An object of the present disclosure is to provide a method for manufacturing a copolymer, wherein a crystal content and a vinyl bond content (or a glass transition temperature) of the copolymer can be controlled. Specifically, the present disclosure provides a method for manufacturing a copolymer, wherein the method comprises a process of copolymerizing ethylene with isoprene under the presence of a polymerization catalyst composition containing a half metallocene cation complex represented by following general formula (I) ##STR00001## (In formula (I), M represents a lanthanoid element, scandium or yttrium; Cp.sup.R represents substituted cyclopentadienyl, substituted indenyl or substituted fluorenyl; X represents hydrogen atom, halogen atom, alkoxy, thiolate, amide, silyl, or a C.sub.1-20 monovalent hydrocarbon group; L represents a neutral Lewis base; w represents an integer in the range of 0 to 3; and [B].sup. represents a non-coordinating anion), wherein Cp.sup.R in general formula (I) has at least two substituent groups.

Processes of polymerizing olefin monomers and catalyst systems. The catalyst systems include a non-hydrogen-generating post-metallocene procatalyst; a co-catalyst; and a hydrogenation procatalyst having the formula Cp.sub.2TiX.sub.nTiCp.sub.2 or Cp.sub.2TiX.sub.n, in which each Cp is cyclopentadienyl substituted with at least one (C.sub.1-C.sub.10)alkyl; each X is independently monoanionic or neutral, wherein each X is independently (C.sub.1-C.sub.40)hydrocarbon, (C.sub.1-C.sub.40)heterohydrocarbon, (C.sub.1-C.sub.40)hydrocarbyl, (C.sub.1-C.sub.40)heterohydrocarbyl, or a halogen atom; and n is 1 or 2.