New laser-based measurements of the isotope shift between hydrogen and deuterium by Haensch [ital et] [ital al]. should determine accurately the deuteron matter radius [ital r][sub [ital m]]. We study the contribution of the deuteron polarizability energy shifts to the isotopic difference and show that this is known in a model independent way. We also make accurate determinations of the asymptotic normalization and the electric dipole polarizability by exploiting empirical linear relations between them and [ital r][sub [ital m]][sup 2].