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Comparison of GEANT4 very low energy cross section models with experimental data in water
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10.1118/1.3476457
/content/aapm/journal/medphys/37/9/10.1118/1.3476457
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/37/9/10.1118/1.3476457

Figures

Image of FIG. 1.
FIG. 1.

Overview of the standard electromagnetic software design adopted by the process and model classes of the GEANT4-DNA extension, shown in the unified modeling language (Ref. 80). This design uses a single static entry point, the singleton G4LossTableManager class which has an abstract base class G4VEmProcess, from which all GEANT4-DNA process classes are derived. The G4VEmProcess class has an abstract base class G4VEmModel, from which all GEANT4-DNA model classes are derived.

Image of FIG. 2.
FIG. 2.

Elastic scattering total cross section for electron in liquid water plotted from 10 eV up to 10 keV as a function of electron incident energy. The two models available in GEANT4-DNA are shown on the figure [the Screened Rutherford model (plain curve) and the Champion model (long dashed curve)] compared to a collection of experimental data in gaseous water from Danjo and Nishimura (Ref. 23) (diamonds), Katase et al. (Ref. 24) (stars), Sueoka et al. (Ref. 29) (multiplication sign), Szmytkowski (Ref. 30) (open circles), Zecca et al. (Ref. 31) (asterisks), Saglam and Aktekin (Refs. 32 and 33) (crosses), Johnstone and Newell (Ref. 25) (squares), Shyn and Grafe (Ref. 26) (up triangles), and Cho et al. (Ref. 27) (down triangles). Experimental data are fully referenced in Champion et al. (Ref. 22) and in ICRU Report No. 77 (Ref. 28). The four ICRU Report No. 77 recommendations are also shown. They have been computed from the static-exchange approximation (P–DF–FM potential) or from the full optical-model potential (P–DF–FM–LDA–A) using either the IAA or the AA.

Image of FIG. 3.
FIG. 3.

Elastic scattering differential cross section for electrons in liquid water plotted for several incident energies (100 eV, 200 eV, 500 eV, and 1 keV) as a function of the scattering angle. The figure compares the two models available in GEANT4-DNA [the Screened Rutherford model (plain curve) and the Champion model (long dashed curve)] to a collection of experimental data in gaseous water from Hilgner et al. (Ref. 34) (solid circles), Danjo and Nishimura (Ref. 23) (open circles), Katase et al. (Ref. 24) (triangles), and Shyn and Grafe (Ref. 26) (asterisks). Scaling factors have been introduced for ease of clarity and are indicated in parentheses. Experimental data are fully referenced in Aouchiche et al. (Ref. 81) and in ICRU Report No. 77 (Ref. 28). Note that for the 100 eV case, the Screened Rutherford model values were scaled to the first experimental point by Katase et al. as only the relative values of the differential cross section which are obtained from the relative Brenner–Zaider formula are used in GEANT4-DNA. Above 200 eV, absolute differential cross section values are implemented in GEANT4-DNA. ICRU Report No. 77 (Ref. 28) recommendations are shown, they have been obtained from the IAA or from the AA, with the F–DF–FM–LDA–A atomic optical-model potentials using effective atomic polarizabilities.

Image of FIG. 4.
FIG. 4.

GEANT4-DNA total cross section for excitation by electrons in liquid water (so-called Born excitation model) plotted up to 1 keV as a function of the incident electron energy obtained with the model based on the work of Emfietzoglou and Nikjoo et al. (Ref. 37) (plain curve). Also shown are low energy experimental data in water vapor from Muñoz et al. (Ref. 35) (circles). An uncertainty bar of 40% has been assigned to the plotted values as suggested by their authors.

Image of FIG. 5.
FIG. 5.

Total cross section for ionization by electrons in liquid water plotted up to 10 keV as a function of electron incident energy obtained from GEANT4-DNA using the Born model (plain curve). Also shown is a collection of experimental data in water vapor from Schutten et al. (Ref. 39) (solid up triangles), Olivero et al. (Ref. 40) (diamonds), Bolorizadeh and Rudd (Ref. 41) (circles), Khare and Meath (Ref. 42) (crosses), Djurić et al. (Ref. 43) (down triangles), Rao et al. (Ref. 44) (stars), and Straub et al. (Ref. 45) (open triangles).

Image of FIG. 6.
FIG. 6.

GEANT4-DNA differential cross sections for ionization by electrons in liquid water (plain curves) obtained with the Born ionization model plotted for several incident electron energies (given in the labels) as a function of the emitted electron energy up to its maximum value. Scaling factors have been introduced for ease of clarity and are indicated in parentheses. Experimental data from Champion (Ref. 46) are shown for the water vapor molecule: Opal et al. (Ref. 48) (open circles), Vroom and Palmer (Ref. 49) (triangles), and Bolorizadeh and Rudd (Ref. 41) (solid circles).

Image of FIG. 7.
FIG. 7.

Comparison between the collision stopping power of electrons in liquid water computed from the GEANT4-DNA electron excitation and ionization models with several recommendations for liquid water. The dotted curve shows the excitation stopping power, the long dashed curve shows the ionization stopping power, and the plain curve shows the total stopping power . Recommendations are obtained from the ICRU Report No. 16 (Ref. 51) (its recommendations are identical to the ones of the Handbook of Radiation Chemistry (Ref. 52) (squares) and the ICRU Report No. 37 (Ref. 53) (circles), from the Handbook of Radiation Measurement and Protection (Ref. 54) (stars), and from the IAEA-TECDOC-0799 (Ref. 55) report (triangles).

Image of FIG. 8.
FIG. 8.

Total ionization cross section for protons in liquid water plotted up to 10 MeV as a function of proton incident energy obtained with the complementary ionization models available in GEANT4-DNA [Rudd model (below 500 keV) and Born model (above 500 keV, plain curve)]. The GEANT4-DNA cross sections are compared to experimental data extracted in water vapor as provided by Rudd et al. (Ref. 60): Low energy accelerator data (addition symbol), early Van de Graaff data (asterisks), late Van de Graaff data (triangles), early University of Nebraska-Lincoln data (squares), late University of Nebraska-Lincoln data (stars), tandem Van de Graaff data (open circles), and Rudd et al. data (solid circles). Bolorizadeh and Rudd (Ref. 61) data (diamonds) are also shown. Hydrogen total ionization cross section is also shown (Rudd model).

Image of FIG. 9.
FIG. 9.

GEANT4-DNA differential cross sections for ionization by protons in liquid water (plain curves) obtained from the Rudd (below 500 keV) and Born (above) ionization models and plotted for several incident proton energies (given in the labels) as a function of the emitted electron energy. Scaling factors have been introduced for clarity and are indicated in parentheses. Experimental data are shown for the water vapor molecule (Ref. 62): Toburen and Wilson (Ref. 63) (triangles at 500 keV and circles at 1.5 MeV) and Bolorizadeh and Rudd (Ref. 61) (squares at 100 keV and stars at 150 keV).

Image of FIG. 10.
FIG. 10.

Electron capture total cross section for proton and electron loss total cross section for hydrogen in liquid water plotted up to 10 MeV as a function of proton or hydrogen incident energy obtained with the models available in GEANT4-DNA [the Dingfelder charge increase model and the Dingfelder charge decrease model (plain curve)] compared to a collection of experimental data in water vapor provided by Chambers [cited by Lindsay et al. (Ref. 64), down triangles], Cable [cited by Koopman, (Ref. 65) diamonds], Toburen et al. (Ref. 66), (squares), Berkner et al. [referenced by Dingfelder et al. (Ref. 59), crosses], Coplan and Ogilvie (Ref. 67) (stars), Dagnac et al. (Ref. 68) (up triangles), and Lindsay et al. (Ref. 64) (circles).

Image of FIG. 11.
FIG. 11.

GEANT4-DNA stopping cross sections for proton and hydrogen in liquid water compared to the recommendations given by the Handbook of Radiation Measurement and Protection (Ref. 54) (stars), by the Handbook of Radiation Chemistry (Ref. 52) (diamond), and by the ICRU Report No. 49 (Ref. 70) (circles for the liquid phase and squares for the vapor phase). The total stopping cross section (solid curve) has been calculated from the sum of the proton ionization (short dashed curve), proton excitation (dotted curve), hydrogen ionization (dashed dotted curve), and charge change (long dashed curve) stopping cross sections.

Image of FIG. 12.
FIG. 12.

Excitation and ionization total cross sections for (plain curve), (dashed curve), and (dotted dashed curve) in liquid water plotted up to 10 MeV as a function of incident energy obtained with the excitation and ionization models available in GEANT4-DNA (named Miller and Green and Rudd, respectively). These models are compared to a collection of experimental data in gaseous water for ionization provided by Rudolph and Melton (Ref. 72) (stars for ), by Toburen et al. (Ref. 73) (squares for and triangles for ), and by Rudd et al. (Refs. 74 and 75) (diamonds for and circles for ). These experimental data are referenced in Dingfelder et al. (Ref. 71).

Image of FIG. 13.
FIG. 13.

GEANT4-DNA differential cross sections for ionization by (plain curve) and (dashed curve) in liquid water obtained with the Rudd ionization model and plotted for two incident particle energies (200 and 500 keV/u, refer to the labels) as a function of the emitted electron energy. A scaling factor of 10 has been applied to the 200 keV/u curves for clarity. Corresponding experimental data provided by Toburen et al. (Ref. 73) are shown for the water vapor molecule and are cited by Uehara and Nikjoo (Ref. 76) (circles for , squares for at 200 keV/u, diamonds for , and triangles for at 500 keV/u).

Image of FIG. 14.
FIG. 14.

Charge increase and charge decrease total cross sections for (plain curves), (long dashed curves), and (dotted dashed curves) in liquid water plotted up to 10 MeV as a function of incident particle energy obtained with the Dingfelder models available in GEANT4-DNA. The corresponding charge exchange is indicated in the labels (from initial charge state to final charge state). The model predictions are compared to a set of experimental data in gaseous water for charge increase or charge decrease provided by Rudd et al. (Refs. 74 and 75) (squares for and circles for ) and by Sataka et al. (Ref. 77) (triangles for and diamonds for ). Experimental data are referenced in Friedland et al. (Ref. 78).

Image of FIG. 15.
FIG. 15.

GEANT4-DNA stopping cross sections for helium and charge states in liquid water compared to the recommendations given by the by the ICRU Report No. 49 (Ref. 70) (circles for the liquid phase and squares for the vapor phase). The total stopping cross section (plain curve) has been calculated from the sum of the charge exchange (dotted-dotted-dotted dashed curve), (short dashed curve), (long dashed curve), and (dotted dashed curve) stopping cross sections.

Tables

Generic image for table
TABLE I.

List of GEANT4-DNA physics processes for liquid water and for all associated particles, which will be fully available in the 2010 release of the GEANT4 Monte Carlo toolkit. Process and model classes are indicated, as well as the applicability energy range of each model class. Low energy limits in bold give the energy threshold below which the incident particle is stopped and deposits its total energy to the liquid (for the other models, the incident particle with an incident energy below the low energy limit does not interact with the medium and is left unchanged). The type of model (analytical or based on interpolated data tables) is also listed.

Generic image for table
TABLE II.

Results of the statistical comparison of each of the two models (Screened Rutherford and Champion) for elastic scattering total cross section for electron in liquid water, available in the GEANT4-DNA extension against the listed references. Both the test statistics value (D) and the corresponding p-value (p) are shown for the entire energy range, for the lower energy range , and the higher energy range . Experimental data are fully referenced in Champion et al. (Ref. 22) and in the ICRU Report No. 77 (Ref. 28). Missing results are due to a lack of sufficient data points in the selected energy range to allow a statistical comparison.

Generic image for table
TABLE III.

Results of the statistical comparison of each of the two models (Screened Rutherford and Champion) of elastic scattering differential cross sections for electrons of several incident energies (100 eV, 200 eV, 500 eV, and 1 keV) against the listed references. Both the test statistics value (D) and the corresponding p-value (p) are shown. Experimental data are fully referenced in Aouchiche et al. (Ref. 81) and in the ICRU Report No. 77 (Ref. 28).

Generic image for table
TABLE IV.

Results of the statistical comparison between the GEANT4-DNA electron ionization total cross section model (Born ionization model) and experimental data for three energy ranges: From 11 eV up to 10 keV, from 11 up to 100 eV, and from 100 eV up to 10 keV. The experimental data from Rao et al. (Ref. 44) deviate significantly from the GEANT4-DNA model and are not taken into account in this analysis. Experimental data agree globally well with the GEANT4-DNA model.

Generic image for table
TABLE V.

Results of the statistical comparison of the differential cross section values (Born ionization model) for ionization by electrons of several incident energies (50 eV, 100 eV, 200 eV, 300 eV, 500 eV, 1 keV, 2 keV, 5 keV, and 10 keV) against the listed references. Both the test statistics value (D) and the corresponding p-value (p) are shown. Experimental data are fully referenced in Champion (Ref. 46). Results are presented for the entire emitted electron energy range and for entire emitted electron energy above 10 eV. The agreement between the GEANT4-DNA model and experimental data is better above 10 eV.

Generic image for table
TABLE VI.

Results of the statistical comparison for proton ionization total cross sections (Rudd ionization model below 500 keV and Born ionization model above) against the listed references. Both the test statistics value (D) and the corresponding p-value (p) are shown. Experimental data are fully referenced in Rudd et al. (Ref. 60) and Bolorizadeh and Rudd (Ref. 61). Some of them deviate significantly from the GEANT4-DNA model (Bolorizadeh and Rudd, early UNL, late UNL, and low energy accelerator).

Generic image for table
TABLE VII.

Results of the statistical comparison of proton ionization differential cross sections (Rudd ionization model below 500 keV and Born ionization model above) against the listed references. Both the test statistics value (D) and the corresponding p-value (p) are shown. Experimental data are fully referenced in Boudrioua et al. (Ref. 62) The analysis is performed on the whole emitted electron energy range and above 10 eV, where the agreement is significantly better. Note that the experimental resonance peak is not taken into account in this statistical analysis since it is not modeled by GEANT4-DNA.

Generic image for table
TABLE VIII.

Results of the statistical comparison for proton and hydrogen charge change total cross sections (Dingfelder charge increase and charge decrease models) against the listed references. Both the test statistics value (D) and the corresponding p-value (p) are shown. Experimental data are provided by Chambers [cited by Lindsay et al. (Ref. 64)], Cable [cited by Koopman (Ref. 65)], Toburen et al. (Ref. 66), Berkner et al. [referenced by Dingfelder et al. (Ref. 59)], Coplan and Ogilvie (Ref. 67), Dagnac et al. (Ref. 68), and Lindsay et al. (Ref. 64). Cable’s and Coplan and Ogilvie’s data are not taken into account in this analysis as they deviate significantly from the GEANT4-DNA proton charge decrease model.

Generic image for table
TABLE IX.

Results of the statistical comparison of and of GEANT4-DNA ionization differential cross section models (Rudd ionization model) against the listed references. Both the test statistics value (D) and the corresponding p-value (p) are shown. Experimental data are provided by Toburen et al. (Ref. 73) and they are cited by Uehara and Nikjoo (Ref. 76). The analysis is performed on the full emitted electron energy range for and and below 100 eV for . Experimental data agree better with GEANT4-DNA ionization differential cross section model below 100 eV.

Generic image for table
TABLE X.

Results of the statistical comparison for alpha charge change total cross section (Dingfelder charge increase and charge decrease models) against the listed references. Both the test statistics value (D) and the corresponding p-value (p) are shown. Experimental data are provided by Friedland et al. (Ref. 78). A general good agreement is observed, except for the Sataka et al. for the transition.

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/content/aapm/journal/medphys/37/9/10.1118/1.3476457
2010-08-17
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Comparison of GEANT4 very low energy cross section models with experimental data in water
http://aip.metastore.ingenta.com/content/aapm/journal/medphys/37/9/10.1118/1.3476457
10.1118/1.3476457
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