ON THE VIOLATION OF THE EXPONENTIAL DECAY LAW IN ATOMIC PHYSICS - AB-INITIO CALCULATION OF THE TIME-DEPENDENCE OF THE HE- 1S2P(2) P-4 NONSTATIONARY STATE

The detailed time dependence of the decay of a three-electron autoioni zing state close to threshold has been obtained ab initio by solving t he time-dependent Schrodinger equation (TDSE). The theory allows the d efinition and computation of energy-dependent matrix elements in terms of the appropriate N-electron wavefunctions, representing the localiz ed initial state, psi(0) the stationary scattering states of the conti nuous spectrum, U(epsilon), and the localized excited states, psi(n), of the effective Hamiltonian QHQ, where Q = \psi(0)><psi(0)\. The time -dependent wavefunction is expanded over these states and the resultin g coupled equations with time-dependent coefficients (in the thousands ) are solved to all orders by a Taylor series expansion technique. Con vergence is checked as a function of the number of the numerically obt ained U(epsilon) that span the continuous spectrum of the free electro n. The robustness of the method was verified by using a model interact ion in analytic form and comparing the results from two different meth ods for integrating the TDSE (appendix B). For the physically relevant application, the chosen state was the He- 1s2p(2) P-4 shape resonance , about which very accurate theoretical and experimental relevant info rmation exists. Calculations using accurate wavefunctions and an energ y grid of 20.000 points in the range 0.0-21.77 eV show that the effect ive interaction depends on energy in a state-specific manner, thereby leading to state-specific characteristics of non-exponential decay (NE D). For the established energy position of 0.01 eV, the results show a n exponential decay over about 6 x 10(4) au of time, from which a widt h of Gamma = 5.2 meV and a lifetime of 1.26 x 10(-13) s is deduced. Th e experimentally obtained width is 7.16 meV (Walter, Seifert and Peter son 1994 Phys. Rev. A 50 664). After 12 lifetimes (about 1400 fs), at which time the survival probability is 10(-6), NED sets in. On the oth er hand, due to the shape of the interaction, the NED appears at earli er times if the energy position happened to be slightly larger. For ex ample, if E were at 0.019 eV, NED would Start after nine exponential l ifetimes. These facts suggest that either in this state or in other au toionizing states close to threshold, NED may have sufficient presence to make the violation of the law of exponential decay observable.