<p>Inelastic collisions are the dominant cause of energy loss in radiotherapy. In the energy range around the Bragg peak, single ionization (SI) and single-electron capture (SC) are the primary inelastic collisions that lead to energy loss. This study employs the classical trajectory Monte Carlo method to study the SI and SC processes of H<InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2024_1629_Article_IEq9.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>O molecules using He<InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2024_1629_Article_IEq10.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{2+}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>2</mn> <mo>+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> and C<InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2024_1629_Article_IEq11.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{6+}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>6</mn> <mo>+</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> projectiles in the energy range of 10 keV/u to 10 MeV/u. The total cross sections, single differential cross sections, impact parameter dependence of SI and SC, and fragmentation cross sections were investigated. Results illustrate that the cross section for SI is the highest when the projectile energy is close to the Bragg peak energy. When the projectile energy is below the Bragg peak energy, the ionized electrons in the forward direction dominate, and the removal of electrons can be associated with large impact parameters. As the projectile energy increases, the emission angle of the electrons gradually transitions from small angles (<InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2024_1629_Article_IEq12.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">\(0^{\circ} \sim 30^{\circ}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>0</mn> <mo>∘</mo> </msup> <mo>∼</mo> <msup> <mn>30</mn> <mo>∘</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>) to large angles (<InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2024_1629_Article_IEq13.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="78" /> </InlineMediaObject> <EquationSource Format="TEX">\(60^{\circ} \sim 120^{\circ}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>60</mn> <mo>∘</mo> </msup> <mo>∼</mo> <msup> <mn>120</mn> <mo>∘</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>), and the removal of electrons is associated with small impact parameters. The energy distributions of the ionized electron are similar when the projectile energy is equal to, below or above the Bragg peak energy. The fragmentation cross sections after SI and SC in the energy range around the Bragg peak were also estimated.</p>

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Investigations of inelastic cross sections of H\(_{2}\)O molecule by He\(^{2+}\) and C\(^{6+}\) projectiles with energy range around the Bragg peak

  • Guo-Zhuang Li,
  • Cheng-Ye Sun,
  • Rui Cheng,
  • Yan-Shi Zhang,
  • Liang-Wen Chen,
  • Sheng Zhang,
  • Xin-Xia Li,
  • Lei Yang

摘要

Inelastic collisions are the dominant cause of energy loss in radiotherapy. In the energy range around the Bragg peak, single ionization (SI) and single-electron capture (SC) are the primary inelastic collisions that lead to energy loss. This study employs the classical trajectory Monte Carlo method to study the SI and SC processes of H \(_{2}\) 2 O molecules using He \(^{2+}\) 2 + and C \(^{6+}\) 6 + projectiles in the energy range of 10 keV/u to 10 MeV/u. The total cross sections, single differential cross sections, impact parameter dependence of SI and SC, and fragmentation cross sections were investigated. Results illustrate that the cross section for SI is the highest when the projectile energy is close to the Bragg peak energy. When the projectile energy is below the Bragg peak energy, the ionized electrons in the forward direction dominate, and the removal of electrons can be associated with large impact parameters. As the projectile energy increases, the emission angle of the electrons gradually transitions from small angles ( \(0^{\circ} \sim 30^{\circ}\) 0 30 ) to large angles ( \(60^{\circ} \sim 120^{\circ}\) 60 120 ), and the removal of electrons is associated with small impact parameters. The energy distributions of the ionized electron are similar when the projectile energy is equal to, below or above the Bragg peak energy. The fragmentation cross sections after SI and SC in the energy range around the Bragg peak were also estimated.