[en] The mathematical model of Cherenkov counter pulse-height spectrum for primary nuclei and their fragments has been developed. It takes into account the counter properties and nuclei interaction with radiator matter. The model has been used for data analysis at the experiment with 4 A GeV/c momentum ¹⁹F beam and provided 1% accuracy of charge-changing cross-sections for various nucleus-targets. The similarity of small charge fragments peak to lognormal distribution leads to possibility of existence of primary nucleus cold breakup for large charge-change interactions. 8 refs.; 2 figs.; 1 tab