Photodetachment cross section of He  „ 1 s 2 s 2 p 4 P o … in the region of the 1 s detachment threshold Jinhua Xi Department of Physics, Vanderbilt University, Nashville, Tennessee 37235 Charlotte Froese Fischer Department of Computer Science, Vanderbilt University, Nashville, Tennessee 37235 Received 16 March 1998 Using a Spline-Garlekin and inverse iteration method, we studied in detail the photodetachment cross section of the He - (1 s 2 s 2 p 4 P o ) state in the region of the 1 s detachment threshold. Details of the cross section from threshold to 44 eV are presented. The effects of core excitation and continuum channel coupling are studied. A very narrow 2 s 3 s 4 s 4 S resonance was found at 42.866 00 eV with a width of 0.103 meV. Other resonance structures are also found and analyzed. We studied the 2 s 2 p 24 P resonance state that lies immedi- ately below the 1 s threshold. The width and position of this state, obtained from this calculation, are 37.669 eV and 9.850 meV, respectively. This result is in good agreement with other theoretical calculations. S1050-29479901001-X PACS numbers: 32.80.Fb, 32.80.Gc I. INTRODUCTION The weakly bound He - negative ion has attracted consid- erable interest in recent years. Because of the weak coupling among electrons, theoretical calculations cannot predict the resonance behavior correctly if the correlations are not prop- erly included. The 1 s 2 s 2 p 4 P metastable state, with an extra electron bound to the 1 s 2 s 3 S state of He, can be studied via the photodetachment process. From this study the quartet 4 S , 4 P , and 4 D excited states of He - can be investigated. The energy of this state was calculated by Bunge and Bunge 1. They obtained the binding energy to be 77.51 0.04 meV. The accuracy of the binding energy was im- proved by a recent experimental and theoretical study of Kristensen et al. 2. The reported theoretical value was 77.5180.011 meV, in agreement with their experimental result of 77.5160.006 meV. There also have been some theoretical 3–7 and experimental 8–14 studies of the photodetachment cross section and angular distribution of the quartet 1 s 2 s 2 p 4 P o state. The 1 s 2 p 24 P sharp reso- nance has drawn particular attention among all these studies. This resonance was reported by Hazi and Reed 3 in a the- oretical study of the photodetachment cross section of the 1 s 2 s 2 p 4 P o state. Thereafter, theoretical 4–6 and experi- mental 10–12 investigations have been performed that de- termined the width and position and the maximum cross sec- tion of the resonance with high accuracy. In our first paper on the photodetachment study of He - 6, we calculated the cross section and angular distribution of the 1 s 2 s 2 p 4 P o state with energy from threshold to 4 eV. We employed an approach that uses a spline basis and multiconfiguration Hartree-Fock MCHF orbitals to calculate the interaction matrix and the wave functions of the system. The 1 s 2 p 24 P sharp resonance was investigated in detail and excellent agreement with the experimental data was obtained. We also predicted the 1 s 3 s 4 s 4 S Feshbach resonance at 2.959 07 eV with a width of 0.19 meV. This result was verified by a recent experiment measurement of Klinkmu ¨ ller et al. 15, which gives 2.959 2557 eV and 0.193 meV for the posi- tion and width, respectively. In this paper we report the calculation of the cross section of the 1 s photodetachment from the He - (1 s 2 s 2 p 4 P o ) state, with photon energy from threshold up to 44 eV. In the recent publication of Kim, Zhou, and Manson 7, the pho- todetachment from the inner 1 s electron to certain selected channels was studied using the R-matrix method with MCHF orbitals, where the energy covered the whole range from threshold to 100 eV. In their paper, the large correlations are considered but fine correlation effects are ignored, so small resonance structures near threshold did not appear. In our calculation described below, however, we intend to provide a more complete study of the resonance structure and photo- detachment property in the threshold region of the 1 s detach- ment. We also report the result of the 2 s 2 p 24 P Feshbach resonance. The 2 s 2 p 24 P state was predicted by Chung 16 using the saddle-point variation method. Later the resonance position and width were investigated by Bylicki and Nico- laides 17,18, Chung 19, and Kim, Zhou, and Manson 7. Recently, Morishita and Lin 20 analyzed the resonance states of the He - system using the hyperspherical idiabatic potential curves. II. THEORY AND COMPUTATIONAL APPROACH We use an interaction matrix inverse iteration approach based on the Galerkin method, using MCHF orbitals for bound orbital functions and splines as basis functions for continuum orbitals. The configuration space consists of bound configurations perturber states that incorporate fine and weak correlations, closed-channel configurations that in- clude the major correlation effects near threshold, and open- channel configurations that represent the behavior of the photoelectrons. In our earlier paper 6 we described the in- teraction matrix and Galerkin approach in detail. Briefly, the PHYSICAL REVIEW A JANUARY 1999 VOLUME 59, NUMBER 1 PRA 59 1050-2947/99/591/3078/$15.00 307 ©1999 The American Physical Society