  The ground-state properties of one-dimensional electron-spin-polarized
hydrogen $^1$H, deuterium $^2$H, and tritium $^3$H are obtained by means of
quantum Monte Carlo methods. The equations of state of the three isotopes are
calculated for a wide range of linear densities. The pair correlation function
and the static structure factor are obtained and interpreted within the
framework of the Luttinger liquid theory. We report the density dependence of
the Luttinger parameter and use it to identify different physical regimes:
Bogoliubov Bose gas, super-Tonks-Girardeau gas, and quasi-crystal regimes for
bosons; repulsive, attractive Fermi gas, and quasi-crystal regimes for
fermions. We find that the tritium isotope is the one with the richest
behaviour. Our results show unambiguously the relevant role of the isotope mass
in the properties of this quantum system.
