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With the complete potential energy curve and dipole moment function at all internuclear distances R, the calculation of dipole moment matrix elements is possible for any vibration-rotation transition desired. we use an improved potential energy curve for the $X1\sum +$ state of HF. It is based on the spectroscopically-determined potential of Coxon and $Hajigeorgiou1$ plus the proper long-range behavior determined by including both dispersion and exchange $effects.2$ The dipole moment function of this work is obtained from CASSCF/MRCI calculations for all R. We report dipole moment absorption matrix elements and Einstein A spontaneous emission coefficients for the vibration rotation bands within the $X1\sum +$ state of HF for all v - 0 - 19 observed levels and the v - 20 unobserved level. $^{1} $ J. A. Coxon and P. G. Hajigeorgiou, J. Mol. Spectrosc. 142, 254 (1990). $\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ W. T. Zemke, W. C. Stwalley, J. A. Coxon and P. G. Hajigeorgiou, Chem. Phys. Lett. 177, 412 (1991).""