Numerical study of magnetic Raman scattering spectra in ladder antiferromagnets - Exchange scatterings from the singlet ground state

The exchange-scattering spectra are reproduced by the numerical calculation for the finite Heisenberg ladder, in which two-legs with antiferromagnetic bond J(c) is connected by rungs with antiferromagnetic bond J(r). The nume rical calculation is made for the system of 12 x 2 sites by Lanczos method. The ratio of J(c)/J(r) is considered to be 0.6-1.0 in order to discuss the experimental work for ladders of Cu2+ ions in oxide compounds Sr14-xCaxCu2 4O47. In addition to the Raman edge about J(r) corresponding twice the sing let-triplet spin gap, the characteristic structure appears around 2 or 3 ti mes of J(r) i.e. 3 or 5 times the spin-gap. We concentrate our attention Oi l characteristic features of excited levels, transitions to which are Raman -active. In particular, the relationship between correlations for spins in those states and corresponding Raman intensities is discussed in the pictur e of triplet pairs excited from singlet dimers. By the perturbation theory, the essential dependence of those intensities on distances between triplet dimers is investigated.