It seemed useful in analyzing the results of scattering experiments to estimate the scattering due purely to the electrostatic force. To estimate the effect of multiple Coulomb scattering through a target, a FORTRAN program was written which uses the Rutherford differential cross section formula to calculate multiple Coulomb scattering of a proton beam through small angles.
The first tests of the program were done by comparing the theta distributions in the plane with a Gaussian distribution published in Physical Review. Several graphs were created and show the program to produce a Gaussian distribution similar to the one given in Physical Review, with bigger tails. Based on the assumptions taken in the Physical Review article and those made in creating the program, these tails are reasonable in a simulation based on the Rutherford scattering formula. See that graph here.
The end product of this program will be databases for targets of a particular composition and thickness which will allow the calculation of theta distributions in the plane for incident protons (and later, other particles, particularly muons). An example of the theta distributions obtained by the program for a 5 cm carbon target is shown below.
This graph shows theta distributions at several energies for a proton beam incident on a 5 cm Carbon target. The distributions were calculated by a program which uses the Rutherford differential cross section formula to calculate multiple Coulomb scattering at small angles.
Tests are being done to establish the validity of linear interpolations between different energies, which will be necessary for the database created to be useful. Results show that the distributions change most rapidly at low energies -- extra runs at lower energies will allow reasonable linear estimates between energies.
This page revised July 14, 1998, by Chase Boulware.