About the existence of the exotic molecular ions $(HeH{)}^{2+}$ and $H{e}_2^{3+}$ in a strong magnetic field

The Coulombic systems $(\text{al}pe)$ and $(\text{al}\text{al}e)$, $(\text{al}ppe)$, $(\text{al}\text{al}pe)$ and $(L{i}^{3+}L{i}^{3+}e)$ placed in a magnetic field $B \gtrsim 10^{11} {G}$ are studied. It is demonstrated a theoretical existence of the exotic ion $(HeH{)}^{2+}$ for $B\gtrsim 5\times {10}^{12}G$ in parallel configuration (the magnetic field is directed along internuclear axis) as optimal as well as its excited states $1\pi ,1\delta$. As for the exotic ion ${He}_2^{3+}$ it is shown that in spite of strong electrostatic repulsion of $\text{al}-$particles this ion can also exist for $B \gtrsim 100 {a.u.} (= 2.35\times 10^{11} {G})$inparallelconfigurationasoptimalinthestates$1\si_g$(groundstate),$1\pi_u, 1\delta_g$. Upon appearance both ions are unstable towards dissociation with $H{e}^{+}$ in the final state but with very large lifetime. However, at $B\gtrsim 10000$ a.u. the ion $(HeH{)}^{2+}$ becomes stable, while at $B\gtrsim 1000$ a.u. the ion ${He}_2^{3+}$ becomes stable. With a magnetic field growth, both exotic ions become more and more tightly bound and compact, their lowest rotational and vibrational energies grow. At the edge of applicability of non-relativistic approximation, $B \sim 4.414 \times 10^{13}$G,thereareindicationsthatthreemoreexoticlinearions$(H-He-H)^{3+}$,$(He-H-He)^{4+}$andeven$Li_2^{5+}$ in parallel configuration may also occur.