Process for making alpha-olefin polymers or copolymers with high isotacticity index

A composition containing titanium chloride, for use in a catalyst to polymerize alpha-olefins, comprising a titanium chloride selected from the group consisting of titanium tetrachloride and titanium trichloride, and an additive consisting of a cyclic polyether of the crown ether type, in which the molecule is made up of from 0 to 20 p groups of the formula --X--C.sub.n H.sub.2n -- and from 0 to 4 q groups of the formula --X--R--, with the number of p groups and q groups together being from 3 to 24, arranged in any order to form a cycle in which any two adjacent groups in the cycle are connected by a bond between the element X in one of these adjacent groups and a carbon atom in the other group, where n is an integer from 1 to 6, R, which may be the same or different from one group to the other, represents divalent radicals, selected from the group consisting of divalent radicals of aliphatic hydrocarbons containing 1 to 6 carbon atoms, divalent radicals of cycloaliphatic hydrocarbons containing 4 to 10 carbon atoms, divalent radicals of aromatic hydrocarbons containing 6 to 20 carbon atoms, and the divalent heterocyclic radicals of furane, thiophene and pyridine, in which both free valences are each borne by a carbon atom in the alpha position in relation to the heteroatom of these heterocycles, or by a carbon atom of an aliphatic hydrocarbon chain containing 1 to 6 carbon atoms fixed to the said carbon atom in the alpha position, X is either identical in all the groups and represents oxygen atoms, or may be different from one group to the other and represents partly oxygen atoms and partly sulphur atoms, nitrogen-containing radicals of the formula >N--R.sub.1, or both, where R.sub.1 is a hydrogen atom or alkyl radical containing 1 to 4 carbon atoms, and the number of oxygen atoms r, sulphur atoms s and nitro radicals t in the cyclic polyether molecule are such that 0.ltoreq.t.ltoreq.r, 0.ltoreq.s.ltoreq. (r+t) and 1.ltoreq.r.ltoreq.28.