Calculation of supercritical Dirac resonances in heavy-ion collisions

Abstract

This resonance is similar in character to other resonances in atomic physics. It is parameterized by its energy and its lifetime. A numerical discretization technique, the mapped Fourier grid method (MFG) is extended to the Dirac equation and is used to solve for the resonance parameters of a quasimolecular supercritical 1S$\sigma$ state which arises, e.g., in a uranium-uranium collision. Direct methods using only the MFG method are shown to give reasonable estimates for the resonance parameters. Analytic continuation methods such as complex scaling (CS) of the coordinate or adding a complex absorbing potential (CAP) are then applied. They allow for more accurate determinations of the supercritical resonance parameters. The (extrapolated) augmented analytic continuation methods are used to investigate the effects of higher-order couplings, beyond the monopole approximation. For the nearly charge symmetric system of U$^{92+}$-Cf$^{98+}$, it is shown that the S-D quadrupole coupling is the next dominant interaction after the monopole interaction. Collisions near the Coulomb barrier, in which supercritical resonance states occur, are also calculated using the MFG. Results are presented for the collision of U$^{92+}$-U$^{92+}$ for a zero-impact-parameter Coulomb trajectory at a center-of-mass energy of 740MeV. The enhancement effects to the positron spectrum due to nuclear sticking at closest approach is examined. Results are given for sticking times of 2,5,10$\times10^{-21}$s. Nuclear sticking is shown to offer the possibility of demonstrating experimentally the existence of supercritical resonance states.