# Technical Note: On the proton range and nuclear interactions in compounds and mixtures

## Abstract

Purpose: Range and probability of nonelastic nuclear interactions (NNIs) for protons can be found only for a limited number of compounds and mixtures in nuclear data tables, and the proton-related analytical studies are therefore restricted to those materials for which the data are provided in these documents. In this paper, the authors present general solutions for calculating the proton range and probability of NNIs for desired compounds and mixtures. Methods: Benefiting from the Bragg–Kleeman approximation of mass stopping power, the authors derive a concise formula for calculating the proton range in materials with arbitrary number of constituent elements. Additionally, the authors propose another relation for obtaining the probability of undergoing NNIs which is suggested to be additive. Results: The examination of the formula presented shows that the authors’ method can be considered as general solutions for analytical evaluation of the range in compounds and mixtures. The formula proposed for probability of NNIs is valid for almost every compound except for those materials containing H. It is shown that this formula can be modified so that it covers these materials. Conclusions: The authors present a general analytical method for calculating the range and probability of NNIs for protons which are mathematicallymore »

- Authors:

- Department of Physics, K.N. Toosi University of Technology, P.O. Box 15875-4416, Tehran 15418-49611 (Iran, Islamic Republic of)
- ICT Radiotherapy Services, Livingston, New Jersey 07039 (United States)

- Publication Date:

- OSTI Identifier:
- 22413553

- Resource Type:
- Journal Article

- Journal Name:
- Medical Physics

- Additional Journal Information:
- Journal Volume: 42; Journal Issue: 5; Other Information: (c) 2015 American Association of Physicists in Medicine; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-2405

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; APPROXIMATIONS; INDIUM COMPOUNDS; MATERIALS; MATHEMATICAL SOLUTIONS; PARTICLE INTERACTIONS; PROTON BEAMS; PROTONS; STOPPING POWER

### Citation Formats

```
Rasouli, Fatemeh S., E-mail: rasouli@mail.kntu.ac.ir, Masoudi, S. Farhad, E-mail: masoudi@kntu.ac.ir, and Jette, David, E-mail: dave@jettes.org.
```*Technical Note: On the proton range and nuclear interactions in compounds and mixtures*. United States: N. p., 2015.
Web. doi:10.1118/1.4917479.

```
Rasouli, Fatemeh S., E-mail: rasouli@mail.kntu.ac.ir, Masoudi, S. Farhad, E-mail: masoudi@kntu.ac.ir, & Jette, David, E-mail: dave@jettes.org.
```*Technical Note: On the proton range and nuclear interactions in compounds and mixtures*. United States. doi:10.1118/1.4917479.

```
Rasouli, Fatemeh S., E-mail: rasouli@mail.kntu.ac.ir, Masoudi, S. Farhad, E-mail: masoudi@kntu.ac.ir, and Jette, David, E-mail: dave@jettes.org. Fri .
"Technical Note: On the proton range and nuclear interactions in compounds and mixtures". United States. doi:10.1118/1.4917479.
```

```
@article{osti_22413553,
```

title = {Technical Note: On the proton range and nuclear interactions in compounds and mixtures},

author = {Rasouli, Fatemeh S., E-mail: rasouli@mail.kntu.ac.ir and Masoudi, S. Farhad, E-mail: masoudi@kntu.ac.ir and Jette, David, E-mail: dave@jettes.org},

abstractNote = {Purpose: Range and probability of nonelastic nuclear interactions (NNIs) for protons can be found only for a limited number of compounds and mixtures in nuclear data tables, and the proton-related analytical studies are therefore restricted to those materials for which the data are provided in these documents. In this paper, the authors present general solutions for calculating the proton range and probability of NNIs for desired compounds and mixtures. Methods: Benefiting from the Bragg–Kleeman approximation of mass stopping power, the authors derive a concise formula for calculating the proton range in materials with arbitrary number of constituent elements. Additionally, the authors propose another relation for obtaining the probability of undergoing NNIs which is suggested to be additive. Results: The examination of the formula presented shows that the authors’ method can be considered as general solutions for analytical evaluation of the range in compounds and mixtures. The formula proposed for probability of NNIs is valid for almost every compound except for those materials containing H. It is shown that this formula can be modified so that it covers these materials. Conclusions: The authors present a general analytical method for calculating the range and probability of NNIs for protons which are mathematically easy to handle and valid for desired compounds or mixtures composed of an arbitrary number of constituent elements, including materials of interest for proton radiotherapy purposes.},

doi = {10.1118/1.4917479},

journal = {Medical Physics},

issn = {0094-2405},

number = 5,

volume = 42,

place = {United States},

year = {2015},

month = {5}

}