Finite Hydrogenic molecular chain H$_3$ and ion H$_2^-$ exist in a strong magnetic field

The existence and stability of the linear hydrogenic chain H$_3$ and H${}_2^-$ in a strong magnetic field is established. Variational calculations for H$_3$ and H${}_2^-$ are carried out in magnetic fields in the range $10^{11}\leq B \leq 10^{13}\,$G with 17-parametric (13-parametric for H${}_2^-$), physically adequate trial function. Protons are assumed infinitely massive, fixed along the magnetic line. States with total spin projection $S_z=-3/2$ and magnetic quantum numbers $M=-3,-4,-5$ are studied. It is shown that for both H$_3$ and H${}_2^-$ the lowest energy state corresponds to $M=-3$ in the whole range of magnetic fields studied. As for a magnetic field $B \gtrsim 10^{11}\,$G both H$_3$ and H${}_2^-$ exist as metastable states, becoming stable for $B \geq 1.9 \times 10^{11}\,$G and for $B \geq 2.7 \times 10^{11}\,$G, respectively. The excited states $^4(-4)^+$, $^4(-5)^+$ of ${\rm H}_3$ and H${}_2^-$ appear at magnetic fields $B > 7 \times 10^{11}$ and $10^{12}$\,G, respectively.