Martin & Doran (2023: 25):
For particulate structure this means bringing nuclearity into the picture and re-interpreting multivariate structures as orbital (with satellites related to a single nucleus) and univariate structures as serial (i.e. multi-nuclear). This additional variable (i.e. nuclearity) allows for the recognition of “heads” in both experiential and logical structures. The canonical “head” in an orbital structure is exemplified by the Thing in nominal groups, the Event in verbal groups or the configuration of Process and Medium in clause structure; the canonical “head” in serial structure is the α variable in hypotactic complexes – e.g. the primary tense choice in an English or Spanish verbal group (Martin et al. 2023) or the projecting clause in a reporting clause complex across languages.
The Process and the Medium together form the nucleus of an English clause; and this nucleus then determines the range of options that are available to the rest of the clause. Thus the nucleus ‘tear + cloth’ represents a small semantic field that may be realised as a clause either alone or in combination with other participant or circumstantial functions.
Importantly, for Halliday, the meaning of 'nucleus' is distinct from the meaning of 'head', which is why he uses the different terms. The nuclear model construes a cline from the most central to the most peripheral. Halliday & Matthiessen (2014: 348):
the nucleus of ‘Process + Medium’ has an inner ring of additional participants as well as an outer ring of circumstances surrounding it: see Figure 5-40.
The primary tense is that functioning as Head, shown as α.