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

Sensitivity of stellar electron-capture rates to parent neutron number: A case study on a continuous chain of twenty Vanadium isotopes