Residual spectral fluence or residual energy of isotropically distributed protons and ions traversing a spherical absorber

The current web calculator allows one to obtain the residual spectral fluence of isotropically distributed protons and ions traversing a spherical shield by exploiting the "SRIM Module.exe" included in SRIM 2013 code (SRIM Tutorials with an upper energy limit of 5 GeV/nucleon), i.e., the used electronic stopping power tables are those provided by SRIM code with a low energy limit of 1 eV. The probabilty distribution of path lenghts in the spherical absorber is obtained by means of a GEANT4 simulation.

EXAMPLE:
Copy and paste the data here to reproduce the following example.
Protons spectral fluence during ESA Juice mission moderated by 50 mils of Al (0.3429 [g cm^-2]):

Shield thickness t is set to 0.127 cm (50 mils), sphere radius R to 50 cm and the number of steps to 10. The distance from center is r= R-t. Spectral fluence data are calculated with JOREM Model implemented in SPENVIS assuming a 4 sr solid angle exposure.
Following is the corresponding probability density of traversed path:

NOTE:

The lower energy limit is 1 eV

The higher energy limit is 5 GeV/nucleon

The default traversed path is that for 50 mils of Al

The lower limit of traversed path is equivalent to about 5 μm of Si (1.16x10^-3 [g cm^-2]), e.g., 0.96 cm in Dry Air at sea level with density equal to 1.20484x10^-3 g/cm³ (as implemented in SRIM from ICRU-37 table 5.5).

Residual energies were obtained disregarding multiple scattering effect, i.e., directions of flight of emerging particles were unchaged with respect to those of impinging directions.

Target selection for the results obtained in the EXAMPLE section
Selection for Protons in Silicon:

Selection for Protons in GaAs:

Selection for Protons in Water Liquid: