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The classical impact theory of Gordon [1] is applied to calculate half-widths and shifts of spectral lines of the pure rotational band of 12C16O broadened by He. Two rotational transitions are examined: J=0->J=1 and J=1->J=2 in the wide temperature range from 2 to 600 K. Dynamical calculations were performed on the most accurate CO-He ab initio potential energy surfaces of Heijmenn et al. [2] developed into Legendre polynomial series up to lmax = 13. The calculation results are in good agreement with experimental data of Beaky et al. [3] with the exception of very low temperatures. It is shown that the origin of these discrepancies between theory and measurements is connected with too high contribution of elastic collisions into broadening and shift in the course of calculations. Some ideas in the spirit of the old Weisskopf theory [4] are tested to diminish this contribution. S. Ivanov and O. Buzykin received financial support from the Ministry of Science and Higher Education within the State assignment FSRC «Crystallography and Photonics» RAS and Russian Science Foundation (Project No.18-55-16006). References: 1. R.G. Gordon, J. Chem. Phys. 44, 3083-3089 (1966); ibid., 45, 1649-1655 (1966). 2. T.G.A. Heijmen, R. Moszynski, P.E.S. Wormer, A. van der Avoird, J. Chem. Phys. 107 9921-9928 (1997). 3. M.M. Beaky, T.M. Goyette, F.C. De Lucia, J. Chem. Phys. 105(10), 3994-4004 (1996). 4. R.G. Breene. The shift and shape of spectral lines. Pergamon Press. Oxford. London. New York. 1964.