VOLUME 79, NUMBER 1 PHYSICAL REVIEW LETTERS 7JULY 1997 Reappraisal of the Existence of Shape Resonances in the Series C 2 H 2 , C 2 H 4 , and C 2 H 6 B. Kempgens, H. M. Köppe, A. Kivimäki, M. Neeb, K. Maier, U. Hergenhahn, and A. M. Bradshaw Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany (Received 28 January 1997) We have measured the main line (single hole) C 1s photoionization cross sections for C 2 H 2 , C 2 H 4 , and C 2 H 6 in the immediate threshold region. These three molecules occupy a central place in the proposed correlation between shape resonance position and molecular geometry. We find no clearly identifiable shape resonances in the single hole cross sections of C 2 H 4 and C 2 H 6 and only weak evidence for one in C 2 H 2 . [S0031-9007(97)03487-X] PACS numbers: 33.80.Eh Following the work of Dehmer and others, e.g., [1–4], various shape resonances have been identified in the pho- toadsorption spectra of diatomic molecules. These occur in the continuum above the core level absorption thresh- old and are usually attributed to the resonant trapping of the emitted photoelectron due to the presence of a poten- tial barrier. The latter results from centrifugal, repulsive forces which give rise to a concentric double well poten- tial. An alternative view of this phenomenon [3,4] is to assign the resonances to virtual, antibonding s   molecu- lar orbitals (m.o.’s) in the continuum. The two descrip- tions are essentially equivalent, as has been discussed in several papers, e.g., [5]. Conforming with the notion that the energy of a shape resonance depends on the details of the molecular potential, Stöhr, Sette, Hitchcock, and others have suggested that there is a correlation between shape resonance position and bond length, even in poly- atomic molecules [6–10]. Piancastelli et al. [11,12] later pointed out that, although such a “bond lengths with a ruler” [8] correlation might be expected (see, e.g., [13]), there were assignment problems in photoabsorption spec- tra and it was suggested that shape resonances should ac- tually be sought in the corresponding main line, or single hole, cross sections. Such measurements for C 2 H 4 and C 6 H 6 using synchrotron radiation on a bending magnet beam line did not, however, give an unequivocal answer to this question [14]. The molecules ethyne, ethene, and ethane (C 2 H 2 , C 2 H 4 , and C 2 H 6 , respectively) occupy a key role in this discussion [7,8,15,16], since there is also a marked varia- tion in C-C bond length with which the apparent position of the shape resonance has been correlated [7,8] (Fig. 1). Moreover, according to the calculations of Farren et al. [17] the C-C s  resonance is expected to dominate the near-edge region. The C-H resonances, on the other hand, are expected to be weak in the core level excitation spectra. In this Letter we report the measurement of the C 1s main line (single hole) cross sections for the three molecules in the near-threshold region. Photoelectron spectra of the three molecules were measured on the X1B undulator beam line [18] at the Brookhaven NSLS x-ray storage ring. The kinetic en- ergies of the emitted photoelectrons were determined with a stationary, angle-resolving magic-angle cylindrical mirror analyzer (CMA), along the axis of which the incident radiation reaches the target region [19]. With this arrangement the total intensity, integrated over all angles around the axis, is independent of the angular distribution of the photoelectrons and the degree of light polarization, enabling partial cross sections to be determined. The angular asymmetry parameter b (not of relevance here) can also be determined by utilizing a specially designed FIG. 1. Carbon K -edge absorption spectra of ethyne, ethene, and ethane measured with electron energy loss spectroscopy, showing the putative shape resonances and their apparent dependence on C-C bond length. From Hitchcock and Brion [16] and Sette et al. [7]. 0031-9007 97 79(1) 35(4)$10.00 © 1997 The American Physical Society 35