Polarizabilities and Other Properties of the td Muons Molecular Ion

Wavefunctions of Hylleraas type were used earlier to calculate energy levels of muonic systems. Recently, we found in the case of the molecular ions H2+, D2+ and HD+ that it was necessary to include high powers of the internuclear distance in the Hylleraas functions to localize the nuclear motion when treating the ions as three-body systems without invoking the Born-Oppenheimer approximation. We try the same approach in a muonic system, td(mu-). Improved convergence is obtained for J = 0 and 1 states for shorter expansions when we use this type of generalized Hylleraas function, but as the expansion length increases the high powers are no longer useful. We obtain good energy values for the two lowest J = 0 and J = 1 states and compare them with the best earlier calculations. Expectation values are obtained for various operators, the Fermi contact parameters, and the permanent quadrupole moment. The cusp conditions are also calculated. The polarizability of the ground state is then calculated using second-order perturbation theory with intermediate J = 1 pseudostates. It should be possible to measure the polarizability by observing Rydberg states of atoms with td(mu-) acting as the nucleus.