Quantum Monte Carlo Study of a Positron in an Electron Gas

Quantum Monte Carlo calculations of the relaxation energy, pair-correlation function, and annihilating-pair momentum density are presented for a positron immersed in a homogeneous electron gas. We find smaller relaxation energies and contact pair-correlation functions in the important low-density regime than predicted by earlier studies. Our annihilating-pair momentum densities have almost zero weight above the Fermi momentum due to the cancellation of electron-electron and electron-positron correlation effects.

Figure 1

Relaxation energy against density parameter from our SJB-DMC calculations and other studies [14, 26, 28, 34, 35], relative to the Boroński-Nieminen expression, $\Delta {\Omega }_{\mathrm{BN}}$ [6] (horizontal dashed line).

Figure 2

Top: APMDs [$\rho (\overline{p})$] for different densities. The solid lines show our VMC data obtained with wave function ${\Psi }_{\mathrm{pair}}^{\mathrm{SJB}}$ and $N=114$ electrons, while the dashed and dash-dotted lines show the data of Kahana [29] and Stachowiak [27], respectively. Bottom: APMDs for the positron in HEG and the HEG at $r_s=8$ and $N=54$ electrons, calculated using ${\Psi }_{\mathrm{PW}}^{\mathrm{SJB}}$.

Figure 3

Deviation of the contact PCF $g(0)$ from the form $g_{\mathrm{BN}}(0)$ of Boroński and Nieminen [6] together with other results in the literature [14, 26, 28, 35, 36, 37, 38].