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A new \delta h method and its application to the asymptotic normalization constants of the 16O bound statesстатья
Дата последнего поиска статьи во внешних источниках: 23 сентября 2021 г.
- Автор: Orlov Yu V.
- Журнал: Nuclear Physics A
- Том: 1014
- Год издания: 2021
- Издательство: Elsevier BV
- Местоположение издательства: Netherlands
- Первая страница: 122257-1
- Последняя страница: 122257-10
- DOI: 10.1016/122174
- Аннотация: A new \delta h method for finding the asymptotic normalization coefficient (ANC) was recently proposed by the author (2021). It was shown that the denominator of the re-normalized scattering amplitude ˜f_l includes the factor d_l(E)=\delta_l(E)+h_r(E)−h(η), where \delta_l(E) is the nuclear interaction part of the effective-range function (ERF) and \delta h(E)=h_r(E)−h(η) is the difference of the related Coulomb terms. Here h_r(E) =Reh(η) for E>0, η=1/a_B k is the Sommerfeld parameter, a_B is the Bohr radius. The equation d_l(E) =0 determines the ˜f_l poles at E=−ε (ε is a binding energy). In the present paper to calculate \delta h(−ε) the function h_r(E) is analytically continued to E<0. For this the series of h_r(E) in powers of (a_Bk)^2 converges if (a_Bk)^2<1 should be used. It is found that the first dominant term [(a_Bk)^2]/12 of the asymptotic series h_{as}(E) is the same for h_r(E) and h(η) (at E<0 for h(η)) when E→0. The subtraction of this dominant term from both h_r(E) and h(η) simplifies the \delta h(−ε) calculation. Here the \delta h method applies to the ground and first excited S-wave bound states of 16O (16O↔4He+12C) which meet the condition |a_Bk|^2<1. For 16O the standard ERF method does not work due to the large product Z_1Z_2 of the 4He and 12C charges. For the P−and D-wave 16O states the binding energies ε are so small that the approximate \delta method, when d_l(E) ≈\delta_l(E), is valid. ANCs for the ground and first excited P-wave bound states of 7Be (7Be↔3He+4He) are also calculated by polynomial fitting the sum \delta_l(E)+h_r(E)up to E^2 in an analogy with the ERF method. The results for \delta h and EFR methods are close to each other. For this system a_B k >1 and the \delta h method has no advantages over the standard ERF method. The \delta h method opens up a new direction for systems with large Z_1Z_2values when the ERF method no longer works.
- Добавил в систему: Орлов Юрий Всеволодович