Autoionizing multiply excited states offer unusual challenges to the theory of electronic structure and spectra because of the presence of strong electron correlations, of their occasional weak binding, of their proximity to more than one threshold, and of their degeneracy with many continua. Here we discuss a theory that addresses these difFiculties in conjunction with the computation of their wave functions and intrinsic properties. Emphasis is given on the justification of the possible presence of self-consistently obtained open-channel-like (OCL) correlating configurations in the square-integrable representation of such states and on their effect on the energy E and the width I . Application of the theory has allowed the prediction of two hitherto unknown He triply excited resonances, the 2s2p P (E=59.71 eV, above the He ground state, I =79 meV) and the 2p D' (E=59.46 eV, I =282 meV) (1 a.u. =27.2116 eV).These resonances are above the singly excited states of He and are embedded in its doubly excited spectrum. The relatively broad 2p D' state interacts strongly with the He 2s2p P' ed continuum. The effect of this interaction has been studied in terms of the coupling with fixed core scattering states as well as with a self-consistently computed OCL bound configuration. The position of the He 2p' D' resonance is below that of the He 2p 'D autoionizing state at 59.91 eV and of the He 2p P bound state at 59.68 eV. The partial decay widths to the three important open channels are y(2s2p P')=252 meV, y(1s2p 'P')=21 meV, y(1s2p 'P')=9 meV. The final core states are also represented by correlated (multiconfigurational Hartree-Fock) functions. The 2s2p P state couples to four neighboring He thresholds, the 2s2p P', 2p P, 'D, and 2s2p 'P'. It is above the He 2s2p P' threshold at 58.31 eV, with respect to which it is a valence shape resonance, and below the He 2p 'D and 2s2p 'P' autoionizing states. In the limit of an exact energy calculation, we suggest that its position would also come below that of the 2p P state, which it overlaps. Its partial widths are y(2s2p P') =60 meV, y(1s2p P') =9 meV, y(1s2p 'P') =10 meV. The present results, considered together with published ones on other n=2 intrashell states, show that the recently measured [R. N. Gosselin and P. Marmet, Phys. Rev. A 41, 1335] closely lying structures at 58.415 and 58.48 eV cannot correspond to the He 2p S' and D' states, as these authors proposed.PACS number(s): 31.50.+w, 31.20.Tz, 32.80.Dz, 34.80.Dp

Singly, doubly, and triply excited states of the Li isoelectronic sequence have been represented by small expansions of self-consistent, state-specific wave functions containing important contributions from localized and asymptotic correlation components. These wave functions have been used for the prediction of wavelengths and probabilities of one-, two-, and three-electron radiative transitions along the sequence, up to Ne +. For Z around 8 -10, the radiative lifetimes of the triply excited states are about 10 "-10 ' s, a fact which might render them observable in emission.PACS number(s): 31.50.+w, 32.70.Fw

Linear and non-linear frequency-dependent polarizabilities are defined as time averages and computed efficiently from a recently developed Floquet theorem based many-electron, many-photon theory. The theory is formulated and implemented in terms of suitably chosen state-specific function spaces and yields the induced total energy shift to all orders for frequencies o below, as well as above the ionization threshold. Application is made to H-, for which the reliable computation of even the static polarizability, (Y, is cumbersome. We have obtained (~(201.8 au), ( ~( o ) , ~( 0 . 7 6 ~ 10'au) and y ( w ) , for w = 0.0-0.260au. The forms of . ( U ) and y ( o ) are the same as those of the recently computed Li-.t As is well known, these quantities are usable in a number of areas of physics and chemistry. For example, see Fowler and Madden (1984a, b) for the use of static polarizabilities and hyperpolarizabilities of negative ions in the analysis of optical properties of crystals. $ These calculations dealt only with frequencies below the ionization threshold.

By identifying a special class of atomic negative ion states where all electron spins are unpaired and where the nuclear charge is partially unscreened, we predict, via large-scale state-specific calculations, that B − , C − , N − and O − have states which belong to the discrete spectrum even though they are very highly excited and embedded in a multitude of ionization thresholds. For example, the O − 1s2s2p 3 3s3p 3 10 S state lies 600.6 eV above the O 1s 2 2s 2 2p 4 3 P ground state and yet it is bound. For N − , the two maximum spin states, 1s2s2p 3 3s3p 2 9 P o and 1s2s2p 3 3p 3 9 S, are connected by an electric dipole transition with λ = 4615.5 Å and with transition rate ∼ 2.7 × 10 8 s −1 . For these unique states, the reliable prediction of the relevant energy differences demanded the execution of systematic all-electron calculations, with interand intra-shell correlations included.

We discuss the theory and computation of the lowest three, nϭ3 intrashell triply excited resonance states of He Ϫ of Li, and of positive ions of the sequence, up to N 4ϩ . These are the 3s 2 3p 2 P o , 3s3p 2 4 P, and 3s3p 2 2 D states, for which wave function characteristics, energies, and widths are reported. Contrary to recently published results for He Ϫ and to earlier ones for N 4ϩ , we found that electron correlation and orthogonality to lower states are such that they make the 2 P o state the lowest nϭ3 triply excited state ͑TES͒, as is the case with the nϭ2 shell. Our predictions for these states of He Ϫ are in harmony with the measurements of Roy ͓Phys. Rev. Lett. 38, 1062 ͑1977͔͒, which were interpreted only recently ͓C. A. Nicolaides and N. A. Piangos, J. Phys. B 34, 99 ͑2001͔͒. In addition, our value for the position of the Li 3s 2 3p 2 P o TES, 175.15 eV, agrees with the measurement (175.165Ϯ0.050 eV) of Diehl et al. ͓Phys. Rev. A 56, R1071 ͑1997͔͒. Apart from specifics, the paper discusses or points to certain basic aspects of computational quantum mechanics of such multiply excited states. For example, it refers to the utility of open-channel-like configurations toward proper convergence to a local energy minimum in the continuous spectrum, where quasibound and unbound states of the same symmetry lie below, and for which the normal eigenvalue properties of the discrete spectrum do not apply. Also, we discuss the possibility that is given by the state-specific theory for carrying out economic and physically transparent calculations and for deducing semiquantitative conclusions about the interplay between electronic structure, interference, and autoionization widths.