Theoretical resolution of the H- resonance spectrum up to the n=4 threshold. I. States of P-1(0), D-1(0), and F-1(0) symmetries - art. no. 052508

We report on a theoretical approach to the calculation of wave functions, e nergies E, and widths Gamma of high-lying resonances of H-, with applicatio n to the identification of 76 states of P-1(0), D-1(0), and F-1(0) symme tr ies up to the n = 4 threshold, with widths down to about 1 x 10(-8)-1 x 10( -10) a.u., depending on symmetry and threshold. The overwhelming majority o f these resonances have not been detected experimentally. Previous calculat ions by different methods allowed the identification of 35 of these states, with only very few cases having a level of accuracy comparable to the one of the present work. We suggest that the measurement of these resonances mi ght become possible via two-step excitation mechanisms using ultrasensitive techniques capable of dealing with the problems of very small widths and p reparation cross-sections. In this work, the D-1 state at 10.872 eV above t he H(-)1s(2) S-1 ground state, already prepared and measured by electron sc attering as well as by two-photon absorption, is considered as the stepping stone for the possible probing of resonances of P-1(0), D-1(0), and F-1(0) symmetries via absorption of tunable radiation of high resolution. By clas sifying the results according to the Gailitis-Damburg model of dipole reson ances (a product of a 1/r(2) -like potential) we find that there are unpert urbed as well as perturbed series, in analogy with the Rydberg spectra of n eutrals and positive ions (a product of a 1/r-like potential). For the form er, the agreement with the Gailitis-Damburg predictions as to the relations hip of the extent of the outer orbital and of the energies and widths of st ates is excellent. The perturbed series result from interchannel coupling a nd the remaining electron correlation. One of the effects is the existence of overlapping resonances. For example, for two P-1(0) states below the n = 3 threshold there is degeneracy on the energy axis (E1 = - 0.0555763612 a. u. and E2 = - 0.0555763099 a.u.) but the widths differ (Gamma(1) = 1.14x10( -4) eV and Gamma(2) = 5.45x10(-6) eV). We also comment on whether considera tion of the relativistic Lamb shift splitting of me hydrogen thresholds is sufficient for deciding the truncation of the resonance series. Our calcula tions were carried out by implementing previously published theories, where by the resonance E's and Gamma's are determined from properly selected comp lex eigenvalues of non-Hermitian Hamiltonian matrices constructed in terms of physically relevant square integrable real and complex function spaces r epresenting the localized and asymptotic parts of the resonance eigenfuncti ons. For the H- series of resonances, the physical relevance of the real fu nctions implies the systematic construction of basis sets with average [r] extending to thousands of atomic units, in order to account for the extreme diffuseness of the outer orbital as each threshold is approached. The comp lex one-electron basis sets are Slater-type orbitals of a complex coordinat e re-(i theta) Their inclusion into the overall calculation and their optim ization via the variation of nonlinear parameters (including theta) account s for the contribution of the asymptotic part of the resonance, and for the energy width and shift beyond the real energy E-0 of the localized part.