Method for manufacturing copolymer

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)
• (In formula (I), M represents a lanthanoid element, scandium or yttrium;
• CpR′ represents substituted cyclopentadienyl, substituted indenyl or substituted fluorenyl;
• X represents hydrogen atom, halogen atom, alkoxy, thiolate, amide, silyl, or a C1-20 monovalent hydrocarbon group;
• L represents a neutral Lewis base;
• w represents an integer in the range of 0 to 3;
• [B]− represents a non-coordinating anion), and
• CpR′ in general formula (I) has at least two substituent groups;
• and
• a process of controllably setting a crystal content, a vinyl bond content or the glass transition temperature, of a copolymer to be manufactured, at desired values by selecting type of at least one of the core metal M and the ligand CpR′,
• wherein the vinyl bond content is the sum of a content of 1,2-bonding unit and a content of 3,4-bonding unit of isoprene, and
• the copolymer thus manufactured has the vinyl bond content in the range of 20 mass % to 50 mass % and the crystal content in the range of 10% to 50%.