Quality distribution detection is regarded as a crucial basis for regulating the rare earth extraction process. The variation of the lanthanum (La), cerium (Ce), praseodymium (Pr), and neodymium (Nd) solution system during the saponified P507-kerosene extraction is significant, showing obvious nonlinear characteristics such as time-varying and strong coupling. Moreover, the solution system exhibits no apparent color change. Existing soft measurement methods based on machine vision and artificial neural networks have shown unsatisfactory application effects. To address these issues, a mechanistic modeling method was first employed to construct a mathematical model for the quantitative analysis of the four components. Subsequently, by measuring the characteristic gamma-ray intensity information of the natural radioactive isotope ¹³⁸ La@1.436 MeV (auxiliary variable), the mass distribution information of the four components (main variable) was predicted simultaneously. Finally, experiments were conducted based on a high-purity germanium detector. The results show that the minimum detectable mass concentration of La is 1.70 g/L. Compared with the experimental results, the relative errors of the predicted mass concentrations of La, Ce, Pr, and Nd are -3.11% ~ 4.23%,-5.81% ~ 3.74%, -8.16% ~ 6.68%, and -19.87% ~ 14.20%, respectively. The relative errors of the sensitivity prediction are 1.33%, 5.56%, -3.20%, and -0.41%, respectively. The proposed "gamma ray-soft measurement" method enables high-accuracy and high-sensitivity prediction of the four components La, Ce, Pr, and Nd. The detection process is not affected by changes in extraction system density, acidity, temperature, and other parameters, providing new technical references for rare earth extraction quality distribution detection.