Neutron capture cross sections and solar abundances of ${}_{}{}^{160,161}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{170,171}{}_{}{}^{}\mathrm{Yb}$, ${}_{}{}^{175,176}{}_{}{}^{}\mathrm{Lu}$, and ${}_{}{}^{176,177}{}_{}{}^{}\mathrm{Hf}$ for the $s$-process analysis of the radionuclide ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$

The neutron capture cross sections and solar abundances of ${}_{}{}^{160,161}{}_{}{}^{}\mathrm{Dy}$, ${}_{}{}^{170,171}{}_{}{}^{}\mathrm{Yb}$, ${}_{}{}^{175,176}{}_{}{}^{}\mathrm{Lu}$, and ${}_{}{}^{176,177}{}_{}{}^{}\mathrm{Hf}$ have been measured. With this data base $s$-process studies have been carried out to determine the $s$-process neutron density and temperature and to investigate the $s$-process nucleosynthesis of the ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$ clock. From various branchings the neutron density was found to be (0.8-1.8)×${10}^8$ neutrons per ${\mathrm{cm}}^3$ and the temperature $\mathrm{kT}$ to be 18—28 keV. On the basis of the present data, ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$ proved not to be applicable as a cosmic clock because of the temperature sensitivity of the ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$ half-life but can be used instead as a stellar thermometer. Constraints for the $s$-process temperature ($kT=20-28\mathrm{}$ keV) were found to be in good agreement with the investigated branchings.