γ
-ray strength function for thallium isotopes relevant to the 
Pb205−Tl205
 chronometry
Photoneutron cross sections were measured for $^{203}\mathrm{Tl}$ and $^{205}\mathrm{Tl}$ at energies between the one- and two-neutron thresholds using quasimonochromatic $\ensuremath{\gamma}$-ray beams produced in laser Compton scattering at the NewSUBARU synchrotron radiation facility. Our measurement results in cross sections significantly different from the previously reported bremsstrahlung experiment, leading to rather different giant dipole resonance (GDR) parameters, in particular to lower GDR peak energies and higher peak cross sections. The photoneutron data are used to constrain the $\ensuremath{\gamma}$-ray strength function on the basis of the Hartree-Fock-Bogolyubov plus quasiparticle random-phase approximation using the Gogny D1M interaction. Supplementing the experimentally constrained $\ensuremath{\gamma}$-ray strength function with the zero-limit $E1$ and $M1$ contributions for the de-excitation mode, we estimate the Maxwellian-averaged cross section for the s-process branching-point nucleus $^{204}\mathrm{Tl}$ in the context of the $^{205}\mathrm{Pb}\ensuremath{-}^{205}\mathrm{Tl}$ chronometry.