  We study Tan's contact, i.e. the coefficient of the high-momentum tails of
the momentum distribution at leading order, for an interacting one-dimensional
Bose gas subjected to a harmonic confinement. Using a strong-coupling
systematic expansion of the ground-state energy of the homogeneous system
stemming from the Bethe-Ansatz solution, together with the local-density
approximation, we obtain the strong-coupling expansion for Tan's contact of the
harmonically trapped gas. Also, we use a very accurate conjecture for the
ground-state energy of the homogeneous system to obtain an approximate
expression for Tan's contact for arbitrary interaction strength, thus
estimating the accuracy of the strong-coupling expansion. Our results are
relevant for ongoing experiments with ultracold atomic gases.

Quantum Gases