Simulation Klein-Nishina cross section using the Monte Carlo method

Eric Ehler
University of Minnesota-Twin Cities, Radiation Oncology
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Project is designed for students learning radiologic physics and radiation dosimetry in a Medical Physics graduate program. The project is designed to reinforce course concepts on the Compton Effect and associated Klein-Nishina cross section. The project is also designed to introduce students to Matlab for those that do not have experience. It will also serve to present ideas to be later used when presenting Monte Carlo simulation of radiation interactions at a later point in the course.

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Learning Goals

Using Matlab, this project is designed to assist the students to understand the relationships between all of the factors involved in the Compton effect. This project improves student learning because it takes some very long equations used to express radiation interaction cross section and encourages the student to think qualitatively about what the meaning and implications are for the expressions. This pushes the students to use critical thinking to understand how and why the cross sections vary with respect to different factors.

Context for Use

The education level for this exercise is medical physics graduate students taking a radiologic physics and radiation dosimetry course (although upper level undergraduate science and engineering majors can be included). The exercise is designed to extend over the first half of the semester as the concepts are presented in class. Students do not need extensive MATLAB experience but some computer programming experience is helpful as basic programming techniques are used such as nested for-loops. A Modern Physics course is a prerequisite for the course.

Description and Teaching Materials

The students utilize equations for Compton effect kinematics as well as differential Klein-Nishina cross sections to describe the probability of a Compton effect interaction under various conditions. All equations are given in the textbook and the first step of the project students are recreating a figure from the book to benchmark their Matlab script. The solutions to the project are covered during course discussion.
Project Assignment (Microsoft Word 2007 (.docx) 17kB Aug15 18)

Teaching Notes and Tips

Students with limited programming experience may need help with understanding basic concepts such as for-loops and use of Matlab functions. I provide office hours for those that need assistance. The project counts as one homework assignment which is about 3% of the total grade for the course


Assessment is largely based on whether the students can demonstrate qualitative and quantitative understanding of Compton effect interactions both in terms of kinematics and interaction cross section.

References and Resources

Required resource is the textbook, Introduction to Radiological Physics and Radiation Dosimetry by Frank Herbert Attix, Wiley-VCH Verlag GmbH & Co., 2004.