Ubiquitous diffraction resonances in positronium formation from fullerenes

Due to the dominant electron capture by positrons from the molecular shell and the spatial dephasing across the shell width, a powerful diffraction effect universally underlies the positronium (Ps) formation from fullerenes. This results in trains of resonances in the Ps formation cross section as a function of the positron beam energy, producing structures in recoil momenta in analogy with classical single-slit diffraction fringes in the configuration space. This work opens a hitherto unknown avenue of Ps spectroscopy with nanomaterials and motivates level-differential measurements.

Figure 1

The scattering potential $V_{2h}^{\text{sc}}$ of the positron from ${\mathrm{C}}_{60}{}^{+}$ after a $7h$ (HOMO) electron is captured, the radial HOMO wave function, and the free ${\mathrm{C}}_{\text{60}}$ ground state LDA radial potential identifying the shell width. The position vectors, from the ${\mathrm{C}}_{60}$ center (0,0) roughly placed in the figure, and momentum vectors (for capture in the forward direction) are shown schematically. A bunch of curves peaking around the ${\mathrm{C}}_{\text{60}}$ radius $r_c$ represents products of scattering potential, radial HOMO, and radial $\mathrm{Ps}\left(1s\right)$ (shown) wave functions for the choices of electron positions marked by correspondingly color-coded dots. See the text for the description of $\alpha$.

Figure 2

(a) $\mathrm{Ps}\left(1s\right)$ formation cross sections for captures from HOMO (H), HOMO-1 (H-1), $2s$ (bottommost $\pi$ level), and $6h$ (a $\sigma$ level) as a function of recoil momentum ($Q$) in the forward direction. The result of hydrogen $1s$ capture is also shown for comparison. (b) The ratios of two pairs of these cross sections illustrate strong resonances. Separations ($\mathrm{\Delta }Q$) between some resonances are marked.

Figure 3

(a) ${\mathrm{C}}_{\text{60}}$ LDA radial potential and the positron scattering potential for the HOMO capture. (b) The Fourier transform magnitudes of $\mathrm{Ps}\left(1s\right)$ cross-section ratios for captures from various ${\mathrm{C}}_{\text{60}}\pi$ levels.