7Be(p,γ)8b reaksiyasi quyosh-neytrino muammosida katta ahamiyatga ega [1] va kosmik qorong'i asrlarning oxirida hosil bo'lgan ilk yulduzlar evolyutsiyasida muhim rol o'ynaydi [2]

7Be(p,γ)8b reaksiyaning modifikatsiyalangan R-matritsa usulida tahlili. Modifikatsiyalangan R-matritsa usulining asosiy formulalari
Modifikatsiyalangan R matritsa usulining astrofizik s omillari uchun zaruriy formulalar ([masalan, Ref ga qarang.[13,15] va unda ma'lumotnomalar) ushbu osti keltirilgan. Astrofizik s omil tomonidan berilgan
, (1)
where is the reaction cross section, E is the relative kinetic energy of colliding particles (p and ⁷Be) and is the Coulomb parameter for p⁷Be scattering. According to the modified R-matrix method [13,15], the cross section for the reaction ⁷Be(p,γ)⁸B is given by
(2)
, (3)
bu yerda J_i - (p+(_ ^7)be ) kanalda kolliziya zarrachalarining umumiy burchak momenti; J_f-8b yadroning spini; J_p (J_(_ ^7)Be) - protonning spini (7Be yadrosi); i,l_i va k=√2µe-kolliziya yadrolarining umumiy spini; j_p (J_ (_^7) be) - (7Be yadrosi) va k = √ 2µe reaksiyada kolliziya zarrachalarining nisbiy aylanasi, mos ravishda kamayadi.
O'tish genliğiyle M_(men l_(i ) J_i J_f ) (E) taqdim etiladi shaklida summasi aks sado va to'g'ridan-to'g'ri amplitudes ( M_(men l_i J_i J_f L)^((R) ) va M_(men l_i J_i J_f L)^((NR) )), mos ravishda, qaerda L bo'lgan elektromagnit-o'tish multipolarity). Bir sathli approksimatsiyada rezonans protonni ushlash amplitudasi ko'rinishda ifodalanishi mumkin [15,16]
(4)
where and are the phase shifts for Coulomb p⁷Be scattering and scattering on an impenetrable sphere, respectively; is the total width; is the protonic partial width of the resonance state of the ⁸B nucleus in the channel; is the radiative width; The energy dependence of the protonic and radiative resonance widths is given by the expressions [15]
(5)
(6)
qaerda k_y hisoblanadi photon tezlashtirish; P_(l_i ) hisoblanadi penetrability omil; S_c hisoblanadi Tomas o'zgarish omili [14]; va γ_(men l_i J_i)^p va γ_(J_i J_f L)^γ bo'lgan tushgan protonic va radiative widths, mos ravishda. Kengligi γ_(J_i J_f L)^γ o'z ichiga oladi, bir ichki va tashqi qismi [γ_(J_i J_f L)^γ (int) va γ_(J_i J_f L)^γ (ext.), mos ravishda]:
. (7)
(J_i J_f L) tashqi tushgan kengligi γ_ bu^γ (ext.) foton-kanal hissasini hisobga oladi. Kuzatiladigan protonik va radiatsion kengliklar tomonidan berilgan


, . (8)
Bizning hisob-kitoblarimiz uchun zarur bo'lgan rezonans-protonik-kenglik va rezonans-radiativ-kenglik qiymatlarini astrofizik s omilining hisoblangan qiymatlarini past energiyalar mintaqasida (e=70 keV gacha pastga) eksperimental sheriklariga moslab aniqlash mumkin.
To'g'ridan-to'g'ri radiativ ushlash uchun amplituda radial integralni o'z ichiga oladi (masalan, [13]),
. (9)
Qaerda W_(-n_f;〖 l〗_f+1/2) (2kr) hisoblanadi Whittaker funktsiyasi; r_c hisoblanadi kanal radiusi; n_f hisoblanadi Coulomb parametr uchun (p+(_ ^7)Bo'lishi ) bog'langan davlat; k=√2με bilan ε bo'lish majburiy energiya 8B yadrosi ichida (p+(_ ^7)Bo'lishi ) kanal; I_(l_i ) (r) (O_(l_i ) (r)) (chiqish) kirish kanali uchun radial Schrodinger tenglama bir yechim hisoblanadi; α=0(1) multipole bir o'tish uchun EL(M1) buyurtma.