f-wave pairing of parallel spins near the transition temperature

A partial solution is found to the problem of minimizing the general fourth-order Ginzburg-Landau free energy for triplet $f$-wave pairing in which only a single spin population is paired. The weak-coupling BCS free energy is found to lie in the interior of a region of the space of fourth-order parameters throughout which the solution of lowest free energy gives no Leggett NMR shift, in contrast to observed behavior in the $A_1$ phase of superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. The solutions in the regions of parameter space that border on the weak-coupling region are also examined.