Precision wavelength calibration for Radial Velocity measurements using Uranium lines between 3800-6900 \AA.

We present here the precise wavelength calibration of a high-resolution spectrum using Uranium lines in the wavelength range of 3809 - 6833 Afor precision radial velocity measurements for exoplanet detection or related astrophysical sciences. The spectrum is acquired using the PARAS spectrograph (R=67,000) attached to a 1.2 meter telescope at Mount Abu Observatory, India. We identify well-resolved 1540 U lines from a high-resolution spectrum of the UAr hollow cathode lamp (HCL) using PARAS spectrograph in the aforesaid wavelength range. We calculate the Ritz wavelength of U from its known energy levels and compare them with our observed central wavelengths. The comparisons do not show any significant offset in our line list on the absolute wavelength scale. The final U line list has an average measurement uncertainty of 0.28 mA. We included these lines to the PARAS data analysis framework to do the wavelength calibration and then calculate the multi-order radial velocity of PARAS spectra. The typical dispersion of residuals around the wavelength solution of a UAr spectrum, using U lines, is found to be 0.8 mA. We show our result in the precision radial velocity of an on-sky source (A RV standard star), and an off-sky source (A HCL) observed with PARAS along with UAr HCL. We measure the dispersion in absolute drift difference between two fibers (inter-fiber drift) for a span of 6.5 hours to be 88 cm s$^{-1}$, and the ${\sigma_{RV}}$ for a RV standard star, HD55575 for 450 days to be 3.2 m s$^{-1}$. Comparing these results with the previous ones measured using ThAr HCL shows that the ThAr HCL with about 99\% pure-Th, usually used for precise wavelength calibration, are replaceable with the UAr HCL in the visible-domain for PARAS like spectrograph (R $\leq$ 67,000) to achieve a radial velocity precision of 1-3 m s$^{-1}$.