  Gamow-Teller (GT) strength distributions (B(GT)) in electron-capture (EC)
daughters stemming from the parent ground state are computed with the
shell-model in the full pf-shell space, with quasi-particle random-phase
approximation (QRPA) in the formalism of Krumlinde and M\"oller and with an
Approximate Method (AM) for assigning an effective B(GT). These are compared to
data available from decay and charge-exchange (CE) experiments across titanium
isotopes in the pf-shell from A=43 to A=62, the largest set available for any
chain of isotopes in the pf-shell. The present study is the first to examine
B(GT) and the associated EC rates across a particular chain of isotopes with
the purpose of examining rate sensitivities as neutron number increases. EC
rates are also computed for a wide variety of stellar electron densities and
temperatures providing concise estimates of the relative size of rate
sensitivities for particular astrophysical scenarios. This work underscores the
astrophysical motivation for CE experiments in inverse kinematics for nuclei
away from stability at the luminosities of future Radioactive Ion Beam
Facilities.
