Elastic $$\alpha $$-$$^{12}$$C Scattering at Low Energies with the Bound States of $$^{16}$$O in EFT

Abstract

The elastic α-12 C scattering for l = 0, 1, 2, 3 channels at low energies is studied, including the energies of excited bound states of 16 O, in effective field theory. We introduce a new renormalization method due to the large suppression factor produced by the Coulomb interaction when fitting the effective range parameters to the phase sift data. After fitting the parameters, we calculate asymptotic normalization constants of the 0 + 2 , 1 − 1 , 2 + 1 , 3 − 1 states of 16 O. We also discuss the uncertainties of the present study when the amplitudes are interpolated to the stellar energy region of the 12 C(α,γ) 16 O reaction.

ANCs of the bound states of 16O deduced from elastic α-12C scattering data

“…EFT has been employed in the studies of many reactions, which are crucial for nuclear astrophysics, e.g., neutron β-decay [10], radiative neutron capture on a proton at big-bang nucleosynthesis energy [11][12][13], proton-proton fusion in hydrogen burning processes [14][15][16], solar-neutrino reactions on the deuteron [17,18], and radiative proton capture on 15 N in the CNO cycle [19]. During the last decade, we have been studying the construction of EFT for the 12 C(α,γ) 16 O reaction and applied the formalism to the studies of various cases of elastic α-12 C scattering at low energy [20][21][22][23], E1 transition of 12 C(α,γ) 16 O reaction [24], and β-delayed α emission from 16 N [4]. In the present contribution, we discuss the calculation of asymptotic normalization coefficients (ANCs) of 0 16 O as twobody α-12 C cluster system, deduced from the phase shift data of elastic α-12 C scattering in cluster EFT [25,26].…”

“…We also obtained a large value of ANC of 2 + 1 state by imposing a condition, dD 2 /dp 2 p=pi+1 < dD 2 /dp 2 p=pi with p i+1 > p i at the energy region, 0 < E α < 2.6 MeV, where the experimental phase shift data do not exist (the condition is that the slope of the inverse of propagator, D 2 (p), is continuously decreasing), but it has large error bar, (1.3 ± 3.0) × 10 5 fm −1/2 (see Table II in Ref. [23] as well). To obtain such a large value of the ANC of 2 + 1 state, the inverse of propagator D 2 (p) should become vanishingly small at the small energy region, where the center values of D 2 (p) become smaller than its error bars in the denominator.…”

Radiative proton capture on $^{15}\mathrm{N}$ within effective field theory

“…EFT methods have been applied to the studies of various reactions including thermonuclear reactions such as 𝛼 capture on C 12 [29], radiative proton capture on C 12 [30], and proton and neutron capture on light nuclei [31][32][33][34][35]. It was also applied to the reactions of C 15 [36], 𝛼-C 12 elastic scattering [37][38][39], and 𝛽 delayed 𝛼 emission from N 16 [40], and so on. Reviews on these topics can be found, for example, in Refs.…”