The process and catalyst of this invention can be utilized to synthesize homo and copolymers of conjugated diene monomers and vinyl aromatic monomers having high trans contents of greater than 60% with low melting points. These homo and copolymers of conjugated diene monomers and vinyl aromatic monomers can be utilized in tire tread and sidewall rubbers that exhibit outstanding wear and tear characteristics in the tread and excellent flexing properties in the sidewall. The rubber polymers of this invention are made utilizing an improved catalyst system. This catalyst system is comprised of (a) organo aluminum compounds, (b) organo lithium compounds, (c) a barium compound selected from barium salts of (i) di(ethylene glycol) ethyl ether, (ii) di(ethylene glycol) propyl ether, (iii) di(ethylene glycol) hexyl ether, (iv) di(N,N-dimethyl amino glycol) ethyl ether, (v) menthol and thymol in the presence of polar modifier consisting of water, alcohols, amines, thiols, phosphates and phosphites. The trans polymers and copolymers of this invention made with the above catalyst system typically have a glass transition temperature ranging from -97.degree. C. to -40.degree. C., a melt temperature ranging from -30.degree. C. to +30.degree. C., and a number average molecular weight from 20,000 to 250,000. The inclusion of such polar modifiers in the barium catalyst system results in a high styrene content in copolymerization, a high trans content, and high molecular weight. Copolymers of conjugated diolefin monomers and vinyl aromatic monomers made with the catalyst system of this invention also have a tapered macrostructure.