Abstract
The method of asymptotic normalization coefficients is a standard approach for studies of two-body non-resonant radiative capture processes in nuclear astrophysics. This method suggests a fully analytical description of the radiative capture cross section in the low-energy region of the astrophysical interest. We demonstrate how this method can be generalized to the case of three-body 2p radiative captures. It was found that an essential feature of this process is the highly correlated nature of the capture. This reflects the complexity of three-body Coulomb continuum problem. Radiative capture 15O+p+p→17Ne+γ is considered as an illustration.
Highlights
In the asymptotic normalization coefficient (ANC) approach the nuclear wave function (WF) is characterized only by the behavior of its asymptotics
We provide a formalism for a complete analytical description of low-energy three-body 2p nonresonant radiative capture processes
The developed approach is a generalization of the ANC method, which has proven itself well for two-body nonresonant radiative captures
Summary
In the asymptotic normalization coefficient (ANC) approach the nuclear wave function (WF) is characterized only by the behavior of its asymptotics This asymptotics is defined in terms of the modified Bessel function of the second kind K in neutral case ψgs(r → ∞) = C2 2qr/π Kl+1/2(qr) ∼ C2 exp[−qr] , or in terms of the Whittaker function W in Coulombic case ψgs(r → ∞) = C2 W−η,l+1/2(2qr) ∼ C2 (2kr)−η exp[−qr] , where η = Z1Z2e2M/q is the Sommerfeld parameter. The related observables are defined just by two parameters: the g.s. binding energy Eb = q2/(2M ) and the 2-body ANC value C2. Such an approximation is valid for highly peripheral processes. The two-body resonant radiative captures σpart,γ v (T ) ∝
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