Determination of the astrophysical factor S17 by using continuum-discretized coupled-channels method and asymptotic normalization coefficient method

The solar neutrino flux observed on the earth is much smaller than the prediction by the standard solar model. This deficit is called the solar neutrino problem and is interpreted to be due to the neutrino oscillation. The solar neutrino is generated by the decay of 8B which is produced by the 7Be(p, γ)8B reaction. The astrophysical factor S17 is defined as the 7Be(p, γ)8B reaction cross section divided by the Coulomb transmission coefficient. Up to the present, the value of S17 has been accompanied with about 15% of error range. If it is reduced below 5%, a great progress of the neutrino physics and the solar neutrino problem is expected. In this review, recent development of the estimation of S17 by using Continuum-Discretized Coupled-Channels method (CDCC) and Asymptotic Normalization Coefficient (ANC) method is presented. In the CDCC method the reacting system is described by a three-body model. The wave function is discretized by using the average method. CDCC equation is formulated. The scattering S matrix is obtained by solving the CDCC equation with a given boundary condition. On the other hand, ANS is applied for indirect determination of the cross section of extremely low energy reactions utilizing other experimental result. In the present case, S17 can be obtained by determining the ANC value choosing the proton transfer reaction 7Be(d, n)8B at 7.5 MeV as the alternative reaction for example. For the practical application of the CDCC and ANS to this reaction, optical potential needed in the calculation was carefully examined. Finally the error range of the S17 value obtained is about 6 to 7% which can be further reduced down to 2% by improving calculation code. As another example, the decomposition reaction of 8B bombarded to 58Ni target was analyzed. The S17 value was obtained with small theoretical error by using the CDCC plus ANS instead of Virtual Photon Theory. In both cases, theoretical error is much smaller than the experimental. (S. Funahashi)