  We investigate the critical exponents $\eta_3(\alpha,M), \eta_1(\alpha,M)$
associated with the singularities in the longitudinal and transverse structure
factors of the one dimensional antiferromagnetic Heisenberg model with nearest
(J_1) and next to nearest (J_2) neighbour coupling of relative strength $\alpha
= {J_2}/{J_1}$ and an external field $B$ with magnetization $M(B)$.
