Study of nonlocality effects in direct capture reactions with Lagrange-mesh R-matrix method

We apply the Lagrange-mesh [Formula: see text]-matrix method to calculate the [Formula: see text]-factor for the [Formula: see text]C[Formula: see text]N and [Formula: see text]O[Formula: see text]F direct radiative capture reactions. By comparing the astrophysical [Formula: see text]-factors calculated with nonlocal and local potentials, we investigate the nonlocality effects coming from the nuclear potentials in the direct capture reactions. Our calculations are in good agreement with the experimental data and indicate a nonnegligible difference in the results of local and nonlocal potentials. The use of small diffuseness narrow potentials also provides a remarkably good fit in the case with multiple broad resonances. Our findings suggest that the nonlocal potential improves the calculated results although the difference between the local and nonlocal potentials is smaller than uncertainties from other sources. We propose the nonlocality potential should be used in the potential model calculation of future astrophysics rates evaluation.

Direct and inverse spectral problems for Dirac systems with nonlocal potentials

The main purposes of this paper are to study the direct and inverse spectral problems of the one-dimensional Dirac operators with nonlocal potentials. Based on informations about the spectrum of the operator, we find the potential and recover the form of the Dirac system. The methods used allow us to reduce the situation to the one-dimensional case. In accordance with the given assumptions and conditions we consider problems in a specific way. We describe the spectrum, the resolvent, the characteristic function etc. Illustrative examples are also given.