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A new Δ method for bound state asymptotic normalization coefficients with a finite limit of the nuclear part of the effective-range function at zero energyстатья
Дата последнего поиска статьи во внешних источниках: 8 сентября 2021 г.
- Автор: Orlov Yu V.
- Журнал: Nuclear Physics A
- Том: 1010
- Год издания: 2021
- Издательство: Elsevier BV
- Местоположение издательства: Netherlands
- Первая страница: 122174-1
- Последняя страница: 122174-11
- Номер статьи: 122174
- DOI: 10.1016/122174
- Аннотация: A new bound state Δ method for finding an asymptotic normalization coefficient (ANC) is proposed. This is valid, while the standard effective-range function (ERF) Kl(k2) method does not work when the product of colliding particles charges increases. The denominator of the strict expression of the re-normalized scattering amplitude f ̃_l includes the factor d_l(E)=Δ_l(E)+h_r(E)-h(\eta), where \eta=1/a_Bk, a_B is the Bohr radius. In the physical region, the Coulomb term h_r=Re h(\eta). So an analytical continuation of h_r(E) from the physical region to E<0 can be found by fitting h_r(E) for E>0. The related analytical continuation of h(\eta) consists in a simple sign change, E->-E, using an explicit dependence of h(\eta) on E. It is important that for E<0, abs(Δh)=abs(h+h_r)=0 at E=0, and this increases when abs(E) does. Thus, a new real equation, \deelta_l(-\epsilon)=0, is obtained for a binding energy \epsilon. It is applied to find a residue W of f ̃_l at the bound state pole E=-\epsilon, the nuclear vertex constant (NVC) and (ANC). The Coulomb-nuclear phase shift δ_l^cs, cot〖 δ〗_l^cs and a finite limit of the nuclear part Δ_l(k^2) of K_l(k^2) are also derived for an arbitrary orbital momentum l when E->0. It is shown that cot〖 δ〗_l^cs has an essential singularity at zero energy, but Δ_l(k^2) does not. The explicit finite limit of Δ_l(k^2) when E->0 is found using the expression for K_l(k^2). These results are in agreement with those for the S-wave scattering, which are widely accepted. The ANCs for ground and first excited bound states for the vertex ^Be<->3He+4He are calculated using the proposed new method, and are compared with those for the approximate method when d_l(E)=Δ_l(E) proposed by Ramírez Suárez and Sparenberg (2017). The fit of Δ_l(k^2) is found from the experimental phase-shift input data and the additional equation d_l(-\epsilon)=0.
- Добавил в систему: Орлов Юрий Всеволодович