  We give new proofs of the rationality of the N=1 superconformal minimal model
vertex operator superalgebras and of the classification of their modules in
both the Neveu-Schwarz and Ramond sectors. For this, we combine the standard
free field realisation with the theory of Jack symmetric functions. A key role
is played by Jack symmetric polynomials with a certain negative parameter that
are labelled by admissible partitions. These polynomials are shown to describe
free fermion correlators, suitably dressed by a symmetrising factor. The
classification proofs concentrate on explicitly identifying Zhu's algebra and
its twisted analogue. Interestingly, these identifications do not use an
explicit expression for the non-trivial vacuum singular vector. While the
latter is known to be expressible in terms of an Uglov symmetric polynomial or
a linear combination of Jack superpolynomials, it turns out that standard Jack
polynomials (and functions) suffice to prove the classification.
