Polarizabilities and other properties of the td mu molecular ion

Wave functions of the Hylleraas type were used earlier to calculate energy levels of muonic systems. Recently, we found in the case of the molecular i ons H-2(+), D-2(+), and HD+ that it was necessary to include high powers of the internuclear distance in the Hylleraas functions to localize the nucle ar motion when treating the ions as three-body systems without invoking the Born-Oppenheimer approximation. We tried the same approach in a muonic sys tem, td mu (-) (triton, deuteron, and muon). Improved convergence was obtai ned for J = 0 and 1 states for shorter expansions when we used this type of generalized Hylleraas function, but as the expansion length increased the high powers were no longer useful. We obtained good energy values for the t wo lowest J = 0 and 1 states and compared them with the best earlier calcul ations. Expectation values were obtained for various operators, the Fermi c ontact parameters, and the permanent quadrupole moment. The cusp conditions were also calculated. The polarizability of the ground state was then calc ulated using second-order perturbation theory with intermediate J = 1 pseud ostates. (It should be possible to measure the polarizability by observing Rydberg states of atoms with td mu (-) acting as the nucleus.) In addition, the initial sticking probability (an essential quantity in the analysis of muon catalyzed fusion) was calculated and compared with earlier results.