Low energy theorems are derived for the coefficients of the effective range
expansion in s-wave nucleon-nucleon scattering valid to leading order in an
expansion in which both mΟβ and 1/a (where a is the scattering length)
are treated as small mass scales. Comparisons with phase shift data, however,
reveal a pattern of gross violations of the theorems for all coefficients in
both the 1S0β and 3S1β channels. Analogous theorems are developed for the
energy dependence Ο΅ parameter which describes 3S1ββ3D1β mixing.
These theorems are also violated. These failures strongly suggest that the
physical value of mΟβ is too large for the chiral expansion to be valid in
this context. Comparisons of mΟβ with phenomenological scales known to
arise in the two-nucleon problem support this conjecture.Comment: 12 pages, 1 figure, 1 table; appendix added to discuss behavior in
chiral limit; minor revisions including revised figure reference to recent
work adde