The leading asymptotic terms of the three-body Coulomb scattering wave function

The asymptotic wave function derived by Alt and Mukhamedzhanov [Phys. Rev. A 47, 2004 (1993)] and Mukhamedzhanov and Lieber [Phys. Rev. A 54, 3078 (1996)] has been refined in the region where the pair $(\beta,\gamma)$ remains close to each other while the third particle $\alpha$ is far away from them $(\rho_{\alpha} \to \infty$, $r_{\alpha}/\rho_{\alpha}\to 0)$. The improved wave function satisfies the Schr\"odinger equation up to the terms of order $O(1/{\rho_{\alpha}}^{3})$, provides the leading asymptotic terms of the three-body scattering wave function with Coulomb interactions and gives further insight into the continuum behavior of the three-charged-particle wave function and helps to obtain $3\to 3$ scattered wave. This opens up further ways of solving and analysing the three-body Schr\"odinger equation by numerical means

Trojan Horse as an indirect technique in nuclear astrophysics. Resonance reactions

The Trojan Horse method is a powerful indirect technique that provides information to determine astrophysical factors for binary rearrangement processes $x + A \to b + B$ at astrophysically relevant energies by measuring the cross section for the Trojan Horse reaction $a + A \to y+ b + B$ in quasi-free kinematics. We present the theory of the Trojan Horse method for resonant binary subreactions based on the half-off-energy-shell R matrix approach which takes into account the off-energy-shell effects and initial and final state interactions.Comment: 6 pages and 1 figur

Asymptotic behavior of the Coulomb three-body scattered wave

Asymptotic forms of the scattered wave for a system of three arbitrary charged particles valid in all domains relevant to breakup are derived. The derivations are based on the relationship between the total wave function of a breakup process in a three-body system with Coulomb interactions and the wave function of the process of scattering of all three particles of the system in the continuum. The results are free from amplitude-phase ambiguity problems associated with previously known forms. A similar technique is used to obtain asymptotic forms of the three-body Coulomb Green’s function

Determination of the astrophysical S factor for C-11(p,gamma)N-12 from the N-12 -> C-11+p asymptotic normalization coefficient

Journals published by the American Physical Society can be found at http://publish.aps.org/The evolution of very low-metallicity, massive stars depends critically on the amount of CNO nuclei that they produce. Alternative paths from the slow 3alpha process to produce CNO seed nuclei could change their fate. The C-11(p,gamma)N-12 reaction is an important branch point in one such alternative path. At energies appropriate to stellar evolution of very low-metallicity, massive stars, nonresonant capture dominates the reaction rate. We have determined the astrophysical S factor for the C-11(p,gamma)N-12 reaction using the asymptotic normalization coefficient for N-12-->C-11+p to fix the nonresonant capture rate. In our experiment, a 110 MeV C-11 radioactive beam was used to study the(14)N(C-11,N-12)C-13 peripheral transfer reaction and the asymptotic normalization coefficient, (C-peff(12N))(2)=(C-p1/2(12N))(2)+(C-p3/2(12N))(2)=1.73+/-0.25 fm(-1), was extracted from the measured cross section. The contributions from the second resonance and interference effects were estimated using an R-matrix approach with the measured asymptotic normalization coefficient and the latest value for Gamma(gamma). We find the S factor for C-11(p,gamma)N-12 is significantly larger than previous estimates. As a result, the required density for it to contribute is reduced, and more CNO material may be produced

Determination of the direct capture contribution for N-13(p,gamma)O-14 from the O-14 -> N-13+p asymptotic normalization coefficient

Journals published by the American Physical Society can be found at http://publish.aps.org/N-13(p, gamma)O-14 is one of the key reactions which trigger the onset of the hot CNO cycle. This transition occurs when the proton capture rate on 13N is faster, due to increasing stellar temperature (greater than or equal to10(9) K), than the N-13 beta-decay rate. The rate of this reaction is dominated by the resonant capture through the first excited state of O-14 (E-r=0.528 MeV). However, through constructive interference, direct capture below the resonance makes a non-negligible contribution to the reaction rate. We have determined this direct contribution by measuring the asymptotic normalization coefficient for O-14 --> N-13+p. In our experiment, an 11.8 MeV/nucleon N-13 radioactive beam was used to study the N-14(N-13, O-14)C-13 peripheral transfer reaction, and the asymptotic normalization coefficient, (C-p1/2(14O))(2)=29.0+/-4.3 fm(-1), was extracted from the measured cross section. The radiative capture cross section was estimated using an R-matrix approach with the measured asymptotic normalization coefficient and the latest resonance parameters. We find the S factor for N-13(p, gamma)O-14 to be larger than previous estimates. Consequently, the transition from the cold to hot CNO cycle for novae would be controlled by the slowest proton capture reaction N-14(p, gamma)O-15

Publisher's Note: Asymptotic normalization coefficients for N-14+p -> O-15 and the astrophysical S factor for N-14(p,gamma)O-15 (vol 67, art no 065804, 2003)

Journals published by the American Physical Society can be found at http://publish.aps.org

Asymptotic normalization coefficients for 14N+p -> O-15 and the astrophysical S factor for N-14(p, gamma)O-15

Journals published by the American Physical Society can be found at http://publish.aps.org/The N-14(p,gamma)O-15 reaction, which controls energy production in the CNO cycle, has contributions from both resonance and direct captures to the ground and excited states. The overall normalization of the direct captures is defined by the corresponding asymptotic normalization coefficients (ANCs). Especially important is the ANC for the subthreshold state in O-15 at -0.504 keV since direct capture through this state dominates the reaction rate at stellar energies. In order to determine the ANCs for N-14+p-->O-15, the N-14(He-3,d)O-15 proton transfer reaction has been measured at an incident energy of 26.3 MeV. Angular distributions for proton transfer to the ground and five excited states were obtained. ANCs were then extracted from comparison to both distorted-wave Born approximation and coupled-channels Born approximation calculations. Using these ANCs, we calculated the astrophysical factor and reaction rates for N-14(p,gamma)O-15. Our analysis favors a low value for the astrophysical factor

Indirect techniques in nuclear astrophysics

Owing to the presence of the Coulomb barrier at astrophysically relevant kinetic energies it is very difficult, or sometimes impossible, to measure astrophysical reaction rates in the laboratory. That is why different indirect techniques are being used along with direct measurements. Here we address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique for calculation of the astrophysical processes in the presence of subthreshold bound states, in particular, two different mechanisms are discussed: direct capture to the subthreshold state and capture to the low-lying bound states through the subthreshold state, which plays the role of the subthreshold resonance. The ANC technique can also be used to determine the interference sign of the resonant and nonresonant (direct) terms of the reaction amplitude. The TH method is unique indirect technique allowing one to measure astrophysical rearrangement reactions down to astrophysically relevant energies. We explain why there is no Coulomb barrier in the sub-process amplitudes extracted from the TH reaction. The expressions for the TH amplitude for direct and resonant cases are presented