Resonant Annihilation and Positron Bound States in Benzene

Positrons attach to molecules in vibrationally resonant two-body collisions that result in greatly enhanced annihilation rates. Measurements of annihilation as a function of positron energy are presented for benzene using a cryogenic, trap-based beam. They establish a positron binding energy of $132\pm 3\mathrm{meV}$ to test state-of-the-art theoretical calculations, and they exhibit many unexpected resonances, likely due to combination and overtone vibrational modes. The relationship of these results to the unique $\pi$-bonded structure of benzene is discussed.

Figure 1

(a) The positron annihilation spectrum of benzene (open circles) as a function of the mean parallel energy of the positron beam. Vertical magenta bars indicate the locations of the downshifted dipole-allowed vibrational modes. The red curve is the convolution of the beam energy distribution with a delta function at the DA mode position [35, 36], downshifted to fit the experimental peak, to yield $E_b=133\pm 3\mathrm{meV}$. The blue line is the downshifted infrared absorption spectrum (in arbitrary units) from Ref. [37]. The green dashed-dot line is the prediction of the VFR theory [16] using the dipole coupling strengths from the IR spectrum [38]. (b) The normalized annihilation spectrum for benzene (black circles; magenta bars for DA modes) compared with that for cyclohexane (open red squares; green bars for DA modes), $E_b=78\mathrm{meV}$. The amplitudes of the large C-H peaks have been normalized, and the cyclohexane data and bars shifted so that the peaks coincide. The peak value for cyclohexane is $Z_{\mathrm{eff}}=1.24\times {10}^5$, a factor of 1.6 larger than benzene.

Figure 2

The annihilation spectrum for benzene-d6. Magenta bars indicate the downshifted DA fundamental modes. The red curve is the convolution of the positron beam with a delta function at the downshifted C-D mode position to yield $E_b=130\pm 3\mathrm{meV}$. The blue line is the downshifted infrared absorption spectrum (in arbitrary units) [37]. The green dashed-dot line is the prediction of the VFR theory [16] using the dipole coupling strengths from the IR spectrum [38].

Figure 3

The annihilation spectrum for (a) benzene-d1, (b) benzene-d3, and (c) benzene-d5. Magenta and blue bars are downshifted DA C-D and C-H modes [35]. The red curve is the convolution of the positron beam with delta functions at the downshifted DA mode positions, yielding (a) $E_b=132$, (b) 134, and (c) 132 meV.