Density-dependent Energy Loss of Protons in Pb and Be Targets and Percent Mass-Stopping Power from Bethe-Bloch Formula and Bichsel-Sternheimer Data Within 1-12 MeV Energy Range: A Comparative Study Based on Bland-Altman Analysis.

Background: This comparative study calculated Bethe-Bloch results with Bichsel-Sternheimer values, employing the Bland-Altman analysis within 95% limit of agreement for the first time. The Bethe-Bloch formula was employed for the physical realization of the density-dependent energy loss of protons in lead (Pb) and beryllium (Be) targets in the energy range 1-12 MeV.

Methods: The mass-stopping power of protons for the given elements was calculated and the corresponding normalized difference and standard deviation was also calculated. The obtained theoretical results were compared with the Bichsel-Sternheimer values for the same targets within the same energy range of the projectile protons in terms of stopping-power percent difference.

Results: As a general trend, as the energy of proton increases the percent normalized difference decreases. For elements having a high atomic number like lead, the percent difference is large. This may mean that calculated values of percent difference for heavy elements like lead are not in agreement with experimental results.

Conclusion: The calculated mass-stopping power in view of the normalized percent difference is consistent with the Bichsel-Sternheimer results for the same projectile of higher energy in Pb and Be targets. However, results deviate from the Bichsel-Sternheimer results for high atomic number materials for the same projectile of lower energy. The difference may be attributed to the adjusted parameters in the Bethe-Bloch formula.