Hadronic and electromagnetic fragmentation of ultrarelativistic heavy ions at LHC

Reliable predictions of yields of nuclear fragments produced in electromagnetic dissociation and hadronic fragmentation of ion beams are of great practical importance in analyzing beam losses and interactions with the beam environment at the Large Hadron Collider (LHC) at CERN as well as for estimating radiation effects of galactic cosmic rays on the spacecraft crew and electronic equipment. The model for predicting the fragmentation of relativistic heavy ions is briefly described, and then applied to problems of relevance for LHC. The results are based on the fluka code, which includes electromagnetic dissociation physics and dpmjet-iii as hadronic event generator. We consider the interaction of fully stripped lead ions with nuclei in the energy range from about one hundred MeV to ultrarelativistic energies. The yields of fragments close in the mass and charge to initial ions are calculated. The approach under discussion provides a good overall description of Pb fragmentation data at 30 and $158A\mathrm{GeV}$ as well as recent LHC data for $\sqrt{s_{\mathrm{NN}}}=2.76\mathrm{TeV}$ Pb-Pb interactions. Good agreement with the calculations in the framework of different models is found. This justifies application of the developed simulation technique both at the LHC injection energy of $177A\mathrm{GeV}$ and at its collision energies of 1.38, 1.58, and $2.75A\mathrm{TeV}$, and gives confidence in the results obtained.

Figure 1

Total electromagnetic dissociation and nuclear cross sections for Pb-Pb collisions as a function of the effective relativistic $\gamma$ factor. The results of calculations of the total EMD cross section and partial cross sections in $1n$ and $2n$ channels are shown by solid, dashed and dotted lines, respectively. Total nuclear cross section calculated in the dpmjet-iii model is shown by dot-dashed line. Results from the ALICE collaboration [22] for the total EMD and nuclear cross sections are shown by the full circle and full box, respectively. The measurements for $1n$ and $2n$ channels are shown by open circles [19] and full triangles [22].

Figure 2

Ratio of the electromagnetic dissociation cross sections in $2n$ and $1n$ channels as a function of the center of mass energy $\sqrt{s_{\mathrm{NN}}}$ for the collisions of gold ions (upper curve) and lead ions (lower curve). Experimental data from the fixed target experiments [47, 51] are shown with diamonds. The data from the RHIC experiments Phobos, Brahms and Phenix are displayed with the filled point, open square and filled triangle, respectively [55]. The filled square corresponds to the results from the ALICE [22] collaboration at the CERN LHC.

Figure 3

(Top) Calculated (solid line) and measured (data points) sum of $1nx$ and $2nx$ electromagnetic dissociation cross sections as a function of the target charge. (Bottom) Calculated (dashed and dot-dashed lines) and measured (open and filled triangles) contributions from $1nx$ and $2nx$ channels, respectively, to the sum of $1nx$ and $2nx$ EMD cross sections. Data points are the measured cross sections of forward $1n$ and $2n$ emission in dissociation of $30A\mathrm{GeV}$ Pb ions on Al, Cu, Sn and Pb targets [19].

Figure 4

Total charge-changing cross sections for the incident $158A\mathrm{GeV}$ Pb ions as a function of target mass number. Electromagnetic contributions calculated by fluka are shown by the dashed line. The nuclear contributions calculated in the framework of dpmjet-iii are shown by a dotted line and the sum of EMD and nuclear cross sections is displayed with the solid line. The data of Ref. [16] and Refs. [17, 18] are shown by the full and open squares, respectively.

Figure 5

Inclusive cross sections for producing a fragment with charge $Z$ by $158A\mathrm{GeV}$ ${}^{208}\mathrm{Pb}$ projectiles on C, Al, Cu, Sn, Au and Pb targets. Experimental data from Ref. [16] and Refs. [17, 18] are shown by the open squares and full circles, respectively. Results of the fluka model for electromagnetic dissociation are shown by the dashed (blue) histograms. The solid (yellow) histograms represent the sum of electromagnetic and hadronic contributions with the latter calculated in the dpmjet-iii model.

Figure 6

Inclusive cross sections for producing a fragment with charge $Z$ by $158A\mathrm{GeV}$ ${}^{208}\mathrm{Pb}$ projectiles on C, Al, Cu, Sn, Au and Pb targets. Experimental data from Refs. [16] and [17] are shown by the open squares and full circles, respectively. Charge pickup cross sections are shown by downward [16] and upward [18] triangles, respectively. The results for electromagnetic dissociation are shown by the dashed (blue) histograms. The solid (yellow) histograms represent the sum of electromagnetic and hadronic contributions evaluated in the framework of the fluka model.

Figure 7

Total (solid line), electromagnetic dissociation (dashed line) and nuclear fragmentation (dot-dashed line) cross sections for the incident lead ions on target nuclei as a function of the nuclear charge $Z$ evaluated for the projected LHC energy of $7\mathrm{TeV}/\text{charge}$.

Figure 8

Cross sections for the production of the heaviest fragments in electromagnetic dissociation of $2750A\mathrm{GeV}$ Pb nuclei on ${}^{12}\mathrm{C}$ (top panel) and ${}^{74}\mathrm{W}$ (bottom panel) targets as a function of the mass-to-charge ratio normalized to that of the main circulating beam. A contribution from nuclear fragments other than indicated by filled bars is shown with unfilled bars.

Figure 9

Cross sections for the production of the heaviest (top panel) and light (bottom panel) fragments (together with ${}^{203}\mathrm{Hg}$) in electromagnetic dissociation of $2750A\mathrm{GeV}$ Pb nuclei on ${}^{12}\mathrm{C}$ target as a function of the momentum-to-charge ratio normalized to that of the main circulating beam.

Figure 10

Cross sections for the production of the heaviest (top panel) and light (bottom panel) fragments (together with ${}^{203}\mathrm{Hg}$) in electromagnetic dissociation of $2750A\mathrm{GeV}$ Pb nuclei on ${}^{74}\mathrm{W}$ target as a function of the momentum-to-charge ratio normalized to that of the main circulating beam.

Figure 11

Longitudinal momentum distribution for the heaviest fragment in electromagnetic dissociation of $2750A\mathrm{GeV}$ ${}^{208}\mathrm{Pb}$ ions interacting with stationary carbon nuclei (lower histogram), and in Pb-Pb beam collisions (upper histogram).

Figure 12

Transverse momentum distribution for the heaviest fragment in electromagnetic dissociation of $2750A\mathrm{GeV}$ ${}^{208}\mathrm{Pb}$ ions interacting with stationary carbon nuclei (lower histogram), and in Pb-Pb beam collisions (upper histogram).