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The $(HeH)^{2+}$ and $He_2^{3+}$ exotic molecular ions can exist in a strong magnetic field

Alexander V. Turbiner, Juan Carlos Lopez Vieyra

Published Dec 16, 2004• 1 citation
OpenAlex

Abstract

The Coulombic systems $(\\al p e)$ and $(\\al\\al e)$, $(\\al p p e)$, $(\\al \\al p e)$ and $(Li^{3+} Li^{3+} e)$ placed in a magnetic field $B \\gtrsim 10^{11} {G}$ are studied. It is demonstrated a theoretical existence of the exotic ion $(He H)^{2+}$ in parallel configuration (the magnetic field is directed along internuclear axis) for $B\\gtrsim 10^{12} {G}$. As for the exotic ion ${\\rm He}_{2}^{3+}$ it is shown that in spite of strong electrostatic repulsion of $\\al-$particles it can exist in parallel configuration for $B \\gtrsim 100 {a.u.} (= 2.35\\times 10^{11} {G})$ in the state $1\\si_g$ (ground state) as well as in the excited states $1\\pi_u, 1\\sigma_g$. With magnetic field growth, both exotic ions become more and more tightly bound and compact. It seems at the edge of applicability of non-relativistic approximation, $B \\sim 4.414 \\times 10^{13}$ G, three more exotic linear ions $(H-He-H)^{3+}$, $(He-H-He)^{4+}$ and $Li_2^{5+}$ in parallel configuration may also exist.

Related papers

EXOTIC MOLECULAR IONS ( He H )2+ AND ${\rm He}_2^{3+}$ IN A STRONG MAGNETIC FIELD: LOW-LYING STATES

Alexander V. Turbiner, Juan Carlos Lopez Vieyra

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.

International Journal of Modern Physics A•Apr 10, 2007•7 citations

He22+ molecular ion can exist in a magnetic field

Alexander V. Turbiner, Nicolais L. Guevara

We present a detailed study of the ground state of the Coulomb system $(\ensuremath{\alpha}\ensuremath{\alpha}ee)$ which corresponds to the ${\mathrm{He}}_{2}^{2+}$ molecular ion in a magnetic field $B=0\ensuremath{-}4.414\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{0.3em}{0ex}}\mathrm{G}$ in parallel configuration (it is assumed that infinitely massive $\ensuremath{\alpha}$ particles are situated along a magnetic-field line). One uses a variational method, introducing a trial function which includes electronic correlation in the form $\mathrm{exp}(\ensuremath{\gamma}{r}_{12})$, where $\ensuremath{\gamma}$ is a variational parameter. It is shown that the quantum numbers of the lowest total-energy state depend on the magnetic-field strength. This state evolves from the spin-singlet $^{1}{\ensuremath{\Sigma}}_{g}$ metastable state at $0\ensuremath{\le}B\ensuremath{\lesssim}0.85\phantom{\rule{0.3em}{0ex}}\mathrm{a}.\mathrm{u}.$ to a repulsive spin-triplet $^{3}{\ensuremath{\Sigma}}_{u}$ state for $0.85\ensuremath{\lesssim}B\ensuremath{\lesssim}1100\phantom{\rule{0.3em}{0ex}}\mathrm{a}.\mathrm{u}.$ and, finally, to a stable strongly bound spin-triplet $^{3}{\ensuremath{\Pi}}_{u}$ state at stronger fields $B\ensuremath{\gtrsim}1100\phantom{\rule{0.3em}{0ex}}\mathrm{a}.\mathrm{u}.$ The lowest vibrational energy for the latter case is calculated.

arXiv:astro-ph/0610928•Physical Review A•Dec 26, 2006•15 citations

He2+ molecular ion and the He− atomic ion in strong magnetic fields

Juan Carlos Lopez Vieyra, Alexander V. Turbiner

We study the question of existence, i.e., stability with respect to dissociation of the spin-quartet permutation- and reflection-symmetric ${}^{4}{(\ensuremath{-}3)}^{+}{}_{g}$ (${S}_{z}=\ensuremath{-}3/2,M=\ensuremath{-}3$) state of the $(\ensuremath{\alpha}\ensuremath{\alpha}eee)$ Coulomb system: the ${{\mathrm{He}}_{2}}^{+}$ molecular ion, placed in a magnetic field $0\ensuremath{\le}B\ensuremath{\le}10\phantom{\rule{0.16em}{0ex}}000$ a.u. We assume that the $\ensuremath{\alpha}$ particles are infinitely massive (Born-Oppenheimer approximation of zero order) and adopt the parallel configuration, when the molecular axis and the magnetic field direction coincide, as the optimal configuration. The study of the stability is performed variationally with a physically adequate trial function. To achieve this goal, we explore several helium-containing compounds in strong magnetic fields, in particular; we study the spin-quartet ground state of the ${\mathrm{He}}^{\ensuremath{-}}$ ion and the ground (spin-triplet) state of the helium atom, both for a magnetic field in $100\ensuremath{\le}B\ensuremath{\le}10\phantom{\rule{0.16em}{0ex}}000$ a.u. The main result is that the ${{\mathrm{He}}_{2}}^{+}$ molecular ion in the state ${}^{4}{(\ensuremath{-}3)}^{+}{}_{g}$ is stable towards all possible decay modes for magnetic fields $B\ensuremath{\gtrsim}120\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$ and with the magnetic field increase the ion becomes more tightly bound and compact with a cigar-type form of electronic cloud. At $B=1000\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$, the dissociation energy of ${{\mathrm{He}}_{2}}^{+}$ into ${\mathrm{He}}^{\ensuremath{-}}+\ensuremath{\alpha}$ is $\ensuremath{\sim}702\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ and the dissociation energy for the decay channel to $\mathrm{He}+\ensuremath{\alpha}+e$ is $\ensuremath{\sim}729\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, and both energies are in the energy window for one of the observed absorption features of the isolated neutron star 1E1207.4-5209.

arXiv:1704.01118•Physical Review A•Aug 9, 2017•3 citations

One-electron atomic–molecular ions containing lithium in a strong magnetic field

Horacio Olivares‐Pilón, D. Baye, Alexander V. Turbiner +1 more

The one-electron lithium-containing Coulomb systems of atomic type Li 2 + and molecular type Li 5 + 2 , LiHe 4 + and LiH 3 + are studied in the presence of a strong magnetic field B ⩽ 10 7 au in a non-relativistic framework. They are considered at the Born–Oppenheimer approximation of zero order (infinitely massive centres) within the parallel configuration (molecular axis parallel to the magnetic field). The variational and Lagrange-mesh methods are employed, complementing each other. It is demonstrated that the molecular systems LiH 3 + , LiHe 4 + and Li 5 + 2 can exist for sufficiently strong magnetic fields B ≳ 10 4 au and that Li 5 + 2 can even be stable at magnetic fields typical of magnetars.

arXiv:0912.1043•Journal of Physics B Atomic Molecular and Optical Physics•Mar 9, 2010•8 citations

H32+ molecular ion in a strong magnetic field: Triangular configuration

Juan Carlos Lopez Vieyra, Alexander V. Turbiner

The existence of the molecular ion ${\mathrm{H}}_{3}^{2+}$ 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 ${10}^{8}<B<{10}^{11}\mathrm{G}$ the system $(\mathrm{pppe}),$ 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 $(\mathrm{H}\mathrm{atom})+p+p$ and ${\mathrm{H}}_{2}^{+}+p.$ The triangular configuration of ${\mathrm{H}}_{3}^{2+}$ complements ${\mathrm{H}}_{3}^{2+}$ in the linear configuration that exists for $B\ensuremath{\gtrsim}{10}^{10}\mathrm{G}.$

arXiv:astro-ph/0203020•Physical Review A•Aug 26, 2002•20 citations

The HeH+molecular ion in a magnetic field

A V Turbiner, N L Guevara

A detailed study of the low-lying electronic states 1 Σ, 3 Σ, 3 Π, 3 Δ of the HeH + molecular ion in parallel to a magnetic field configuration (when α-particle and proton are situated on the same magnetic line) is carried out for B = 0 − 4.414 × 10 13 G in the Born–Oppenheimer approximation. The variational method is employed using a physically adequate trial function. It is shown that for the Σ states the parallel configuration is stable with respect to small deviations. The quantum numbers of the ground state depend on the magnetic field strength. The ground state evolves from the spin-singlet 1 Σ state for small magnetic fields B ≲ 0.5 au to the spin-triplet 3 Σ (unbound or weakly bound) state for intermediate fields and to the spin-triplet strongly bound 3 Π state for B ≳ 15 au. When the HeH + molecular ion exists, it is stable with respect to dissociation.

arXiv:physics/0703090•Journal of Physics B Atomic Molecular and Optical Physics•Aug 6, 2007•10 citations
The (HeH)2+(HeH)^{2+}(HeH)2+ and He23+He_2^{3+}He23+​ exotic molecular ions can exist in a strong magnetic field
The Coulombic systems (alpe)(\\al p e)(alpe) and (alale)(\\al\\al e)(alale), (alppe)(\\al p p e)(alppe), (alalpe)(\\al \\al p e)(alalpe) and (Li3+Li3+e)(Li^{3+} Li^{3+} e)(Li3+Li3+e) placed in a magnetic field Bgtrsim1011GB \\gtrsim 10^{11} {G}Bgtrsim1011G are studied. It is demonstrated a theoretical existence of the exotic ion (HeH)2+(He H)^{2+}(HeH)2+ in parallel configuration (the magnetic field is directed along internuclear axis) for Bgtrsim1012GB\\gtrsim 10^{12} {G}Bgtrsim1012G. As for the exotic ion rmHe23+{\\rm He}_{2}^{3+}rmHe23+​ it is shown that in spite of strong electrostatic repulsion of al−\\al-al−particles it can exist in parallel configuration for Bgtrsim100a.u.(=2.35times1011G)B \\gtrsim 100 {a.u.} (= 2.35\\times 10^{11} {G})Bgtrsim100a.u.(=2.35times1011G) in the state 1sig1\\si_g1sig​ (ground state) as well as in the excited states 1piu,1sigmag1\\pi_u, 1\\sigma_g1piu​,1sigmag​. With magnetic field growth, both exotic ions become more and more tightly bound and compact. It seems at the edge of applicability of non-relativistic approximation, Bsim4.414times1013B \\sim 4.414 \\times 10^{13}Bsim4.414times1013 G, three more exotic linear ions (H−He−H)3+(H-He-H)^{3+}(H−He−H)3+, (He−H−He)4+(He-H-He)^{4+}(He−H−He)4+ and Li25+Li_2^{5+}Li25+​ in parallel configuration may also exist.
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.
We present a detailed study of the ground state of the Coulomb system $(\ensuremath{\alpha}\ensuremath{\alpha}ee)$ which corresponds to the He22+{\mathrm{He}}_{2}^{2+}He22+​ molecular ion in a magnetic field $B=0\ensuremath{-}4.414\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{0.3em}{0ex}}\mathrm{G}$ in parallel configuration (it is assumed that infinitely massive $\ensuremath{\alpha}$ particles are situated along a magnetic-field line). One uses a variational method, introducing a trial function which includes electronic correlation in the form $\mathrm{exp}(\ensuremath{\gamma}{r}_{12})$, where $\ensuremath{\gamma}$ is a variational parameter. It is shown that the quantum numbers of the lowest total-energy state depend on the magnetic-field strength. This state evolves from the spin-singlet $^{1}{\ensuremath{\Sigma}}_{g}$ metastable state at $0\ensuremath{\le}B\ensuremath{\lesssim}0.85\phantom{\rule{0.3em}{0ex}}\mathrm{a}.\mathrm{u}.$ to a repulsive spin-triplet $^{3}{\ensuremath{\Sigma}}_{u}$ state for $0.85\ensuremath{\lesssim}B\ensuremath{\lesssim}1100\phantom{\rule{0.3em}{0ex}}\mathrm{a}.\mathrm{u}.$ and, finally, to a stable strongly bound spin-triplet $^{3}{\ensuremath{\Pi}}_{u}$ state at stronger fields $B\ensuremath{\gtrsim}1100\phantom{\rule{0.3em}{0ex}}\mathrm{a}.\mathrm{u}.$ The lowest vibrational energy for the latter case is calculated.
We study the question of existence, i.e., stability with respect to dissociation of the spin-quartet permutation- and reflection-symmetric ${}^{4}{(\ensuremath{-}3)}^{+}{}_{g}$ (${S}_{z}=\ensuremath{-}3/2,M=\ensuremath{-}3$) state of the $(\ensuremath{\alpha}\ensuremath{\alpha}eee)$ Coulomb system: the He2+{{\mathrm{He}}_{2}}^{+}He2​+ molecular ion, placed in a magnetic field $0\ensuremath{\le}B\ensuremath{\le}10\phantom{\rule{0.16em}{0ex}}000$ a.u. We assume that the $\ensuremath{\alpha}$ particles are infinitely massive (Born-Oppenheimer approximation of zero order) and adopt the parallel configuration, when the molecular axis and the magnetic field direction coincide, as the optimal configuration. The study of the stability is performed variationally with a physically adequate trial function. To achieve this goal, we explore several helium-containing compounds in strong magnetic fields, in particular; we study the spin-quartet ground state of the ${\mathrm{He}}^{\ensuremath{-}}$ ion and the ground (spin-triplet) state of the helium atom, both for a magnetic field in $100\ensuremath{\le}B\ensuremath{\le}10\phantom{\rule{0.16em}{0ex}}000$ a.u. The main result is that the He2+{{\mathrm{He}}_{2}}^{+}He2​+ molecular ion in the state ${}^{4}{(\ensuremath{-}3)}^{+}{}_{g}$ is stable towards all possible decay modes for magnetic fields $B\ensuremath{\gtrsim}120\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$ and with the magnetic field increase the ion becomes more tightly bound and compact with a cigar-type form of electronic cloud. At B=1000a.u.B=1000\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.B=1000a.u., the dissociation energy of He2+{{\mathrm{He}}_{2}}^{+}He2​+ into ${\mathrm{He}}^{\ensuremath{-}}+\ensuremath{\alpha}$ is $\ensuremath{\sim}702\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ and the dissociation energy for the decay channel to $\mathrm{He}+\ensuremath{\alpha}+e$ is $\ensuremath{\sim}729\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, and both energies are in the energy window for one of the observed absorption features of the isolated neutron star 1E1207.4-5209.
The one-electron lithium-containing Coulomb systems of atomic type Li 2 + and molecular type Li 5 + 2 , LiHe 4 + and LiH 3 + are studied in the presence of a strong magnetic field B ⩽ 10 7 au in a non-relativistic framework. They are considered at the Born–Oppenheimer approximation of zero order (infinitely massive centres) within the parallel configuration (molecular axis parallel to the magnetic field). The variational and Lagrange-mesh methods are employed, complementing each other. It is demonstrated that the molecular systems LiH 3 + , LiHe 4 + and Li 5 + 2 can exist for sufficiently strong magnetic fields B ≳ 10 4 au and that Li 5 + 2 can even be stable at magnetic fields typical of magnetars.
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 $B\ensuremath{\gtrsim}{10}^{10}\mathrm{G}.$
A detailed study of the low-lying electronic states 1 Σ, 3 Σ, 3 Π, 3 Δ of the HeH + molecular ion in parallel to a magnetic field configuration (when α-particle and proton are situated on the same magnetic line) is carried out for B = 0 − 4.414 × 10 13 G in the Born–Oppenheimer approximation. The variational method is employed using a physically adequate trial function. It is shown that for the Σ states the parallel configuration is stable with respect to small deviations. The quantum numbers of the ground state depend on the magnetic field strength. The ground state evolves from the spin-singlet 1 Σ state for small magnetic fields B ≲ 0.5 au to the spin-triplet 3 Σ (unbound or weakly bound) state for intermediate fields and to the spin-triplet strongly bound 3 Π state for B ≳ 15 au. When the HeH + molecular ion exists, it is stable with respect to dissociation.