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arXiv:1903.06533 · Physical Review A

Existence of the finite hydrogenic molecular chain H3 and ion H2− in a strong magnetic field

Daniel Julian Nader, Juan Carlos Lopez Vieyra, Alexander V. Turbiner

Published Jul 11, 2019• 4 citations
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Abstract

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

DOI
10.1103/physreva.100.012508

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The existence of the molecular ion H32+{\mathrm{H}}_{3}^{2+}H32+​ in a magnetic field in a triangular configuration is revised. A variational method with an optimization of the form of the vector potential (gauge fixing) is used. It is shown that in the range of magnetic fields 108<B<1011G{10}^{8}<B<{10}^{11}\mathrm{G}108<B<1011G the system (pppe),(\mathrm{pppe}),(pppe), with the protons forming an equilateral triangle perpendicular to the magnetic line, has a well-pronounced minimum in the total energy. This configuration is unstable under the decays (Hatom)+p+p(\mathrm{H}\mathrm{atom})+p+p(Hatom)+p+p and H2++p.{\mathrm{H}}_{2}^{+}+p.H2+​+p. The triangular configuration of H32+{\mathrm{H}}_{3}^{2+}H32+​ complements H32+{\mathrm{H}}_{3}^{2+}H32+​ in the linear configuration that exists for $B\ensuremath{\gtrsim}{10}^{10}\mathrm{G}.$
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EXOTIC MOLECULAR IONS ( He H )2+ AND He23+{\rm He}_2^{3+}He23+​ IN A STRONG MAGNETIC FIELD: LOW-LYING STATES
The Coulombic systems (αpe) and (ααe), (αppe), (ααpe) and ( Li 3+ Li 3+e) placed in a magnetic field B ≳ 1011 G are studied. It is demonstrated a theoretical existence of the exotic ion ( He H )2+ for B ≳ 5 × 1012 G in parallel configuration (the magnetic field is directed along internuclear axis) as optimal as well as its excited states 1π, 1δ. As for the exotic ion [Formula: see text] it is shown that in spite of strong electrostatic repulsion of α-particles this ion can also exist for B ≳ 100 a.u. (= 2.35 × 1011 G ) in parallel configuration as optimal in the states 1σg (ground state), 1πu, 1δg. Upon appearance both ions are unstable towards dissociation with He + in the final state but with very large lifetime. However, at B ≳ 10000 a.u. , the ion ( He H )2+ becomes stable, while at B ≳ 1000 a.u. , the ion [Formula: see text] becomes stable. For both ions the vibrational and rotational energies are calculated. With a magnetic field growth, both exotic ions become more and more tightly bound and compact, their lowest rotational and vibrational energies grow drastically. At the edge of applicability of nonrelativistic approximation, B ~ 4.414 × 1013 G , there are indications that three more exotic linear ions ( H – He – H )3+, ( He – H – He )4+ and even [Formula: see text] in parallel configuration may also occur.
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