Effect of the atomic electric quadrupole moment on positron binding

The effect of an electric quadrupole moment $Q$ is studied for positron-atom bound systems. It is demonstrated that for $Q>50$ a.u. the electric quadrupole potential is sufficiently strong to bind a positron (or an electron) even in the absence of the dipole polarization potential. Such large values of $Q$ are not known for atomic ground states; however, they exist in molecules and excited atoms. In the $2s2p^3{P}_2^o$ state of beryllium, the quadrupole contribution makes the difference between a stable bound state and an unstable state, which decays to a $\mathrm{Be}{}^{+}$ ion and positronium. In the majority of atoms the quadrupole contribution is small and can be neglected.

Figure 1

The distance of the boundary of the wave function of the positron from the nucleus $a$ (in a.u.) vs the required minimum electric quadrupole moment $Q$ to get a bound state with the energy $E=-100$ meV when the dipole polarizability is supposed to be zero, $\alpha =0$.