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\(\text{He}^{3+}_{2}\) and \(\text{HeH}^{2+}\) molecular ions in a strong magnetic field: The Lagrange-mesh approach. (English) Zbl 1260.81336

Summary: Accurate calculations for the ground state of the molecular ions \(\text{He}^{3+}_{2}\) and \(\text{HeH}^{2+}\) placed in a strong magnetic field B\(\gtrsim 10^{2}\) a.u. \(\approx 2.35\times 10^{11} G\)) using the Lagrange-mesh method are presented. The Born-Oppenheimer approximation of zero order (infinitely massive centers) and the parallel configuration (molecular axis parallel to the magnetic field) are considered. Total energies are found with 9-10 s.d. The obtained results show that the molecular ions \(\text{He}^{3+}_{2}\) and \(\text{HeH}^{2+}\) exist at \(B>100\) a.u. and \(B>1000\) a.u., respectively, as predicted in A. V. Turbiner and J. C. López Vieyra wile a saddle point in the potential curve appears for the first time at \(B\sim 80\) a.u. and \(B\sim 740\) a.u., respectively.

MSC:

81V55 Molecular physics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs

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References:

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