Ch. 8 of Introduction to Radiological Physics and Radiation Dosimetry by Frank Attix does a good job of explaining stopping power and mass stopping power. The mass stopping power is dependent on properties of both the incident particle and the medium. The mass stopping power is directly proportional to the atomic number of the medium and the square of the charge of the incident particle, and inversely proportional to the atomic mass of the medium and the square of the beta value of the incident particle.
In high energy heavy ion collisions, we used some model, so that by using a relativistic transport model, we study the stopping power for the formation of super dense hadronic matter as well as the strength of transverse and radial flow in such collisions at ultra-relativistic energy..
S toping power is the energy lost by charged particle completely when it traversing ,in a medium per unit length.Which is dependent on the density of the medium,if the density is more loss of energy of the charge particle is more,if density is less lose of energy of the charged particle is less.So to make it as independent of density we are defining mass stopping power.It is nothing but stopping power /density of the medium.