢ R t –
ɮɭɧɤɰɢɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ.
(ɚ) ɫɯɟɦɚɬɢɱɟɫɤɨɟ ɢɡɨɛɪɚɠɟɧɢɟ ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ.
ɉɭɧɤɬɢɪɧɵɦɢ ɥɢɧɢɹɦɢ ɩɨɤɚɡɚɧ ɤɨɪɢɞɨɪ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ, ɫɩɥɨɲɧɨɣ ɥɢɧɢɟɣ – R t –ɮɭɧɤɰɢɹ; Zc - ɝɪɚɧɢɰɚ ɯɜɨɫɬɚ, Zcc - ɜɟɪɯɧɹɹ ɝɪɚɧɢɰɚ ɢɡɦɟɪɟɧɧɵɯ ɞɚɧɧɵɯ, Zc ÷ Zɚ – ɞɢɚɩɚɡɨɧ ɚɞɟɤɜɚɬɧɨɫɬɢ
R t -ɮɭɧɤɰɢɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ, Zmin ÷ Zmax
– ɨɛɥɚɫɬɶ ɩɨɞɝɨɧɤɢ R t -ɮɭɧɤɰɢɢ.
(ɛ) ɡɚɜɢɫɢɦɨɫɬɶ D(Zmin) ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɮɢɤɫɢɪɨɜɚɧɧɵɯ ɡɧɚɱɟɧɢɹɯ Zmax.
(ɜ) ɡɚɜɢɫɢɦɨɫɬɶ D(Zmɚɯ) ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɦ ɡɧɚɱɟɧɢɢ Zmin.
D
(ɧɚ ɪɢɫ.1ɚ ɞɚɧɧɵɟ ɩɪɢ Z ! Zc, ɝɞɟ Zc ɝɪɚɧɢɰɚ ɨɛɥɚɫɬɢ ɯɜɨɫɬɚ). ɉɪɢ ɷɬɨɦ ɨɪɢɟɧɬɚɰɢɹ ɧɚ ɜɟɥɢɱɢɧɭ ɡɧɚɱɟɧɢɹ ɦɢɧɢɦɚɥɶɧɨɝɨ F2 ɹɜɥɹɟɬɫɹ ɧɟɨɛɯɨɞɢɦɵɦ, ɧɨ ɧɟɞɨɫɬɚɬɨɱɧɵɦ ɭɫɥɨɜɢɟɦ.
Ɍɚɤ ɤɚɤ R t-ɮɭɧɤɰɢɹ ɞɨɥɠɧɚ ɚɩɩɪɨɤɫɢɦɢɪɨɜɚɬɶ ɜɟɫɶ ɯɜɨɫɬ
ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ, ɬɨ ɦɨɠɧɨ ɩɨɬɪɟɛɨɜɚɬɶ, ɱɬɨɛɵ ɩɨɥɭɱɚɟɦɵɟ
ɢɡ ɩɨɞɝɨɧɤɢ ɡɧɚɱɟɧɢɹ ɜɚɪɶɢɪɭɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ ɧɟ ɡɚɜɢɫɟɥɢ
ɨɬ ɜɵɛɨɪɚ ɞɢɚɩɚɡɨɧɚ Z, ɞɚɧɧɵɟ ɢɡ ɤɨɬɨɪɨɝɨ ɭɱɚɫɬɜɭɸɬ ɜ ɩɨɞɝɨɧɤɟ (ɞɚɧɧɵɟ ɢɡ ɨɛɥɚɫɬɢ Z ! Zc). Ȼɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɷɬɨ
ɬɪɟɛɨɜɚɧɢɟ ɤɚɤ ɤɪɢɬɟɪɢɣ ɚɞɟɤɜɚɬɧɨɫɬɢ ɚɧɚɥɢɬɢɱɟɫɤɨɣ ɮɭɧɤɰɢɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ.
Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɩɨɞɝɨɧɤɚ R t-ɮɭɧɤɰɢɢ ɞɚɥɚ ɧɟ ɫɥɢɲɤɨɦ
ɛɨɥɶɲɭɸ ɨɲɢɛɤɭ ɜɚɪɶɢɪɭɟɦɨɝɨ ɩɚɪɚɦɟɬɪɚ, ɞɢɚɩɚɡɨɧ ɩɟɪɟɞɚɧɧɵɯ ɷɧɟɪɝɢɣ, ɜ ɤɨɬɨɪɨɦ ɧɚɯɨɞɹɬɫɹ ɭɱɚɫɬɜɭɸɳɢɟ ɜ ɩɨɞɝɨɧɤɟ ɞɚɧɧɵɟ, ɢ ɢɯ ɤɨɥɢɱɟɫɬɜɨ ɞɨɥɠɧɵ ɛɵɬɶ ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɨɡɧɢɤɚɟɬ ɡɚɞɚɱɚ ɨɩɪɟɞɟɥɟɧɢɹ ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɤɚɠɞɨɣ ɢɡ ɩɨɞɝɨɧɨɤ ɤɨɥɢɱɟɫɬɜɚ ɞɚɧɧɵɯ, ɞɢɚɩɚɡɨɧɚ ɷɬɢɯ ɞɚɧɧɵɯ ɩɨ Z, ɚ ɬɚɤ ɠɟ ɜɨɩɪɨɫ ɨ ɝɪɚɧɢɰɟ ɨɛɥɚɫɬɢ, ɨɬɤɭɞɚ ɷɬɢ ɞɚɧɧɵɟ ɜɵɛɢɪɚɸɬɫɹ, ɬɨ ɟɫɬɶ ɨ ɡɧɚɱɟɧɢɢ Zc.
Ɉɞɧɢɦ ɢɡ ɭɞɨɛɧɵɯ ɞɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɚɧɚɥɢɡɚ ɪɟɲɟɧɢɣ
ɹɜɥɹɟɬɫɹ ɫɥɟɞɭɸɳɢɣ ɩɨɞɯɨɞ. ɉɭɫɬɶ Zmin ɧɢɠɧɹɹ ɝɪɚɧɢɰɚ
ɞɢɚɩɚɡɨɧɚ ɞɚɧɧɵɯ ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɩɨɞɝɨɧɤɟ ɢ Zmax ɟɝɨ
ɜɟɪɯɧɹɹ ɝɪɚɧɢɰɚ, ɚ ɜɫɹ ɨɛɥɚɫɬɶ ɢɡɦɟɪɟɧɧɨɝɨ ɯɜɨɫɬɚ ɮɭɧɤɰɢɢ
ɨɬɤɥɢɤɚ Zc y Zcc, ɝɞɟ Zcc ɦɚɤɫɢɦɚɥɶɧɚɹ ɩɟɪɟɞɚɧɧɚɹ ɷɧɟɪɝɢɹ,
ɩɪɢ ɤɨɬɨɪɨɣ ɩɨɥɭɱɟɧɵ ɞɚɧɧɵɟ (ɫɦ. ɪɢɫ. 1ɚ). ȼɨɡɶɦɟɦ ɜ ɤɚɱɟɫɬɜɟ Zmax ɡɧɚɱɟɧɢɟ ɛɥɢɡɤɨɟ ɤ Zcc ɢ ɡɚɮɢɤɫɢɪɭɟɦ ɟɝɨ. Ⱦɚɥɟɟ
ɩɪɨɜɟɞɺɦ ɪɹɞ ɩɨɞɝɨɧɨɤ ɜ ɞɢɚɩɚɡɨɧɚɯ ɨɝɪɚɧɢɱɟɧɧɵɯ ɷɬɢɦ
Zmax ɢ ɪɚɡɥɢɱɧɵɦɢ Zmin. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɧɚɣɞɺɦ ɡɧɚɱɟɧɢɹ
ɜɚɪɶɢɪɭɟɦɨɝɨ ɩɚɪɚɦɟɬɪɚ D, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɦɢɧɢɦɚɥɶɧɵɦ
F2, ɢ ɩɨɥɭɱɢɦ ɡɚɜɢɫɢɦɨɫɬɶ D(Zmin) (ɫɩɥɨɲɧɚɹ ɥɢɧɢɹ ɧɚ
ɪɢɫ. 1ɛ). Ɍɟɩɟɪɶ ɩɪɟɞɥɨɠɟɧɧɵɣ ɤɪɢɬɟɪɢɣ ɚɞɟɤɜɚɬɧɨɫɬɢ R tɮɭɧɤɰɢɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ
ɤɚɤ ɬɪɟɛɨɜɚɧɢɟ ɩɨɫɬɨɹɧɫɬɜɚ ɜ ɩɪɟɞɟɥɚɯ r'Di(Zmin) ɡɧɚɱɟɧɢɣ
Di(Zmin) ɩɪɢ Zmin ! Zc. Ɉɬɦɟɬɢɦ, ɱɬɨ ɟɫɥɢ ɩɥɚɬɨ ɜ ɮɭɧɤɰɢɢ
Di(Zmin) ɧɚɛɥɸɞɚɟɬɫɹ, ɬɨ ɟɝɨ ɤɪɚɣ ɫɨ ɫɬɨɪɨɧɵ ɦɚɥɵɯ Z ɨɩɪɟɞɟɥɹɟɬ ɡɧɚɱɟɧɢɟ ɜɟɥɢɱɢɧɵ Zc.
ɉɪɢ ɢɫɫɥɟɞɨɜɚɧɢɢ R t-ɡɚɜɢɫɢɦɨɫɬɢ ɫɥɟɞɭɟɬ ɭɱɢɬɵɜɚɬɶ
ɜɨɡɦɨɠɧɨɫɬɶ ɩɪɢɫɭɬɫɬɜɢɹ ɜ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɡɧɚɱɟɧɢɹɯ
RT/L ɧɟɭɱɬɺɧɧɵɯ ɫɢɫɬɟɦɚɬɢɱɟɫɤɢɯ ɨɲɢɛɨɤ. ɇɚɢɛɨɥɟɟ ɫɭɳɟɫɬɜɟɧɧɨɣ ɢɡ ɜɨɡɦɨɠɧɵɯ ɫɢɫɬɟɦɚɬɢɱɟɫɤɢɯ ɨɲɢɛɨɤ ɦɨɠɟɬ
ɛɵɬɶ ɬɚ, ɱɬɨ ɫɜɹɡɚɧɚ ɫ ɜɵɱɢɬɚɧɢɟɦ ɮɨɧɚ ɢɡ ɫɩɟɤɬɪɚ ɪɚɫɫɟɹɧɧɵɯ ɷɥɟɤɬɪɨɧɨɜ. ɗɬɚ ɨɲɢɛɤɚ ɩɪɨɹɜɥɹɟɬɫɹ ɜ ɨɛɥɚɫɬɢ ɯɜɨɫɬɨɜ
ɮɭɧɤɰɢɣ ɨɬɤɥɢɤɚ ɤɚɤ ɜɟɥɢɱɢɧɚ ɩɨɫɬɨɹɧɧɚɹ ɢɥɢ ɤɚɤ ɧɚɪɚɫɬɚɸɳɚɹ ɫɨ ɡɧɚɱɟɧɢɟɦ Z.
Ɉɰɟɧɢɦ ɜɥɢɹɧɢɟ ɷɬɨɣ ɨɲɢɛɤɢ ɧɚ ɜɟɥɢɱɢɧɭ ɩɚɪɚɦɟɬɪɚ
D. Ⱦɥɹ ɷɬɨɝɨ ɪɚɫɫɦɨɬɪɢɦ ɞɜɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɡɧɚɱɟɧɢɹ
ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ: R(Z1) ɢ R(Z2) ɩɪɢ q = const. ɋɨɝɥɚɫɧɨ
ɜɵɪ.(3) R(Z1) = CD(q) Z1D ɢ R(Z2) = CD(q) Z2D. Ɋɚɡɞɟɥɢɜ ɩɟɪɜɨɟ ɪɚɜɟɧɫɬɜɨ ɧɚ ɜɬɨɪɨɟ ɢ ɩɪɨɥɨɝɚɪɢɮɦɢɪɨɜɚɜ ɨɬɧɨɲɟɧɢɹ,
ɧɚɣɞɺɦ
R (Z1 )
1
ln
.
ln Z 2 ln Z1 R(Z 2 )
(4)
ɉɭɫɬɶ ɜ ɨɛɨɢɯ ɡɧɚɱɟɧɢɹɯ ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ ɢɦɟɟɬɫɹ ɨɞɢɧɚɤɨɜɚɹ ɨɲɢɛɤɚ '. ɉɨɞɫɬɚɜɢɜ ɜ ɭɪɚɜɧɟɧɢɟ (4) ɜɦɟɫɬɨ
R(Z1) ɢ R(Z2) ɜɟɥɢɱɢɧɵ R(Z1)+' ɢ R(Z2)+', ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɧɟ ɬɪɭɞɧɨ ɩɨɥɭɱɢɬɶ
D dD
1
ln Z2 ln Z1
ª R(Z1 )
1 ' R (Z1 ) º
ln
«ln
».
1 ' R (Z2 ) »¼
¬« R (Z2 )
(5)
47
ñåð³ÿ ô³çè÷íà «ßäðà, ÷àñòèíêè, ïîëÿ», âèï. 2 /27/
Ýêñòðàïîëÿöèÿ ýêñïåðèìåíòàëüíûõ ôóíêöèé ...
ɉɪɢɦɟɦ Z1 = Zc ɢ Z2 = Zcc. Ɍɚɤ ɤɚɤ ɜ ɪɟɚɥɶɧɵɯ ɞɚɧɧɵɯ R(Zc) !! R(Zcc), ɬɨ ɢɡ ɭɪɚɜɧɟɧɢɣ (4) ɢ (5) ɫɥɟɞɭɟɬ
dĮ |
1
1
ɑln
.
ln Ȧcc - ln Ȧc
1+ ǻ R (Ȧcc)
(6)
ɍɪɚɜɧɟɧɢɟ (6) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɜɨɡɦɨɠɧɚɹ ɨɲɢɛɤɚ ɩɚɪɚɦɟɬɪɚ, ɫɜɹɡɚɧɧɚɹ ɫ ɜɵɱɢɬɚɧɢɟɦ ɮɨɧɚ, ɨɩɪɟɞɟɥɹɟɬɫɹ ɡɧɚɱɟɧɢɹɦɢ R(Z) ɢɡ ɨɤɪɟɫɬɧɨɫɬɢ Zcc. Ɋɨɥɶ ɷɬɨɣ ɨɲɢɛɤɢ ɦɟɧɶɲɟ ɩɪɢ ɩɨɞɝɨɧɤɟ ɤ ɞɚɧɧɵɦ ɢɡ ɲɢɪɨɤɨɝɨ ɞɢɚɩɚɡɨɧɚ Z, ɝɞɟ
ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ '/R(Z) ɧɟ ɜɟɥɢɤɨ, ɨɞɧɚɤɨ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɩɥɚɬɨ Di(Zmin) ɦɨɠɟɬ ɛɵɬɶ ɜɵɪɚɠɟɧɨ ɯɭɠɟ (ɲɬɪɢɯɨɜɚɹ
ɥɢɧɢɹ ɧɚ ɪɢɫ.1ɛ). Ɂɚɦɟɬɢɦ, ɱɬɨ ɟɫɥɢ ɟɫɬɶ ɪɚɫɫɦɨɬɪɟɧɧɵɟ ɜɵɲɟ ɨɲɢɛɤɢ ɢɡɦɟɪɟɧɢɣ, ɬɨ ɧɚɲ ɩɨɞɯɨɞ ɩɨɡɜɨɥɹɟɬ, ɩɨ
ɤɪɚɣɧɟɣ ɦɟɪɟ, ɨɩɪɟɞɟɥɢɬɶ ɝɪɚɧɢɰɭ ɨɛɥɚɫɬɢ ɯɜɨɫɬɚ ɡɧɚɱɟɧɢɟ Zc.
ȿɫɥɢ ɩɪɟɞɥɨɠɟɧɧɵɣ ɩɨɞɯɨɞ ɧɟ ɩɨɤɚɡɵɜɚɟɬ ɩɥɚɬɨ, ɬɨ ɫɥɟɞɭɸɳɢɦ ɷɬɚɩɨɦ ɚɧɚɥɢɡɚ ɹɜɥɹɟɬɫɹ ɩɨɫɬɪɨɟɧɢɟ ɡɚɜɢɫɢɦɨɫɬɢ Di(Zmax) ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɦ Zmin = Zc, ɝɞɟ ɡɧɚɱɟɧɢɟ Zc ɭɠɟ ɧɚɣɞɟɧɨ (ɪɢɫ.1ɜ). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɚ ɛɨɥɶɲɟɣ
ɱɚɫɬɢ ɨɛɥɚɫɬɢ ɩɨɞɝɨɧɤɢ ɧɟ ɩɪɨɹɜɥɹɟɬɫɹ ɜɥɢɹɧɢɟ ɜɟɥɢɱɢɧɵ '/R(Z) (ɧɚ ɪɢɫ.1ɜ ɢɧɬɟɪɜɚɥ Zc y Zɚ). Ʉɨɝɞɚ ɠɟ
Zmax ! Zɚ, ɬɨ ɜɤɥɚɞ ɞɚɧɧɵɯ ɢɡ ɨɛɥɚɫɬɢ Z ! Zɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟ ɜɟɥɢɤ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɜɤɥɚɞɨɦ ɢɡ Zc y Zɚ ɢ ɨɬɤɥɨɧɟɧɢɟ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɚ D(Zmax) ɨɬ ɩɥɚɬɨ ɦɟɧɟɟ ɡɧɚɱɢɬɟɥɶɧɨ, ɱɟɦ ɜ ɡɚɜɢɫɢɦɨɫɬɢ D(Zmin).
ɗɄɋɉȿɊɂɆȿɇɌȺɅɖɇɕȿ ɁɇȺɑȿɇɂə ɉȺɊȺɆȿɌɊȺ D
ȼ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɟ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ R t-ɮɭɧɤɰɢɢ ɢɫɩɨɥɶɡɭɸɬɫɹ ɩɨɩɟɪɟɱɧɚɹ ɢ ɩɪɨɞɨɥɶɧɚɹ ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ ɹɞɟɪ 2ɇ ɢ 4ɇɟ, ɤɨɬɨɪɵɟ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɢɡ ɢɡɦɟɪɟɧɢɣ ɧɚ ɭɫɤɨɪɢɬɟɥɟ ɷɥɟɤɬɪɨɧɨɜ Ʌɍɗ-300 ɏɎɌɂ (ɨɩɢɫɚɧɢɟ
ɷɤɫɩɟɪɢɦɟɧɬɚ ɢ ɨɛɪɚɛɨɬɤɢ ɞɚɧɧɵɯ ɩɪɢɜɟɞɟɧɵ ɜ [4]), ɢ
ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ RT/L-ɮɭɧɤɰɢɢ 4ɇɟ ɪɚɛɨɬ [2,3]. ɋɥɟɞɭɹ ɢɡɥɨɠɟɧɧɨɣ ɜɵɲɟ ɦɟɬɨɞɢɤɟ, ɧɚɣɞɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ
DT/L(Zmin) ɢ DT/L(Zmax) ɞɥɹ ɮɭɧɤɰɢɣ ɨɬɤɥɢɤɚ ɩɪɢ q = 0,88
y 1,52 ɮɦ1 (ɞɚɧɧɵɟ ɩɪɢ q = 1,52 ɮɦ1 ɩɨɥɭɱɟɧɵ ɜ Bates
[2] ɢ Saclay [3]).
ɇɚ ɪɢɫ.2 ɩɨɤɚɡɚɧɚ RL-ɮɭɧɤɰɢɹ ɹɞɪɚ 2ɇ ɩɪɢ q =
1,05 ɮɦ1 ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɟɣ ɡɚɜɢɫɢɦɨɫɬɶ D(Zmin).
ɗɬɨ ɫɥɭɱɚɣ, ɤɨɝɞɚ, ɜɜɢɞɭ ɯɨɪɨɲɨ ɧɚɛɥɸɞɚɟɦɨɝɨ ɩɥɚɬɨ
ɜ ɡɧɚɱɟɧɢɹɯ Di(Zmin), ɪɚɫɫɦɨɬɪɟɧɢɟ ɡɚɜɢɫɢɦɨɫɬɢ
D(Zmax) ɢɡɥɢɲɧɟ. ɇɚ ɪɢɫ.3 ɢ 4 ɬɚɤɨɝɨ ɠɟ ɪɨɞɚ ɞɚɧɧɵɟ ɢ
ɡɚɜɢɫɢɦɨɫɬɶ D(Zmax) ɞɥɹ RT-ɮɭɧɤɰɢɢ ɹɞɪɚ 4ɇɟ ɩɪɢ q =
1,125 ɮɦ1 ɢ q = 1,52 ɮɦ1, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. Ɋɢɫ. 2, 3, 4
ɞɟɦɨɧɫɬɪɢɪɭɸɬ ɚɞɟɤɜɚɬɧɨɫɬɶ ɫɬɟɩɟɧɧɨɣ ɮɭɧɤɰɢɢ ɞɚɧɧɵɦ ɢɡɦɟɪɟɧɢɣ. ɉɨɞɨɛɧɚɹ ɚɞɟɤɜɚɬɧɨɫɬɶ ɧɚɛɥɸɞɚɥɚɫɶ
ɧɚ 10 ɢɡ 14 ɢɫɩɨɥɶɡɨɜɚɧɧɵɯ ɜ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɮɭɧɤɰɢɣ ɨɬɤɥɢɤɚ. ȼ ɱɚɫɬɧɨɫɬɢ, ɷɬɚ ɚɞɟɤɜɚɬɧɨɫɬɶ ɢɦɟɥɚ ɦɟɫɬɨ ɜɨ ɜɫɟɯ ɩɹɬɢ RT-ɮɭɧɤɰɢɹɯ ɹɞɪɚ
4
ɇɟ. ɗɬɨɬ ɮɚɤɬ, ɚ ɬɚɤɠɟ ɬɨ, ɱɬɨ ɜ ɫɥɭɱɚɟ ɤɚɠɞɨɝɨ ɢɡ
ɹɞɟɪ ɛɥɢɡɤɢɟ ɩɨ ɩɟɪɟɞɚɧɧɨɦɭ ɢɦɩɭɥɶɫɭ RT/L-ɮɭɧɤɰɢɢɢ
ɢɦɟɸɬ ɧɟ ɩɨɞɨɛɧɨɟ ɞɪɭɝ ɞɪɭɝɭ ɩɨɜɟɞɟɧɢɟ (ɚɞɟɤɜɚɬɧɨɟ
ɫɬɟɩɟɧɧɨɣ ɮɭɧɤɰɢɢ ɢ ɧɟɚɞɟɤɜɚɬɧɨɟ), ɦɨɝɥɨ ɛɵ ɤɚɡɚɬɶɫɹ
ɭɞɢɜɢɬɟɥɶɧɵɦ. Ɉɞɧɚɤɨ ɢɫɫɥɟɞɭɟɦɚɹ ɚɞɟɤɜɚɬɧɨɫɬɶ ɧɟ
ɧɚɛɥɸɞɚɥɚɫɶ ɢɦɟɧɧɨ ɜ ɬɟɯ ɫɥɭɱɚɹɯ, ɤɨɝɞɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ ɢɦɟɥɢ ɛɨɥɶɲɨɣ ɪɚɡɛɪɨɫ
ɡɧɚɱɟɧɢɣ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɩɨɜɟɞɟɧɢɹ ɞɚɧɧɵɯ, ɝɞɟ ɚɞɟɤɜɚɬɧɨɫɬɶ ɧɚɛɥɸɞɚɥɚɫɶ.
Ȼɵɥɨ ɡɚɦɟɱɟɧɨ, ɱɬɨ ɜ ɬɟɯ ɫɥɭɱɚɹɯ, ɤɨɝɞɚ ɧɚɛɥɸɞɚɥɚɫɶ ɚɞɟɤɜɚɬɧɨɫɬɶ ɫɬɟɩɟɧɧɨɣ ɮɭɧɤɰɢɢ ɤ ɞɚɧɧɵɦ, ɝɪɚɧɢɰɚ ɯɜɨɫɬɚ (Zc) ɩɪɢɯɨɞɢɬɫɹ ɧɚ ɩɨɥɭɜɵɫɨɬɭ ɩɢɤɚ ɮɭɧɤɰɢɢ ɨɬɤɥɢɤɚ ɢɥɢ ɧɟɫɤɨɥɶɤɨ ɜɵɲɟ ( R(Zc) t ½ max(R) ).
ɂɫɯɨɞɹ ɢɡ ɷɬɨɝɨ, ɞɥɹ ɫɥɭɱɚɟɜ ɞɚɧɧɵɯ ɫ ɛɨɥɶɲɢɦ ɪɚɡɛɪɨɫɨɦ ɡɧɚɱɟɧɢɣ ɛɵɥɢ ɩɪɢɦɟɧɟɧɵ ɩɨɞɝɨɧɤɢ ɜ ɲɢɪɨɤɨɦ ɞɢɚɩɚɡɨɧɟ ɩɟɪɟɞɚɧɧɵɯ ɷɧɟɪɝɢɣ, ɝɞɟ ɷɬɨɬ ɪɚɡɛɪɨɫ
ɞɨɥɠɟɧ ɜ ɡɧɚɱɢɬɟɥɶɧɨɣ ɦɟɪɟ ɧɢɜɟɥɢɪɨɜɚɬɶɫɹ. Ⱥ ɢɦɟɧɊɢɫ.2. Ɉɩɪɟɞɟɥɟɧɢɟ ɡɧɚɱɟɧɢɹ DL ɞɥɹ ɹɞɪɚ 2ɇ ɩɪɢ q =
ɧɨ,
ɨɬ ɡɧɚɱɟɧɢɹ Z, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɩɨɥɭɜɵɫɨɬɟ ɩɢɤɚ
1,05 ɮɦ –1.
R(Z), ɞɨ ɜɟɪɯɧɟɣ ɝɪɚɧɢɰɵ ɢɡɦɟɪɟɧɢɣ ɩɨ ɩɟɪɟɞɚɧɧɨɣ
(ɚ) RL-ɞɚɧɧɵɟ, ɤɪɢɜɚɹ – ɫɬɟɩɟɧɧɚɹ ɮɭɧɤɰɢɹ.
ɷɧɟɪɝɢɢ (Zcc). ɇɚɣɞɟɧɧɵɟ ɬɚɤɢɦ ɨɛɪɚɡɨɦ ɡɧɚɱɟɧɢɹ ɩɚ(ɛ) ɩɚɪɚɦɟɬɪ DL ɤɚɤ ɮɭɧɤɰɢɹ Zmin , ɩɪɹɦɚɹ – ɩɥɚɬɨ ɮɭɧɤɪɚɦɟɬɪɚ D ɨɤɚɡɚɥɢɫɶ ɛɥɢɡɤɢ ɤ ɡɧɚɱɟɧɢɹɦ, ɩɨɥɭɱɟɧɧɵɦ
ɰɢɢ.
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À.Þ. Áóêè, È.À. Íåíüêî, Í.Ã. Øåâ÷åíêî ...
«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 664, 2005
ɜ ɫɥɭɱɚɹɯ ɚɞɟɤɜɚɬɧɨɫɬɢ ɫɬɟɩɟɧɧɨɣ ɮɭɧɤɰɢɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ R-ɮɭɧɤɰɢɢɹɦ. ɗɬɨɬ ɪɟɡɭɥɶɬɚɬ ɦɨɠɧɨ ɫɱɢɬɚɬɶ
ɩɨɞɬɜɟɪɠɞɟɧɢɟɦ ɩɪɚɜɢɥɶɧɨɫɬɢ ɦɟɬɨɞɢɤɢ, ɢɫɩɨɥɶɡɨɜɚɧɧɨɣ ɜ ɚɧɚɥɢɡɟ ɦɟɧɟɟ ɤɚɱɟɫɬɜɟɧɧɵɯ ɞɚɧɧɵɯ.
Ɋɢɫ. 3. Ɉɩɪɟɞɟɥɟɧɢɟ ɡɧɚɱɟɧɢɹ DɌ ɞɥɹ ɹɞɪɚ
ɇɟ ɩɪɢ q = 1,125 ɮɦ –1.
(ɚ) RɌ-ɞɚɧɧɵɟ, ɤɪɢɜɚɹ – ɫɬɟɩɟɧɧɚɹ ɮɭɧɤɰɢɹ.
(ɛ) ɩɚɪɚɦɟɬɪ DɌ ɤɚɤ ɮɭɧɤɰɢɹ Zmin , ɩɪɹɦɚɹ – ɩɥɚɬɨ ɮɭɧɤɰɢɢ.
(ɫ) ɩɚɪɚɦɟɬɪ DɌ ɤɚɤ ɮɭɧɤɰɢɹ Zmɚɯ , ɩɪɹɦɚɹ – ɩɥɚɬɨ ɮɭɧɤɰɢɢ.
4
Ɋɢɫ. 4. Ɉɩɪɟɞɟɥɟɧɢɟ ɡɧɚɱɟɧɢɹ DɌ ɞɥɹ ɹɞɪɚ
ɇɟ ɩɪɢ q = 1,52 ɮɦ –1.
(ɚ) RɌ-ɞɚɧɧɵɟ ɢɡ ɪɚɛɨɬɵ [3], ɤɪɢɜɚɹ – ɫɬɟɩɟɧɧɚɹ
ɮɭɧɤɰɢɹ.
(ɛ) ɩɚɪɚɦɟɬɪ DɌ ɤɚɤ ɮɭɧɤɰɢɹ Zmin , ɩɪɹɦɚɹ – ɩɥɚɬɨ ɮɭɧɤɰɢɢ.
(ɫ) ɩɚɪɚɦɟɬɪ DɌ ɤɚɤ ɮɭɧɤɰɢɹ Zmɚɯ , ɩɪɹɦɚɹ – ɩɥɚɬɨ ɮɭɧɤɰɢɢ.
4
ɈȻɋɍɀȾȿɇɂȿ ɊȿɁɍɅɖɌȺɌɈȼ
ɉɨɥɭɱɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ DT/L ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɚ ɪɢɫ.5: (ɚ) ɡɧɚɱɟɧɢɹ ɢɡ RT/L-ɮɭɧɤɰɢɣ, ɤɨɬɨɪɵɦ ɫɬɟɩɟɧɧɚɹ ɮɭɧɤɰɢɹ ɚɞɟɤɜɚɬɧɚ; (ɛ) ɡɧɚɱɟɧɢɹ ɢɡ ɜɫɟɯ ɢɫɩɨɥɶɡɨɜɚɧɧɵɯ RT/L-ɮɭɧɤɰɢɣ. ɇɚ ɷɬɨɦ ɪɢɫɭɧɤɟ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ DT/L, ɩɨɥɭɱɟɧɧɵɟ ɩɨ ɞɚɧɧɵɦ ɥɚɛɨɪɚɬɨɪɢɢ Bates, ɩɪɢɜɟɞɟɧɵ ɜ ɜɢɞɟ D = (DT + DL)/2. ɗɬɨ ɫɜɹɡɚɧɨ ɫɨ ɫɥɟɞɭɸɳɢɦ. Ʉɚɤ ɜ ɫɥɭɱɚɟ 2ɇ, ɬɚɤ ɢ 4ɇɟ ɩɪɢ ɨɞɢɧɚɤɨɜɵɯ ɩɟɪɟɞɚɧɧɵɯ ɢɦɩɭɥɶɫɚɯ ɡɧɚɱɟɧɢɹ DT ɢ DL ɛɥɢɡɤɢ. Ɍɚɤɚɹ ɠɟ
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ñåð³ÿ ô³çè÷íà «ßäðà, ÷àñòèíêè, ïîëÿ», âèï. 2 /27/
Ýêñòðàïîëÿöèÿ ýêñïåðèìåíòàëüíûõ ôóíêöèé ...
Ɋɢɫ. 5. ɉɚɪɚɦɟɬɪɵ D ɞɥɹ ɩɪɨɞɨɥɶɧɵɯ (ɨɬɤɪɵɬɵɟ ɫɢɦɜɨɥɵ) ɢ
ɩɨɩɟɪɟɱɧɵɯ (ɡɚɤɪɵɬɵɟ ɫɢɦɜɨɥɵ) ɮɭɧɤɰɢɣ ɨɬɤɥɢɤɚ.
(ɚ) ɡɧɚɱɟɧɢɹ D ɢɡ RT/L-ɮɭɧɤɰɢɣ, ɤɨɬɨɪɵɦ ɫɬɟɩɟɧɧɚɹ ɮɭɧɤɰɢɹ ɚɞɟɤɜɚɬɧɚ.
(ɛ) ɡɧɚɱɟɧɢɹ D ɢɡ ɜɫɟɯ ɢɫɩɨɥɶɡɨɜɚɧɧɵɯ RT/L-ɮɭɧɤɰɢɣ.
ɢ
– D ɞɥɹ ɹɞɟɪ 2ɇ ɢ 4ɇɟ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɩɨɥɭɱɟɧɧɵɟ ɢɡ ɧɚɲɢɯ
ɞɚɧɧɵɯ;
– D ɞɥɹ ɹɞɪɚ 4ɇɟ ɢɡ ɨɛɪɚɛɨɬɤɢ ɞɚɧɧɵɯ Saclay [3];
ȝ – D = (DɌ+DL)/2 ɞɥɹ ɹɞɪɚ 4ɇɟ ɢɡ ɨɛɪɚɛɨɬɤɢ ɞɚɧɧɵɯ Bates [2];
– ɫɪɟɞɧɢɟ ɡɧɚɱɟɧɢɹ DɌ/L ɞɥɹ 2ɇ ɢ ɞɥɹ 4ɇɟ;
– ɪɚɫɱɟɬ D ɪɚɛɨɬɵ [5];
– ɪɚɫɱɟɬ D (ɫɥɭɱɚɣ 2ɇ) ɪɚɛɨɬɵ [1].
GS t ,( k )
GD
.
k 1
1
GD
D
ɫɢɬɭɚɰɢɹ ɢɦɟɟɬ ɦɟɫɬɨ ɞɥɹ DT ɢ DL ɢɡ
ɞɚɧɧɵɯ Saclay, ɤɨɬɨɪɵɟ ɞɭɛɥɢɪɭɸɬ
ɢɡɦɟɪɟɧɢɹ Bates. ɂɡ ɷɬɨɣ ɫɢɫɬɟɦɚɬɢɤɢ ɜɵɩɚɞɚɸɬ ɬɨɥɶɤɨ ɡɧɚɱɟɧɢɹ D,
ɩɨɥɭɱɟɧɧɵɟ ɢɡ ɞɚɧɧɵɯ Bates: DT =
1,46 ɢ DL = 2,70. ȼɨɡɦɨɠɧɨ, ɫɟɱɟɧɢɹ
ɢɡɦɟɪɟɧɧɵɟ ɜ Bates ɧɟɫɤɨɥɶɤɨ ɢɫɤɚɠɟɧɵ ɜ ɨɛɥɚɫɬɢ ɯɜɨɫɬɚ, ɚ ɬɚɤ ɤɚɤ ɜ
ɩɪɨɰɟɞɭɪɟ ɪɚɡɞɟɥɟɧɢɹ R-ɮɭɧɤɰɢɣ,
ɡɧɚɱɟɧɢɹ RT ɢ RL ɤɨɦɩɨɧɟɧɬɨɜ ɧɟ
ɧɟɡɚɜɢɫɢɦɵ ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɬɨ ɡɚɧɢɠɟɧɢɟ ɨɞɧɨɣ ɢɡ ɧɢɯ ɜɵɡɵɜɚɟɬ ɡɚɜɵɲɟɧɢɟ ɞɪɭɝɨɣ. ɉɨɷɬɨɦɭ ɦɵ ɪɚɫɫɦɚɬɪɢɜɚɟɦ ɪɟɡɭɥɶɬɚɬɵ ɨɛɪɚɛɨɬɤɢ
ɞɚɧɧɵɯ Bates ɤɚɤ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɣ
ɦɚɬɟɪɢɚɥ, ɚ ɡɧɚɱɟɧɢɟ D ɢɡ ɷɬɢɯ ɞɚɧɧɵɯ ɛɟɪɟɦ ɤɚɤ ɫɪɟɞɧɟɟ DT ɢ DL.
ɂɡ ɪɢɫ.5 ɜɢɞɧɨ, ɱɬɨ ɡɧɚɱɟɧɢɹ
D, ɫ ɬɨɱɧɨɫɬɶɸ ɞɨ ɫɬɚɬɢɫɬɢɱɟɫɤɨɝɨ
ɪɚɡɛɪɨɫɚ, ɨɞɢɧɚɤɨɜɵ ɞɥɹ ɤɚɠɞɨɝɨ ɢɡ
ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɹɞɟɪ. ɉɪɨɜɟɞɟɧɧɨɟ
ɭɫɪɟɞɧɟɧɢɟ ɩɚɪɚɦɟɬɪɨɜ D (ɧɟ ɜɤɥɸɱɚɸɳɟɟ D ɢɡ ɞɚɧɧɵɯ Bates) ɩɨɤɚɡɵɜɚɟɬ:
D = 3,03 r 0,15 ɞɥɹ 2ɇ;
D = 2,19 r 0,10 ɞɥɹ 4ɇɟ.
Ɋɚɫɫɦɨɬɪɢɦ, ɤɚɤ ɧɚɣɞɟɧɧɵɟ
ɡɧɚɱɟɧɢɹ ɢ ɩɨɝɪɟɲɧɨɫɬɢ ɩɚɪɚɦɟɬɪɚ
D ɩɪɨɹɜɥɹɸɬɫɹ ɜ ɩɪɨɛɥɟɦɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɮɭɧɤɰɢɢ
ɨɬɤɥɢɤɚ: ɩɨɝɪɟɲɧɨɫɬɶ S (k) ɢ ɡɧɚɱɟɧɢɟ kmax.
ɉɨɝɪɟɲɧɨɫɬɢ ɡɧɚɱɟɧɢɣ D ɨɬɪɚɠɚɸɬɫɹ ɧɚ ɬɨɱɧɨɫɬɢ ɡɧɚɱɟɧɢɹ ɬɨɣ
ɱɚɫɬɢ ɢɧɬɟɝɪɚɥɚ (ɨɛɨɡɧɚɱɢɦ ɟɺ
S t,(k)), ɝɞɟ ɩɨɞɵɧɬɟɝɪɚɥɶɧɨɣ ɮɭɧɤɰɢɟɣ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɹ ɷɤɫɬɪɚɩɨɥɹɰɢɢ. Ɉɬɧɨɫɢɬɟɥɶɧɭɸ ɩɨɝɪɟɲɧɨɫɬɶ
ɜɟɥɢɱɢɧɵ S t,(k) ɧɟ ɬɪɭɞɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɮɭɧɤɰɢɟɣ ɨɬ GD ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɩɨɝɪɟɲɧɨɫɬɢ ɩɚɪɚɦɟɬɪɚ D
(7)
ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ, ɢɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɭ (7) ɞɥɹ ɫɥɭɱɚɹ 4ɇɟ ɢ k = 0 ɧɚɯɨɞɢɦ, ɱɬɨ GS t,(0) = 0,07. Ɍɚɤ ɤɚɤ ɨɛɵɱɧɨ
ɬɨɱɧɨɫɬɶ ɧɨɪɦɢɪɨɜɨɱɧɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ CD(q) ɢɡ ɜɵɪ.(3) ɨɤɨɥɨ 10%, ɬɨ ɩɨɥɧɨɟ ɡɧɚɱɟɧɢɟ GS t,(0) d 0,13. Ʉɚɤ ɨɬɦɟɱɚɥɨɫɶ ɜɨ ɜɜɟɞɟɧɢɢ, GS t,(0) ɫɨɫɬɚɜɥɹɟɬ (10 y 20)% ɨɬ S(0). Ɉɬɫɸɞɚ ɫɜɹɡɚɧɧɚɹ ɫ ɷɤɫɬɪɚɩɨɥɹɰɢɟɣ ɩɨɝɪɟɲɧɨɫɬɶ ɜ
ɡɧɚɱɟɧɢɢ ɧɭɥɟɜɨɝɨ ɦɨɦɟɧɬɚ ɨɤɨɥɨ 2%. Ɂɚɦɟɬɢɦ, ɱɬɨ ɬɚɤɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɧɟ ɡɧɚɱɢɬɟɥɶɧɚ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɩɨɝɪɟɲɧɨɫɬɶɸ ɜ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɢɡɦɟɪɹɟɦɨɣ ɱɚɫɬɢ ɧɭɥɟɜɨɝɨ ɦɨɦɟɧɬɚ, ɜɟɥɢɱɢɧɚ ɤɨɬɨɪɨɣ (6 y 15)%.
Ʉɚɤ ɧɟ ɬɪɭɞɧɨ ɜɢɞɟɬɶ, ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɞɥɹ ɷɤɫɬɪɚɩɨɥɹɰɢɢ R-ɮɭɧɤɰɢɢ ɫɬɟɩɟɧɧɨɣ ɮɭɧɤɰɢɢ ɨɝɪɚɧɢɱɢɜɚɟɬ ɧɨɦɟɪ ɦɨɦɟɧɬɚ, ɤɨɬɨɪɵɣ ɢɦɟɟɬ ɤɨɧɟɱɧɨɟ ɡɧɚɱɟɧɢɟ [8]
­ ent(Į) 1 ɟɫɥɢ Į z ent(Į)
kmax = ®
,
ɟɫɥɢ Į ent(Į)
¯ Į2
(8)
ɝɞɟ ent(D) ɰɟɥɚɹ ɱɚɫɬɶ ɡɧɚɱɟɧɢɹ D. ɉɨɥɭɱɟɧɧɵɦ D, ɫɨɝɥɚɫɧɨ ɜɵɪ.(8), ɫɨɨɬɜɟɬɫɬɜɭɟɬ kmax = 1. ɗɬɨ ɜɟɫɶɦɚ ɢɧɬɟɪɟɫɧɵɣ ɪɟɡɭɥɶɬɚɬ, ɬɚɤ ɤɚɤ ɜ ɪɹɞɟ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɪɚɛɨɬ (ɫɦ. ɧɚɩɪɢɦɟɪ [1, 9, 10]) ɦɨɦɟɧɬɵ ɮɭɧɤɰɢɣ ɨɬɤɥɢɤɚ ɪɚɫ-
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ɫɱɢɬɵɜɚɸɬɫɹ ɞɥɹ k ɪɚɜɧɨɝɨ 2 ɢ 3. Ɉɬɦɟɬɢɦ, ɱɬɨ ɭɤɚɡɚɧɧɨɟ ɩɪɨɬɢɜɨɪɟɱɢɟ ɫɥɟɞɭɟɬ ɧɟ ɬɨɥɶɤɨ ɢɡ ɧɚɣɞɟɧɧɵɯ ɜ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɡɧɚɱɟɧɢɣ D, ɧɨ ɢ ɢɡ ɪɚɫɱɺɬɨɜ ɷɬɨɝɨ ɩɚɪɚɦɟɬɪɚ ɜ ɪɚɛɨɬɚɯ [1, 5], ɝɞɟ D d 3.
ȼɕȼɈȾɕ
ɗɤɫɩɟɪɢɦɟɧɬ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ:
1. DT | DL ɞɥɹ ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɹɞɟɪ;
2. DT/L ɤɚɠɞɨɝɨ ɢɡ ɹɞɟɪ ɜ ɢɫɫɥɟɞɭɟɦɨɦ ɞɢɚɩɚɡɨɧɟ ɩɟɪɟɞɚɧɧɵɯ ɢɦɩɭɥɶɫɨɜ ɩɨɫɬɨɹɧɧɵ;
3. ɡɧɚɱɟɧɢɹ DT/L ɹɞɟɪ 2ɇ ɢ 4ɇɟ ɪɚɡɥɢɱɧɵ.
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɪɟɡɭɥɶɬɚɬɵ (1) ɢ (2) ɧɟ ɩɪɨɬɢɜɨɪɟɱɚɬ ɜɵɜɨɞɚɦ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɪɚɛɨɬ [1,5]. Ɋɚɫɫɱɢɬɚɧɧɨɟ ɜ
ɪɚɛɨɬɟ [1] ɡɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɚ D ɞɥɹ 2ɇ, ɫɨɝɥɚɫɭɟɬɫɹ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ, ɚ ɧɚɣɞɟɧɧɨɟ ɡɧɚɱɟɧɢɟ D ɞɥɹ 4ɇɟ ɞɨɜɨɥɶɧɨ ɛɥɢɡɤɨ ɤ ɪɚɫɫɱɢɬɚɧɧɨɦɭ ɜ [5].
ȼ ɡɚɤɥɸɱɟɧɢɟ ɧɚɞɨ ɫɤɚɡɚɬɶ, ɱɬɨ, ɫɨɝɥɚɫɧɨ ɪɚɛɨɬɟ [5], ɜɟɥɢɱɢɧɚ D ɦɚɥɨ ɢɡɦɟɧɹɟɬɫɹ ɜɩɥɨɬɶ ɞɨ ɫɪɟɞɧɟɬɹɠɺɥɵɯ ɹɞɟɪ, ɩɨɷɬɨɦɭ ɧɚɣɞɟɧɧɨɟ ɞɥɹ 4ɇɟ ɡɧɚɱɟɧɢɟ ɷɬɨɝɨ ɩɚɪɚɦɟɬɪɚ ɦɨɝɥɨ ɛɵ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɨ ɜ ɨɩɪɟɞɟɥɟɧɢɢ
ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɡɧɚɱɟɧɢɣ S(k)T/L(q) ɜɫɟɯ ɷɬɢɯ ɹɞɟɪ. Ɉɞɧɚɤɨ ɧɚɦ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ, ɱɬɨ ɩɪɨɛɥɟɦɚ ɷɤɫɬɪɚɩɨɥɹɰɢɢ
ɮɭɧɤɰɢɣ ɨɬɤɥɢɤɚ ɬɪɟɛɭɟɬ ɞɚɥɶɧɟɣɲɟɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ.
ɋɉɂɋɈɄ ɅɂɌȿɊȺɌɍɊɕ
Orlandini G. and Traini M. Sum rules for electron-nucleus scattering // Rep. Prog. Phys. 1991. V.54. P.257-338.
von Reden K.F., Alcorn C., Dytman S.A. et. al. Quasielastic electron scattering and Coulomb sum rule in 4He // Phys. Rev. 1990. V.ɋ41. ʋ3. P.1084-1094.
3. Zghiche A., Danelet J.F., Bernhheim M. et al. Longitudinal and transverse responses in quasi-elastic electron scattering from
208
Pb and 4He // Nucl. Phys. 1994. V.A572. P.513-559.
4. Ȼɭɤɢ Ⱥ.ɘ., ɒɟɜɱɟɧɤɨ ɇ.Ƚ., ɇɟɧɶɤɨ ɂ.Ⱥ. ɢ ɞɪ. Ɇɨɦɟɧɬɵ ɮɭɧɤɰɢɣ ɨɬɤɥɢɤɚ ɹɞɪɚ 2ɇ ɩɪɢ q = 1,05 Ɏɦ-1 // əɞɟɪɧɚɹ ɮɢɡɢɤɚ.
2002. Ɍ.65. ʋ5. ɋ.787-796.
5. Tornow V., Orlandini G., Traini M. et. al. A study of electronuclear sum rules in light and medium-weight nuclei // Nucl. Phys.
1980. V.A348. ʋ2. P.157-178.
6. Buki A.Yu., Efros V.D., Shevchenko N.G. et al. Electronuclear transversal sum rule in 4He at moderate transfer momenta and
high-Z extrapolation of response functions. Moscow, 1991. 17p. (Preprint / I.V. Kurchatov Institute of Atomic Energy.:
IAE-5397/2).
7. Marschand C., Barreau P., Bernheim M. et. al. Transverse and longitudinal response functions in deep inelastic electron scattering from 3He // Phys. Lett. 1985. V.B153. P.29-32.
8. Buki A.Yu., Nenko I.A. Response Functions Extrapolation of 2H Nucleus in the Region of High Transfer Energy // ȼɨɩ. ɚɬɨɦ.
ɧɚɭɤɢ ɢ ɬɟɯ. ɋɟɪ.: ɹɞ.-ɮɢɡ. ɢɫɫɥɟɞ. ɏɚɪɶɤɨɜ. 2000. Ɍ.2(36). ɋ.13-15.
9. ɗɮɪɨɫ ȼ.Ⱦ. ɉɪɚɜɢɥɚ ɫɭɦɦ ɜ ɪɚɫɫɟɹɧɢɢ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɹɞɪɚɯ // əɞɟɪɧɚɹ ɮɢɡɢɤɚ. 1973. Ɍ.18. ɋ.1184-1203.
10. Shiavilla R., Pandharipande V.R., Fabrocini A. Coulomb sum rule of A = 2, 3, and 4 nuclei // Phys. Rev. 1989. V.C40. ʋ3. P.1484-1490.
1.
2.
POWER EXTRAPOLATION OF EXPERIMENTAL RESPONSE FUNCTIONS
OF 2H AND 4He NUCLEI
A.Yu. Buki, I.A. Nenko, N.G. Shevchenko, I.S. Timchenko
National Science Center “Kharkov Institute of Physics and Technology”,
1 Akademicheskaya St., 61108 Kharkov, Ukraine
E-mail: [email protected]
To solve the problem of determining experimentally the moments of nuclear response functions, it is essential to extrapolate these
functions to the region of high energy transfers, where the measurements are impossible. The present paper is concerned with the extrapolation of the response function through the use of the power function. For the purpose, the measured data on the 2H and 4He nuclei at momentum transfers between 0.9 and 1.5 fm-1 were used. The derived exponent values of the extrapolation function are compared with the results of theoretical calculations.
KEY WORDS: atomic nuclei, electron scattering, response functions, extrapolation, power function.