Spallation residues in the reaction ${}^{56}\mathrm{Fe}+p$ at $0.3A,0.5A,0.75A,1.0A$, and $1.5A$ GeV

The spallation residues produced in the bombardment of ${}^{56}\mathrm{Fe}$ at $1.5A,1.0A,0.75A,0.5A$, and $0.3A$ GeV on a liquid-hydrogen target have been measured using the reverse kinematics technique and the fragment separator at GSI (Darmstadt). This technique has permitted the full identification in charge and mass of all isotopes produced with cross sections larger than ${10}^{-2}$ mb down to $Z=8$. Their individual production cross sections and recoil velocities at the five energies are presented. Production cross sections are compared with previously existing data and with empirical parametric formulas, often used in cosmic-ray astrophysics. The experimental data are also extensively compared with the results of different combinations of intranuclear cascade and deexcitation models. It is shown that the yields of the lightest isotopes cannot be accounted for by standard evaporation models. The GEMINI model, which includes an asymmetric fission decay mode, gives an overall good agreement with the data. These experimental data can be directly used for the estimation of composition modifications and damages in materials containing iron in spallation sources. They are also useful for improving high-precision cosmic-ray measurements.

Figure 1

Schematic layout of fragment spectrometer. Fragments are analyzed by the four large dipole magnets. Scintillators at S2 and S4 measure the time of flight over the second half of the spectrometer as well as the horizontal positions in the dispersive focal planes at S2 and at S4. The MUSIC detector (ionization chamber) gives information about the energy loss of the fragment. Multiwire proportional chambers (MWPCs) are used for beam tuning and removed for production measurements.

Figure 2

Complete isotope coverage in $Z$ vs. $A/Q$ (actually identical to $A/Z$) for $1A$ GeV ${}^{56}\mathrm{Fe}$ on the liquid-hydrogen target. The plot is built from data of overlapping settings, normalized to the primary beam intensity and superimposed.

Figure 3

Longitudinal velocity distribution of ${}^{38}\mathrm{K}$ detected as a residual nucleus at $1A$ GeV and expressed in the rest frame of the iron beam. Five different settings of the FRS were needed to reconstruct the complete distribution. The yield (here in arbitrary units) detected in each setting is normalized by the number of incident iron nuclei and corrected for the acquisition dead time.

Figure 4

Transmission factor as a function of the mass number of the residue for the five energies presented in this work (see text).

Figure 5

Isotopic production cross sections of fragments from the reaction ${}^{56}\mathrm{Fe}+p$ at $1.5A$ GeV as a function of the neutron number.

Figure 6

Same as Fig. 5, but at $1.0A$ GeV.

Figure 7

Same as Fig. 5, but at $0.75A$ GeV.

Figure 8

Same as Fig. 5, but at $0.5A$ GeV.

Figure 9

Same as Fig. 5, but at $0.3A$ GeV.

Figure 10

Mass distribution of the residual nuclei in the spallation reaction ${}^{56}\mathrm{Fe}+p$ at the five different beam energies.

Figure 11

Nuclear-charge distribution of the residual nuclei for the five energies with scaling factors (2/1/0.5/0.25/0.125, respectively, from $1500A$ to $300A$ MeV) applied for clarity. Points correspond to the present data, and solid histograms are data from Webber et al. [4, 5, 7] at close energies: $(1512,1086,724,520,\text{and}330)A$ MeV.

Figure 12

Ratio between isotopic cross sections measured by Webber et al. at $573A$ MeV [3, 4] and the present experiment at $500A$ MeV for each element as a function of the mass number. Lines are theoretical predictions from INCL4-GEMINI for this ratio.

Figure 13

Ratio of mean nuclear-mass value to the charge for each element measured by Webber et al. at $573A$ MeV [3, 4] and in the present experiment at $500A$ MeV, and for the same quantity evaluated from all isotopes measured in this experiment.

Figure 14

Excitation functions of some residual nuclei produced in the spallation reaction of proton on iron. Open dots are the data of R. Michel et al. [34, 35] obtained by a direct irradiation; solid triangles correspond to the present experimental data at five energies. Independent isotopes are indicated (Ind.).

Figure 15

Same as Fig. 14, but for additional nuclei.

Figure 16

Comparison between present results at five energies (symbols) and the results obtained with the Webber formula (solid lines). Scaling factors (2/1/0.5/0.25/0.125, respectively, from $1500A$ to $300A$ MeV) are applied for clarity.

Figure 17

Comparison between the present measured mass distributions (symbols) and the results obtained with the EPAX formula (solid line).

Figure 18

Comparison between present experimental results at the five energies (symbols) and the results obtained with the Silberberg-Tsao formula (solid lines). Scaling factors ($2/1/0.5/0.25/0.125$, respectively, from $1500A$ to $300A$ MeV) are applied for clarity.

Figure 19

Mean values and widths of the mass-over-charge distributions as a function of element charge measured at 1500 MeV per nucleon compared with predictions of the Webber, Silberberg-Tsao, and EPAX parametric formulas.

Figure 20

Total reaction cross sections of protons on iron as a function of the bombarding energy (energy per nucleon for this experiment in reverse kinematics). Our five experimental data are compared with the compilation of previous experimental data from Barashenkhov [59] and the values given by the three INC models: Bertini, ISABEL (not available for $E>1$ GeV in LAHET3), and INCL4.

Figure 21

Mass distribution of the spallation residues of iron at $1A$ GeV compared with the Bertini and INCL4 INC models combined with the Dresner evaporation model.

Figure 22

Mass distribution of the spallation residues of iron at $1A$ GeV compared with predictions of two different INC models (INCL4 [44] and ISABEL [43]) combined with the ABLA evaporation model [51].

Figure 23

Spallation residue cross sections of iron as a function of mass number compared with calculations with INCL4 coupled with GEM (dashed lines) or GEMINI (continuous lines). Points are data of the present paper complemented for low masses at 1 GeV by data from Ref. [29] obtained during the same experiment.

Figure 24

Charge distribution of the spallation residues of iron at $1A$ GeV compared with predictions by INCL4 coupled with deexcitation models GEM, GEMINI, and ABLA.

Figure 25

Cross sections calculated with INCL4 and SMM compared with data points at $1A$ GeV. Multifragmentation contribution to the calculation is also shown.

Figure 26

Selected isotopic distributions of cross sections measured at $1A$ GeV compared with INCL4-GEMINI calculations (continuous lines) and INCL4-ABLA (dashed lines).

Figure 27

$\langle A\rangle /Z$ and rms $\sigma (A)$ of the isotopic cross-section distributions as a function of $Z$, at the five bombarding energies, compared with calculations done with INCL4 coupled with GEMINI. Calculated values have been averaged over the actually measured isotopes.

Figure 28

Same as Fig. 27, but only at $1A$ GeV for comparison with calculations done with INCL4 coupled with ABLA, GEM, and SMM.

Figure 29

Mean and rms values of the longitudinal recoil velocity distribution for spallation residues at $1A$ GeV vs their atomic mass, comparing experimental values with predictions from INCL4-ABLA, ISABEL-ABLA, and INCL4-GEMINI. Velocities are expressed in the beam (${}^{56}\mathrm{Fe}$) rest frame and with a minus sign as being opposite to the iron beam direction.

Figure 30

Mean values and rms of the longitudinal recoil velocity distribution for spallation residues vs their atomic mass at all beam energies, comparing experimental values (open circles) with predictions from INCL4-GEMINI (solid triangles). The lines are the Morrissey systematics [64].