Analysis of the energy dependences of the P- and D-wave phase shifts for α 12C scattering in the threshold region on the basis of N/D equations

Abstract

The energy dependences of the P- and D-wave phase shifts for α 12C scattering in the region of low energies are studied on the basis of N/D equations, in which effects of Coulomb interaction are taken into account. For the vertex constants G 11 and G 12 in the 16O(7.12 MeV, 1−) ↔ α + 12C and 16O(6.92 MeV, 2+) ↔ α + 12C vertex functions and for the corresponding asymptotic normalization coefficients C 11 and C 12, the regions of values that are compatible with the required analytic properties of the partial-wave scattering amplitudes T l CN (s) (l = 1, 2) and with the condition of a satisfactory description of data available from a partial-wave analysis of α 12C scattering are determined. It is shown that, in the region G 11 2 > 0.283 fm (C 11 > 3.45 × 1014 fm−1/2), the P-wave amplitude T l CN (s) develops, on the physical sheet, a second pole, which corresponds to a ghost state; therefore, these regions of values of the constants G 11 2 and C 11 are not admissible. In the case of scattering in the D-wave state, it is shown on the basis of the analytic approach being considered that, for values of the square of the vertex constant G 12 2 in the range 0.031–0.122 fm [the corresponding values of the asymptotic normalization coefficient fall within the range C 12 = (1.15–2.30) × 105 fm−1/2], the results of our calculation of the phase shifts are in satisfactory agreement with partial-wave-analysis data.