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

TL;DR

This paper calculates the bound rotational-vibrational energy levels and electric quadrupole transition probabilities of the T$_2^+$ molecular ion using the Lagrange-mesh method, providing highly accurate data for multiple vibrational and rotational states.

Contribution

It presents the first detailed calculation of quadrupole transitions in T$_2^+$, extending previous work on isotopomers and including quasibound states with high precision.

Findings

Calculated energies for vibrational states v=0 to 3 and rotational states up to L=68.

Provided electric quadrupole transition probabilities across the entire rotational bands.

Presented high-accuracy ground state energies for various symmetric systems.

Abstract

The nonrelativistic energies of the homonuclear ion T$_2^+$ are calculated for the ground state using the Lagrange-mesh method as was done for the isotopomers H$_2^+$ and D$_2^+$ ({\it J. Phys. B: At. Mol. Opt. Phys.} {\bf 45} 065101 and {\it J. Phys. B: At. Mol. Opt. Phys.} {\bf 46} 245101). Energies and eigenfunctions are obtained up to four of the lowest bound vibrational states ($v=0,1,2,3$) which support 62, 61, 60 and 58 bound rotational states, respectively. Some quasibound sates are also presented until $L =$ 68. From the obtained wave functions, electric quadrupole transitions per time unit are calculated between those states over the whole rotational bands. Extensive results are presented with 6 significant digits. The ground state energy of the symmetric systems $^{\infty}$H$_2^+$, $^{\infty}$H$^-$, Ps$^{-}$, H$^-$, D$^-$, T$^-$, $\mu^+\mu^+e$ and $\mu^+e\,e$ is presented with high accuracy as a function of $\beta=m_3/(2m+m_3)$.