ЯДЕРНАЯ ФИЗИКА, 2011, том 74, № 1, с. 139-150
ЭЛЕМЕНТАРНЫЕ ЧАСТИЦЫ И ПОЛЯ
ELECTROMAGNETIC AND HADRONIC INTERACTIONS OF ULTRARELATIVISTIC NUCLEI
©2011 I. A. Pshenichnov1)*, E. V. Karpechev1)**, A. B. Kurepin1), I. N. Mishustin2)'3)
Received February 10, 2010; in final form, May 13, 2010
Beam nuclei accelerated at the Large Hadron Collider (LHC) at CERN are lost due to interactions with the counter-rotating beam, residual gas, and accelerator elements. Proper modelling of the beam transport and radiation load on accelerator components requires reliable prediction of the yields of nuclear fragments produced in electromagnetic dissociation and hadronic fragmentation of beam nuclei. We investigate electromagnetic and hadronic fragmentation of lead nuclei in collisions with various nuclei and single electrons at the injection and collision energies of the LHC. The consideration is based on the RELDIS and abrasion—ablation models. Since this approach well describes Pb fragmentation data at 30 and 158 A GeV, its validity for Pb nuclei at the LHC collision energy is also expected.
1. INTRODUCTION
The advent of the Large Hadron Collider (LHC) at CERN puts forward new challenges to accelerator physics and theory of ion propagation in extended media. In particular, the interaction of the most energetic nuclei available on the Earth with the counter-rotating beam and various materials has to be understood and precisely simulated. It is expected that first lead nuclei with the design energy of 2.75 A GeV (2.75 GeV/nucleon) of each beam will collide in 2010-2011.
Hadronic collisions of lead nuclei will be studied by means of various detectors built, in particular, by the ALICE Collaboration [1, 2]. Such collisions are characterized by an overlap of nuclear densities of colliding nuclei, intense hadron production in the mid-rapidity region and violent nuclear fragmentation. There exist several theoretical approaches which predict various characteristics of violent PbPb collisions and draw conclusions on the existence of new states of hadronic matter (quark—gluon plasma) during such collision events, see, e.g., [3].
Since the LHC is designed with the primary goal to collide protons, its collimator system is currently well tuned to clean proton beams, see, e.g., [4]. However, the same LHC collimator system, possibly with minor modifications, will also be used to accelerate
'-'Institute for Nuclear Research, Russian Academy of Sciences, Moscow.
2)Frankfurt Institute for Advanced Studies, J.-W. Goethe
University, Frankfurt am Main, Germany
3)Kurchatov Institute, Russian Research Center, Moscow.
E-mail: pshenich@inr.ru
E-mail: karpeche@inr.ru
and collide nuclei. In this operation mode very peripheral hadronic collisions and distant electromagnetic interactions of nuclei do not destroy projectile nuclei completely. In addition to a few hadrons, such collisions result in heavy fragments of beam nuclei propagating in very forward direction beyond the acceptance of the ALICE detectors. Since produced fragments are close in mass and charge to initial ions, they propagate nearby to undisturbed beam nuclei and may pass through the collimator system. This gives rise to specific well localized radiation and heat loads on certain elements of the LHC, see [5] for details.
First of all, the LHC luminosity is restricted by the process of the bound-free pair production (BFPP), which is due to copious creation of e+e- pairs and subsequent capture of an electron by the 208Pb82+ projectile resulting in a 208Pb81+ ion. The BFPP process was investigated in several theoretical and experimental studies, see [6] for a detailed review of these results.
Due to a high BFPP cross section (272 b, see, e.g., [7]), this process is very frequent. However, the change in magnetic rigidity of 208Pb81+ ions is not enough for separating them from the beam nuclei immediately after the interaction point, see [8]. This finally leads to a well-localized impact of 208Pb81+ ions on superconducting dipole magnets of the LHC, which possibly result in their quenching at the design luminosity of the LHC, see [9] for details.
The electromagnetic dissociation (EMD) of nuclei is the second important source of ions with their magnetic rigidity close to the beam nuclei. The emission of one or two neutrons is a dominant process of EMD of Pb nuclei at the LHC, but other
channels with emission of charged particles cannot be neglected [10, 11]. On the contrary to the BFPP process, the EMD process leads to a wide spectrum of nuclear fragments. Therefore, accurate calculations of heat loads on critical elements of the LHC require reliable predictions of the fragmentation yields of ultrarelativistic Pb nuclei.
As the fragments produced in peripheral and ultraperipheral nuclear collisions at the LHC cannot be registered directly by the ALICE detectors, these collision events have received much less attention compared to central nucleus—nucleus collisions. However, their impact on the LHC operation in ionion collision mode is crucial [4, 5, 8, 9].
We propose a set of models to describe peripheral and ultraperipheral nuclear collisions at the injection and collision energies of the LHC. The models are validated by comparison with available experimental data on Pb fragmentation on various nuclei. Electro-disintegration of lead nuclei in collisions with atomic electrons is also considered. The predicted yields of nuclear fragments can be used as input for various transport models describing the interaction of Pb beams with various materials.
Ultraperipheral collisions of fully-stripped Pb ions with various nuclei are studied within the framework of the Relativistic ELectromagnetic DISsociation (RELDIS) model [10-12]. Peripheral hadronic collisions, which are characterized by a small overlap of the nuclear densities of colliding nuclei, are described by a modified version of the abrasion—ablation model [13]. In Sections 2 and 3 brief surveys of relevant physics processes are given together with descriptions of the abrasion—ablation and RELDIS models. In Section 4 the calculational methods are validated by comparison of their results with the experimental data obtained at the CERN SPS on fragmentation of relativistic Pb nuclei [13—17]. Fragmentation of lead nuclei on fixed targets at the LHC injection energy of 175 A GeV and at the nominal beam energy of 2750 A GeV is considered in Section 5, where the predictions for the total fragmentation cross sections in various materials are given. The simulation results for beam—beam interactions at the LHC are presented in Section 6, where the mass, charge, and momentum distributions of heavy secondary fragments are given. Finally, Section 7 contains a summary of results and suggestions for future development of the models.
2. REVISITED ABRASION—ABLATION MODEL FOR HADRONIC FRAGMENTATION
In hadronic interactions of nuclei the collision impact parameter b varies from b ~ 0 in central collisions, which are characterized by a complete overlap
of nuclei, till b ~ R1 + R2 in peripheral collision events described as grazing interactions. Here the nuclear radii of colliding nuclei are denoted as Ri and R2. We use a revisited abrasion—ablation model to describe the production of nuclear fragments in peripheral nuclear collisions.
According to the abrasion—ablation model, each collision event consists of two stages. On the first abrasion stage nucleons from overlapping parts of the colliding nuclei (participant nucleons) are split-ted ("abraded") from nonoverlapping parts of nuclei called spectators. At relativistic collision energies nucleons from the participant zone are kinematically well separated from spectator nucleons, which form excited remnants of the initial nuclei treated as pre-fragments. The cross section for the abrasion of a given number of nucleons from the projectile nucleus in a collision with the target nucleus is derived from the Glauber semiclassical theory of multiple scattering [ 18]. We use a similar approach for calculating the probabilities to remove a given number of protons and neutrons in the collision, see [ 13] for details.
Excited remnants of projectile and target nuclei (prefragments) decay at the second "ablation" stage of each nucleus—nucleus collision event. Cold nuclei in their ground states and several lighter nuclear fragments (mostly nucleons) are usually produced in such decays. It is quite common to describe the ablation process by the statistical evaporation and fission models [18—20]. A key point in abrasion— ablation calculations consists in a reliable estimation of the excitation energy of prefragments E*. Several prescriptions for E* are proposed, see [18—22], which estimate E* per each abraded nucleon as 13—26 MeV on the average.
This approach is aimed mostly at the description of heavy nuclear fragments consisting of spectator nucleons, and it is well known for heavy-ion collisions at intermediate energies of A GeV [18—22]. The production of secondary hadrons in collisions of participant nucleons is neglected. Therefore, the predictions of the abrasion—ablation model for secondary hadrons become inaccurate above the pion production threshold. Nevertheless, we believe that spectator matter still can be satisfactorily described by this model even at high collision energies.
As found [13], the abrasion—ablation picture of nuclear collisions remains valid also for production of heavy nuclear fragments at ultrarelativistic energies of ~10—100 A GeV. In this case the excitation energy of prefragments may be well described by the Ericson formula, see [13] for details. This gives ^40 MeV per each abraded nucleon, with some increase in this value compared to fragmentation of intermediate energy heavy ions. We attribute this increase to
additional heating of spectators by secondary hadrons produced at high collision energies.
Presently we follow the approach [13] to describe the production
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