Is there a less colloquial term for the phenomenon known as "brain zaps"?
Short answer
Brain zaps are a colloquial term for certain symptoms of antidepressant discontinuation syndrome. 

Background
'Brain zaps' are associated with sudden shakes, or vibrations, tremors, jolts, electric shocks, or 'zaps' of the head and/or brain. As SydneyMaples rightfully commented, these are scientifically recognized as symptoms of 


  Antidepressant discontinuation syndrome, or Antidepressant withdrawal syndrome


Withdrawal from a wide range of antidepressants, including the tricyclic antidepressants (TCAs), monoamine oxidase inhibitors (MAOIs) and selective serotonin reuptake inhibitors (SSRIs) can produce somatic and psychological distress, influenza-like syndromes, gastrointestinal adverse effects, arrhythmias, anxiety, sleep disturbances, movement disorders, mania or hypomania, panic attacks and delirium (Lejoyeux et al., 1996).

Reference
- Lejoyeux et al. CNS Drugs (1996); 5(4): 278–92