Pilón, Horacio Olivares \(\text{He}^{3+}_{2}\) and \(\text{HeH}^{2+}\) molecular ions in a strong magnetic field: The Lagrange-mesh approach. (English) Zbl 1260.81336 Phys. Lett., A 376, No. 19, 1608-1611 (2012). 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. Cited in 1 Document 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 Keywords:strong magnetic field; exotic molecular ions Software:JADAMILU PDFBibTeX XMLCite \textit{H. O. Pilón}, Phys. Lett., A 376, No. 19, 1608--1611 (2012; Zbl 1260.81336) Full Text: DOI arXiv References: [1] Turbiner, A. V.; López Vieyra, J. C., Int. J. Mod. Phys. A, 22, 1605 (2007) [2] Lai, D., Rev. Mod. Phys., 73, 629 (2001) [3] Turbiner, A. V.; López Vieyra, J. C., Phys. Rep., 424, 309 (2006) [4] Turbiner, A. V.; López Vieyra, J. C.; Guevara, N. L., Phys. Rev. A, 81, 042503 (2010) [5] Turbiner, A. V., A helium-hydrogenic molecular atmosphere of neutron star 1E1207.4-5209 (2005) [6] Olivares-Pilón, H.; Baye, D.; Turbiner, A. V.; López Vieyra, J. C., J. Phys. B, 43, 065702 (2010) [7] Baye, D.; Joos de ter Beerst, A.; Sparenberg, J.-M., J. Phys. B, 42, 225102 (2009) [8] Vincke, M.; Baye, D., J. Phys. B, 39, 2605 (2006) [9] Melezhik, V., Phys. Rev. A, 48, 4528 (1993) [10] Guan, X.; Li, B.; Taylor, K. T., J. Phys. B, 36, 3569 (2003) [11] Baye, D.; Heenen, P.-H., J. Phys. A, 19, 2041 (1986) [12] Baye, D.; Vincke, M.; Hesse, M., J. Phys. B, 41, 055005 (2008) [13] Bollhoefer, M.; Notay, Y., Comput. Phys. Commun., 177, 951 (2007) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.