# Utilization of Random Walk MC Diagnostics for Calculations in the Glauber Model

## Grade Level at Time of Presentation

Senior

## Major

Physics

## Minor

Religious Study

## Institution

Western Kentucky University

## KY House District #

20

## KY Senate District #

32

## Faculty Advisor/ Mentor

Dr. Ivan Novikov

## Department

Department of Physics and Astronomy

## Abstract

The Random Walk MC algorithm returns a sequence of random numbers from a desired probability distribution by making random steps in an appropriate space. We are using obtained random numbers to calculate reaction and interaction cross sections for nuclei with A < 40 in the framework of the Glauber Model. Calculated cross sections are then compared to the experimental results to estimate parameters of the nuclear density distribution. It is clear that the accuracy of integration, and, hence, the accuracy of parameter estimation, depends on how well a finite random sequence converges to the desired distribution, i.e. on the efficiency of sampling. In the ideal case, the correlation between neighboring elements of the chain should be zero, and the power spectrum should be a constant. In the presented work, we demonstrate how variation in quality of the random number sequence affects results of the reaction cross section calculations.

Utilization of Random Walk MC Diagnostics for Calculations in the Glauber Model

The Random Walk MC algorithm returns a sequence of random numbers from a desired probability distribution by making random steps in an appropriate space. We are using obtained random numbers to calculate reaction and interaction cross sections for nuclei with A < 40 in the framework of the Glauber Model. Calculated cross sections are then compared to the experimental results to estimate parameters of the nuclear density distribution. It is clear that the accuracy of integration, and, hence, the accuracy of parameter estimation, depends on how well a finite random sequence converges to the desired distribution, i.e. on the efficiency of sampling. In the ideal case, the correlation between neighboring elements of the chain should be zero, and the power spectrum should be a constant. In the presented work, we demonstrate how variation in quality of the random number sequence affects results of the reaction cross section calculations.