Nuclear energy levels are characterized in part by their isospin quant
um numbers. Ordinary nuclides are well described by an independent-par
ticle model with ground-state isospins equal to the minimum possible v
alue T-min = abs(A/2 - Z). It has been suggested that extremely neutro
n rich nuclei constitute a second branch of the table of isotopes whos
e ground states have the maximum possible isospin T-max = A/2 and that
neutral members of the T-max branch (i.e., polyneutrons) serve as med
iating particles for the new class of nuclear reactions discovered by
Fleischmann and Pons. The energetics of the new reactions have been qu
alitatively described by a liquid-drop model. Recent measurements of t
he mass spectrum of reaction products produced in the new reactions ma
ke possible a refinement of the model, providing an explanation for ga
ps of instability separating ranges of stability in the mass spectrum.