Charge-changing interactions of ultrarelativistic $\mathrm{Pb}$ nuclei

Experimental data and theoretical results on charge loss $-27⩽\Delta Z⩽-1$, charge pickup $\Delta Z=+1$, and total charge-changing cross sections for $158A\mathrm{GeV}$ ${}_{82}{}^{208}\mathrm{Pb}$ ions on ${\mathrm{CH}}_2$, $\mathrm{C}$, $\mathrm{Al}$, $\mathrm{Cu}$, $\mathrm{Sn}$, and $\mathrm{Au}$ targets are presented. Calculations based on the revisited abrasion-ablation model for hadronic interaction and the relativistic electromagnetic dissociation (RELDIS) model for electromagnetic interaction describe the data. The decay of excited nuclear systems created in both types of interaction is described by the statistical multifragmentation model (SMM), which includes evaporation, fission, and multifragmentation channels. We show that at very high projectile energy the excitation energy of residual nuclei may be described on average as $\sim 40\mathrm{MeV}$ per removed nucleon, with some increase in this value compared to fragmentation of intermediate energy heavy ions at $\sim 1A\mathrm{GeV}$. The importance of the electromagnetic interaction in production of ${}_{80}\mathrm{Hg}$, ${}_{81}\mathrm{Tl}$, and ${}_{83}\mathrm{Bi}$ projectile fragments on heavy targets is shown. A strong increase of nuclear-charge pickup cross sections, forming ${}_{83}\mathrm{Bi}$, is observed in comparison to similar measurements at $10.6A\mathrm{GeV}$. This process is attributed to the electromagnetic production of a negative pion by an equivalent photon, which is quantitatively described by the RELDIS model.

Figure 1

Schematic view of the experimental setup. The reaction targets are placed between two multiple-sampling ionization chambers (MUSIC) with fourfold segmented anodes. A trigger signal of the incoming beam is obtained from the scintillator detector.

Figure 2

(Color online) Energy-deposition spectra obtained with MUSIC 2 for an incoming $158A\mathrm{GeV}$ $\mathrm{Pb}$ ion beam and two different targets (upper spectrum: $1\mathrm{g}∕{\mathrm{cm}}^2$ carbon target, lower spectrum: $6\mathrm{g}∕{\mathrm{cm}}^2$ gold target). The inset in the lower spectrum shows an enlarged part of the spectrum with the heaviest reaction products. The bismuth peak, which arises from nuclear-charge pickup $\left(\Delta Z=+1\right)$ is clearly visible.

Figure 3

(Color online) Measured partial charge-changing cross sections for charge-loss ($\Delta Z<0$, full squares) and charge-pickup ($\Delta Z=+1$, full triangles) cross sections of $158A\mathrm{GeV}$ ${}^{208}\mathrm{Pb}$ ions on $\mathrm{H}$, $\mathrm{C}$, $\mathrm{Al}$, $\mathrm{Cu}$, $\mathrm{Sn}$, and $\mathrm{Au}$ targets from the present work. For comparison, the data of Ref. 6 for charge-loss and charge-pickup cross sections are shown by the open circles and triangles, respectively. The data on $\mathrm{PbPb}$ interactions [6] are presented in the bottom panel to be compared with our $\mathrm{PbAu}$ measurements Error bars are plotted in the figure, but are in most cases smaller than the size of the symbols and may thus be not visible.

Figure 4

(Color online) Total charge-changing cross sections of the present work (full squares) for $158A\mathrm{GeV}$ $\mathrm{Pb}$ ions as a function of target mass number $A_2$. The data of Ref. 6 are shown by the open squares. Electromagnetic contribution calculated by the RELDIS code and nuclear contribution calculated within the abrasion-ablation model are shown by the dashed and dotted lines, respectively. The solid curve is the sum of both contributions.

Figure 5

Prefragment excitation-energy distributions created after the abrasion of a given number of nucleons. Top panel: distribution given by the Gaimard-Schmidt formula, Eq. (13), with $g_0=16{\mathrm{MeV}}^{-1}$, $g_1=0.4{\mathrm{MeV}}^{-2}$ for $a=1–5,10,15,20$, and 25. Bottom panel: distribution given by the Ericson formula $\left(g_1=0\right)$ with $E_{max}=40\mathrm{MeV}$ for $a=1–5$.

Figure 6

Correlation between excitation energy per nucleon of prefragment, $E∕A_{pf}$, and its relative mass, $A_{pf}∕A_1$, for $158A\mathrm{GeV}$ $\mathrm{Pb}$ ions on $\mathrm{C}$, $\mathrm{Cu}$, and $\mathrm{Pb}$ targets. Results for the Gaimard-Schmidt formula with $g_0=16{\mathrm{MeV}}^{-1}$, $g_1=0.4{\mathrm{MeV}}^{-2}$ and the Ericson formula for $E_{max}=40\mathrm{MeV}$ are given in the first and second columns, respectively. The same correlation based on the empirical parametrization of Ref. 28 is given in the third column.

Figure 7

Mass distributions of excited prefragments (arbitrary units) produced in $158A\mathrm{GeV}$ $\mathrm{PbC}$ collisions after the abrasion step. Prefragment distributions calculated by the Gaimard-Schmidt formula, the Ericson formula, and the ALADIN parametrization, are given by the dashed, solid, and dotted histograms, respectively. Top panel: prefragments with $E∕A_{pf}<2\mathrm{MeV}$, which undergo decay via evaporation-fission competition. Bottom panel: highly excited prefragments with $E∕A_{pf}>4\mathrm{MeV}$, which undergo explosive multifragment breakup.

Figure 8

Product of the virtual photon spectrum and the total photoabsorption cross section used in RELDIS calculations for $10.6A\mathrm{GeV}$ $\mathrm{Au}$ ions (dotted line) and for $158A\mathrm{GeV}$ $\mathrm{Pb}$ ions (solid line). The domains of photoabsorption via GDR excitation, quasideuteron mechanism, and $\Delta$ excitation are shown. The product of the ${}_{83}\mathrm{Bi}$ photoproduction cross section and the virtual photon spectrum for $158A\mathrm{GeV}$ ions is shown by the dashed line.

Figure 9

Cross sections for photoproduction of ${}_{83}{}^A\mathrm{Bi}$ isotopes by monoenergetic photons on ${}^{208}\mathrm{Pb}$ as predicted by the RELDIS model. The results for photon energies of $E_{\gamma }=190,260,520$, and $960\mathrm{MeV}$ are shown by the solid, dashed, dotted, and dash-dotted lines, respectively.

Figure 10

(Color online) Inclusive cross sections for producing a fragment with charge $Z$ by $158A\mathrm{GeV}$ ${}^{208}\mathrm{Pb}$ projectiles on $\mathrm{C}$, $\mathrm{Al}$, $\mathrm{Cu}$, $\mathrm{Sn}$, $\mathrm{Au}$, and $\mathrm{Pb}$ targets. Experimental data are shown by the full squares (this work) and by the open circles (Refs. 3, 6). Results of calculations with the abrasion-ablation model with ${\rho }_a\left(E\right)$ given by the Gaimard-Schmidt formula, Eq. (13), with $g_0=16{\mathrm{MeV}}^{-1}$, $g_1=0.4{\mathrm{MeV}}^{-2}$, and with the RELDIS model are shown by the dotted and dashed histograms, respectively. The solid histograms represent their sums.

Figure 11

(Color online) Same as Fig. 10, but for calculations made with ${\rho }_a\left(E\right)$ given by the Ericson formula, Eq. (14), and with a factor of $K=0.3$ used in fission calculations.

Figure 12

(Color online) Same as in Fig. 11, but for the calculations made with prefragment excitation energy $E$ estimated from ALADIN data [28].

Figure 13

Inclusive cross sections for producing a fragment with charge $Z$ by $10.6A\mathrm{GeV}$ ${}^{197}\mathrm{Au}$ projectiles on $\mathrm{C}$, $\mathrm{Al}$, $\mathrm{Cu}$, $\mathrm{Sn}$, and $\mathrm{Pb}$ targets. Experimental data are shown by the open circles [46]. Calculations were made with ${\rho }_a\left(E\right)$ given by the Ericson formula, Eq. (14), and with a factor of $K=0.3$ used in fission calculations. Other notations are the same as in Fig. 10.

Figure 14

(Color online) Energy dependence of charge-pickup cross sections for $\mathrm{Au}$ and $\mathrm{Pb}$ projectiles on $\mathrm{C}$, $\mathrm{Cu}$, $\mathrm{Au}$, or $\mathrm{Pb}$ targets. Experimental data [46, 48, 49] for $\mathrm{Au}$ projectiles at $10.6A\mathrm{GeV}$ and below are given by the open triangles, present data for $\mathrm{Pb}$ projectiles at $158A\mathrm{GeV}$ by the full triangles. Fit results of Ref. 2 are given by the dashed lines. The solid lines represent the dashed curves plus an electromagnetic contribution calculated by the RELDIS model.

Figure 15

(Color online) Nuclear-charge pickup $\left(\Delta Z=+1\right)$ cross sections as a function of target atomic number $Z_2$. The data for $158A\mathrm{GeV}$ $\mathrm{Pb}$ ions are shown by the full (present work) and open triangles (Ref. 3). The solid curve is the sum of the electromagnetic contribution (EM, dashed line) and the nuclear contribution to the $\Delta Z=+1$ cross section. For comparison, data obtained with $10.6A\mathrm{GeV}$ $\mathrm{Au}$ ions [46, 50] are depicted with the light-colored triangles and squares, which are connected by the dotted line to guide the eye.