Particle production in nucleon induced reactions above 14 MeV with an intranuclear cascade model

We present an intranuclear cascade (INC) model which includes the dynamics of the cascade particles and uses in-medium $\mathit{NN}$ elastic cross sections. Our model is still based on the impulse approximation and does not have the complexity of other sophisticated nuclear models. Nevertheless, its results of angle-energy distributions of emitted nucleons in continuum are in good agreement with experimental data for nucleon induced reactions from low intermediate energy to high energy, between 14 MeV and 1.6 GeV, and for light to heavy target nuclei. Comparisons with results of Bertini's INC model and of a previous version of our INC model show the clear contribution of the combined effects of better dynamics and the in-medium $\mathit{NN}$ cross sections. From our results, we conclude that our INC model effectively includes the preequilibrium emission.

Figure 1

Time-dependent mean excitation energies $\langle U_{\mathrm{exc}}\rangle$ and $\langle E_{\mathrm{exc}}\rangle$ defined by Eqs. (22) and (23), respectively, for proton induced reactions on ${}^{208}\mathrm{Pb}$ at six incident energies.

Figure 2

Distribution of the end of INC step for proton induced reactions on ${}^{208}\mathrm{Pb}$ at six incident energies. Ordinate is number of events in arbitrary units. The end of INC step is determined when no more quasifree hadrons are inside the nuclear volume of radius $R_{\mathrm{limit}}$. Events with at least one quasifree hadron inside the nucleus after 400 fm/$c$ are not shown here.

Figure 3

Distribution of excitation energies $U_{\mathrm{exc}}$ and $E_{\mathrm{exc}}$ defined by Eqs. (22) and (23), respectively, at six different times for the 800 MeV proton induced reaction on ${}^{208}\mathrm{Pb}$.

Figure 4

Differential cross section of proton production for reaction of 65 MeV proton on ${}^{93}\mathrm{Nb}$ as a function of the outgoing proton energy for the angles indicated. Results are from (a) BRIC 1.0 and (b) BRIC 1.4. Filled area is the INC component of our model; solid histogram is the INC + evaporation sum. Hashed line in (a) is the result of the sum of Bertini's INC plus evaporation. Symbols are data of Sakai et al. [68].

Figure 5

Same as in Fig. 4, but for 62 MeV proton on ${}^{54}\mathrm{Fe}$. Data are from Ref. [17].

Figure 6

Double differential cross sections of neutron production in ${}^{90}\mathrm{Zr}$$(p,\mathit{xn})$ reaction at (a) 45 MeV and (b) 80 MeV. Symbols are data from Ref. [69] (45 MeV proton) and [70] (80 MeV proton). Hashed histograms are the results of BRIC 1.0; solid histograms, BRIC 1.0 with the in-medium $\mathit{NN}$ elastic cross sections [Eq. (12)]. Evaporation component is not included.

Figure 7

Same reactions as in Fig. 6, but showing results for BRIC 1.0 (hashed histograms), and BRIC 1.4 with the free $\mathit{NN}$ elastic cross sections and without taking into account $Q(p,n)$ (solid histograms).

Figure 8

Same as in Fig. 7, but with our current BRIC 1.4.

Figure 9

Same as in Fig. 8, but for proton induced reactions on ${}^{208}\mathrm{Pb}$. Symbols are experimental data of (a) Galonsky et al. [19] and (b) Cowley et al. [71].

Figure 10

Differential cross section of neutron production for the reactions (a) ${}^{90}\mathrm{Zr}$$(p,\mathit{xn})$ at 120 MeV and (b) ${}^{208}\mathrm{Pb}$$(p,\mathit{xn})$ at 160 MeV as a function of the c.m. energy of the outgoing neutrons for the indicated laboratory angles. Results of BRIC 1.4 (no evaporation) (solid histograms) and BRIC 1.0 (hashed histograms). Experimental data (stars) are from Ref. [72].

Figure 11

Differential cross section of neutron production for the reactions ${}^{27}\mathrm{Al}$$(p,\mathit{xn})$ at (a) 113 MeV and (b) 256 MeV as a function of the energy of the outgoing neutrons for the angles indicated in the laboratory frame. The results at two successive angles are shifted by a 0.1 factor. The solid, hashed, and dotted histograms are the results of BRIC 1.4, BRIC 1.0, and Bertini's INC, respectively, plus evaporation. Data at 113 and 256 MeV are from Refs. [20] and [21], respectively.

Figure 12

Same as in Fig. 11, but for ${}^{238}\mathrm{U}$$(p,\mathit{xn})$.

Figure 13

Differential cross section of proton production for proton induced reactions on ${}^{58}\mathrm{Ni}$ at (a) 100 MeV and (b) 200 MeV as a function of the laboratory angles of the outgoing protons for the energies indicated. Results of BRIC 1.4 (no evaporation) (solid histograms) and BRIC 1.0 (hashed histograms). Experimental data (stars) are from Richter et al. [73].

Figure 14

Same as in Fig. 13, but for ${}^{197}\mathrm{Au}$.

Figure 15

Differential cross section of proton production for the reaction of 300 MeV proton on (a) ${}^9\mathrm{Be}$ and (b) ${}^{107}\mathrm{Ag}$ as a function of the energy of the proton for the angles indicated. Hashed histograms are BRIC 1.0 results; solid histograms, BRIC 1.4. Data of ${}^9\mathrm{Be}(p,\mathit{xp})$ and ${}^{107}\mathrm{Ag}(p,\mathit{xp})$ are from Refs. [76] and [77], respectively. No data are available at ${10}^{°}$.

Figure 16

Same as in Fig. 15, but for reactions (a) ${}^{40}\mathrm{Ca}(p,\mathit{xp})$ at 392 MeV with the data of Ref. [78] and (b) ${}^{58}\mathrm{Ni}(p,\mathit{xp})$ at 400 MeV with the data of Ref. [79].

Figure 17

Differential cross section of neutron production for reactions (a) ${}^{56}\mathrm{Fe}$$(p,\mathit{xn})$ and (b) ${}^{208}\mathrm{Pb}$$(p,\mathit{xn})$ at 597 MeV as a function of outgoing neutron energy for the angles indicated. The results of two angles are shifted by a 0.1 factor with increasing angles. The results are given in the laboratory frame. Hashed and solid histograms are the results of BRIC 1.0 and BRIC 1.4, respectively, plus evaporation. Data are from Ref. [83]. No data are available at $7.5^{°}$.

Figure 18

Same as in Fig. 17, but for (a) 800 MeV proton on ${}^{\mathrm{nat}}$Fe and (b) 1200 MeV proton on ${}^{27}\mathrm{Al}$. Calculations were done with the TIERCE code [66] to take account of target thickness. Data are from Ref. [82].

Figure 19

Same as in Fig. 18, but for (a) 1200 MeV proton on ${}^{\mathrm{nat}}$Zr and (b) 1600 MeV proton on ${}^{\mathrm{nat}}$Pb. Calculations were done with the TIERCE code. Data are from Ref.[82].

Figure 20

Double differential cross section of outgoing (a) ${\pi }^{+}$ and (b) ${\pi }^{-}$ in 730 MeV proton induced reactions on ${}^{208}\mathrm{Pb}$. Hashed and solid histograms are the results of BRIC 1.0 and BRIC 1.4, respectively. Symbols are data of Ref. [84].

Figure 21

Double differential cross section of neutron production in 18 MeV neutron induced reaction on ${}^{238}\mathrm{U}$ with BRIC 1.4 for two cuts of the time of reaction: (a) 100 fm/$c$ and (b) 200 fm/$c$. Data are from Ref. [86]. No data are available at ${160}^{°}$. Filled area is the INC component; solid histograms, sum of INC and deexcitation components (including evaporation of fission fragments).

Figure 22

Same as in Fig. 21, but for 14 MeV neutrons on ${}^{209}\mathrm{Bi}$. Data are from Ref. [87]. No data available at ${165}^{°}$.

Figure 23

Double differential cross section of neutron production for four outgoing energies in the 14 MeV neutron induced reaction on ${}^{209}\mathrm{Bi}$. Results of BRIC 1.4 are shown at four $t_{\mathrm{cut}}$ levels as indicated in legend.

Figure 24

Some trajectories of backward emitted neutrons in 14 MeV neutron induced reaction on ${}^{209}\mathrm{Bi}$. Positions of incident neutron at $t=0$ (black dots) and of effective collision at time $t_{\mathrm{coll}}$ (black crosses) are given in [$\pm (x^2+y^2){}^{1/2},z$] plane and in nucleus rest frame. Dotted line circle is the nucleus edge ($R_{\mathrm{limit}}=9.58$ fm). Momentum of incident neutron is along $z$ axis with $p_z>0$, and arrows indicate direction. $E_{\mathrm{out}},{\theta }_{\mathrm{lab}}$, and $t_{\mathrm{out}}$ are the kinetic energy of emitted neutron (MeV), angle of emission (deg), and time of emission (fm/$c$), respectively.