FESHBACH RESONANCES AND VIRTUAL STATES IN ELECTRON
SCATTERING BY Rb, Cs, AND Fr ATOMS AT LOW-ENERGIES

Cristian Bahrim, Uwe Thumm
Department of Physics, Kansas State University, Manhattan, KS 66506-2604, USA

Ilya I. Fabrikant
Department of Physics and Astronomy, University of Nebraska, Lincoln, NE 68588-0111, USA

In the last decades, negative ions have attracted much interest from both theorists and experimentalists and some reviews have been devoted to this subject¹. Nevertheless, the spectra of many negative ions, especially the heavy anions, have not been investigated in detail. Based on the Dirac R-matrix method², we analyze the spectra of Rb-, Cs-, and Fr- anions below the first np excitation thresholds of Rb(5p), Cs(6p), and Fr(7p), in electron scattering calculations.

The model potential we use to describe the electrostatic interaction between the projectile electron and the atomic targets (Rb, Cs, and Fr) is based on an effective two-electrons approach, in which the valence and scattered electron of the electron-alkali atom system move in the field of a polarizable noble-gas-like core^2,3. The available data provided by both theory and experiment suggest that the low-lying spectra of different negative alkali-metal ions are similar¹. Recently, we have confirmed in elaborate Dirac R-matrix calculations that the lowest ³P^o excited state for Rb- and Cs- ions is a shape resonance rather than a bound state, in excellent agreement with electron scattering and photodetachment measurements³. We have predicted that the lowest ³P^o state of Fr- is also a resonance, at 32 meV above the detachment threshold³.

Our new relativistic Dirac R-matrix calculations for electron scattering at energies below the Rb(5p), Cs(6p), and Fr(7p) excitation thresholds allow to identify the ³P^e and ¹P^o₁ Feshbach resonances . For Cs and Fr targets, our calculation indicates the presence of a new ¹D^o₂ resonance at a few meV below the lowest np_3/2 atomic excitation threshold. We provide the positions, widths, and shape for all these resonances in both partial and total elastic cross sections. The influence of the long-range electrostatic interaction and the short-range electron correlations on the ³P^e, ¹P^o₁ and ¹D^o₂ Feshbach states is investigated. Comparison with available experiments is done⁴. We find that the splitting ΔE(J,J-1) between adjacent fine-structure components J of same triplet resonance located below the first Rb(5p_1/2), Cs(6p_1/2), and Fr(7p_1/2) thresholds, increases linearly with Z⁴/n³, as in the case of hydrogenic ions. Here n is the principal quantum number which defines the dominant nl n'l' configurations (n=5(Rb), 6(Cs), and 7(Fr)) for each resonance, and Z is the charge of the nucleus.

Figure 1 shows this linear dependence for the ³P^o, shape and ³P^e Feshbach states of Rb-, Cs-, and Fr-.

Based on the relativistic version of the modified effective range theory⁵, which extrapolates eigenphases provided by the Dirac R-matrix calculations toward energies below 1 meV, we compute highly accurate ³S^e and ¹S^e scattering lengths in e- + Rb(5s), Cs(6s), and Fr(7s) elastic collisions.

Figures:

Figure 1: The splitting ΔE_J(1,0) between the J=0 and J=1 terms
of the ³P^o (triangles) and ³P^e (circles) resonances vs. Z⁴/n³.

References:

1) S.J. Buckman and Ch.W. Clark, Rev. Mod. Phys. 66, 539 (1994);
T. Andersen, H.K. Haugen, and H. Hotop, J. Phys. Chem. Ref. Data 28, 1511 (1999).
2) U. Thumm and D.W. Norcross, Phys.Rev.A 45, 6349 (1992).
3) C. Bahrim and U. Thumm, Phys. Rev. A 61, 022722 (2000).
4) C. Bahrim, U. Thumm, and I.I. Fabrikant, Phys. Rev. A, in press
5) C. Bahrim, U. Thumm, and I.I. Fabrikant, J. Phys. B, in press

This work was supported by the Chemical Sciences, Geosciences and Biosciences Division,
Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy.

Submitted to ICPEAC 2001, July 2001 in Santa Fe, NM.

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