Quantum-mechanical equivalent-photon spectrum for heavy-ion physics

Abstract

In a previous paper, we calculated the fully quantum-mechanical cross section for electromagnetic excitation during peripheral heavy-ion collisions. Here, we examine the sensitivity of that cross section to the detailed structure of the projectile and target nuclei. At the transition energies relevant to nuclear physics, we find the cross section to be weakly dependent on the projectile charge radius, and to be sensitive to only the leading momentum-transfer dependence of the target transition form factors. We exploit these facts to derive a quantum-mechanical "equivalent-photon spectrum" valid in the long-wavelength limit. This improved spectrum includes the effects of projectile size, the finite longitudinal momentum transfer required by kinematics, and the response of the target nucleus to the off-shell photon.In the previous decade, relativistic heavy-ion beams have become a useful tool for the study of electromagnetic processes in nuclei. Applications have included studies of nuclear astrophysics[1], nuclei far from stability [2], and searches for multi-phonon excitations in nuclei [3]. In these experiments, cross sections that are difficult to measure by other means are amplified by the projectile charge, and, in the case of relativistic projectiles, by the contraction of the projectile's electric field into a sharp pulse.Almost exclusively, the data from these experiments have been analyzed using the semiclassical Weizsäcker-Williams method of virtual quanta [4], in which the cross section for the heavy-ion-induced reaction is calculated by integrating the cross section for the analogous real-photon process over a flux of photons that is "equivalent" to those that make up the electric field of the projectile. In its simplest form, the pulse of equivalent photons is obtained from the boosted Coulomb field of the projectile by equating the classical Poynting flux onto the target to the energy flux carried by the pulse of equivalent photons. The semi-classical spectrum has been generalized to include arbitrary multipoles[5], projectile structure [6] and Coulomb scattering effects [7]. Attempts to move beyond the semi-classical picture of these processes have been thwarted by lack of information about the structure of the target nucleus [8]. Furthermore, there has been little motivation for improvement because the semi-classical spectrum, when used in conjunction with data from real-photon processes, provides model-independent results for cross sections measured in heavy-ion collisions [9].Recently, we have undertaken a program to systematically examine corrections to the semi-classical picture[10] [11], and have found significant deviations from the predictions of the Weizsäcker-Williams method for the mildly relativistic collisions (γ < 2 − 3) that constitute a significant fraction of the available data. The aim of the present work is to expand on the results of reference 10, examining the sensitivity of the cross section to nuclear structure inputs. Having determined which inputs are essential to extracting...

Electromagnetic dissociation of Au targets by Au beams in E862

“…The preliminary measured results for crtot, the nuclear contribution unuc and UED are given in Table 1. [15]. The basic folding method of the WW procedure was recovered as well as the effects of both the El and E2…”

Probing the quantum-mechanical equivalent-photon spectrum for electromagnetic dissociation of relativistic uranium projectiles

“…Recently, Benesh, Hayes, and Friar have presented new quantum-mechanical descriptions of the equivalentphoton spectra for electromagnetic heavy-ion collisions * Electronic address: TRubehn@lbl.gov [25]. This recent work has extended previous studies [26,27] by examining the sensitivity of nuclear structure inputs.…”

“…The indices E1 and E2 indicate the multipolarities. While most semi-classical calculations make use of a cutoff parameter, b min , in coordinate space to account for electromagnetic contributions only, the quantum-mechanical description introduces a cutoff parameter in momentum space [25]:…”

“…In this paper, we will not discuss the quantummechanical ansatz per se which has been presented in Ref. [25]; this issue will be addressed elsewhere [30]. However, we shall apply the given quantum-mechanical virtual photon spectra to calculate electromagnetic dissociation cross sections of relativistic heavy-ion collisions.…”

“…In particular, it will be shown that due to uncertainties in various input parameters, no unambiguous conclusions on the excitation of the double giant dipole resonance (DGDR) can be drawn by only investigating the electromagnetic 1n removal cross sections as it has been done in Ref. [25]. [17]).…”