High-precision measurements of \(\gamma\) -ray angular distributions and cross sections from neutron inelastic scattering are essential for both fundamental nuclear physics and nuclear technology applications. However, such measurements at white neutron sources are severely hampered by intense pulse pileup, particularly in the fast-neutron region. This work presents a comprehensive investigation of \((\textrm{n},\textrm{n}^{\prime }\gamma )\) reactions on \(^{56}\textrm{Fe}\) , \(^{48}\textrm{Ti}\) , and \(^{52}\textrm{Cr}\) at the CSNS Back-n beamline. A key innovation was the deployment of a high-performance LaBr \(_3\) (Ce) detector array coupled with an advanced pulse pileup recovery algorithm, which successfully reconstructs individual events at extreme counting rates up to \(6\times 10^7\) s \(^{-1}\) and resolves pulses separated by as little as 10 ns. This capability eliminated the need for traditional, model-dependent pileup-loss corrections and enabled the extraction of clean \(\gamma\) -ray spectra across the entire neutron energy range. We report the incident-energy-dependent Legendre coefficients ( \(a_2\) , \(a_4\) ) for five characteristic E2 transitions from 0.9 to 14 MeV. Furthermore, the absolute inelastic-scattering cross sections for the first excited 847-keV state in \(^{56}\textrm{Fe}\) and the first excited 1434-keV state in \(^{52}\textrm{Cr}\) were determined using a relative normalization method. Our results show excellent agreement with previous experimental data and provide an experimental benchmark for validating and constraining theoretical nuclear-reaction models.
