Free-Radical Polymerization of Ethylene Proceeds with the Following Propagation Steps

Essay

Free-radical polymerization of ethylene proceeds with the following propagation steps.
It turns out that polyethylene made by free-radical polymerization contains some branches, for example,
(a) Give a plausible mechanism, complete with "fishhooks," for propagation steps that can account for formation of these branches.
(b) It is possible (by a completely different method) to form polyethylene with unbranched chains. Which do you think would have higher density, branched-chain polyethylene or polyethylene with unbranched chains? Explain briefly.