Moleculelike metastable states of antiprotonic and mesic helium

Abstract

The exotic helium atom, consisting of a helium nucleus ${\mathrm{He}}^{2+}$, an electron ${\mathit{e}}^{\mathrm{-}}$, and a massive, negatively charged particle ${\mathit{X}}^{\mathrm{-}}$, such as an antiproton (p¯) or a kaon (${\mathit{K}}^{\mathrm{-}}$), is studied theoretically. This exotic atom is more like a polar molecule with two nuclei ${\mathrm{He}}^{2+}$ and ${\mathit{X}}^{\mathrm{-}}$, if ${\mathit{e}}^{\mathrm{-}}$ is in a low-lying orbital and ${\mathit{X}}^{\mathrm{-}}$ is in a highly excited orbital. Such states are generally formed in the capture of ${\mathit{X}}^{\mathrm{-}}$ by helium. The Born-Oppenheimer (BO) separation of the ${\mathit{e}}^{\mathrm{-}}$ motion and the ${\mathrm{He}}^{2+}$-${\mathit{X}}^{\mathrm{-}}$ motion is a good approximation for these states, and affords a transparent, unified perspective of exotic helium with different ${\mathit{X}}^{\mathrm{-}}$ and different isotopes of ${\mathrm{He}}^{2+}$. A propensity rule that favors small transition energies (except for the smallest one) is found for radiative emission by low vibrational and high rotational levels. This rule resembles the selection rule for infrared emission by the usual diatomic polar molecules, and contradicts the conventional expectation that radiative transitions in exotic atoms favor larger transition energies. The radiative lifetimes τ of highly excited states formed immediately after the capture of ${\mathit{X}}^{\mathrm{-}}$ are of the order of μsec for ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$-p¯-${\mathit{e}}^{\mathrm{-}}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$-p¯-${\mathit{e}}^{\mathrm{-}}$, and those for ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$-${\mathit{K}}^{\mathrm{-}}$-${\mathit{e}}^{\mathrm{-}}$ are about half the values for the antiprotonic helium.