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«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 777, 2007 ñåð³ÿ ô³çè÷íà «ßäðà, ÷àñòèíêè, ïîëÿ», âèï.2 /34/

Þ.À. Áåðåæíîé, Â.Â. Ïèëèïåíêî Àíàëèç çàðÿäîâûõ ôîðìôàêòîðîâ ÿäðà...

ɍȾɄ 539.172

ȺɇȺɅɂɁ ɁȺɊəȾɈȼɕɏ ɎɈɊɆɎȺɄɌɈɊɈȼ əȾɊȺ 6Li ɇȺ ɈɋɇɈȼȿ ɄɅȺɋɌȿɊɇɈɃ ɆɈȾȿɅɂ
ɏɚɪɶɤɨɜɫɤɢɣ ɧɚɰɢɨɧɚɥɶɧɵɣ ɭɧɢɜɟɪɫɢɬɟɬ ɢɦ. ȼ.ɇ. Ʉɚɪɚɡɢɧɚ, ɩɥ. ɋɜɨɛɨɞɵ 4, ɏɚɪɶɤɨɜ 61077 ɇɚɰɢɨɧɚɥɶɧɵɣ ɧɚɭɱɧɵɣ ɰɟɧɬɪ "ɏɚɪɶɤɨɜɫɤɢɣ ɮɢɡɢɤɨ-ɬɟɯɧɢɱɟɫɤɢɣ ɢɧɫɬɢɬɭɬ", ɭɥ. Ⱥɤɚɞɟɦɢɱɟɫɤɚɹ 1, ɏɚɪɶɤɨɜ 61108 ɉɨɫɬɭɩɢɥɚ ɜ ɪɟɞɚɤɰɢɸ 7 ɦɚɹ 2007 ɝ.
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ɘ.Ⱥ. Ȼɟɪɟɠɧɨɣ1, ȼ.ȼ. ɉɢɥɢɩɟɧɤɨ2

2

Ɋɚɫɫɦɨɬɪɟɧɨ ɩɪɢɦɟɧɟɧɢɟ ɪɚɡɥɢɱɧɵɯ ɜɚɪɢɚɧɬɨɜ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɨɣ ɤɥɚɫɬɟɪɧɨɣ ɦɨɞɟɥɢ ɹɞɪɚ 6Li – ɦɨɞɟɥɢ D+d ɧɭɤɥɨɧɧɵɯ ɚɫɫɨɰɢɚɰɢɣ ɢ ɤɥɚɫɬɟɪɧɨɣ ɦɨɞɟɥɢ ɫ ɞɢɫɩɟɪɫɢɟɣ ɞɥɹ ɫɢɫɬɟɦ D+d ɢ D+p+n – ɞɥɹ ɨɩɢɫɚɧɢɹ ɭɩɪɭɝɨɝɨ ɡɚɪɹɞɨɜɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ ɹɞɪɚ 6Li ɢ ɮɨɪɦɮɚɤɬɨɪɚ ɧɟɭɩɪɭɝɨɝɨ ɪɚɫɫɟɹɧɢɹ ɫ ɜɨɡɛɭɠɞɟɧɢɟɦ ɜ ɹɞɪɟ ɦɢɲɟɧɢ ɩɟɪɜɨɝɨ ɫɨɫɬɨɹɧɢɹ 3+. ɂɡ ɚɧɚɥɢɡɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɢɡɦɟɪɟɧɧɵɯ ɮɨɪɦɮɚɤɬɨɪɨɜ ɧɚɣɞɟɧɵ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɢɡɭɱɚɟɦɵɯ ɦɨɞɟɥɟɣ. ɉɨɤɚɡɚɧɨ, ɱɬɨ ɪɚɫɫɦɨɬɪɟɧɧɵɟ ɤɥɚɫɬɟɪɧɵɟ ɦɨɞɟɥɢ ɞɚɸɬ ɯɨɪɨɲɟɟ ɨɩɢɫɚɧɢɟ ɤɚɤ ɭɩɪɭɝɨɝɨ, ɬɚɤ ɢ ɧɟɭɩɪɭɝɨɝɨ ɮɨɪɦɮɚɤɬɨɪɨɜ, ɩɪɢɱɟɦ ɧɚɢɛɨɥɟɟ ɩɪɟɞɩɨɱɬɢɬɟɥɶɧɨɣ ɜɵɝɥɹɞɢɬ ɤɥɚɫɬɟɪɧɚɹ D+d ɦɨɞɟɥɶ ɫ ɞɢɫɩɟɪɫɢɟɣ. ɄɅɘɑȿȼɕȿ ɋɅɈȼȺ: ɹɞɪɨ 6Li, ɤɥɚɫɬɟɪɧɚɹ ɦɨɞɟɥɶ, ɡɚɪɹɞɨɜɵɣ ɮɨɪɦɮɚɤɬɨɪ, ɧɟɭɩɪɭɝɢɣ ɮɨɪɦɮɚɤɬɨɪ, ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɵɣ ɪɚɞɢɭɫ, ɩɚɪɚɦɟɬɪ ɞɢɫɩɟɪɫɢɢ

əɞɪɚ ɢɡɨɬɨɩɨɜ ɥɢɬɢɹ ɩɪɢɧɚɞɥɟɠɚɬ ɤ ɱɢɫɥɭ ɥɟɝɱɚɣɲɢɯ ɚɬɨɦɧɵɯ ɹɞɟɪ. ɂɫɫɥɟɞɨɜɚɧɢɟ ɢɯ ɫɬɪɭɤɬɭɪɵ ɩɪɟɞɫɬɚɜɥɹɟɬ ɡɧɚɱɢɬɟɥɶɧɵɣ ɢɧɬɟɪɟɫ, ɩɨɫɤɨɥɶɤɭ ɨɧɢ ɹɜɥɹɸɬɫɹ ɦɚɥɨɧɭɤɥɨɧɧɵɦɢ ɫɢɫɬɟɦɚɦɢ, ɜ ɤɨɬɨɪɵɯ ɦɨɝɭɬ ɩɪɨɹɜɥɹɬɶɫɹ ɷɮɮɟɤɬɵ ɤɥɚɫɬɟɪɢɡɚɰɢɢ (ɫɦ., ɧɚɩɪɢɦɟɪ, [1 ɝɥ. 5, 2 ɝɥ. XI]). ɉɨɷɬɨɦɭ ɢɡɭɱɟɧɢɸ ɹɞɟɪ ɥɢɬɢɹ ɩɨɫɜɹɳɟɧɨ ɡɧɚɱɢɬɟɥɶɧɨɟ ɤɨɥɢɱɟɫɬɜɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɢ ɬɟɨɪɟɬɢɱɟɫɤɢɯ ɪɚɛɨɬ. Ȼɨɥɶɲɨɟ ɡɧɚɱɟɧɢɟ ɢɦɟɟɬ ɢɡɭɱɟɧɢɟ ɩɪɨɹɜɥɟɧɢɣ ɷɮɮɟɤɬɨɜ ɤɥɚɫɬɟɪɢɡɚɰɢɢ ɹɞɟɪ ɜ ɩɪɨɰɟɫɫɚɯ ɹɞɟɪɧɨɝɨ ɪɚɫɫɟɹɧɢɹ ɢ ɹɞɟɪɧɵɯ ɪɟɚɤɰɢɹɯ [3, 4]. Ⱦɥɹ ɨɩɢɫɚɧɢɹ ɤɥɚɫɬɟɪɧɨɣ ɫɬɪɭɤɬɭɪɵ ɹɞɟɪ ɩɪɢɦɟɧɹɸɬɫɹ ɪɚɡɥɢɱɧɵɟ ɩɨɞɯɨɞɵ [4], ɜ ɱɚɫɬɧɨɫɬɢ, ɫɥɨɠɧɵɟ ɦɢɤɪɨɫɤɨɩɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɛɚɡɢɪɭɸɬɫɹ ɧɚ ɞɢɧɚɦɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɹɯ, ɤɨɬɨɪɵɟ ɨɩɢɫɵɜɚɸɬ ɤɚɤ ɞɜɢɠɟɧɢɟ ɤɥɚɫɬɟɪɨɜ ɜ ɹɞɪɚɯ, ɬɚɤ ɢ ɧɭɤɥɨɧɧɵɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ. Ɍɟɦ ɧɟ ɦɟɧɟɟ ɞɥɹ ɨɩɢɫɚɧɢɹ ɫɬɨɥɤɧɨɜɟɧɢɣ ɱɚɫɬɢɰ ɜɵɫɨɤɨɣ ɷɧɟɪɝɢɢ ɫ ɹɞɪɚɦɢ ɩɪɢ ɧɟ ɨɱɟɧɶ ɛɨɥɶɲɢɯ ɩɟɪɟɞɚɧɧɵɯ ɢɦɩɭɥɶɫɚɯ q ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɛɨɥɟɟ ɩɪɨɫɬɨɣ ɩɨɞɯɨɞ, ɜ ɤɨɬɨɪɨɦ ɹɞɪɨ ɨɩɢɫɵɜɚɟɬɫɹ ɤɚɤ ɫɢɫɬɟɦɚ ɢɡ ɧɟɫɤɨɥɶɤɢɯ ɤɥɚɫɬɟɪɨɜ ɫ ɩɨɦɨɳɶɸ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɢɯ ɜɨɥɧɨɜɵɯ ɮɭɧɤɰɢɣ ɢɥɢ ɩɥɨɬɧɨɫɬɟɣ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤɥɚɫɬɟɪɨɜ ɜ ɹɞɪɟ ɦɢɲɟɧɢ. ȼɵɫɨɤɚɹ ɷɮɮɟɤɬɢɜɧɨɫɬɶ ɷɬɨɝɨ ɦɟɬɨɞɚ ɛɵɥɚ ɩɨɤɚɡɚɧɚ ɜ ɪɚɛɨɬɚɯ, ɜ ɤɨɬɨɪɵɯ ɛɵɥɚ ɪɚɡɜɢɬɚ D-ɤɥɚɫɬɟɪɧɚɹ ɦɨɞɟɥɶ ɫ ɞɢɫɩɟɪɫɢɟɣ ɞɥɹ ɧɟɫɤɨɥɶɤɢɯ ɥɟɝɤɢɯ ɹɞɟɪ [5–8]. ɉɨɷɬɨɦɭ ɜɵɝɥɹɞɢɬ ɩɪɢɜɥɟɤɚɬɟɥɶɧɨɣ ɪɚɡɪɚɛɨɬɤɚ ɚɧɚɥɨɝɢɱɧɨɝɨ ɩɨɞɯɨɞɚ ɞɥɹ ɨɩɢɫɚɧɢɹ ɫɬɨɥɤɧɨɜɟɧɢɣ ɜɵɫɨɤɨɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɱɚɫɬɢɰ ɫ ɹɞɪɚɦɢ ɥɢɬɢɹ. ɉɪɢ ɷɬɨɦ, ɩɪɟɠɞɟ ɜɫɟɝɨ, ɧɟɨɛɯɨɞɢɦɨ ɧɚɣɬɢ ɤɨɪɪɟɤɬɧɵɟ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɢɟ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤɥɚɫɬɟɪɨɜ ɜ ɹɞɪɚɯ ɥɢɬɢɹ. ɉɚɪɚɦɟɬɪɵ ɷɬɢɯ ɮɭɧɤɰɢɣ ɦɨɠɧɨ ɧɚɣɬɢ ɢɡ ɚɧɚɥɢɡɚ ɡɚɪɹɞɨɜɵɯ ɮɨɪɦɮɚɤɬɨɪɨɜ ɷɬɢɯ ɹɞɟɪ, ɩɨɥɭɱɟɧɧɵɯ ɢɡ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨ ɪɚɫɫɟɹɧɢɸ ɷɥɟɤɬɪɨɧɨɜ. Ⱦɚɧɧɚɹ ɪɚɛɨɬɚ ɩɨɫɜɹɳɟɧɚ ɪɚɫɫɦɨɬɪɟɧɢɸ ɬɚɤɨɣ ɡɚɞɚɱɢ ɞɥɹ ɹɞɟɪ ɢɡɨɬɨɩɚ 6Li. ɄɅȺɋɌȿɊɇɕȿ ɆɈȾȿɅɂ əȾɊȺ 6Li ȿɫɬɟɫɬɜɟɧɧɨ ɨɠɢɞɚɬɶ, ɱɬɨ ɨɞɧɢɦ ɢɡ ɫɬɪɭɤɬɭɪɧɵɯ ɷɥɟɦɟɧɬɨɜ ɹɞɟɪ ɥɢɬɢɹ ɹɜɥɹɟɬɫɹ D-ɤɥɚɫɬɟɪ, ɤɨɬɨɪɵɣ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɜɵɫɨɤɨɣ ɫɬɚɛɢɥɶɧɨɫɬɶɸ ɢ ɫɢɦɦɟɬɪɢɟɣ. ɉɪɢ ɷɬɨɦ ɤɥɚɫɬɟɪɧɵɟ ɷɮɮɟɤɬɵ ɧɚɢɛɨɥɟɟ ɹɪɤɨ ɩɪɨɹɜɥɹɸɬɫɹ ɜ ɹɞɪɟ ɢɡɨɬɨɩɚ 6Li, ɤɨɬɨɪɨɟ ɦɵ ɪɚɫɫɦɚɬɪɢɜɚɟɦ ɧɢɠɟ. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɡɚɪɹɞɚ ɜ ɹɞɪɟ 6Li ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɞɨɜɨɥɶɧɨ ɞɥɢɧɧɵɦ “ɯɜɨɫɬɨɦ” [1], ɤɨɬɨɪɵɣ ɧɟɥɶɡɹ ɨɛɴɹɫɧɢɬɶ ɜ ɪɚɦɤɚɯ ɩɪɨɫɬɨɣ ɨɛɨɥɨɱɟɱɧɨɣ ɦɨɞɟɥɢ. əɞɪɨ 6Li ɢɦɟɟɬ ɬɚɤɠɟ ɞɨɜɨɥɶɧɨ ɛɨɥɶɲɨɟ ɡɧɚɱɟɧɢɟ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɝɨ ɪɚɞɢɭɫɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɡɚɪɹɞɚ ɹɞɟɪ Li ɫɜɢɞɟɬɟɥɶɫɬɜɭɸɬ ɬɚɤɠɟ ɛɨɥɶɲɨɟ ɡɧɚɱɟɧɢɟ ɩɪɢɜɟɞɟɧɧɨɣ ɜɟɪɨɹɬɧɨɫɬɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɟɪɟɯɨɞɚ B(E2) ɢ ɞɚɧɧɵɟ ɨ ɧɢɡɲɢɯ ɜɨɡɛɭɠɞɟɧɧɵɯ ɫɨɫɬɨɹɧɢɹɯ ɷɬɨɝɨ ɹɞɪɚ. ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɭɫɬɚɧɨɜɥɟɧɧɵɦ, ɱɬɨ ɞɨɦɢɧɢɪɭɸɳɟɣ ɤɥɚɫɬɟɪɧɨɣ ɦɨɞɨɣ ɜ ɹɞɪɚɯ 6Li ɹɜɥɹɟɬɫɹ ɤɨɧɮɢɝɭɪɚɰɢɹ ɢɡ D-ɤɥɚɫɬɟɪɚ ɢ ɞɟɣɬɪɨɧɚ (D+d), ɬɨɝɞɚ ɤɚɤ ɤɨɧɮɢɝɭɪɚɰɢɹ ɢɡ ɬɪɢɬɨɧɚ t ɢ 3He, ɤɨɬɨɪɚɹ ɬɚɤɠɟ ɪɚɫɫɦɚɬɪɢɜɚɥɚɫɶ ɜ ɥɢɬɟɪɚɬɭɪɟ, ɢɝɪɚɟɬ ɧɟɡɧɚɱɢɬɟɥɶɧɭɸ ɪɨɥɶ [1, 2]. ɗɬɨɬ ɜɵɜɨɞ ɩɨɞɬɜɟɪɠɞɚɟɬɫɹ ɬɚɤɠɟ ɜɟɥɢɱɢɧɚɦɢ ɷɧɟɪɝɢɣ ɫɜɹɡɢ: 31,99 Ɇɷȼ ɞɥɹ ɹɞɪɚ 6 Li ɜ ɰɟɥɨɦ, 28,29 Ɇɷȼ ɞɥɹ D-ɱɚɫɬɢɰɵ, 2,224 Ɇɷȼ ɞɥɹ ɞɟɣɬɪɨɧɚ ɢ 1,474 Ɇɷȼ ɞɥɹ ɫɢɫɬɟɦɵ D- ɢ d-ɤɥɚɫɬɟɪɨɜ. ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɷɧɟɪɝɢɹ ɫɜɹɡɢ ɹɞɪɚ 3He ɪɚɜɧɚ 7,717 Ɇɷȼ, ɹɞɪɚ 3H – 8,48 Ɇɷȼ ɢ ɫɢɫɬɟɦɵ t- ɢ 3He-ɤɥɚɫɬɟɪɨɜ – 15,80 Ɇɷȼ. ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɫɱɢɬɚɬɶ, ɱɬɨ ɹɞɪɨ 6Li ɹɜɥɹɟɬɫɹ ɫɢɫɬɟɦɨɣ D- ɢ d-ɤɥɚɫɬɟɪɨɜ, ɤɨɬɨɪɵɟ ɧɚɯɨɞɹɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɞɚɥɟɤɨ ɞɪɭɝ ɨɬ ɞɪɭɝɚ. Ȼɭɞɟɦ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɹɞɪɨ 6Li ɤɚɤ ɫɢɫɬɟɦɭ ɤɥɚɫɬɟɪɨɜ D+d ɜ S-ɫɨɫɬɨɹɧɢɢ, ɤɨɬɨɪɚɹ ɨɩɢɫɵɜɚɟɬɫɹ ɩɥɨɬɧɨɫɬɶɸ
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«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 777, 2007

Þ.À. Áåðåæíîé, Â.Â. Ïèëèïåíêî

( rD ɢ rd – ɪɚɞɢɭɫɵ- ɜɟɤɬɨɪɵ ɤɥɚɫɬɟɪɨɜ). ɉɨɫɤɨɥɶɤɭ ɹɞɪɨ 6Li ɢɦɟɟɬ ɫɩɢɧ 1, ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɞɥɹ ɨɩɢɫɚɧɢɹ ɭɩɪɭɝɨɝɨ ɪɚɫɫɟɹɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɷɬɨɦ ɹɞɪɟ ɫɥɟɞɭɟɬ ɜɜɟɫɬɢ ɬɪɢ ɮɨɪɦɮɚɤɬɨɪɚ: ɦɨɧɨɩɨɥɶɧɵɣ ɢ ɤɜɚɞɪɭɩɨɥɶɧɵɣ ɡɚɪɹɞɨɜɵɟ ɮɨɪɦɮɚɤɬɨɪɵ ɢ ɦɚɝɧɢɬɧɵɣ ɮɨɪɦɮɚɤɬɨɪ [9 ɝɥ. 3]. ɇɢɠɟ ɦɵ ɧɟ ɪɚɫɫɦɚɬɪɢɜɚɟɦ ɨɩɢɫɚɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ, ɚ ɩɪɢ ɨɩɢɫɚɧɢɢ ɡɚɪɹɞɨɜɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ ɩɪɟɧɟɛɪɟɝɚɟɦ ɤɜɚɞɪɭɩɨɥɶɧɵɦ ɜɤɥɚɞɨɦ, ɩɪɢɧɢɦɚɹ ɜɨ ɜɧɢɦɚɧɢɟ ɦɚɥɨɫɬɶ ɡɧɚɱɟɧɢɣ ɤɜɚɞɪɭɩɨɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɞɟɣɬɪɨɧɚ (2,86 ɦɛɧ) ɢ 6Li ɜ ɰɟɥɨɦ (–0,83 ɦɛɧ). Ɂɚɪɹɞɨɜɭɸ ɩɥɨɬɧɨɫɬɶ

U (ch) r  Li
6

ɹɞɪɚ 6Li ɩɪɟɞɫɬɚɜɢɦ ɱɟɪɟɡ ɩɥɨɬɧɨɫɬɢ ɡɚɪɹɞɚ D-ɱɚɫɬɢɰɵ

(ch ) UD r 

ɢ ɞɟɣɬɪɨɧɚ

(ch ) Ud r  :

U (ch) r  Li
6

ȼ ɮɨɪɦɭɥɟ (1) ɦɵ ɭɱɥɢ, ɱɬɨ ɡɚɪɹɞɵ ɹɞɪɚ 6Li, D-ɱɚɫɬɢɰɵ ɢ ɞɟɣɬɪɨɧɚ ɪɚɜɧɵ Z

1 3 (ch ) (ch ) 2 UD d [ª r  ɨ / 3   Ud   r  2ɨ / 3 º ³ ¬ ¼U 6 Li [  . 3
3 , ZD

(1)
2 ɢ Zd 1 , ɚ ɞɥɹ ɢɯ

ɦɚɫɫ ɩɪɢɛɥɢɠɟɧɧɨ ɦɨɠɧɨ ɩɨɥɨɠɢɬɶ M D / M | 2 / 3 , M d / M | 1/ 3 . ȼ ɪɟɡɭɥɶɬɚɬɟ ɡɚɪɹɞɨɜɵɣ ɮɨɪɦɮɚɤɬɨɪ ɹɞɪɚ 6Li ɩɪɢɨɛɪɟɬɚɟɬ ɜɢɞ:

F6 Li  q 
ɝɞɟ FD  q  ɢ
6

3 (ch) ³ d r exp  iqr  U Li  r  3 FD  q  S Li  q / 3  3 Fd  q  S Li  2q / 3 , Fd  q  – ɡɚɪɹɞɨɜɵɟ ɮɨɪɦɮɚɤɬɨɪɵ D-ɱɚɫɬɢɰɵ ɢ ɞɟɣɬɪɨɧɚ, ɚ ɫɬɪɭɤɬɭɪɧɵɣ ɮɨɪɦɮɚɤɬɨɪ
6 6 6

2

1

(2)

ɹɞɪɚ Li ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ

S 6 Li  q 
(3)

S 6 Li  q 
ɉɪɢ ɜɵɛɨɪɟ ɩɥɨɬɧɨɫɬɢ

3 ³ d [ exp  iqɨ U Li [  .
6

U

6

ɦɨɞɟɥɟɣ. ɉɪɨɫɬɟɣɲɢɟ ɢɡ ɧɢɯ ɨɬɜɟɱɚɸɬ ɨɫɰɢɥɥɹɬɨɪɧɨɣ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɤɥɚɫɬɟɪɨɜ ɜ ɦɨɞɟɥɢ ɧɭɤɥɨɧɧɵɯ ɚɫɫɨɰɢɚɰɢɣ (ɆɇȺ, ɫɦ. [1, 2]), ɤɨɬɨɪɚɹ ɡɚɜɢɫɢɬ ɨɬ ɨɞɧɨɝɨ ɩɚɪɚɦɟɬɪɚ E . ɉɟɪɜɵɣ ɜɚɪɢɚɧɬ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ D+d ɫɢɫɬɟɦɵ (ɆɇȺ1) ɢɦɟɟɬ ɜɢɞ:

Li

[  ɦɵ ɪɚɫɫɦɨɬɪɟɥɢ ɧɟɫɤɨɥɶɤɨ ɤɨɧɤɪɟɬɧɵɯ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɢɯ ɤɥɚɫɬɟɪɧɵɯ

\ [ 

3 § 4E · 4 § 8 2 · § 2 · ¨ ¸ ¨ 1  E[ ¸ exp ¨  E[ ¸ , 2 © 3S ¹ © 9 ¹ © 3 ¹

3

(4)
0 . ɉɨɞɫɬɚɜɢɜ

ɢ ɨɬɜɟɱɚɟɬ ɫɥɭɱɚɸ, ɤɨɝɞɚ ɧɚɢɛɨɥɟɟ ɜɟɪɨɹɬɧɨ ɩɨɥɨɠɟɧɢɟ ɤɥɚɫɬɟɪɨɜ ɜ ɨɞɧɨɣ ɬɨɱɤɟ [

U

6

Li

[  \ [ 

2

ɜ (3), ɧɚɯɨɞɢɦ ɹɜɧɵɣ ɜɢɞ ɞɥɹ ɫɬɪɭɤɬɭɪɧɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ

§ 3q 2 § 1 2 1 4· S 6 Li  q  ¨1  q  q exp ¨ ¸ 64 E 2 ¹ © 4E © 16 E

· ¸. ¹

(5)

Ⱦɥɹ ɜɬɨɪɨɝɨ ɜɚɪɢɚɧɬɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɦɨɞɟɥɢ ɆɇȺ2 ɜɨɥɧɨɜɭɸ ɮɭɧɤɰɢɸ D+d ɫɢɫɬɟɦɵ ɜɨɡɶɦɟɦ ɜ ɮɨɪɦɟ

\ [ 

64 § 4 E · 4 § 2 · 2 ¨ ¸ E[ exp ¨  E[ ¸ . 135 © 3S ¹ © 3 ¹

3

(6)

ȼɵɪɚɠɟɧɢɟ (6) ɨɬɜɟɱɚɟɬ ɧɚɢɛɨɥɟɟ ɜɟɪɨɹɬɧɨɦɭ ɪɚɫɫɬɨɹɧɢɸ ɦɟɠɞɭ ɤɥɚɫɬɟɪɚɦɢ
6

[ {d

3 (2 E ) . ɋɨɛɫɬɜɟɧɧɨ

ɝɨɜɨɪɹ, ɢɦɟɧɧɨ ɜɚɪɢɚɧɬ ɦɨɞɟɥɢ ɆɇȺ2 ɨɩɢɫɵɜɚɟɬ ɤɨɧɮɢɝɭɪɚɰɢɸ ɹɞɪɚ Li ɫ ɜɵɪɚɠɟɧɧɨɣ ɤɥɚɫɬɟɪɢɡɚɰɢɟɣ, ɜ ɤɨɬɨɪɨɣ D- ɢ d-ɤɥɚɫɬɟɪɵ ɯɨɪɨɲɨ ɨɬɞɟɥɟɧɵ ɞɪɭɝ ɨɬ ɞɪɭɝɚ ɢ ɮɨɪɦɢɪɭɸɬ ɫɬɪɭɤɬɭɪɭ ɬɢɩɚ ɝɚɧɬɟɥɢ ɫ ɞɥɢɧɨɣ d. Ⱦɥɹ ɜɚɪɢɚɧɬɚ ɆɇȺ2 ɫɬɪɭɤɬɭɪɧɵɣ ɮɨɪɦɮɚɤɬɨɪ ɪɚɜɟɧ

§ 3q 2 § 1 2 3 4· S 6 Li  q  ¨1  q  q exp ¨ ¸ 320 E 2 ¹ © 4E © 16E

· ¸. ¹

(7)

Ⱦɥɹ ɨɛɨɢɯ ɜɚɪɢɚɧɬɨɜ ɆɇȺ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɵɣ ɡɚɪɹɞɨɜɵɣ ɪɚɞɢɭɫ ɹɞɪɚ 6Li ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ:

 r 2 ! 6 Li
ɝɞɟ

2 1 7  r 2 !D   r 2 ! d  , 3 3 12E

(8)

2 1/ 2 2  r 2 !1/ D ɢ  r ! d – ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɵɟ ɡɚɪɹɞɨɜɵɟ ɪɚɞɢɭɫɵ D-ɱɚɫɬɢɰɵ ɢ ɞɟɣɬɪɨɧɚ.

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ñåð³ÿ ô³çè÷íà «ßäðà, ÷àñòèíêè, ïîëÿ», âèï. 2 /34/

Àíàëèç çàðÿäîâûõ ôîðìôàêòîðîâ ÿäðà...

Ɋɚɫɫɦɨɬɪɢɦ ɞɚɥɟɟ D+d ɤɥɚɫɬɟɪɧɭɸ ɦɨɞɟɥɶ ɫ ɞɢɫɩɟɪɫɢɟɣ (ɄɆȾ1) ɞɥɹ ɹɞɪɚ 6Li, ɤɨɬɨɪɚɹ ɹɜɥɹɟɬɫɹ ɛɨɥɟɟ ɪɟɚɥɶɧɨɣ, ɱɟɦ ɨɩɢɫɚɧɧɵɟ ɜɵɲɟ ɞɜɚ ɜɚɪɢɚɧɬɚ ɆɇȺ. ɉɨ ɚɧɚɥɨɝɢɢ ɫ D-ɤɥɚɫɬɟɪɧɨɣ ɦɨɞɟɥɶɸ ɫ ɞɢɫɩɟɪɫɢɟɣ ɢɡ ɪɚɛɨɬ [5–8] ɩɪɟɞɫɬɚɜɢɦ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤɥɚɫɬɟɪɨɜ ɜ 6Li ɜ ɮɨɪɦɟ

U

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Li

[  { U ' [  ³ d 3[ cU0 [ c  ) '  ɨ  ɨc ,
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(9) (10)

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Ɂɞɟɫɶ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɞɥɢɧɨɣ d , ɚ ɪɚɡɦɵɜɚɸɳɚɹ ɮɭɧɤɰɢɹ

ɨɬɜɟɱɚɟɬ ɤɨɧɮɢɝɭɪɚɰɢɢ ɫɢɫɬɟɦɵ D+d ɜ ɜɢɞɟ ɠɟɫɬɤɨɣ ɝɚɧɬɟɥɢ ɨɩɢɫɵɜɚɟɬ ɜɨɡɦɨɠɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɢɫɬɟɦɵ ɨɬ

ɷɬɨɣ ɠɟɫɬɤɨɣ ɮɨɪɦɵ, ɜɟɪɨɹɬɧɨɫɬɶ ɤɨɬɨɪɵɯ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɩɚɪɚɦɟɬɪɨɦ ɞɢɫɩɟɪɫɢɢ '. ɉɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ (9) ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ:

U ' [ 

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§ [ 2  d 2 · '2 exp ¨  sh [ d / ' 2  . ¸ 2 2' ¹ [ d ©

(11)

ɉɨɞɫɬɚɜɥɹɹ ɜɵɪɚɠɟɧɢɹ (9) ɢ (10) ɜ ɮɨɪɦɭɥɭ (3), ɧɚɯɨɞɢɦ ɫɬɪɭɤɬɭɪɧɵɣ ɮɨɪɦɮɚɤɬɨɪ ɞɥɹ ɹɞɪɚ 6Li ɜ ɮɨɪɦɟ

S 6 Li  q 

§ 1 · j0  qd  exp ¨  q 2 ' 2 ¸ . © 2 ¹

(12)

ɋɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɵɣ ɡɚɪɹɞɨɜɵɣ ɪɚɞɢɭɫ ɹɞɪɚ 6Li ɜ ɷɬɨɣ ɦɨɞɟɥɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ

 r 2 ! 6 Li

2 1 2 2  r 2 !D   r 2 ! d  d 2  ' 2 . 3 3 9 3

(13)

ɉɨɫɤɨɥɶɤɭ ɞɟɣɬɪɨɧ ɹɜɥɹɟɬɫɹ ɫɥɚɛɨ ɫɜɹɡɚɧɧɨɣ ɫɢɫɬɟɦɨɣ, ɦɨɠɧɨ ɞɨɩɭɫɬɢɬɶ, ɱɬɨ d-ɤɥɚɫɬɟɪ ɦɨɠɟɬ ɢɫɩɵɬɵɜɚɬɶ ɡɧɚɱɢɬɟɥɶɧɭɸ ɞɟɮɨɪɦɚɰɢɸ ɜɧɭɬɪɢ ɹɞɪɚ 6Li. ɉɨɷɬɨɦɭ ɪɚɫɫɦɨɬɪɢɦ ɬɚɤɠɟ ɷɬɨ ɹɞɪɨ ɤɚɤ ɤɥɚɫɬɟɪɧɭɸ ɫɢɫɬɟɦɭ D+p+n, ɤɨɬɨɪɭɸ ɛɭɞɟɦ ɨɩɢɫɵɜɚɬɶ ɩɥɨɬɧɨɫɬɶɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤɥɚɫɬɟɪɨɜ U 6 Li  ɨ, ɡ  , ɡɚɜɢɫɹɳɟɣ ɨɬ ɤɨɨɪɞɢɧɚɬ əɤɨɛɢ ɞɥɹ ɬɪɟɯ ɤɥɚɫɬɟɪɨɜ ɩɪɨɬɨɧɚ

ɨ rp  rn , ɡ

rD  (rp  rn ) / 2 . ɉɪɟɧɟɛɪɟɝɚɹ ɜɤɥɚɞɨɦ ɡɚɪɹɞɨɜɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ

ɧɟɣɬɪɨɧɚ, ɩɪɟɞɫɬɚɜɢɦ ɡɚɪɹɞɨɜɭɸ ɩɥɨɬɧɨɫɬɶ

U

(ch ) p

r  :

U (ch) r  Li
6

ɹɞɪɚ 6Li ɱɟɪɟɡ ɩɥɨɬɧɨɫɬɢ ɡɚɪɹɞɚ D-ɱɚɫɬɢɰɵ

(ch ) UD r 

ɢ

(ɄɆȾ2):

1 3 3 (ch ) ) (14) 2 UD d [d K ª r  ɡ / 3   U (ch   r  2ɡ / 3  ɨ / 2 º ³ p ¬ ¼U 6 Li  ɨ, ɡ  . 3 ɂɫɤɨɦɭɸ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤɥɚɫɬɟɪɨɜ U 6 Li  ɨ, ɡ  ɡɚɩɢɲɟɦ ɜ ɤɥɚɫɬɟɪɧɨɣ ɦɨɞɟɥɢ ɫ ɞɢɫɩɟɪɫɢɟɣ

U (ch) r  Li
6

U

6

Li

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U0  ɨ, ɡ 

(15) (16)

8S

2

d N dD  G [  d N  G K  dD  G  ɨ ˜ ɡ  ,
1

) ' [ ,K 
Ɂɞɟɫɶ ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ

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3

§ · 1 1 exp ¨  2 [ 2  2 K 2 ¸ . 2 'D ¹ © 2' N

(17)

U0  ɨ, ɡ 

ɨɩɢɫɵɜɚɟɬ ɫɢɫɬɟɦɭ D+p+n ɜ ɮɨɪɦɟ ɠɟɫɬɤɨɝɨ ɪɚɜɧɨɛɟɞɪɟɧɧɨɝɨ

ɬɪɟɭɝɨɥɶɧɢɤɚ ɫ ɨɫɧɨɜɚɧɢɟɦ d N (ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɩɪɨɬɨɧɨɦ ɢ ɧɟɣɬɪɨɧɨɦ) ɢ ɜɵɫɨɬɨɣ dD , ɚ ɜɟɪɨɹɬɧɨɫɬɶ ɨɬɤɥɨɧɟɧɢɹ ɤɥɚɫɬɟɪɨɜ ɨɬ ɩɨɥɨɠɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɜ ɜɟɪɲɢɧɚɯ ɷɬɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ɨɩɢɫɵɜɚɟɬɫɹ ɪɚɡɦɵɜɚɸɳɟɣ ɮɭɧɤɰɢɟɣ ) '  [ ,K  ɫ ɩɚɪɚɦɟɬɪɚɦɢ ɞɢɫɩɟɪɫɢɢ ' N ɢ 'D . ɩɪɨɬɨɧɚ Fp  q  ɫɨɨɬɧɨɲɟɧɢɟɦ ȼ ɞɚɧɧɨɣ ɦɨɞɟɥɢ ɡɚɪɹɞɨɜɵɣ ɮɨɪɦɮɚɤɬɨɪ ɹɞɪɚ 6Li ɜɵɪɚɠɚɟɬɫɹ ɱɟɪɟɡ ɮɨɪɦɮɚɤɬɨɪɵ D-ɱɚɫɬɢɰɵ FD  q  ɢ

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«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 777, 2007

Þ.À. Áåðåæíîé, Â.Â. Ïèëèïåíêî

F6 Li  q 
) S 6(D q Li

2 1 ) ) FD  q  S 6(D  q   Fp  q  S 6(N q , Li Li 3 3 1 1

(18)

ɝɞɟ ɞɜɚ ɫɬɪɭɤɬɭɪɧɵɯ ɮɨɪɦɮɚɤɬɨɪɚ ɹɞɪɚ 6Li ɨɩɪɟɞɟɥɹɸɬɫɹ ɮɨɪɦɭɥɚɦɢ

§ · § 3 3 2 2 · ³ d [ d K exp  iqɨ/3 U Li  ɨ, ɡ  j0 ¨ 3 qdD ¸ exp ¨  18 q 'D ¸ , © ¹ © ¹
6

(19)

) S 6(N q Li

3 3 ³ d [ d K exp «iq ¨ 2 ɨ  3 ɡ ¸ » U Li  ɨ, ɡ 
6

ª §1 ¬ ©

2 ·º ¹¼

(20)

Ⱦɥɹ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɝɨ ɡɚɪɹɞɨɜɨɝɨ ɪɚɞɢɭɫɚ ɹɞɪɚ 6Li ɫɨɝɥɚɫɧɨ ɄɆȾ2 ɥɟɝɤɨ ɧɚɣɬɢ ɬɚɤɨɟ ɜɵɪɚɠɟɧɢɟ

§ 4 2 1 2 j0 ¨ dD  d N ¨q 9 4 ©

· ª 2 § 2 2 1 2 ·º exp ¸ «  q ¨ 9 'D  8 ' N ¸ » . ¸ © ¹¼ ¬ ¹

 r 2 ! 6 Li
2 1/ 2

2 1 2 2 1 2 2 2 1 2  r 2 !D   r 2 ! p  dD  d N  'D  ' N , 3 3 9 12 3 4

(21)

ɝɞɟ  r ! p – ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɵɣ ɡɚɪɹɞɨɜɵɣ ɪɚɞɢɭɫ ɩɪɨɬɨɧɚ. Ʉɪɨɦɟ ɨɩɢɫɚɧɢɹ ɭɩɪɭɝɨɝɨ ɡɚɪɹɞɨɜɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ ɹɞɪɚ 6Li, ɜ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɟ ɪɚɫɫɦɨɬɪɟɧɨ ɬɚɤɠɟ ɩɪɢɦɟɧɟɧɢɟ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɨɣ ɤɥɚɫɬɟɪɧɨɣ ɦɨɞɟɥɢ ɞɥɹ ɨɩɢɫɚɧɢɹ ɤɜɚɞɪɭɩɨɥɶɧɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ ɧɟɭɩɪɭɝɨɝɨ ɪɚɫɫɟɹɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɹɞɪɚɯ 6Li, ɨɬɜɟɱɚɸɳɟɝɨ ɩɟɪɟɯɨɞɭ 1+o3+ ɫ ɜɨɡɛɭɠɞɟɧɢɟɦ ɜ ɹɞɪɟ ɩɟɪɜɨɝɨ ɭɪɨɜɧɹ 3+, * E3 2,18 Ɇɷȼ. ɉɪɢ ɷɬɨɦ ɦɵ ɨɝɪɚɧɢɱɢɥɢɫɶ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɬɨɥɶɤɨ ɬɪɟɯ ɜɚɪɢɚɧɬɨɜ ɤɥɚɫɬɟɪɧɨɣ ɦɨɞɟɥɢ D+d: ɆɇȺ1, ɆɇȺ2 ɢ ɄɆȾ1. ȼ ɬɚɤɨɦ ɩɨɞɯɨɞɟ ɤɨɧɟɱɧɵɣ ɭɪɨɜɟɧɶ 3+ ɹɞɪɚ 6Li ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɜɪɚɳɚɬɟɥɶɧɨɟ ɫɨɫɬɨɹɧɢɟ ɫɢɫɬɟɦɵ D+d ɫ ɨɪɛɢɬɚɥɶɧɵɦ ɦɨɦɟɧɬɨɦ l = 2. ȼ ɨɛɳɟɦ ɜɢɞɟ ɤɭɥɨɧɨɜɫɤɢɣ ɮɨɪɦɮɚɤɬɨɪ ɞɥɹ ɧɟɭɩɪɭɝɨɝɨ ɩɟɪɟɯɨɞɚ ɫɢɫɬɟɦɵ D+d ɢɡ ɫɨɫɬɨɹɧɢɹ < J i M i  ɨ  ɜ ɫɨɫɬɨɹɧɢɟ < J f M f  ɨ  , ɝɞɟ J i , M i ɢ J f , M f – ɧɚɱɚɥɶɧɵɟ ɢ ɤɨɧɟɱɧɵɟ ɡɧɚɱɟɧɢɹ ɦɨɦɟɧɬɚ ɢ ɟɝɨ ɩɪɨɟɤɰɢɢ, ɞɚɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɜɵɪɚɠɟɧɢɟɦ

FM f M i  q 

1 3 (ch ) (ch ) d r exp  iqr  ³ d 3[ ª r  [ / 3   Ud r  2[ / 3  º <* 2 UD   ³ J f M f  ɨ < Ji M i  ɨ . ¬ ¼ 3

(22)

ȼɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɤɥɚɫɬɟɪɨɜ ɜ ɹɞɪɟ 6Li ɢɦɟɟɬ ɜɢɞ:

< JM  ɨ 

¦  l 1 mP | JM Ml [  Ylm  n[  F1P ,
mP

(23) – ɪɚɞɢɚɥɶɧɚɹ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ

ɝɞɟ l , m – ɨɪɛɢɬɚɥɶɧɵɣ ɦɨɦɟɧɬ ɫɢɫɬɟɦɵ ɤɥɚɫɬɟɪɨɜ ɢ ɟɝɨ ɩɪɨɟɤɰɢɹ, ɞɜɢɠɟɧɢɹ ɤɥɚɫɬɟɪɨɜ,

Ml  [ 

F1P

– ɫɩɢɧɨɜɚɹ ɮɭɧɤɰɢɹ ɞɟɣɬɪɨɧɚ.

ɉɪɨɟɤɰɢɢ ɦɨɦɟɧɬɚ

M i ɢ M f ɧɟ ɮɢɤɫɢɪɭɸɬɫɹ ɜ ɷɤɫɩɟɪɢɦɟɧɬɟ. ɉɨɷɬɨɦɭ ɩɨ ɧɢɦ ɧɚɞɨ ɩɪɨɜɟɫɬɢ

ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɭɫɪɟɞɧɟɧɢɟ, ɤɨɬɨɪɨɟ ɞɚɟɬ ɞɥɹ ɩɟɪɟɯɨɞɚ 1+o3+ ɧɟɭɩɪɭɝɢɣ ɤɜɚɞɪɭɩɨɥɶɧɵɣ ɮɨɪɦɮɚɤɬɨɪ ɜ ɮɨɪɦɟ

F1o3  q  {
2

2 1 ¦ FM f M i  q  2 Ji  1 Mi M f

2 1 FD  q  S1(2) Fd  q  S1(2) o3  q 3   o3  2q 3  . 3 3
6

2

(24)

Ɂɞɟɫɶ ɫɬɪɭɤɬɭɪɧɵɣ ɤɜɚɞɪɭɩɨɥɶɧɵɣ ɮɨɪɦɮɚɤɬɨɪ ɹɞɪɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ

Li ɞɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɧɟɭɩɪɭɝɨɝɨ ɩɟɪɟɯɨɞɚ (25)

S1(2) 4S 7 3 ³ d[[ 2 j2  q[  U1o3 [  , o3  q 

ɝɞɟ ɪɚɞɢɚɥɶɧɚɹ ɩɟɪɟɯɨɞɧɚɹ ɩɥɨɬɧɨɫɬɶ ɫɜɹɡɚɧɚ ɫ ɪɚɞɢɚɥɶɧɵɦɢ ɜɨɥɧɨɜɵɦɢ ɮɭɧɤɰɢɹɦɢ ɫɨɨɬɧɨɲɟɧɢɟɦ * U1o3 [  M 2 [  M0 [  / 4S . ɉɪɟɞɩɨɥɚɝɚɹ, ɱɬɨ ɩɪɢ ɜɪɚɳɟɧɢɢ ɜ ɤɨɧɟɱɧɨɦ ɫɨɫɬɨɹɧɢɢ ɫɢɫɬɟɦɚ D+d ɧɟ ɩɪɟɬɟɪɩɟɜɚɟɬ ɡɧɚɱɢɬɟɥɶɧɨɣ ɞɟɮɨɪɦɚɰɢɢ, ɩɨɥɨɠɢɦ ɩɟɪɟɯɨɞɧɚɹ ɩɥɨɬɧɨɫɬɶ ɪɚɜɧɚ U1o3 [ 
2

M2 [  | M0 [  { M [  . ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɦɵ ɩɨɥɭɱɚɟɦ, ɱɬɨ

M [  / 4S
6

\ [ 

2

U

6

ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤɥɚɫɬɟɪɨɜ ɜ ɨɫɧɨɜɧɨɦ ɫɨɫɬɨɹɧɢɢ ɹɞɪɚ Li. Ⱦɥɹ ɜɚɪɢɚɧɬɚ ɆɇȺ1, ɢɫɩɨɥɶɡɭɹ ɜɵɪɚɠɟɧɢɟ (4) ɞɥɹ ɜɨɥɧɨɜɨɣ ɮɭɧɤɰɢɢ ɩɟɪɟɯɨɞɧɵɣ ɫɬɪɭɤɬɭɪɧɵɣ ɮɨɪɦɮɚɤɬɨɪ ɜ ɜɢɞɟ

Li

[  ,

ɬ.ɟ. ɫɨɜɩɚɞɚɟɬ ɫ ɩɥɨɬɧɨɫɬɶɸ

\ [  ,

ɩɨɥɭɱɚɟɦ ɢɡ (25)

37
ñåð³ÿ ô³çè÷íà «ßäðà, ÷àñòèíêè, ïîëÿ», âèï. 2 /34/

Àíàëèç çàðÿäîâûõ ôîðìôàêòîðîâ ÿäðà...

S

(2) 1o3

q

8 7S E

32

§ 3 q· § 1 4E § 3q 2 · q2 q4 · 1 erf ¨ ¨ E 4¸ ¸  21 ¨ 2  q 2  48E  128E 2 ¸ exp ¨  16 E ¸ . q3 © ¹ © ¹ © ¹

(26)

Ⱥɧɚɥɨɝɢɱɧɨ ɞɥɹ ɜɚɪɢɚɧɬɚ ɆɇȺ2, ɢɫɩɨɥɶɡɭɹ ɜɵɪɚɠɟɧɢɟ (6), ɧɚɯɨɞɢɦ

S1(2) o3  q 

§ 3q 2 21q 2 2 q  56 3 exp E   ¨  16E 960 E 2 ©

· ¸. ¹

(27)

Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɫɬɪɭɤɬɭɪɧɨɝɨ ɩɟɪɟɯɨɞɧɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ ɜ ɄɆȾ1 ɢɫɩɨɥɶɡɭɟɦ ɜɵɪɚɠɟɧɢɹ (9), (10) ɞɥɹ ɩɥɨɬɧɨɫɬɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤɥɚɫɬɟɪɨɜ, ɱɬɨ ɞɚɟɬ

S1(2) o3  q 

§ d2 · § [2 · 14 1 exp ¨  2 ¸ ³ d [[ j2  q[  exp ¨  2 ¸ sh [ d ' 2  . 3S 'd © 2' ¹ © 2' ¹

(28)

ɊȿɁɍɅɖɌȺɌɕ ɊȺɋɑȿɌɈȼ ɎɈɊɆɎȺɄɌɈɊɈȼ ɇɚ ɨɫɧɨɜɟ ɨɩɢɫɚɧɧɨɝɨ ɜɵɲɟ ɩɨɞɯɨɞɚ ɜ ɪɚɦɤɚɯ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɨɣ ɤɥɚɫɬɟɪɧɨɣ ɦɨɞɟɥɢ ɧɚɦɢ ɛɵɥ ɩɪɨɜɟɞɟɧ ɬɟɨɪɟɬɢɱɟɫɤɢɣ ɚɧɚɥɢɡ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɩɨ ɡɚɪɹɞɨɜɨɦɭ ɮɨɪɦɮɚɤɬɨɪɭ ɹɞɪɚ 6Li, ɧɚɣɞɟɧɧɵɯ ɢɡ ɭɩɪɭɝɨɝɨ ɪɚɫɫɟɹɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɧɚ ɹɞɪɚɯ 6Li, ɚ ɬɚɤɠɟ ɞɚɧɧɵɯ ɩɨ ɧɟɭɩɪɭɝɨɦɭ ɮɨɪɦɮɚɤɬɨɪɭ ɞɥɹ ɪɚɫɫɟɹɧɢɹ * ɷɥɟɤɬɪɨɧɨɜ ɫ ɜɨɡɛɭɠɞɟɧɢɟɦ ɜ ɹɞɪɚɯ ɦɢɲɟɧɢ ɩɟɪɜɨɝɨ ɭɪɨɜɧɹ 3+, E3 2,18 Ɇɷȼ. ɉɪɢ ɷɬɨɦ ɚɧɚɥɢɡ ɭɩɪɭɝɨɝɨ ɡɚɪɹɞɨɜɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ ɩɪɨɜɨɞɢɥɫɹ ɧɚ ɨɫɧɨɜɟ ɜɫɟɯ ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɜɵɲɟ ɤɥɚɫɬɟɪɧɵɯ ɦɨɞɟɥɟɣ ɫ ɩɨɦɨɳɶɸ ɮɨɪɦɭɥɵ (2) ɢ ɮɨɪɦɭɥ (5) ɞɥɹ ɆɇȺ1, (7) ɞɥɹ ɆɇȺ2 ɢ (12) ɞɥɹ ɄɆȾ1, ɚ ɬɚɤɠɟ ɩɨ ɮɨɪɦɭɥɚɦ (18)–(20) ɞɥɹ ɄɆȾ2. ɇɟɭɩɪɭɝɢɣ ɮɨɪɦɮɚɤɬɨɪ ɪɚɫɫɱɢɬɵɜɚɥɫɹ ɩɨ ɮɨɪɦɭɥɟ (24) ɢ ɮɨɪɦɭɥɚɦ (26) ɞɥɹ ɆɇȺ1, (27) ɞɥɹ ɆɇȺ2 ɢ (28) ɞɥɹ ɄɆȾ1. Ɂɚɪɹɞɨɜɵɟ ɮɨɪɦɮɚɤɬɨɪɵ D- ɢ d-ɤɥɚɫɬɟɪɨɜ, ɤɨɬɨɪɵɟ ɜɯɨɞɹɬ ɜ ɮɨɪɦɭɥɭ (2), ɦɵ ɫɱɢɬɚɥɢ ɫɨɜɩɚɞɚɸɳɢɦɢ ɫ ɮɨɪɦɮɚɤɬɨɪɚɦɢ ɫɜɨɛɨɞɧɵɯ ɹɞɟɪ ɢ ɜɵɛɢɪɚɥɢ ɞɥɹ ɧɢɯ ɛɟɡɦɨɞɟɥɶɧɵɟ ɜɵɪɚɠɟɧɢɹ ɜ ɜɢɞɟ ɫɭɦɦɵ ɝɚɭɫɫɢɚɧɨɜ ɞɥɹ Dɱɚɫɬɢɰɵ [10, 11]

FD  q  exp   q 2J 2 / 4  ¦
i

Qi ªcos  qRi   2 Ri2 sin  qRi  /  J 2 qRi  º , 2 2 ¬ ¼ 1  2 Ri / J ª1   q / q0 2 º ª1  ¦ ai q 2i º . » ¬ ¼« ¬ i1 ¼
5
1

(29)

ɢ ɬɚɤ ɧɚɡɵɜɚɟɦɨɣ ɉɚɪɚɦɟɬɪɢɡɚɰɢɢ I ɢɡ ɪɚɛɨɬɵ [12] ɞɥɹ ɞɟɣɬɪɨɧɚ

Fd  q 

(30)

Ʉɨɧɫɬɚɧɬɵ ɜ ɮɨɪɦɭɥɚɯ (29), (30) ɹɜɥɹɸɬɫɹ ɨɩɪɟɞɟɥɟɧɧɵɦɢ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɢɦɢ ɩɚɪɚɦɟɬɪɚɦɢ, ɨɩɪɟɞɟɥɟɧɧɵɦɢ ɢɡ ɚɧɚɥɢɡɚ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨ ɪɚɫɫɟɹɧɢɸ ɷɥɟɤɬɪɨɧɨɜ. ɂɫɩɨɥɶɡɨɜɚɧɧɵɟ ɛɟɡɦɨɞɟɥɶɧɵɟ 2 1/ 2 1,676 ɮɦ ɢ ɮɨɪɦɮɚɤɬɨɪɵ D- ɢ d-ɤɥɚɫɬɟɪɨɜ (29) ɢ (30) ɨɬɜɟɱɚɸɬ ɡɧɚɱɟɧɢɹɦ ɡɚɪɹɞɨɜɵɯ ɪɚɞɢɭɫɨɜ  r !D
2  r 2 !1/ 2,093 ɮɦ. Ⱦɥɹ ɜɯɨɞɹɳɟɝɨ ɜ ɮɨɪɦɭɥɭ (18) ɡɚɪɹɞɨɜɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ ɩɪɨɬɨɧɚ ɦɵ ɢɫɩɨɥɶɡɨɜɚɥɢ d ɯɨɪɨɲɨ ɢɡɜɟɫɬɧɭɸ ɞɢɩɨɥɶɧɭɸ ɮɨɪɦɭ [9] ɫ r0 0,234 ɮɦ:

F q

2 2 ª ¬1  r0 q º ¼ , 2 1/ 2

2

(31)

12r0 0,811 ɮɦ. ɱɬɨ ɨɬɜɟɱɚɟɬ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɦɭ ɡɚɪɹɞɨɜɨɦɭ ɪɚɞɢɭɫɭ ɩɪɨɬɨɧɚ  r ! p Ɋɚɫɫɱɢɬɚɧɧɵɟ ɮɨɪɦɮɚɤɬɨɪɵ ɫɪɚɜɧɢɜɚɥɢɫɶ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɢɡɦɟɪɟɧɧɵɦɢ ɭɩɪɭɝɢɦ ɢ ɧɟɭɩɪɭɝɢɦ ɡɚɪɹɞɨɜɵɦɢ ɮɨɪɦɮɚɤɬɨɪɚɦɢ ɹɞɪɚ 6Li ɢɡ ɪɚɛɨɬ [13, 14]. ɇɚ ɨɫɧɨɜɟ ɚɧɚɥɢɡɚ ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɧɚɦɢ ɛɵɥɢ ɨɩɪɟɞɟɥɟɧɵ ɜɟɥɢɱɢɧɵ ɩɚɪɚɦɟɬɪɨɜ ɞɥɹ ɢɫɩɨɥɶɡɨɜɚɧɧɵɯ ɦɨɞɟɥɶɧɵɯ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɤɥɚɫɬɟɪɨɜ, ɤɨɬɨɪɵɟ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. 1 ɜɦɟɫɬɟ ɫɨ ɡɧɚɱɟɧɢɹɦɢ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɝɨ ɡɚɪɹɞɨɜɨɝɨ ɪɚɞɢɭɫɚ ɹɞɪɚ 6 Li, ɜɵɱɢɫɥɟɧɧɵɦɢ ɩɨ ɮɨɪɦɭɥɟ (8) ɞɥɹ ɆɇȺ1 ɢ ɆɇȺ2, (13) ɞɥɹ ɄɆȾ1 ɢ (21) ɞɥɹ ɄɆȾ2, ɢ ɜɟɥɢɱɢɧɵ F 2 ɞɥɹ ɨɩɢɫɚɧɢɹ ɭɩɪɭɝɨɝɨ ɢ ɧɟɭɩɪɭɝɨɝɨ ɮɨɪɦɮɚɤɬɨɪɨɜ. Ⱦɥɹ ɫɪɚɜɧɟɧɢɹ ɩɪɢɜɟɞɟɦ ɬɚɤɠɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ 2 1/2 2 1/2 ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɝɨ ɪɚɞɢɭɫɚ:  r ! 6 Li = 2,56r0,05 ɮɦ-1 ɢɡ [13] ɢ  r ! 6 Li = 2,57r0,10 ɮɦ-1 ɢɡ [14]. ɉɟɪɜɨɟ ɢɡ

ɧɢɯ ɩɨɥɭɱɟɧɨ ɢɡ ɨɛɪɚɛɨɬɤɢ ɞɚɧɧɵɯ ɩɨ ɪɚɫɫɟɹɧɢɸ ɷɥɟɤɬɪɨɧɨɜ ɜ ɞɢɚɩɚɡɨɧɟ 0,56 ɮɦ-1 d q d 3,66 ɮɦ-1, ɚ ɜɬɨɪɨɟ – ɜ ɞɢɚɩɚɡɨɧɟ 0,09 ɮɦ-1 d q d 0,90 ɮɦ-1. Ɋɟɡɭɥɶɬɚɬɵ ɩɪɨɜɟɞɟɧɧɵɯ ɧɚɦɢ ɪɚɫɱɟɬɨɜ ɮɨɪɦɮɚɤɬɨɪɨɜ ɹɞɪɚ 6Li ɜɦɟɫɬɟ ɫ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 1–4. ɇɚ ɝɪɚɮɢɤɚɯ ɭɩɪɭɝɨɝɨ ɡɚɪɹɞɨɜɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ 6Li ɞɥɹ ɫɪɚɜɧɟɧɢɹ ɬɚɤɠɟ ɩɨɤɚɡɚɧɵ ɤɪɢɜɵɟ ɞɥɹ ɡɚɪɹɞɨɜɵɯ ɮɨɪɦɮɚɤɬɨɪɨɜ ɤɥɚɫɬɟɪɨɜ, ɫɨɫɬɚɜɥɹɸɳɢɯ ɹɞɪɨ ɥɢɬɢɹ. ɉɪɢ ɪɚɫɱɟɬɚɯ ɩɨ ɦɨɞɟɥɹɦ ɆɇȺ1 ɢ ɆɇȺ2 ɫɧɚɱɚɥɚ ɢɫɩɨɥɶɡɨɜɚɥɨɫɶ ɡɧɚɱɟɧɢɟ E = 0,176 ɮɦ-2 (ɫɦ. ɜɚɪɢɚɧɬɵ 2 1/2 ɪɚɫɱɟɬɨɜ 1, ɲɬɪɢɯɨɜɵɟ ɤɪɢɜɵɟ ɧɚ ɪɢɫ. 1, 2), ɨɩɪɟɞɟɥɟɧɧɨɟ ɜ [15] ɢɡ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ  r ! 6 Li .

38
«Â³ñíèê Õàðê³âñüêîãî óí³âåðñèòåòó», ¹ 777, 2007

Þ.À. Áåðåæíîé, Â.Â. Ïèëèïåíêî

Ɂɚɬɟɦ ɛɵɥɨ ɩɪɨɜɟɞɟɧɨ ɭɬɨɱɧɟɧɢɟ ɩɚɪɚɦɟɬɪɚ E ɩɭɬɟɦ ɮɢɬɢɪɨɜɚɧɢɹ ɭɩɪɭɝɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ (ɫɦ. ɜɚɪɢɚɧɬɵ 2 1/2 ɪɚɫɱɟɬɨɜ 2, ɫɩɥɨɲɧɵɟ ɤɪɢɜɵɟ ɧɚ ɪɢɫ. 1, 2). ɗɬɨ ɩɪɢɜɟɥɨ ɤ ɧɟɤɨɬɨɪɨɦɭ ɭɜɟɥɢɱɟɧɢɸ  r ! 6 Li ɞɥɹ ɆɇȺ1 ɢ ɟɝɨ ɭɦɟɧɶɲɟɧɢɸ ɞɥɹ ɆɇȺ2. Ɂɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɞɥɹ ɄɆȾ1 (d ɢ ǻ) ɢ ɄɆȾ2 ( dD , d N , 'D ɢ ' N ) ɬɚɤɠɟ ɛɵɥɢ ɧɚɣɞɟɧɵ ɢɡ ɮɢɬɢɪɨɜɚɧɢɹ ɭɩɪɭɝɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ. ȼɫɟ ɪɚɫɫɦɨɬɪɟɧɧɵɟ ɦɨɞɟɥɢ ɩɨɡɜɨɥɢɥɢ ɨɩɢɫɚɬɶ ɢɡɭɱɚɟɦɵɟ 2 2 Ɇɨɞɟɥɶ ɮɨɪɦɮɚɤɬɨɪɵ ɹɞɪɚ 6Li ɩɪɢ ɩɟɪɟɞɚɧɧɵɯ F el F in ɢɦɩɭɥɶɫɚɯ q < 3 ɮɦ-1, ɜ ɫɜɹɡɢ ɫ ɱɟɦ ɜɟɥɢɱɢɧɵ F 2 ɜ ɬɚɛɥ. 1 ɜɵɱɢɫɥɟɧɵ ɞɥɹ ɆɇȺ1, 1 2,579 46,2 9,9 E=0,1760 ɮɦ–2 ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɬɨɱɟɤ, ɥɟɠɚɳɢɯ ɜ ɆɇȺ1, 2 2,637 16,0 9,2 E=0,1611 ɮɦ–2 ɷɬɨɣ ɨɛɥɚɫɬɢ q. ɉɪɢ ɷɬɨɦ, ɨɞɧɚɤɨ, ɦɨɞɟɥɶ ɫ ɜɵɪɚɠɟɧɧɵɦ ɪɚɡɞɟɥɟɧɢɟɦ DɆɇȺ2, 1 2,579 51,6 2.4 E=0,1760 ɮɦ–2 ɢ d-ɤɥɚɫɬɟɪɨɜ ɆɇȺ2 ɩɨ ɫɪɚɜɧɟɧɢɸ ɆɇȺ1 ɞɚɟɬ ɧɟɫɤɨɥɶɤɨ ɥɭɱɲɟɟ ɆɇȺ2, 2 2,504 11,6 3,8 E=0,1987 ɮɦ–2 ɨɩɢɫɚɧɢɟ ɭɩɪɭɝɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ ɢ ɄɆȾ1 2,586 2,7 2,9 d=2,991 ɮɦ, '=1,429 ɮɦ ɡɚɦɟɬɧɨ ɭɥɭɱɲɚɟɬ ɨɩɢɫɚɧɢɟ ɧɟɭɩɪɭɝɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ . Ʉɥɚɫɬɟɪɧɚɹ 2,588 1,8 – ɄɆȾ2 dD=3,239 ɮɦ, 'D=1,116 ɮɦ ɦɨɞɟɥɶ ɫ ɞɢɫɩɟɪɫɢɟɣ ɄɆȾ1 dN=0,0023 ɮɦ, 'N=2,400 ɮɦ ɨɛɟɫɩɟɱɢɜɚɟɬ ɫɭɳɟɫɬɜɟɧɧɨ ɥɭɱɲɟɟ ɫɨɝɥɚɫɢɟ ɪɚɫɫɱɢɬɚɧɧɨɝɨ ɭɩɪɭɝɨɝɨ ɡɚɪɹɞɨɜɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ ɫ ɷɤɫɩɟɪɢɦɟɧɬɨɦ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɨɛɟɢɦɢ ɦɨɞɟɥɹɦɢ ɆɇȺ ɢ ɧɟ ɦɟɧɟɟ ɯɨɪɨɲɟɟ ɨɩɢɫɚɧɢɟ ɧɟɭɩɪɭɝɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ, ɱɟɦ ɆɇȺ2. ɉɪɢ ɷɬɨɦ ɄɆȾ1 ɞɚɟɬ ɬɚɤɠɟ ɥɭɱɲɟɟ ɡɧɚɱɟɧɢɟ ɞɥɹ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɝɨ ɡɚɪɹɞɨɜɨɝɨ ɪɚɞɢɭɫɚ 6Li. Ɉɬɦɟɬɢɦ, ɱɬɨ ɆɇȺ2 (ɫɦ. ɬɚɛɥ. 1, ɜɚɪɢɚɧɬ ɪɚɫɱɟɬɨɜ 2) ɞɚɟɬ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ D- ɢ d-ɤɥɚɫɬɟɪɚɦɢ d = 2,748 ɮɦ, ɚ ɄɆȾ1 – d = 2,991 ɮɦ. ɉɪɢ ɷɬɨɦ ɩɚɪɚɦɟɬɪ ɞɢɫɩɟɪɫɢɢ ɜ ɄɆȾ1 ɢɦɟɟɬ ɛɨɥɶɲɨɟ ɡɧɚɱɟɧɢɟ ' = 1,429 ɮɦ, ɱɬɨ ɫɜɢɞɟɬɟɥɶɫɬɜɭɟɬ ɨ ɛɨɥɶɲɨɣ ɜɟɪɨɹɬɧɨɫɬɢ ɨɬɤɥɨɧɟɧɢɹ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɤɥɚɫɬɟɪɚɦɢ ɨɬ ɪɚɜɧɨɜɟɫɧɨɝɨ ɡɧɚɱɟɧɢɹ. Ⱦɪɭɝɚɹ ɤɥɚɫɬɟɪɧɚɹ ɦɨɞɟɥɶ ɫ ɞɢɫɩɟɪɫɢɟɣ, ɄɆȾ2, ɪɚɫɫɦɚɬɪɢɜɚɸɳɚɹ ɹɞɪɨ 6Li ɤɚɤ ɫɢɫɬɟɦɭ D+p+n, ɞɚɟɬ ɪɟɡɭɥɶɬɚɬɵ ɞɥɹ ɭɩɪɭɝɨɝɨ ɮɨɪɦɮɚɤɬɨɪɚ 6Li, ɛɥɢɡɤɢɟ ɤ ɪɟɡɭɥɶɬɚɬɚɦ ɄɆȾ1. ɉɪɢ ɷɬɨɦ ɜɟɥɢɱɢɧɚ ɩɚɪɚɦɟɬɪɚ d N , ɯɚɪɚɤɬɟɪɢɡɭɸɳɟɝɨ ɧɚɢɛɨɥɟɟ ɜɟɪɨɹɬɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɩɪɨɬɨɧɨɦ ɢ ɧɟɣɬɪɨɧɨɦ, ɨɤɚɡɵɜɚɟɬɫɹ ɨɱɟɧɶ ɦɚɥɨɣ, ɚ ɜɟɥɢɱɢɧɚ ɩɚɪɚɦɟɬɪɚ ɞɢɫɩɟɪɫɢɢ ' N = 2,400 ɮɦ ɛɥɢɡɤɚ ɤ ɯɚɪɚɤɬɟɪɧɨɦɭ ɪɚɡɦɟɪɭ ɞɟɣɬɪɨɧɚ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɨɥɭɱɟɧɧɚɹ ɜ ɷɬɨɣ ɦɨɞɟɥɢ ɤɨɧɮɢɝɭɪɚɰɢɹ ɛɥɢɡɤɚ ɤ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɜ ɄɆȾ1 ɤɨɧɮɢɝɭɪɚɰɢɢ D+d. Ɍɚɛɥ. 1. ɉɚɪɚɦɟɬɪɵ ɪɚɫɱɟɬɨɜ. ɉɚɪɚɦɟɬɪɵ ɦɨɞɟɥɢ , ɮɦ  r 2 !1/2 6 Li

|F(q)| 10 10 10 10 10 10

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|F1o3(q)| 10 10 10 10
-2

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0,0

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0,0

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Ɂɚɦɟɬɢɦ, ɱɬɨ ɜ ɪɚɛɨɬɚɯ [5–8] ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ D-ɤɥɚɫɬɟɪɧɨɣ ɦɨɞɟɥɢ ɫ ɞɢɫɩɟɪɫɢɟɣ ɞɥɹ ɨɩɢɫɚɧɢɹ ɡɚɪɹɞɨɜɵɯ ɮɨɪɦɮɚɤɬɨɪɨɜ ɞɪɭɝɢɯ ɥɟɝɤɢɯ ɹɞɟɪ (ɧɚɩɪɢɦɟɪ, 12C ɢ 16O) ɯɨɪɨɲɟɟ ɫɨɝɥɚɫɢɟ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɬɚɤɠɟ ɢɦɟɥɨ ɦɟɫɬɨ ɜ ɬɨɣ ɠɟ ɨɛɥɚɫɬɢ ɩɟɪɟɞɚɧɧɵɯ ɢɦɩɭɥɶɫɨɜ q < 3 ɮɦ-1. ɇɚɛɥɸɞɚɟɦɨɟ ɪɚɫɯɨɠɞɟɧɢɟ

Ɋɢɫ. 1. Ɂɚɪɹɞɨɜɵɟ ɮɨɪɦɮɚɤɬɨɪɵ ɹɞɪɚ 6Li, ɪɚɫɫɱɢɬɚɧɧɵɟ ɩɨ ɦɨɞɟɥɢ ɆɇȺ1, ɤɚɤ ɮɭɧɤɰɢɢ ɩɟɪɟɞɚɧɧɨɝɨ ɢɦɩɭɥɶɫɚ q (ɮɦ-1). Ʉɨɪɨɬɤɢɟ ɲɬɪɢɯɢ – ɜɚɪɢɚɧɬ ɪɚɫɱɟɬɨɜ 1, ɫɩɥɨɲɧɵɟ ɤɪɢɜɵɟ – ɜɚɪɢɚɧɬ ɪɚɫɱɟɬɨɜ 2. ɚ) ɭɩɪɭɝɢɣ ɮɨɪɦɮɚɤɬɨɪ, ɞɥɢɧɧɵɟ ɲɬɪɢɯɢ ɢ ɬɨɱɟɱɧɚɹ ɤɪɢɜɚɹ – ɡɚɪɹɞɨɜɵɟ ɮɨɪɦɮɚɤɬɨɪɵ D-ɱɚɫɬɢɰɵ ɢ ɞɟɣɬɪɨɧɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ; ɛ) ɧɟɭɩɪɭɝɢɣ ɮɨɪɦɮɚɤɬɨɪ ɞɥɹ ɩɟɪɟɯɨɞɚ * 2,18 Ɇɷȼ). ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɞɚɧɧɵɟ ɢɡ ɪɚɛɨɬ [13, 14]. 1+(g.s.)o3+ ( E3

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ñåð³ÿ ô³çè÷íà «ßäðà, ÷àñòèíêè, ïîëÿ», âèï. 2 /34/

Àíàëèç çàðÿäîâûõ ôîðìôàêòîðîâ ÿäðà...

ɪɚɫɫɱɢɬɚɧɧɵɯ ɢ ɢɡɦɟɪɟɧɧɵɯ ɮɨɪɦɮɚɤɬɨɪɨɜ ɩɪɢ ɛɨɥɶɲɢɯ ɡɧɚɱɟɧɢɹɯ q > 3 ɮɦ–1 ɨɛɴɹɫɧɹɟɬɫɹ ɬɟɦ, ɱɬɨ ɜ ɷɬɨɣ ɨɛɥɚɫɬɢ q ɜ ɤɚɪɬɢɧɟ ɪɚɫɫɟɹɧɢɹ ɷɥɟɤɬɪɨɧɨɜ ɞɨɥɠɧɵ ɭɠɟ ɩɪɨɹɜɥɹɬɶɫɹ ɢɦɟɸɳɢɟɫɹ ɨɬɤɥɨɧɟɧɢɹ ɨɬ ɤɪɭɩɧɨɦɚɫɲɬɚɛɧɨɣ ɤɥɚɫɬɟɪɧɨɣ ɫɬɪɭɤɬɭɪɵ ɢ ɧɚɛɥɸɞɚɬɶɫɹ ɛɨɥɟɟ ɬɨɧɤɢɟ ɞɟɬɚɥɢ ɫɬɪɭɤɬɭɪɵ ɹɞɪɚ, ɧɟ ɨɩɢɫɵɜɚɟɦɵɟ ɩɪɨɫɬɵɦɢ ɤɥɚɫɬɟɪɧɵɦɢ ɦɨɞɟɥɹɦɢ.

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Ɋɢɫ. 2. Ɍɨ ɠɟ ɫɚɦɨɟ, ɱɬɨ ɧɚ ɪɢɫ. 1, ɞɥɹ ɪɚɫɱɟɬɨɜ ɩɨ ɦɨɞɟɥɢ ɆɇȺ2.

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Ɋɢɫ. 3. Ɍɨ ɠɟ ɫɚɦɨɟ, ɱɬɨ ɧɚ ɪɢɫ. 1, ɞɥɹ ɪɚɫɱɟɬɨɜ ɩɨ ɦɨɞɟɥɢ ɄɆȾ1.

ȼɕȼɈȾɕ ɇɚ ɨɫɧɨɜɟ ɫɨɜɪɟɦɟɧɧɵɯ ɩɪɟɞɫɬɚɜɥɟɧɢɣ ɨ ɤɥɚɫɬɟɪɧɨɣ ɫɬɪɭɤɬɭɪɟ ɹɞɟɪ 6Li ɛɵɥ ɢɡɭɱɟɧ ɪɹɞ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɤɥɚɫɬɟɪɨɜ ɜ ɷɬɢɯ ɹɞɪɚɯ. Ɋɚɫɫɦɨɬɪɟɧɵ ɞɜɚ ɜɚɪɢɚɧɬɚ ɤɥɚɫɬɟɪɧɨɣ ɦɨɞɟɥɢ D+d, ɞɥɹ ɤɨɬɨɪɵɯ ɜɨɥɧɨɜɚɹ ɮɭɧɤɰɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɤɥɚɫɬɟɪɨɜ ɨɬɜɟɱɚɟɬ ɦɨɞɟɥɢ ɧɭɤɥɨɧɧɵɯ ɚɫɫɨɰɢɚɰɢɣ, ɩɪɢɱɟɦ ɜɚɪɢɚɧɬ ɆɇȺ1 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɢɥɶɧɨɦɭ ɩɟɪɟɤɪɵɬɢɸ ɤɥɚɫɬɟɪɨɜ, ɚ ɆɇȺ2 – ɯɨɪɨɲɨ ɪɚɡɞɟɥɟɧɧɵɦ ɤɥɚɫɬɟɪɚɦ. Ɍɚɤɠɟ ɩɪɟɞɥɨɠɟɧɵ ɞɜɚ ɜɚɪɢɚɧɬɚ ɤɥɚɫɬɟɪɧɨɣ ɦɨɞɟɥɢ ɫ ɞɢɫɩɟɪɫɢɟɣ. ȼ ɩɟɪɜɨɦ ɢɡ ɧɢɯ (ɄɆȾ1) ɞɥɹ ɹɞɪɚ 6Li ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɨɧɮɢɝɭɪɚɰɢɹ D+d ɜ ɮɨɪɦɟ ɧɟɠɟɫɬɤɨɣ ɝɚɧɬɟɥɢ, ɚ ɜɨ ɜɬɨɪɨɦ (ɄɆȾ2) ɹɞɪɨ

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Þ.À. Áåðåæíîé, Â.Â. Ïèëèïåíêî

Li ɨɩɢɫɵɜɚɟɬɫɹ ɤɚɤ ɫɢɫɬɟɦɚ D+p+n ɜ ɮɨɪɦɟ ɪɚɜɧɨɛɟɞɪɟɧɧɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ɫ ɜɨɡɦɨɠɧɵɦɢ ɨɬɤɥɨɧɟɧɢɹɦɢ ɤɥɚɫɬɟɪɨɜ ɨɬ ɩɨɥɨɠɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɜ ɜɟɪɲɢɧɚɯ ɷɬɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ. Ɂɚɪɹɞɨɜɵɟ ɮɨɪɦɮɚɤɬɨɪɵ ɜɯɨɞɹɳɢɯ ɜ ɫɨɫɬɚɜ ɹɞɪɚ 6Li ɤɥɚɫɬɟɪɨɜ ɡɚɞɚɸɬɫɹ ɜ ɜɢɞɟ ɢɡɜɟɫɬɧɵɯ ɢɡ ɥɢɬɟɪɚɬɭɪɵ ɛɟɡɦɨɞɟɥɶɧɵɯ ɚɩɩɪɨɤɫɢɦɚɰɢɣ. 2 ɉɨɤɚɡɚɧɨ, ɱɬɨ ɪɚɫɫɦɨɬɪɟɧɧɵɟ ɤɥɚɫɬɟɪɧɵɟ |F(q)| ɦɨɞɟɥɢ ɞɚɸɬ ɜɨɡɦɨɠɧɨɫɬɶ ɭɫɩɟɲɧɨ ɨɩɢɫɚɬɶ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɢɡɦɟɪɟɧɧɵɟ ɭɩɪɭɝɢɣ ɡɚɪɹɞɨɜɵɣ -1 10 ɮɨɪɦɮɚɤɬɨɪ ɹɞɪɚ 6Li ɢ ɧɟɭɩɪɭɝɢɣ ɮɨɪɦɮɚɤɬɨɪ ɞɥɹ ɩɟɪɟɯɨɞɚ ɫ ɜɨɡɛɭɠɞɟɧɢɟɦ ɜ ɹɞɪɟ ɦɢɲɟɧɢ ɩɟɪɜɨɝɨ -2 * 10 ɫɨɫɬɨɹɧɢɹ 3+, E3 2,18 Ɇɷȼ, ɜ ɨɛɥɚɫɬɢ ɩɟɪɟɞɚɧɧɵɯ ɢɦɩɭɥɶɫɨɜ q < 3 ɮɦ-1. Ɍɚɤɨɣ ɞɢɚɩɚɡɨɧ q ɹɜɥɹɟɬɫɹ -3 10 ɯɚɪɚɤɬɟɪɧɨɣ ɨɛɥɚɫɬɶɸ ɩɪɢɦɟɧɢɦɨɫɬɢ ɩɪɨɫɬɵɯ ɤɥɚɫɬɟɪɧɵɯ ɦɨɞɟɥɟɣ, ɧɟ ɭɱɢɬɵɜɚɸɳɢɯ ɩɪɨɰɟɫɫɵ -4 ɨɛɦɟɧɚ ɧɭɤɥɨɧɚɦɢ ɦɟɠɞɭ ɤɥɚɫɬɟɪɚɦɢ ɢ ɢɦɟɸɳɢɟɫɹ 10 ɨɬɤɥɨɧɟɧɢɹ ɪɟɚɥɶɧɨɣ ɫɬɪɭɤɬɭɪɵ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɹɞɟɪ ɨɬ ɤɥɚɫɬɟɪɧɨɣ ɤɨɧɮɢɝɭɪɚɰɢɢ. -5 10 ɂɡ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɚɧɚɥɢɡɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ ɛɵɥɢ ɨɩɪɟɞɟɥɟɧɵ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ, -6 ɜɯɨɞɹɳɢɯ ɜ ɩɪɟɞɥɨɠɟɧɧɵɟ ɜɵɪɚɠɟɧɢɹ ɞɥɹ 10 ɩɥɨɬɧɨɫɬɟɣ ɪɚɫɩɪɟɞɟɥɟɧɢɣ ɤɥɚɫɬɟɪɨɜ. Ɋɚɫɱɟɬɵ ɩɨɤɚɡɚɥɢ, ɱɬɨ ɦɨɞɟɥɢ ɫ ɜɵɪɚɠɟɧɧɵɦ ɪɚɡɞɟɥɟɧɢɟɦ -7 10 ɤɥɚɫɬɟɪɨɜ ɞɚɸɬ ɧɟɫɤɨɥɶɤɨ ɥɭɱɲɟɟ ɫɨɝɥɚɫɢɟ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ. ɇɚɢɥɭɱɲɟɟ ɨɩɢɫɚɧɢɟ ɢɡɭɱɚɟɦɵɯ ɮɨɪɦɮɚɤɬɨɪɨɜ ɞɚɟɬɫɹ ɤɥɚɫɬɟɪɧɵɦɢ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 q ɦɨɞɟɥɹɦɢ ɫ ɞɢɫɩɟɪɫɢɟɣ, ɩɪɢɱɟɦ ɄɆȾ2 ɞɥɹ ɤɨɧɮɢɝɭɪɚɰɢɢ D+p+n ɮɚɤɬɢɱɟɫɤɢ ɷɤɜɢɜɚɥɟɧɬɧɚ Ɋɢɫ. 4. ɍɩɪɭɝɢɣ ɡɚɪɹɞɨɜɵɣ ɮɨɪɦɮɚɤɬɨɪ (ɫɩɥɨɲɧɚɹ ɤɪɢɜɚɹ), ɄɆȾ1 ɞɥɹ ɤɨɧɮɢɝɭɪɚɰɢɢ D+d. ɉɪɟɞɥɨɠɟɧɧɵɟ ɦɨɞɟɥɢ ɪɚɫɫɱɢɬɚɧɧɵɣ ɩɨ ɦɨɞɟɥɢ ɄɆȾ2, ɤɚɤ ɮɭɧɤɰɢɹ ɩɟɪɟɞɚɧɧɨɝɨ ɢɦɩɭɥɶɫɚ q (ɮɦ-1). ɒɬɪɢɯɨɜɚɹ ɢ ɬɨɱɟɱɧɚɹ ɤɪɢɜɵɟ – ɞɥɹ ɨɩɢɫɚɧɢɹ ɤɥɚɫɬɟɪɧɨɣ ɫɬɪɭɤɬɭɪɵ ɹɞɟɪ 6Li ɦɨɝɭɬ ɡɚɪɹɞɨɜɵɟ ɮɨɪɦɮɚɤɬɨɪɵ D-ɱɚɫɬɢɰɵ ɢ ɩɪɨɬɨɧɚ ɞɚɥɟɟ ɛɵɬɶ ɩɪɢɦɟɧɟɧɵ ɞɥɹ ɨɩɢɫɚɧɢɹ ɩɪɨɰɟɫɫɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɞɚɧɧɵɟ ɢɡ [13, 14]. ɪɚɫɫɟɹɧɢɹ ɜɵɫɨɤɨɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɩɪɨɬɨɧɨɜ ɧɚ ɷɬɢɯ ɹɞɪɚɯ.
6

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

ɋɉɂɋɈɄ ɅɂɌȿɊȺɌɍɊɕ ȼɢɥɶɞɟɪɦɭɬ Ʉ., Ɍɚɧ ə. ȿɞɢɧɚɹ ɬɟɨɪɢɹ ɹɞɪɚ. -Ɇ.: Ɇɢɪ, 1980. – 502 ɫ. ɇɟɭɞɚɱɢɧ ȼ. Ƚ., ɋɦɢɪɧɨɜ ɘ. Ɏ. ɇɭɤɥɨɧɧɵɟ ɚɫɫɨɰɢɚɰɢɢ ɜ ɥɟɝɤɢɯ ɹɞɪɚɯ. -Ɇ: ɇɚɭɤɚ, 1969. – 414 ɫ. Antonov A.N., Hodgson P.E., Petkov I.Zh. Nucleon correlations in nuclei. -Berlin: Springer-Verlag, 1993. -293 p. Levin F.S. Clusters and reactions // Nucl. Phys. A. -1987. -V. 463, No 1, 2. -P. 487-501. Berezhnoy Yu.A., Mikhailyuk V.P., Pilipenko V.V. Scattering of protons antiprotons and pions on 12C and 16O nuclei // Acta. Phys. Pol. B. -1990. -V. 21, No 9. -P. 723-740. Berezhnoy Yu.A., Mikhailyuk V.P., Pilipenko V.V. Elastic and inelastic intermediate-energy proton multiple scattering on 12C and 16O nuclei // J. Phys. G: Nucl. Part. Phys. -1992. -V. 18, No 1. -P. 85-97. Ȼɟɪɟɠɧɨɣ ɘ.Ⱥ., Ɇɢɯɚɣɥɸɤ ȼ.ɉ. ɍɩɪɭɝɨɟ ɪɚɫɫɟɹɧɢɟ ɩɪɨɬɨɧɨɜ ɫ ɷɧɟɪɝɢɟɣ 800 Ɇɷȼ ɹɞɪɚɦɢ 20Ne // əɎ. - 2000. -Ɍ. 63, ɜɵɩ. 5. -ɋ. 783-786. Berezhnoy Yu.A., Mikhailyuk V.P. 1 GeV proton elastic scattering on 9Be nuclei in the D-cluster model with dispersion // Eur. Phys. J.A. -2004. -V. 22, No. 3. -P. 443-447. Ⱥɯɢɟɡɟɪ Ⱥ. ɂ., ɋɢɬɟɧɤɨ Ⱥ. Ƚ., Ɍɚɪɬɚɤɨɜɫɤɢɣ ȼ. Ʉ. ɗɥɟɤɬɪɨɞɢɧɚɦɢɤɚ ɹɞɟɪ. - Ʉɢɟɜ: ɇɚɭɤɨɜɚ ɞɭɦɤɚ, 1989. – 432 ɫ. De Vries H. et al. Nuclear charge-density-distribution parameters from elastic electron scattering // Atom. Data & Nucl. Data Tabl. -1987. - V. 36, No 3. - P. 495–536. Sick I. Precise nuclear radii from electron scattering // Phys. Lett. B. -1982. -V. 116, No 4. -P. 212-214. Abbott D. Phenomenology of the deuteron electromagnetic form factors // Eur. Phys. J. A. -2000. -V. 7. - P. 421-427. Li G.C., Sick I., Whitney R.R., Yerian M.R. High-energy electron scattering from 6Li // Nucl. Phys. A. - 1971. -V. 162, No 6. P. 583-592. Bumiller F.A., Buskirk F.R., Dyer J.N., Monson W.A. Elastic electron scattering from 6Li and 7Li at low momentum transfer // Phys. Rev. C. -1972. –V. 5, No 2. - P. 391-395. ɉɟɪɟɫɵɩɤɢɧ ȼ.ȼ. Ɋɚɫɫɟɹɧɢɟ ɩɪɨɬɨɧɨɜ ɢ ɞɟɣɬɪɨɧɨɜ ɧɚ ɹɞɪɟ 6Li ɜ ɨɛɥɚɫɬɢ ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɷɧɟɪɝɢɣ // əɎ. - 1983. -Ɍ. 38, ɜɵɩ. 10. - ɋ. 895-900.

1 Kharkov National University, Svobody Sq. 4, Kharkov 61077, Ukraine National Science Center "Kharkov Institute of Physics and Technology", Akademichna Str. 1, Kharkov 61108, Ukraine Several variants of the phenomenological cluster model of the 6Li nucleus – namely, the D+d model of nucleon associations and the cluster model with dispersion for the D+d and D+p+n systems – have been considered to be applied to description of the elastic charge form factor of the 6Li nucleus and of the form factor of inelastic scattering with excitation of the first 3+ state in the target nucleus. The values of the model parameters have been determined from the analysis of experimentally measured form factors. It has been shown that the cluster models under consideration provide a good description of both elastic and inelastic form factors but the cluster model with dispersion looks to be most preferable. KEY WORDS: the 6Li nucleus, cluster model, charge form factor, inelastic form factor, root-mean-square radius, dispersion parameter. 2

ANALYSIS OF CHARGE FORM FACTORS OF THE 6Li NUCLEUS ON THE BASIS OF CLUSTER MODEL Yu.A. Berezhnoy1, V.V. Pilipenko2