Step 1: Understanding the Concept
An action potential at the axon terminal depolarises the presynaptic membrane.
Step 2: Sequence of events
The voltage change opens voltage-gated \(\text{Ca}^{2+}\) channels and calcium ions enter the terminal.
The rise in \(\text{Ca}^{2+}\) makes the synaptic vesicles fuse with the membrane and release neurotransmitter by exocytosis.
Step 3: Why the other options fail
\(\text{K}^{+}\) outflow, \(\text{Na}^{+}\) inflow and the \(\text{Na}^{+}\)-\(\text{K}^{+}\) pump relate to the impulse itself, not to vesicle release.
Final Answer:
Release is due to opening of calcium channels by a change in voltage.
\[ \boxed{\text{(A) }\text{opening of }\text{Ca}^{++}\text{ channels due to change in voltage.}} \]