  We study the magnetic excitation spectra of L-edge resonant inelastic x-ray
scattering (RIXS) from the spin singlet ground state in one-dimensional undoped
cuprates. Analyzing the transition amplitudes of the magnetic excitations in
the second-order dipole allowed process, we find that the magnetic excitations
are brought about not only on the core-hole site but also on the neighboring
sites. The RIXS spectra are expressed by the one-spin correlation function in
the scattering channel with changing polarization, and the two-spin correlation
function in the scattering channel without changing polarization. The latter
could not be brought about within the so-called UCL approximation. We calculate
these correlation functions on a finite-size ring. An application to the
possible RIXS spectra in Sr_2CuO_3 demonstrates that the contribution of the
two-spin correlation function could be larger than that of the one-spin
correlation function in the \sigma polarization for the momentum transfer
around the zone center.

Strongly Correlated Electrons