Isotopic production cross sections of spallation-evaporation residues from reactions of ${}^{238}\mathrm{U}$($1A$ GeV) with deuterium

Isotopic production cross sections and momentum distributions of 602 residual nuclei produced in the collision of ${}^{238}\mathrm{U}$($1A$ GeV) with deuterium have been measured. These data are relevant for a better understanding of spallation reactions for use as neutron sources for accelerator-driven systems or to produce radioactive nuclear beams. Access to primary residue production makes it possible to study the main reaction mechanisms involved: intranuclear cascade, particle evaporation, and fission. The characteristics of the reaction investigated and the high fissility of the ${}^{238}\mathrm{U}$ and the dinucleon projectile system are discussed and compared with other available experimental data.

Figure 1

Schematic representation of the FRS, where only the dipole magnets and main detectors are depicted. The intermediate (F2) and final (F4) focal planes are indicated. The energy degrader was placed just after the plastic scintillator SC2.

Figure 2

(a) Energy loss measured with one MUSIC chamber, corrected for velocity and horizontal position dependences inside the chambers, and calibrated to reproduce the ionic charge $Q$. Beam value is indicated. (b) Position measured in the dispersion coordinate at the FRS exit (F4) vs energy loss measured by one ionization chamber, in arbitrary units. Two elements are marked. We can observe how the charge resolution allows us to clearly separate elements with $Z$ below ∼70. The band just below the most populated area corresponds to those nuclides carrying one electron in the second stage of the FRS. These residues were transmitted in one FRS magnetic setting centered on ${}^{180}\mathrm{Re}$.

Figure 3

Scatter plot of the atomic number $Z$ value obtained from the energy loss measured with the MUSIC chambers, as a function of the $A/Z$ value deduced from the magnetic rigidity and the TOF measurements, for a magnetic setting of the FRS centered in ${}_{75}^{165}$Re. Each spot corresponds to a single nuclide. Some isotopes of ${}^{65}\mathrm{Tb}$ and ${}^{75}\mathrm{Re}$ are indicated.

Figure 4

(a) Energy loss measured with one MUSIC chamber for the ${}^{238}\mathrm{U}$ beam with an energy of about 600$A$ MeV. Three bumps in the distribution correspond to three charge states populated by the beam. Corresponding average position of charges 90–92 are marked. (b) Scatter plot of energy loss measured in two ionization chambers. Spots correspond to atomic charges 84–87, the mean position is indicated for values 85 and 87.

Figure 5

Scatter plot of energy loss in the intermediate degrader $\Delta E_d$ as a function of energy loss, calibrated in charge, measured with two ionization chambers $Q_{\mathrm{eff}}^{max}$. The FRS magnetic setting was centered around ${}_{82}^{195}$Pb. The most populated spots correspond to those nuclides that are bare along the spectrometer. The element $Z$ = 82 is indicated. Spots above the most populated ones correspond to nuclides with one electron before the degrader and bare after; those below, to nuclides bare before the degrader and with one electron after. The case corresponding to a nuclide with one electron unchanged all along the FRS path, indicated as +1$e$, is also separated in the less populated spots near the main line.

Figure 6

Scatter plot of $A/Z$ obtained from the magnetic rigidity and the TOF measurements, as a function of the position of the dispersion coordinate at the intermediate FRS focal plane (F2). The FRS magnetic setting was centered around the nuclide ${}^{216}\mathrm{Ra}$, with the selection $Q=Z=88$.

Figure 7

Longitudinal-momentum distribution $p_L$, in the frame defined by the projectile in the middle of the target, for the nucleus ${}_{70}^{160}$Yb, produced in the reaction ${}^{238}\mathrm{U}$($1A$ GeV) + $d$. The different areas correspond to the momentum intervals measured in different FRS magnetic settings. Overlapping these different measurements allows us to reconstruct the whole momentum distribution.

Figure 8

Corrections applied to the measured yields. (a) Correction factor $f_q$, inverse of the survival probability of fully stripped ions through the FRS and the ionization chambers, as a function of atomic number. Dispersion of values is due to mass dependence. The shift below $Z=70$ corresponds to the settings without the degrader. (b) Correction factor $f_{\mathrm{loss}}$, inverse of the survival probability to reactions of ions in all layers of matter along the FRS to the ionization chambers, as a function of atomic number. Shifts are due to the change in the degrader thickness, adjusted to the range of residue nuclides. For $Z$ below 70, the degrader is not used. (c) Isobaric distribution of yields for the total target assembly (triangles) and for a deuterium-free target container (circles). Deuterium production is typically 97% of total production. (d) Correction factor $f_{\mathrm{mr}}$, ratio of the primary to multiple reaction production within the target, plotted as a function of the mass number of the residue. Line corresponds to the average value weighted by each isobar production. Symbols are the isotopic values of $f_{\mathrm{mr}}$ for elements ${}^{65}\mathrm{Tb}$, ${}^{75}\mathrm{Re}$, ${}^{85}\mathrm{At}$.

Figure 9

Isotopic production cross sections of residues of ${}^{75}\mathrm{Re}$ and ${}^{70}\mathrm{Yb}$ as measured with (full symbols) and without (open symbols) degrader. Lower panels show the relative differences of these values.

Figure 10

Measured longitudinal momentum distribution in the projectile frame for (a) ${}_{85}^{205}$At, (b) ${}_{66}^{156}$Dy, and (c) ${}_{62}^{152}$Sm. The change of shape from a Gaussian to a flat distribution is associated with the different reaction mechanisms contributing to the production of the nuclides.

Figure 11

Isotopic cross sections of residual nuclei ${}^{93}\mathrm{Np}$ to ${}^{74}\mathrm{W}$ produced in reactions induced by ${}^{238}\mathrm{U}$($1A$ GeV) with deuterium. Error bars for statistical uncertainty, are visible only when larger than the symbol size.

Figure 12

Same as Fig. 11, but for residual nuclei ${}^{73}\mathrm{Ta}$ to ${}^{58}\mathrm{Ce}$.

Figure 13

Production cross sections of the residues measured in the reaction ${}^{238}\mathrm{U}$($1A$ GeV)+$d$ plotted as function of the residue mass number and atomic number. Total error bars are visible only if larger than the symbols.

Figure 14

Production cross sections of residues measured in the reaction ${}^{238}\mathrm{U}$($1A$ GeV) on deuteron plotted in gray scale (color scale in the online edition) on top of a chart of nuclides. Black boxes are stable nuclides.

Figure 15

Average $N/Z$ ratio of the residual nuclei measured work as a function of their mass number. Solid line represents the prediction of the EPAX formula [42]. Dashed line is the stability line.

Figure 16

Isotopic cross sections of residual nuclides of ${}^{92}\mathrm{U}$, ${}^{90}\mathrm{Th}$, ${}^{85}\mathrm{At}$, and ${}^{80}\mathrm{Hg}$, produced in reactions of ${}^{238}\mathrm{U}$($1A$ GeV)+$d$ (triangles) and ${}^{238}\mathrm{U}$($1A$ GeV)+$p$ [8] (circles).

Figure 17

Isobaric distribution of production of evaporation residues in the reactions induced by ${}^{208}\mathrm{Pb}$ ($1A$ GeV)+$d$ [4] (squares), ${}^{238}\mathrm{U}$($1A$ GeV)+$p$ (circles) [8], and ${}^{238}\mathrm{U}$($1A$ GeV)+$d$ (triangles). These distributions are represented as a function of the difference in residue mass with respect to the projectile. Only statistical error bars are shown (visible if larger than the symbols).

Figure 18

(a) Measured longitudinal momentum $\langle p_L\rangle$ plotted as function of mass difference $\Delta A=A_{\mathrm{projectile}}-A_{\mathrm{residue}}$. Line corresponds to the Morrissey systematics [46]. (b) Unfolded width ${\sigma }_L$ of the $\langle p_L\rangle$ distribution plotted as function of Δ$A$. Lines correspond to the Morrissey systematics [46] (solid line) and the Goldhaber model [48] (dashed line). Insert shows data of the one-, two-, and three-proton removal channels (triangles) and one additional neutron removal (circles).

Figure 19

Recoil kinetic energy $T$ obtained after the measured values of $\langle p_L\rangle$ and ${\sigma }_L$, as function of mass difference $A_{\mathrm{projectile}}-A_{\mathrm{residue}}$. Solid line is the value given by the Morrissey systematics [46].