Light nuclides produced in the proton-induced spallation of ${}^{238}\mathrm{U}$ at 1 GeV

The production of light and intermediate-mass nuclides formed in the reaction ${}^1\mathrm{H}+{}^{238}\mathrm{U}$ at 1 GeV was measured at the Fragment Separator at GSI, Darmstadt. The experiment was performed in inverse kinematics, by shooting a 1 A GeV ${}^{238}\mathrm{U}$ beam on a thin liquid-hydrogen target. A total of 254 isotopes of all elements in the range $7\le Z\le 37$ were unambiguously identified, and the velocity distributions of the produced nuclides were determined with high precision. The results show that the nuclides are produced in a very asymmetric binary decay of heavy nuclei originating from the spallation of uranium. All the features of the produced nuclides merge with the characteristics of the fission products as their mass increases.

Figure 1

(Color online) Schematic view from above of the horizontal section of the experimental setup. In the analysis, the orthogonal Cartesian reference axes were set as follows: $z$ axis along the beam line, y axis perpendicular to the sheet, and x axis on the plane of the sheet.

Figure 2

(Color online) Identification pattern of the measured data. The vertical line at $A/Z=$2 gives the mass calibration. The inverse of the length of the generic horizontal line, which represents the distance between two close isotopes, gives the atomic number Z (10 in the example) and provides the charge calibration. The plot collects the counts (given on a logarithmic scale) from the hydrogen target, including the contribution from the titanium windows of the container, for the present measurement (fragments with atomic number around $Z=20$).

Figure 3

(Color online) Left: Longitudinal-velocity spectrum for ${}^{58}\mathrm{Fe}$. The experimental data were fitted with three Gaussian curves. Right: Two-dimensional cluster plot of the velocity distribution as a function of the neutron number for iron ($Z=26$). The dashed line encloses the events collected in one $B\rho$ measurement. In both figures, the data refer to the interaction of the uranium beam with ${}^1\mathrm{H}$ + Ti. The velocity is presented in the beam frame (${\upsilon }_{{}^{238}U}$ = 0 cm/ns). The counts are normalized to the beam dose.

Figure 4

(Color online) Top: Schematic representation of the velocity distributions of fragmentation and fission residues of one isotope, together with the FRS angular acceptance. Bottom: Projection of the accepted events on the longitudinal axis.

Figure 5

(Color online) Two-dimensional cluster plot of the experimental velocities of fragments produced in the interaction of the uranium beam with the hydrogen-plus-titanium-window target. The velocity is presented in the beam frame (${\upsilon }_{{}^{238}U}=0$ cm/ns).

Figure 6

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Figure 7

(Color online) Two-dimensional cluster plot of the nuclide production cross sections in the reaction ${}^{238}\mathrm{U}+{}^1\mathrm{H}$ at 1 A GeV obtained in this work superposed on a chart of the nuclides. The numerical values of the measured data are collected in Table . For those nuclides, that could not be measured, the cross sections were interpolated from the existing data by smoothing the isotopic distributions. The open black squares correspond to stable nuclides. The lines indicate the limit of the known nuclides.

Figure 8

(Color online) Experimental results for the reaction ${}^{238}\mathrm{U}+{}^1\mathrm{H}$ at 1 A GeV. Top: Mean recoil velocities of the mother nuclei of all fragments measured in this experiment presented in the beam frame: this work (full dots), Ref. 12 (empty squares). Bottom: Mean values of the velocities of the fragments in the frame of the mother nuclei: This work (full dots), Ref. 12 (empty squares). Values are drawn as a function of the atomic number of the fragment.

Figure 9

Measured standard deviations ${\sigma }_{\upsilon }^{\mathrm{meas}}$ of the velocities of fragments emitted in the backward direction (full dots) and forward direction (empty dots), produced in the reaction ${}^{238}\mathrm{U}+{}^1\mathrm{H}$ at 1 A GeV. The lines are the results given by the fitting procedure. The data are affected by the FRS angular transmission and by the location straggling in the target (see text). Values are drawn as a function of the atomic number of the fragment.

Figure 10

Measured cross sections of potassium isotopes ($Z=19$) from 1 A GeV ${}^{238}\mathrm{U}$ in hydrogen of this work (full dots) compared with the yields of potassium isotopes from the reaction of 600-MeV protons in a thick uranium-carbide target (open dots), measured at ISOLDE [57]. The yields from the ISOLDE experiment (right scale) were normalized to the cross sections of this work (left scale).

Figure 11

Mass and charge distributions of binary-decay products measured in the reaction of ${}^{238}\mathrm{U}+{}^1\mathrm{H}$ at 1 GeV. Dots: this work; squares: Taken from Ref. 12 in the range not covered by the present work.

Figure 12

Left: Schematic presentation of the fission-barrier height for a given mass split for light, intermediate, and heavy systems. Right: Corresponding yields (in arbitrary units).

Figure 13

Measured mean values of the velocities of fission fragments in the frame of the fissioning nucleus ($\mathbf{·}$). The lines represent the expected values of the velocity of fragments originating from the compound nuclei ${}^{238}\mathrm{U}$ and ${}^{185}\mathrm{Au}$. The solid lines represent the expected velocities for the scission-point model (deformed nuclei) and the dashed lines the values obtained by the nucleus-nucleus fusion approach (undeformed nuclei).

Figure 14

(Color online) Cross sections for the nuclei produced in ${}^{238}\mathrm{U}$ (1 A GeV) + ${}^1\mathrm{H}$. Top: Prediction of ABRABLA presented on the chart of the nuclides. Bottom: Experimental data (full dots) (this work, [11, 12, 13]) compared with the results of ABRABLA (solid line). The solid line is obtained by the sum of the three components: the evaporated IMF, the fission fragments, and the heavy evaporation residues (solid lines).

Figure 15

Cross sections for the isotopes of the eight lightest elements measured in the reaction ${}^{238}\mathrm{U}$ (1 A GeV) + p. The dots represent the experimental data measured in this work, the solid lines are the prediction of ABRABLA, which includes the evaporation of IMFs.

Figure 16

(Color online) Top: Mean neutron-to-proton ratio of isotopic distributions as a function of the atomic number, compared with the stability line (dashed line) and to the ABRABLA prediction (solid line). Bottom: FWHM of the isotopic distributions compared to the prediction of the ABRABLA code (solid line).