In the present work, we calculate the total reaction cross sections for the reactions of the following projectiles:
P, 12C, 14 N, 16O, 22Ne, 24Mg, 28Si, and 32S with emulsion nuclei, at incident energy ELab = 3.7 GeV/n, in the framework of
the modified Glauber models I and II (Gl-I and Gl-II approaches). At the same time the number of interacted nucleons
from these projectiles and the emulsion target nuclei beside the number of their binary collisions are calculated. Also the
multiplicity of the shower particles produced in these reactions are calculated. A comparison between the calculated values
of these total reaction cross sections and their multiplicities of the produced shower particles in these reactions, with the
corresponding measured values, had been done within both: Gl-I and Gl-II approaches and in accordance to the zero-range
considerations. As a result of this comparison we have not obtained an agreement between the calculated values and the
corresponding experimental data in case of the total reaction cross sections, but we have got, in general, a good agreement
for the comparison in the case of the particle multiplicities calculations. It should be noted, for the last comparison, that
the theoretical calculations in the framework of Gl-II approach give, in general, agreement with the corresponding experi-
mental data better than those we have obtained for the theoretical calculations in the framework of the Gl-I approach.