Bremsstrahlung from Relativistic Heavy Ions in a Fixed Target Experiment at the LHC

Hindawi Publishing Corporation Advances in High Energy Physics Volume 2015, Article ID 625473, 4 pages http://dx.doi.org/10.1155/2015/625473 Research Article Bremsstrahlung from Relativistic Heavy Ions in a Fixed Target Experiment at the LHC Rune E. Mikkelsen, Allan H. Sørensen, and Ulrik I. Uggerhøj Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C, Denmark Correspondence should be addressed to Rune E. Mikkelsen; Received 20 March 2015; Accepted 13 May 2015 Academic Editor: Gianluca Cavoto Copyright © 2015 Rune E. Mikkelsen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3 . We calculate the emission of bremsstrahlung from lead and argon ions in ultraperipheral collisions in a fixed target experiment (AFTER) that uses the LHC beams. With nuclear charges of Ze equal to 82e and 18e, respectively, these ions are accelerated to energies of 7 Tev × Z. The bremsstrahlung peaks around ≈100 GeV and the spectrum exposes the nuclear structure of the incoming ion. The peak structure is significantly different from the flat power spectrum pertaining to a point charge. Photons are predominantly emitted within an angle of 1/𝛾 to the direction of ion propagation. Our calculations are based on the WeizsäckerWilliams method of virtual quanta with application of existing experimental data on photonuclear interactions. 1. Introduction The structure of stable nuclei, in particular the charge distribution, may be investigated by impact of photons and electrons as, for example, shown in pioneering works by McAllister and Hofstadter; see, for example, [1]. This method, however, is not possible for unstable nuclei with short lifetimes as, for example, hypernuclei. Instead, essentially with a change of reference frame, one may let the nucleus under investigation impinge on a suitable target, for example, an amorphous foil, and measure the delta electrons and/or photons emitted in the process. The interaction thus proceeds between the nucleus and a target electron or a virtual photon similarly originating from the target. With this method the charge distribution may be measured, in this case of the projectile, which might be a nucleus of very short lifetime, 𝛾𝑐𝜏 ≃ 1 mm, where 𝛾 is the Lorentz factor, 𝑐 the speed of light, and 𝜏 the lifetime. With the proposal to extract protons and heavy ions from the LHC for fixed target physics, the socalled AFTER@LHC, such measurements would in principle enable charge distributions, or at least sphericity, for nuclei with lifetimes down to femtoseconds to be extracted. We report calculations of bremsstrahlung emission from Pb and Ar nuclei, with energies corresponding to the maximum of the LHC. We are restricted to cases where the projectile is left intact, that is, to ultraperipheral collisions in which projectile and target nuclei do not overlap. The interaction between the collision partners is electromagnetic but the structure of the composite projectile nucleus, namely, the strong nuclear force, plays a significant role in the photon emission through the giant dipole resonance. 2. Bremsstrahlung We study bremsstrahlung emission by relativistic heavy ions. When traversing an amorphous target, the projectile ions interact with the target electrons and nuclei. This causes radiation emission and energy loss to the projectiles. We focus on the radiation and assume the ion beam to be monoenergetic; that is, we consider targets sufficiently thin that the projectile energy loss is minimal. We further assume impact parameters in excess of the sum of the radii of collision partners. To establish a reference value for the cross section, we first consider the incoming ion as a point particle of electric charge 𝑍𝑒 colliding with target atoms of nuclear charge 𝑍𝑡 𝑒. The major part of the radiation is due to the interaction of the projectile with target nuclei which, in turn, are screened by target electrons at distances beyond the Thomas-Fermi 2 Advances in High Energy Physics distance, 𝑎TF . The cross section differential in energy for the emission of bremsstrahlung photons from an ion with atomic number 𝐴 then reads [2] where 𝛾 ≡ 𝐸/𝑀𝑐2 , 𝛾󸀠 ≡ (𝐸 − ℏ𝜔)/𝑀𝑐2 , 𝑚 is the electron mass, and 𝑀 is the mass of the projectile. The materialdependent factor 𝐿 accounts for the electronic screening of the target nuclei. It is essentially the logarithm of the ratio between the effective maximum (∼2𝑀𝑐) and minimum (∼ℏ/𝑎TF ) momentum transfers to the scattering center. The reference power spectrum extends all the way up to the energy of the primary ion and varies only slightly with energy. However, as we will study in this paper, photons with energy ℏ𝜔 ≳ 𝛾ℏ𝑐/𝑅 have wavelengths smaller than the radius of the ions which cause the emission, making them sensitive to the nuclear structure and collective dynamics of the constituent protons. Taking this into account causes significant change in the shape of the bremsstrahlung spectrum. this with the photonuclear scattering cross section differential in angle results in the scattering cross section differential in energy and angle. The transformation to the laboratory frame is performed by utilizing an invariance relation [2] and produces the bremsstrahlung power spectrum differential in energy and angle; for details, see [6–8]. In [6], one of us used this procedure to calculate the bremsstrahlung spectrum of relativistic bare lead ions. This was possible by using the photonuclear interaction data provided in [9]. However, data for other nuclei is not abundantly available. We therefore developed a procedure to derive the necessary elastic scattering cross sections taking total photonuclear absorption cross sections as input; these are available in the ENDF database for about 100 different nuclei [10]. We obtain the elastic scattering cross sections at low to moderate energies, that is, at energies covering the giant dipole resonance by applying the optical theorem and a dispersion relation to the total photonuclear absortion data; see [7]. At higher energies additional constraints are invoked to ensure coherence. With this construct, the bremsstrahlung spectrum can be calculated for any ion for which the total photon absorption cross section is known. Due to the available data, our approach is most exact for lead ions which have already been successfully accelerated to 4 TeV × 𝑍 in the LHC machine. Also, this allowed us to cross-check the earlier calculations for the bremsstrahlung from lead. It has not been finally decided if other ions will ever be used in the LHC. But argon ions are frequently discussed as a possibility if the physics case requires lower mass ions to be accelerated [11]. Supporting this idea, in 2015, the CERN accelerator complex is successfully ac (...truncated)