The Hyades cluster is key for the study of rotational, activity, and chemical evolution of solar-like low-mass stars. Here we present quantitative surface-activity information for a sequence of 21 Hyades dwarf stars with effective temperatures 6160K to 3780K (all cooler than the red edge of the Li dip), rotation periods 5d to 16d and normalized Rossby numbers (Ro_n_) between 0.14 to 0.54 with respect to the Sun (Ro(Sun)=1). High-resolution Stokes-V spectra and least-squares deconvolution of thousands of spectral lines per spectrum are employed for measuring longitudinal surface magnetic field. From Stokes-I spectra we obtain velocities, lithium abundances, metallicity, and chromospheric CaII infrared-triplet (IRT) fluxes. The average metallicity, +0.186+/-0.045 (rms), for our stars with Teff>=4200K is in good agreement with the metallicity in the recent literature. Lithium abundances A(Li) range from 95-times solar (A(Li)~+3.0) on the warm end of the sample to 1/25 solar (A(Li)~-0.4) on the cool end. We confirm the tight relation of A(Li) with Teff and extend it to K-M stars with even smaller Li abundances than previously measurable. A formal relation with rotational period and velocity in the sense higher Li abundance for faster rotators is present. Targets rotating faster than vsini of 6km/s (Prot~8d) appear Li saturated at A(Li)~3.0dex. CaII IRT fluxes for our sample indicate (logarithmic) chromospheric radiative losses R_IRT_ in the range -4.0 to -4.9 in units of the bolometric flux. These radiative losses also show a relation with Teff, Prot, and vsini, but opposite to A(Li) in an inverse sense with higher radiative losses for the slower=cooler rotators. Longitudinal magnetic-field strengths were measured in the range zero to -100G and +150G with phase-averaged, disk-integrated, unsigned values of 15.4+/-3.6(rms) G for targets warmer than ~5000K and 91+/-61(rms)G for targets cooler than this. These unsigned field strengths relate to Prot , vsini, and Ro_n_, but in a dual-slope fashion. The short-period bonafide single M-target RSP 348 was found to be a double-lined spectroscopic binary of dM3e+dM5e classification. We conclude that the Rossby-number dependencies of the surface activity tracers A(Li), R'IRT , and on our Hyades dwarf sequence primarily originate from convective motions, expressed by its turnover time, and only to a smaller and sometimes inverse extent from surface rotation and its related extra mixing.
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