Quadrupole transitions in the bound rotational-vibrational spectrum of the deuterium molecular ion

Abstract

After the study of the three body molecular system H${}_2^{+}$ ({\it J. Phys. B: At. Mol. Opt. Phys.} {\bf 45} 065101), its isotopomer, the deuterium molecular ion D${}_2^{+}$ is studied. The three-body Schrödinger equation is solved using the Lagrange-mesh method in perimetric coordinates. Energies and wave functions for four vibrational states $v=0-3$ and bound or quasibound states for total orbital momenta from 0 to 56 are calculated. The 1986 fundamental constant $m_d=3670.483014m_e$ is used. The obtained energies have an accuracy from about 13 digits for the lowest vibrational state to at least 9 digits for the third vibrational excited state. Quadrupole transition probabilities per time unit between those states over the whole rotational bands were calculated. Extensive results are presented with six significant figures.

19 pages, 5 figures

Cited by in corpus (4)

• Nuclear critical charge for two-electron ion in Lagrange mesh method
• Trapping and Ground-State Cooling of a Single H${}_2^{+}$
• Hyperfine structure and electric quadrupole transitions in the deuterium molecular ion
• Quantum control of a single ${\mathrm{H}}_2^{+}$ molecular ion