Stable He${}^{-}$ can exist in a strong magnetic field

The existence of bound states of the system $(\text{al},e,e,e)$ in a magnetic field $B$ is studied using the variational method. It is shown that for $B \gtrsim 0.13,{\rm a.u.}$thissystemgetsboundwithtotalenergybelowtheoneofthe$(\al,e,e)$system\mathrm{.}ItmanifeststheexistenceofthestableHe$^-$ atomic ion. Its ground state is a spin-doublet ${}^2(-1{)}^{+}$ at $0.74, {\rm a.u.} \gtrsim B \gtrsim 0.13, {\rm a.u.}$anditbecomesaspin-quartet$^4(-3)^{+}$ for larger magnetic fields. For $0.8, {\rm a.u.} \gtrsim B \gtrsim 0.7, {\rm a.u.}$theHe$^-$ionhastwo(stable)boundstates$^2(-1)^{+}$and$^4(-3)^{+}$.