  The magnetic radiation of the fully-condensed states of $^{23}$Na condensates
have been studied. A narrow characteristic spectral line with a wave length
proportional to N^(-2/5) (N is the number of particles) and with a probability
of transition proportional to N^(17/5) emitted (absorbed) by the condensate was
found. It implies that short wave radiation with a huge probability of
transition can be obtained if numerous atoms are trapped. A new technique
developed by the authors, namely, the analytical forms of the fractional
parentage coefficients, was used to calculate analytically the matrix elements
between the total spin-states.
