  The astrophysically important electric quadrupole (E2) and magnetic dipole
(M1) transitions for the low-lying states of triply ionized titanium (Ti IV)
are calculated very accurately using a state-of-art all-order many-body theory
called Coupled Cluster (CC) theory in the relativistic frame-work. Different
many-body correlations of the CC theory has been estimated by studying the core
and valence electron excitations to the unoccupied states. The calculated
excitation energies of different states are in very good agreement with the
measurements. Also we compare our calculated electric dipole (E1) transition
amplitudes of few transitions with recent many-body calculations by different
groups. We have also carried out the calculations for the lifetimes of the
low-lying states of Ti IV. A long lifetime is found for the first excited
3d$^{2}D_{5/2}$ state, which suggested that Ti IV may be one of the useful
candidates for many important studies. Most of the results reported here are
not available in the literature, to the best of our knowledge.
