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.

Spectral collapse in multiqubit two-photon Rabi model

We have shown that the smallest possible singel-qubit critical coupling strength of the N-qubit two-photon Rabi model is only 1/N times that of the two-photon Rabi model. The spectral collapse can thus occur at a more attainable value of the critical coupling. For both of the two-qubit and three-qubit cases, we have also rigorously demonstrated that at the critical coupling the system not only has a set of discrete eigenenergies but also a continuous energy spectrum. The discrete eigenenergy spectrum can be derived via a simple one-to-one mapping to the bound state problem of a particle of variable effective mass in the presence of a finite potential well and a nonlocal potential. The energy difference of each qubit, which specifies both the depth of the finite potential well and the strength of the nonlocal potential, determines the number of bound states available, implying that the extent of the incomplete spectral collapse can be monitored in a straightforward manner.

Non-real eigenvalues of nonlocal indefinite Sturm–Liouville problems

The present paper deals with non-real eigenvalues of regular nonlocal indefinite Sturm–Liouville problems. The existence of non-real eigenvalues of indefinite Sturm–Liouville differential equation with nonlocal potential $K(x,t)$K(x,t) associated with self-adjoint boundary conditions is studied. Furthermore, a priori upper bounds of non-real eigenvalues for a class of indefinite differential equation involving nonlocal point interference potential function is obtained.