Extension of the Liège intranuclear-cascade model to reactions induced by light nuclei

The purpose of this paper is twofold. First, we present the extension of the Liège intranuclear-cascade model to reactions induced by light ions. We describe here the ideas upon which we built our treatment of nucleus-nucleus reactions and we compare the model predictions against a vast set of heterogeneous experimental data. In spite of the discussed limitations of the intranuclear-cascade scheme, we find that our model yields valid predictions for a number of observables and positions itself as one of the most attractive alternatives available to geant4 users for the simulation of light-ion-induced reactions. Second, we describe the c++ version of the code, which is physicswise equivalent to the legacy version, is available in geant4, and will serve as the basis for all future development of the model.

Figure 1

Distributions of the dynamical pseudopotential used in the preparation of different light projectiles. Mean values and standard deviations are $(8\pm 18)$ MeV for deuteron, $(25\pm 10)$ MeV for triton, $(29\pm 9)$ MeV for ${}^4\mathrm{He}$, and $(30\pm 5)$ MeV for ${}^{12}\mathrm{C}$.

Figure 2

Distribution of the total relativistic nucleon energy in the laboratory frame $e_i$ minus the nominal kinetic energy per nucleon of the projectile for a ${}^{12}\mathrm{C}$ nucleus at $1A$ GeV (black line) or $10A$ MeV (red line).

Figure 3

Double-differential cross section for ${\pi }^{+}$ production from the 730-MeV $p+\text{Cu}$ reaction. Red (black) lines represent the incl++ (incl4.6) result. Data taken from Ref. [41].

Figure 4

Double-differential cross section for neutron production from the 800-MeV $p+\text{Pb}$ reaction. The different model calculations are described in the text (G4EH in the plot legend stands for g4excitationhandler). Data taken from Refs. [42, 43].

Figure 5

Fragmentation cross sections for the $1A$ GeV ${}^{208}\mathrm{Pb}+{}^1\mathrm{H}$ reaction, as a function of the fragment mass number. The different model calculations are described in the text (G4EH in the plot legend stands for g4excitationhandler). Data taken from Refs. [44, 45].

Figure 6

Excitation function for the ${\pi }^{+}+{}^{209}\text{Bi}$ reaction cross section, calculated with incl++ (red line), incl4.6 (black line), and geant4's semiempirical reaction-cross-section model (blue line). Experimental data taken from Ref. [46].

Figure 7

Same as Fig. 6, for ${\pi }^{-}+{}^{12}\mathrm{C}$. Experimental data taken from Refs. [46, 47, 48, 49].

Figure 8

Double-differential cross section for proton emission in 220-MeV ${\pi }^{+}+{}^{12}\mathrm{C}$, calculated with incl++ (red line) and incl4.6 (black line). Experimental data taken from Refs. [50].

Figure 9

Double-differential cross section for neutron emission in 870-MeV ${\pi }^{-}+{}^{208}\mathrm{Pb}$, calculated with incl++ (red line) and incl4.6 (black line). Experimental data taken from Refs. [51].

Figure 10

Excitation function for the $d+{}^{56}\text{Fe}$ reaction cross section, calculated with two versions of incl++ (red and green lines), incl4.6 (black line), and geant4's Glauber-Gribov semiempirical reaction-cross-section model (blue line). Experimental data refer to ${}^{56–58}\text{Fe}$ and ${}^{58–60}\text{Ni}$ targets and are taken from Refs. [53, 54, 55, 56].

Figure 11

Excitation function for the ${}^4\mathrm{He}+{}^{208}\mathrm{Pb}/{}^{209}\mathrm{Bi}$ reaction cross section, calculated with two versions of incl++ (red and green lines), incl4.6 (black line), and geant4's Glauber-Gribov semiempirical reaction-cross-section model (blue line). Experimental data refer to ${}^{208}\mathrm{Pb}$ and ${}^{209}\mathrm{Bi}$ targets and are taken from Refs. [57, 58, 59].

Figure 12

Excitation functions for ${}^{209}\mathrm{Bi}{(}^3\text{He},xn)$ cross sections. Different colors refer to different values of $x$, while the line styles denote calculations performed with incl4.6 (solid lines), incl++ v5.1.14 (dashed lines), and incl++ v5.1.14 with the ${}^3\mathrm{He}$ Coulomb radius as in incl4.6 (dotted lines). Data taken from Refs. [60, 61, 62].

Figure 13

Excitation function for the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ reaction cross section, calculated with incl++ v5.1.9 (green line), incl++ v5.1.14 (solid red line), incl++ v5.1.14 with Pauli blocking and a hard Fermi sphere in the projectile (dashed red line), and geant4's Glauber-Gribov semiempirical reaction-cross-section model (blue line). Experimental data taken from Refs. [70, 71, 72, 73, 74, 75].

Figure 14

Double-differential cross sections for neutron production at (a) $5^{\circ }$, (b) ${10}^{\circ }$, (c) ${20}^{\circ }$, (d) ${30}^{\circ }$, (e) ${40}^{\circ }$, (f) ${60}^{\circ }$, and (g) ${80}^{\circ }$, from a $290A$ MeV ${}^{12}\mathrm{C}+\text{C}$ reaction. The incl++ calculations are presented in accurate-target (black lines) and accurate-projectile (solid red lines) modes, coupled with the g4excitationhandler deexcitation model. We also show an accurate-projectile calculation with ablav3 (dashed red lines) and a calculation with a modified value of the Fermi momentum (green lines; see text). Experimental data are taken from Ref. [76].

Figure 15

Double-differential cross sections for neutron production at (a) $4^{\circ }$, (b) $9^{\circ }$, (c) ${20}^{\circ }$, (d) ${30}^{\circ }$, (e) ${40}^{\circ }$, (f) ${60}^{\circ }$, and (g) ${80}^{\circ }$, from a $230A$ MeV ${}^4\mathrm{He}+\text{Cu}$ reaction. The incl++ calculations are presented in accurate-target mode (solid black lines), coupled with the g4excitationhandler deexcitation model. We also show a calculation with ablav3 (dashed black lines) and a calculation with a modified value of the Fermi momentum (green lines; see text). Experimental data are taken from Ref. [78].

Figure 16

Same as Fig. 14 for incl++ (accurate-projectile mode, red lines), geant4's qmd model (blue lines), and bic model (green lines). All models are coupled to g4excitationhandler.

Figure 17

Same as Fig. 15 for incl++ (accurate-projectile mode, red lines), geant4's qmd model (blue lines), bic (green lines), and bertini+precompound (cyan lines) models. All models except bertini+precompound are coupled to g4excitationhandler.

Figure 18

Angle-differential cross section for the production of (a) protons, (b) ${}^4\mathrm{He}$, (c) ${}^7\mathrm{Li}$, and (d) ${}^{11}\mathrm{C}$ from the $95A$ MeV ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ reaction. Calculations with incl++ (accurate-projectile mode, solid red lines; accurate-target mode, dashed red lines; randomly symmetrized, cyan lines), qmd (blue lines), and bic (green lines) are shown. Experimental data are taken from Ref. [79].

Figure 19

Double-differential cross sections for the production of protons at (a) $4^{\circ }$, (b) ${13}^{\circ }$, (c) ${21}^{\circ }$, (d) ${29}^{\circ }$, and (e) ${43}^{\circ }$, from the $95A$ MeV ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ reaction. Calculations with incl++ (accurate-projectile mode, solid red lines; accurate-target mode, dashed red lines), qmd (blue lines), and bic (green lines) are shown. Experimental data are taken from Ref. [79].

Figure 20

Same as Fig. 19, for ${}^4\mathrm{He}$ ejectiles.

Figure 21

Same as Fig. 19, for ${}^7\mathrm{Li}$ ejectiles.

Figure 22

Same as Fig. 19, for ${}^{11}\mathrm{C}$ ejectiles.

Figure 23

Rapidity spectra of (a) protons, (b) ${}^4\mathrm{He}$, (c) ${}^7\mathrm{Li}$, and (d) ${}^{11}\mathrm{C}$ fragments produced in $100A$ MeV ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$, as calculated by incl++/g4excitationhandler in accurate-target mode. The vertical dotted lines denote the central rapidity.

Figure 24

Same as Fig. 23, for $400A$ MeV ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$.

Figure 25

Fragmentation cross sections for the $1A$ GeV ${}^{208}\mathrm{Pb}+{}^2\mathrm{H}$ reaction, as a function of the fragment mass number. Model calculations are compared to the data taken from Refs. [45, 88]. In the plot legend, G4EH stands for g4excitationhandler.

Figure 26

Isotopic distributions from the fission region $\left(32\le Z\le 39\right)$ for the $1A$ GeV ${}^{208}\mathrm{Pb}+{}^2\mathrm{H}$ reaction. Model calculations are compared to the data taken from Ref. [88]. In the plot legend, G4EH stands for g4excitationhandler.

Figure 27

Same as Fig. 26, for isotopic distributions from the spallation region $\left(68\le Z\le 75\right)$.

Figure 28

Fragmentation cross sections for the $500A$ MeV ${}^{86}\mathrm{Kr}+{}^9\mathrm{Be}$ reaction, as a function of the fragment mass number. Model calculations are compared to the data taken from Refs. [91]. In the plot legend, G4EH stands for g4excitationhandler.

Figure 29

Isotopic distributions $\left(24\le Z\le 31\right)$ for the $500A$ MeV ${}^{86}\mathrm{Kr}+{}^9\mathrm{Be}$ reaction. Model calculations are compared to the data taken from Ref. [91]. In the plot legend, G4EH stands for g4excitationhandler.

Figure 30

Fragmentation cross sections for the $140A$ MeV ${}^{58}\mathrm{Ni}+{}^9\mathrm{Be}$ reaction, as a function of the fragment mass number. Model calculations are compared to the data taken from Refs. [92, 93]. In the plot legend, G4EH stands for g4excitationhandler.

Figure 31

Isotopic distributions $\left(21\le Z\le 28\right)$ for the $140A$ MeV ${}^{58}\mathrm{Ni}+{}^9\mathrm{Be}$ reaction. Model calculations are compared to the data taken from Refs. [92, 93]. In the plot legend, G4EH stands for g4excitationhandler.

Figure 32

Distributions of the excitation energy of the cascade remnants, as calculated by incl++, for the reactions shown in this section.

Figure 33

Partial charge-changing cross sections for the $1.05A$ GeV ${}^{56}\mathrm{Fe}+{}^{12}\mathrm{C}$ reaction. Model calculations are compared to the data taken from Refs. [94].

Figure 34

Map of models used by the incl++-based physics lists in geant4 v10.0. Physics lists whose name ends in _HP use the neutronhp model for neutron transport at low energies (represented as “HP” on the map); those starting with qgsp_ (ftfp_) use the quark-gluon-string model (the fritiof model) at high energy. “PC” stands for precompound.

Figure 35

Same as Fig. 34 for the incl++-based physics lists in geant4 $\text{v}10.1\beta$.

Figure 36

Double-differential cross sections for the production of ${\pi }^{+}$ (top) and ${\pi }^{-}$ (bottom) at (a) ${25}^{\circ }$, (b) ${37}^{\circ }$, (c) ${48}^{\circ }$, (d) ${60}^{\circ }$, (e) ${71}^{\circ }$, (f) ${83}^{\circ }$, (g) ${94}^{\circ }$, (h) ${105}^{\circ }$, and (i) ${117}^{\circ }$ from an 8 $\mathrm{GeV}/c$ $\mathit{p}+{}^{181}\mathrm{Ta}$ reaction. The incl++ calculations are compared to the data from Ref. [96].