Step 1: Understanding the Concept:
High density polyethylene (HDPE) is a linear polymer with little branching. It is made at low pressure (\(6\) to \(7\) atm) and \(333\) to \(343\) K.
Step 2: Catalyst:
The catalyst is the Ziegler-Natta catalyst, a mixture of triethylaluminium \(\text{Al(C}_2\text{H}_5)_3\) and titanium tetrachloride \(\text{TiCl}_4\).
Low density polyethylene (LDPE) is instead made at high pressure with free radical initiators such as peroxides.
Step 3: Other options:
Zinc chloride, nickel chloride and stannic chloride are not used with triethylaluminium for this process.
Final Answer:
The catalyst is triethylaluminium with titanium tetrachloride, option (A).
\[ \boxed{\text{Al(C}_2\text{H}_5)_3 + \text{TiCl}_4} \]