Exact analytical solution of the lateral spread of a particle beam in matter within a nonsmall angle limit

IKEGAMI, Seiji

doi:10.51094/jxiv.269

##article.authors##

IKEGAMI, Seiji Department of Theoretical Physics, Seiji IKEGAMI Resarch Laboratory

DOI:

https://doi.org/10.51094/jxiv.269

キーワード:

Lateral spread、 nonsmall angle limit、 Thomas-Fermi-Moliere Potential

抄録

This work is the construction of an analytical theory of lateral spread within a nonsmall angle limit of an ionic or atomic beam in a target medium. The exact angular distribution theory was developed by Goudsmit and Saunderson; however, exact lateral spread model has not been constructed. Recently, ion beam cancer therapy is widely studied. Thus, the author is motivated to make a lateral spread theory involving small to large scattering angles and including the energy loss effect. The present study is successfully performed using the Bessel function, and exact analytical and numerical results are given in this text. The present research is expected to be useful for particle beam cancer treatment.

利益相反に関する開示

Conflict of Interest My work is only personal study. I, therefore, have no conflict of interest on my investigation.

ダウンロード *前日までの集計結果を表示します

ダウンロード実績データは、公開の翌日以降に作成されます。

引用文献

S. Goudsmit and J. L. Saunderson. 1940. Multiple scattering of electrons. Phys. Rev., Vol. 57, p. 24. https://doi.org/10.1103/PhysRev.57.24

S. Goudsmit and J. L. Saunderson. 1940. Multiple scattering of electrons II. Phys. Rev., Vol. 58, p. 36. https://doi.org/10.1103/PhysRev.58.36

P. Sigmund and K. B. Winterbon. 1974. Small-angle multiple scattering of ions in the screened coulomb region: I. angular distributions. Nucl. Instr. and Meth., V ol. 119, p. 541. https://doi.org/10.1016/0029- 554X(74)90805-2

A. D. Marwick and P. Sigmund. 1975. Small-angle multiple scattering of ions in the screened coulomb region: 2. lateral spread. Nucl. Instr. and Meth., Vol. 126, p. 317. https://doi.org/10.1016/0029-554X(75)90693-X 5. K. Noda, T. Furukawa, T. Fujimoto, Y. Hara, T. Inaniwa, Y . Iwata, K. Katagiri, N. Kanematsu, K. Mizushima, S. Mori, and N. Saotome. 2017. Recent progress and future plans of heavy-ion cancer radiotherapy with HIMAC. Nucl. Instr. and Meth. B, Vol. 406, p. 374. https://doi.org/10.1016/j.nimb.2017.04.021 6. T. Furukawa, Y. Hara, K. Mizushima, N. Saotome, R. Tansho, Y. Saraya, T. Inaniwa, S. Mori, Y. Iwata, T. Shirai, and K. Noda. 2017. Development of NIRS pencil beam scanning system for carbon ion radiotherapy. Nucl. Instr . and Meth. B, V ol. 406, p. 361. https://doi.org/10.1016/j.nimb.2016.10.029

Y. Iwata, T. Fujimoto, S. Matsuba, T. Fujita, S. Sato, T. Furukawa, Y. Hara, K. Mizushima, Y. Saraya, R. Tansho, and N. Saotome. 2017. Recent progress of a superconducting rotating-gantry for carbon-ion radiotherapy Nucl. Instr. and Meth. B, Vol. 406, p. 338. https://doi.org/10.1016/j.nimb.2016.10.040

S. Ikegami. 2017. Extension and applications of switching model: range theory, multiple scattering model of Goudsmit–Saunderson, and lateral spread treatment of Marwick–Sigmund. Rad. Phys. Chem., Vol. 138, p. 37. https://doi.org/10.1016/j.radphyschem.2017.05.002

S. Ikegami. 2013. Angular and lateral distributions from small angle multiple scattering including elastic and inelastic energy loss effects based on the Valdes and Arista model. Nucl. Instr. and Meth B, Vol. 316, p. 222. https://doi.org/10.1016/j.nimb.2013.09.019

J. H. Liang. 1998. Theoretical formulation for calculating lateral spread of implanted ions. Nucl. Instr.

and Meth B, V ol. 134, p. 157. https://doi.org/10.1016/S0168-583X(98)80008-6

J. E. Valdés and N. R. Arista. 1994. Energy-loss effects in multiple-scattering angular distributions of ions in matter. Phys. Rev. A, Vol. 49, p. 2690. https://doi.org/10.1103/PhysRevA.49.2690

Lindhard, J., Vibeke Nielsen, and M. Scharff. 1968. Cross sections for ion-atom collisions in solids. K. Dan. Vidensk. Selsk. Mat. Fys. Medd., Vol. 36, p. 10.

Meyer, L. 1971. Plural and multiple scattering of low- energy heavy particles in solids. Phys. Stat. Sol. B, Vol. 44, p. 253. https://doi.org/10.1002/pssb.2220440127

Kaneko, T. 1990. Energy loss and straggling of low- velocity heavy atoms in matter. Phys. Rev. A, Vol. 41, p. 4889. https://doi.org/10.1103/PhysRevA.41.4889

G. Sidenius and N. Andersen, 1975. Multiple scattering of keV ions: lateral distributions in Xenon. Nucl. Instr. And Meth, Vol. 128 p. 271.