The existence of bound states of the system $(\al,e,e,e)$ in a magnetic field $B$ is studied using the variational method. It is shown that for $B \gtrsim 0.13\,{ \rm a.u.}$ this system gets bound with total energy below the one of the $(\al,e,e)$ system. It manifests the existence of the stable He$^-$ atomic ion. Its ground state is a spin-doublet $^2(-1)^{ +}$ at $0.74\, { \rm a.u.} \gtrsim B \gtrsim 0.13\, { \rm a.u.}$ and it becomes a spin-quartet $^4(-3)^{ +}$ for larger magnetic fields. For $0.8\, { \rm a.u.} \gtrsim B \gtrsim 0.7\, { \rm a.u.}$ the He$^-$ ion has two (stable) bound states $^2(-1)^{ +}$ and $^4(-3)^{ +}$.
Categories: physics.atom-ph astro-ph.HE physics.chem-ph quant-ph