Isotopic and velocity distributions of ${}_{83}\mathrm{Bi}$ produced in charge-pickup reactions of ${}_{82}{}^{208}\mathrm{Pb}$ at $1A\mathrm{GeV}$

Isotopically resolved cross sections and velocity distributions have been measured in charge-pickup reactions of $1A\mathrm{GeV}$ ${}^{208}\mathrm{Pb}$ with proton, deuterium, and titanium targets. The total and partial charge-pickup cross sections in the reactions ${}^{208}\mathrm{Pb}+{}^1\mathrm{H}$ and ${}^{208}\mathrm{Pb}+{}^2\mathrm{H}$ are measured to be the same within the limits of the error bars. A weak increase in the total charge-pickup cross section is seen in the reaction of ${}^{208}\mathrm{Pb}$ with the titanium target. The measured velocity distributions show different contributions—quasielastic scattering and $\Delta$-resonance excitation—to the charge-pickup production. Data on total and partial charge-pickup cross sections from these three reactions are compared with other existing data and also with model calculations based on the coupling of different intranuclear cascade codes and an evaporation code.

Figure 1

Schematic drawing of the fragment separator FRS with the associated detector equipment. For more details see text.

Figure 2

(Color online) Charge and mass identification of bismuth products measured in the reaction ${}^{208}\mathrm{Pb}+{}^1\mathrm{H}$. Upper part: Two-dimensional spectrum of the position at S4 versus the position at S2. Bands corresponding to different charges are marked according to $Z$. Lower part: Two-dimensional spectrum of the time of flight in the second half of the FRS versus the position at S2 for the events corresponding to $Z=83$; the different windows correspond to different bismuth isotopes ($A=202$, 203, 204, 205, 206). Both figures show data measured for only one setting of the magnetic fields. Therefore, due to the limited momentum acceptance of the FRS, the isotopes ${}^{202}\mathrm{Bi}$ and ${}^{206}\mathrm{Bi}$ are only partly transmitted.

Figure 3

Total projectile charge-pickup cross section as a function of the target mass: open triangles, ${}^{197}\mathrm{Au}$ at $0.915A\mathrm{GeV}$ [11]; full squares, ${}^{208}\mathrm{Pb}$ at $1A\mathrm{GeV}$ from the present work (note: for the reaction ${}^{208}\mathrm{Pb}+“\mathrm{Ti}”$ the data point is shown for the weighted mean mass of all materials composing this target); open dots, ${}^{197}\mathrm{Au}$ at $1.2A\mathrm{GeV}$ [9]; and full triangles, ${}^{208}\mathrm{Pb}$ at $1A\mathrm{GeV}$ [27]. The full($\mathrm{Au}$ projectile) and dashed ($\mathrm{Pb}$ projectile) lines are obtained by using the following relation: $\sigma =0.12\left(A_p^{1∕3}+A_t^{1∕3}\right)A_p^{2∕3}$, where $A_p$ and $A_t$ are the values of projectile and target mass, respectively.

Figure 4

Production cross sections of bismuth isotopes from the $1A\mathrm{GeV}$ reactions ${}^{208}\mathrm{Pb}+{}^1\mathrm{H}$, full squares; ${}^{208}\mathrm{Pb}+{}^2\mathrm{H}$, open dots; and ${}^{208}\mathrm{Pb}+“\mathrm{Ti}”$, open triangles. Error bars correspond to total uncertainties, statistical plus systematic.

Figure 5

Velocity of ${}^{207}\mathrm{Bi}$ produced in the reaction ${}^{208}\mathrm{Pb}+{}^1\mathrm{H}$ measured in the present work. The dashed histogram shows the raw velocity spectrum, while the full histogram shows the velocity after applying the deconvolution mentioned in the text.

Figure 6

Longitudinal velocities (lower scale) of several bismuth isotopes produced in the interaction of $1A\mathrm{GeV}$ lead with the proton (full line), deuteron (dashed line), and “$\mathrm{Ti}$” targets (dotted line). The velocity distributions are normalized to the corresponding production cross sections. The upper scale represents the energy transfer in the laboratory frame.

Figure 7

Mean values of measured longitudinal velocities of bismuth isotopes produced in the reactions ${}^{208}\mathrm{Pb}+{}^1\mathrm{H}$ (full squares), ${}^{208}\mathrm{Pb}+{}^2\mathrm{H}$ (open dots), and ${}^{208}\mathrm{Pb}+“\mathrm{Ti}”$ (open triangles) at $1A\mathrm{GeV}$, and the empirical systematics of Morrissey [30], full line. Velocities are shown in the rest frame of the ${}^{208}\mathrm{Pb}$ projectile.

Figure 8

Total charge-pickup cross section as a function of the projectile energy per nucleon: open triangles, ${}^{197}\mathrm{Au}+{}^1\mathrm{H}$ [11]; full dot, ${}^{197}\mathrm{Au}+{}^1\mathrm{H}$ [25]; full square, ${}^{208}\mathrm{Pb}+{}^1\mathrm{H}$ from the present work; and open dots, ${}^{197}\mathrm{Au}+{}^1\mathrm{H}$ [9]. The data from Refs. 9, 11 were extracted from measurements performed with ${\mathrm{CH}}_2$ and $\mathrm{C}$ targets.

Figure 9

Comparison between the partial charge-pickup cross sections from the present work and available data. Data are shown as a function of the difference between the mass numbers of the resulting fragment and of the projectile for the following reactions: ${}^{208}\mathrm{Pb}+{}^1\mathrm{H}$ at $1A\mathrm{GeV}$ from the present work (full squares), ${}^{208}\mathrm{Pb}+\mathrm{Cu}$ at $1A\mathrm{GeV}$ [27] (open triangles), ${}^{197}\mathrm{Au}+{}^1\mathrm{H}$ at $0.8A\mathrm{GeV}$ [25] (full dots), ${}^{129}\mathrm{Xe}+{}^{27}\mathrm{Al}$ at $0.79A\mathrm{GeV}$ [13] (open diamonds), and ${}^{86}\mathrm{Kr}+{}^9\mathrm{Be}$ at $0.5A\mathrm{GeV}$ [14] (stars). All these measurements were performed at GSI. As the data on ${}^{208}\mathrm{Pb}+{}^2\mathrm{H}$ and ${}^{208}\mathrm{Pb}+“\mathrm{Ti}”$ from the present work are already shown in Fig. 4, they are not repeated here.

Figure 10

Partial charge-pickup cross sections for ${}^{204–207}\mathrm{Bi}$ from the reaction $p+{}^{\mathrm{nat}}\mathrm{Pb}$ at different proton-beam energies. The data are taken from Ref. 32.

Figure 11

Partial cross sections for bismuth production. Comparison between experimental data: full squares, ${}^{208}\mathrm{Pb}+{}^1\mathrm{H}$; open dots, ${}^{208}\mathrm{Pb}+{}^2\mathrm{H}$; and open triangles, ${}^{208}\mathrm{Pb}+“\mathrm{Ti}”$; and different model calculations: full line, INCL4 [37] $+$ABLA [38], and dashed line,ISABEL [36] $+$ABLA. Error bars represent total (systematic plus statistical) uncertainties.

Figure 12

Calculated velocity distributions of several bismuth isotopes produced in the interaction of $1A\mathrm{GeV}$ lead with the proton (full line) and the deuteron (dashed line). The velocity distributions are normalized to the corresponding calculated production cross sections. The calculations were performed with INCL4 $+$ABLA. The upper x axis shows the energy transfer in the laboratory frame.