Subthreshold resonances and resonances in the $R$-matrix method for binary reactions and in the Trojan Horse method

Abstract

In this paper we discuss the $R$-matrix approach to treat the subthreshold resonances for the single-level and one channel, and for the single-level and two channel cases. In particular, the expression relating the ANC with the observable reduced width, when the subthreshold bound state is the only channel or coupled with an open channel, which is a resonance, is formulated. Since the ANC plays a very important role in nuclear astrophysics, these relations significantly enhance the power of the derived equations. We present the relationship between the resonance width and the ANC for the general case and consider two limiting cases: wide and narrow resonances. Different equations for the astrophysical S-factors in the $R$-matrix approach are presented. After that we discuss the Trojan Horse Method (THM) formalism. The developed equations are obtained using the surface-integral formalism and the generalized $R$-matrix approach for the three-body resonant reactions. It is shown how the Trojan Horse (TH) double differential cross section can be expressed in terms of the on-the-energy-shell astrophysical S-factor for the binary sub-reaction. Finally, we demonstrate how the THM can be used to calculate the astrophysical S-factor for the neutron generator ${}^{13}\mathrm{C}(\alpha ,n{)}^{16}\mathrm{O}$ in low-mass AGB stars. At astrophysically relevant energies this astrophysical S-factor is controlled by the threshold level $1/2^{+},E_x=6356$ keV. Here, we reanalyzed recent TH data taking into account more accurately the three-body effects and using both assumptions that the threshold level is a subthreshold bound state or it is a resonance state.

11 pages, 3 figures, Accepted for Publication in Physical Review C

References in corpus (5)

• Frontiers in Nuclear Astrophysics
• New determination of the 13C(a, n)16O reaction rate and its influence on the s-process nucleosynthesis in AGB stars
• Concurrent application of ANC and THM to assess the ${}^{13}\mathrm{C}(\alpha ,n{)}^{16}\mathrm{O}$ absolute cross section at astrophysical energies and possible consequences for neutron production in low-mass AGB stars
• Broad levels in ${}^{17}$O and their relevance for the astrophysical s-process
• New $\alpha$ ANC measurement of the 1/2${}^{+}$ state in ${}^{17}$O at 6.356 MeV, that dominates the ${}^{13}$C($\alpha$,n)${}^{16}$O reaction rate at temperatures relevant for the s-process

Cited by in corpus (8)

• The importance of the 13C(alpha,n)16O reaction in Asymptotic Giant Branch stars
• Deep underground laboratory measurement of ${}^{13}$C($\alpha$,$n$)${}^{16}$O in the Gamow windows of the $s$- and $i$-processes
• Characterization of the LUNA neutron detector array for the measurement of the 13C(a,n)16O reaction
• Connection between asymptotic normalization coefficients and resonance widths of mirror states
• Trojan horse method as surrogate indirect approach to study resonant reactions in nuclear astrophysics
• Resonant spectra of multipole-bound anions
• Spin-parities of sub-threshold resonances in the ${}^{18}$F(p, $\alpha$)${}^{15}$O reaction
• Radiative capture reactions via indirect method