TIME-DEPENDENCE AND PROPERTIES OF NONSTATIONARY STATES IN THE CONTINUOUS-SPECTRUM OF ATOMS

The recently measured Li- 1s(2)2s2p(3)P degrees shape resonance, the C a KLM 3d5p F-3 degrees doubly excited autoionizing state and the long- lived He- 1s2s2p (4)P(5/2)degrees metastable level were treated as non stationary states satisfying the time-dependent Schrodinger equation ( TDSE). The lifetimes of the first two are short, of the order of 10(-1 4) s, and the solution of the TDSE well into times where nonexponentia l decay (NED) is established, is achievable via the state-specific exp ansion approach (SSEA), according to which the time-dependent solution has the form Psi(t) = c(t)Psi(0) + X(t). Psi(0) is the square-integra ble wavefunction of the localized state at t = 0 and X(t) is composed mainly of energy normalized scattering functions with time-dependent c oefficients. The coefficient c(t) is related to the survival amplitude , alpha(t), by c(t) = alpha(f) - [Psi(0)\X(t)], where the overlap matr ix element appears when the function spaces are not completely orthono rmal. For the diffuse Li- 1s(2)2s2p(3)P degrees resonance, its analysi s as a decaying state has as a prerequisite the calculation of a relia ble Psi(0), with correlation between the two valence electrons. This h as been achieved by a special procedure and a related discussion is gi ven. The proximity of the energy E to threshold (similar to 50 meV), t he closeness of the ratio E/Gamma to unity (Gamma is the resonance wid th) and the energy dependence of the bound-free matrix element, produc ed the result that NED should appear after only two lifetimes, when th e probability of finding the system in the initial state is still non- negligible. From the exponential part of the decay curve, the width wa s found to be Gamma = 53 meV, in agreement with the recent width of 64 +/- 25 meV derived from measured cross sections in recent collision e xperiments (Lee et al 1996). The shortness of the time for which expon ential decay (ED) holds and the fact that the survival probability, P( t), is still significant at the beginning of the NED, does not allow t he rigorous justification of the definition of the lifetime from tau = (h) over bar/Gamma, or the equivalence of this Gamma with the observe d energy width. Thus, we propose that a mean life, tau, should be obta ined from <(tau)over bar> = [t] = integral(0)tP(t)dt/integral(0)P(t)dt Calculation produces tau = 1.2 x 10-(14) s and <(tau)over bar> = 1.7 x 10(-14) s. For the Ca F-3 degrees state, whose bound-free interactio n is smooth and nearly constant from zero to about 5.5 eV, NED appears after 17 lifetimes. The lifetime of Ca F-3 degrees is deduced from th e exponential decay (ED) part of P(t) to be 3.5 x 10(-14) s. From our examination of the case of the He(- 4)P(5/2)degrees level by a number of methods based on the use of state-specific wavefunctions, we conclu de that for metastable states whose lifetimes are in the range 10(-4)- 10(-8) s, the ab initio calculation of P(t) is, at present, prohibited by the huge requirements for computer time. Finally, having computed the amplitude alpha(t), we obtain numerically the energy distribution function, g(E) = \[E\Psi(0)]\(2), of the two autoionizing states. In t he case of Ca it is a perfect Lorentzian.