Virtual Photon Spectrum Research Articles

Virtual photon approach of cathodoluminescence and ion-beam induced luminescence of solids

A novel analysis of cathodoluminescence (CL) and ion-beam induced luminescence (IBIL) is presented on the basis of virtual photon spectra (VPS) produced by charged particles (electrons or ions) passing by luminescent species such as defects or impurities, in wide band-gap ionic-covalent solids. A discussion is provided for irradiations in a wide range of charged particle kinetic energy by using the Weizsäcker-Williams theory. The computed VPS are found to decay rapidly as a function of virtual photon (VP) energy regardless of particle energy, for close or distant collisions. The electron-energy dependence of experimental CL spectra of sapphire (α-Al2O3) is discussed in relation to the computed VPS for the primary and secondary electrons. The experimental IBIL spectra of α-Al2O3 are also analyzed in this framework for protons and helium ions in the MeV energy range. The variations of stopping power are consistent with the variation of the number of emitted VPs. The decay of IBIL yield versus ion stopping power is discussed on the basis of the variation of the computed VPS, and ionization and excitation induced by primary ions and secondary electrons. This decay is accounted for by a decrease of the yield of low-energy secondary electrons with the subsequent VP emission.

Multi-differential pattern of low-mass e+e− excess from [formula omitted] Au+Au collisions with HADES

The matter formed in central heavy-ion collisions at a few GeV per nucleon is commonly understood as resonance matter, a gas of nucleons and excited baryon states with a substantial contribution from mesonic, mostly pionic excitations. Yet, in the initial phase of the reaction the system is compressed to beyond nuclear ground state density and hence substantial modifications of the hadron properties are expected to occur. The spectral distribution of virtual photons measured in Au+Au collisions at 2.4 GeV center of mass energy indicates strong medium effects beyond pure superposition of individual NN collisions. We present multi-differential distributions of low-mass electron pairs. This radiation is remarkably well described assuming emission from a thermalized system. To gain deeper understanding of the microscopic origin of the radiation, we extracted the centrality dependent true (not blue-shifted) temperature, its azimuthal distribution, as well as mass-dependent effective slope parameter. Virtual photon spectra are confronted with available model calculations.

Spectrum of Virtual Photons in the Electroproduction of Negatively Charged Pions on Deuterons

Numerical and analytical calculations of the virtual photon spectrum have been performed for the electroproduction of negatively charged pions on a deuteron. The numerical calculations of the virtual photon spectrum were performed without recourse to any approximations while a number of approximations were admitted in the derivation of the analytical expression. A comparison of the results of an exact numerical calculation of the virtual photon spectrum with the results of a calculation obtained using an approximate analytical expression for the virtual photon spectrum has been performed for the first time. It is shown that the discrepancy between the virtual photon spectra obtained with the help of numerical and analytical methods can reach 10% in the kinematic region of photoproduction of pions with intermediate energies. It follows from the obtained results that in the statistical modeling of the yields of the reaction of photoproduction of negatively charged pions on a deuteron it is necessary to use the exact virtual photon spectrum obtained with the help of numerical methods whereas in the statistical modeling of the asymmetry of reactions of photoproduction of negatively charged pions on a deuteron it is sufficient to use the approximate analytical expression for the virtual photon spectrum.

Statistical and direct aspects of64Zn(γ,n)and(γ,np)decay channels in the giant dipole resonance and quasideuteron energy regions

The investigation of statistical and direct aspects related to the $(\ensuremath{\gamma},n)$ and $(\ensuremath{\gamma},np)$ decay channels of ${}^{64}\mathrm{Zn}$ in the giant dipole resonance (GDR) and quasideuteron (QD) energy regions was performed by a trial function fitting to the respective $(e,n)$ and $(e,np)$ electrodisintegration yields measured by residual activity. The trial function incorporated the GDR and QD models to describe the initial photoabsorption mechanism and the geometry dependent hybrid exciton model used in the ALICE/LIVERMORE-82 code to calculate the relevant branching ratios, with the $E1$ virtual photon spectra being calculated in the distorted wave Born approximation. We compared our results for the $(\ensuremath{\gamma},n)$ cross section with other existing experimental measurements, and the long-standing normalization issue among different laboratories was revisited and addressed. We obtained for the first time the absolute $(\ensuremath{\gamma},np)$ cross section from threshold to 60 MeV. We succeeded in separating statistical and direct contributions of the $(\ensuremath{\gamma},np)$ process, the latter being remarkably well described by the QD model in the interval 40--60 MeV. A possible direct contribution for the $(\ensuremath{\gamma},n)$ decay in the GDR is also addressed. Finally, the total photoabsorption cross section of ${}^{64}\mathrm{Zn}$ was reevaluated up to 21 MeV, and the results were compared with previous estimates performed by other groups.

Electromagnetic dissociation of [formula omitted] GeV 24Mg and 28Si projectiles in nuclear emulsion

This paper presents exhaustively the results of the electromagnetic dissociation of 3.7 A GeV 24Mg and 28Si projectiles in nuclear emulsion. The reaction mechanism involved in the electromagnetic collisions and the virtual photon spectra are discussed in the framework of the classical model of Weizsäcker and Williams. The number of electromagnetic interactions, the mean free paths, the production cross sections, the charge spectra of projectile fragments and the decay modes of the visible channels are analyzed and their dependences on the projectile charge and the incident energy are investigated. The present values are obtained in systematic agreement with those found experimentally and theoretically. The emission of a single hydrogen isotope is the dominant process in all samples and shows a similar energy spectrum. The relative rate as a function of the threshold energy for various reaction channels are parameterized in terms of an exponential function.

Two proton and two neutron photoemission cross sections of 63Cu.

The ({ital e},2{ital p}) and ({ital e},2{ital n}) cross sections and the ({ital e}+{gamma},2{ital p}) and ({ital e}+{gamma},2{ital n}) yields have been measured for {sup 63}Cu in the electron energy range 28--60 MeV. The experimental results have been analyzed using distorted-wave Born approximation {ital E}1 and {ital E}2 virtual photon spectra in order to derive the {ital E}1 and isovector {ital E}2 components of the ({gamma},2{ital p}) and ({gamma},2{ital n}) cross sections. In the 2{ital n} channel the {ital E}1 component exhausts 12.4(11)% of the {ital E}1 energy weighted sum, while the isovector {ital E}2 component exhausts 52(15)% of its sum. The 2{ital p} channel exhausts 1.03(8)% of the energy weighted sum for {ital E}1 and we were able to establish an upper limit for the isovector {ital E}2 contribution of 0.58% of its sum.

Projectile multifragments break-up and the electromagnetic-field effect of target nucleus

This work presents a special type of interactions produced in emulsion targets exposed to different incident beams of light ions at a few GeV per nucleon. The events characterised by multifragment break-up of the projectile nucleus which are produced via peripheral collisions or due to the effect of the Coulomb field of the target nucleus have been selected. The size of the impact parameter must be considered for determining the type of the interaction. The results are compared with other collected data at energies up to 200 GeV/nucleon. The dependence of electromagnetic dissociation cross-section on the incident projectile energy is investigated. Also, a comparison of the experimental data with the assumed virtual-photon spectrum using Weizsacker-Williams (WW) method is made.

Electromagnetic dissociation of relativistic 28Si.

We have studied in detail the electromagnetic dissociation of [sup 28]Si projectiles at 14.6 GeV/([ital c] nucleon), interacting with Pb, Sn, Cu, and Al targets. Exclusive cross sections were measured for several decay channels, including final states involving the emission of protons, neutrons, and [alpha] particles. Excitation energy distributions for the 1[ital n]+[sup 27]Si and 2[ital p]+[sup 26]Mg decay channels were reconstructed with a resolution of 2 MeV, using a constrained kinematic fit. The energy distributions obtained for 1[ital n]+[sup 27]Si are in good agreement with the [sigma]([gamma],[ital n]) photoneutron cross sections multiplied by the virtual photon spectrum obtained in the Weizsaecker-Williams approximation. A search for the double photon excitation process, based on the dependence of the cross sections on the target atomic number, was performed.

One neutron photoemission cross section of 238U.

The ([ital e],[ital n]) cross section and the ([ital e]+[gamma],[ital n]) yield have been measured for [sup 238]U in the electron energy range 12--60 MeV. The experimental results have been analyzed using distorted-wave Born approximation [ital E]1 and [ital E]2 virtual photon spectra for a finite nucleus in order to derive the [ital E]1 and [ital E]2 components of the ([gamma],[ital n]) cross section. The [ital E]1 component exhausts 40% of the [ital E]1 energy weighted sum rule while the isoscalar [ital E]2 exhausts 70--80 % of its sum.

Fragment angular distributions in electron- and positron-induced fission of 232Th : A specific test of virtual photon spectra★

Fragment angular distributions have been measured for electron- and positron-induced fission of 232Th in the energy range 8–16 MeV. The quite different angular distribution patterns for electron and positron bombardments are compared with photofission data to test recently calculated virtual photon spectra for E11 and E2 excitations of heavy nuclei in electron- and positron-induced electrodisintegration experiments.

Higgs-boson production in nucleus-nucleus collisions.

Cross-section calculations are presented for the production of intermediate-mass Higgs bosons produced in ultrarelativistic nucleus-nucleus collisions via two-photon fusion. The calculations are performed in position space using Baur's method for folding together the Weizsacker-Williams virtual-photon spectra of the two colliding nuclei. It is found that two-photon fusion in nucleus-nucleus collisions is a plausible way of finding intermediate-mass Higgs bosons at the Superconducting Super Collider or the CERN Large Hadron Collider.

Proton emission cross sections of silicon isotopes

Measurements of the electrodisintegration cross sections, (e,p) and (e,2p), and their corresponding electrodisintegration-plus-photodisintegration yields for $^{29}\mathrm{Si}$ and $^{30}\mathrm{Si}$ are presented. The experiment covers the range from 20 to 60 MeV electron incident energies. The experimental results were analyzed using E1 and E2 distorted-wave Born approximation virtual photon spectra for a finite nucleus in order to obtain the corresponding photodisintegration cross sections for both channels and isotopes. For $^{29}\mathrm{Si}$ the integrated (\ensuremath{\gamma},p) cross sections is 47% bigger than (\ensuremath{\gamma},n) while for $^{30}\mathrm{Si}$ they are of the same order of magnitude. For both isotopes the (\ensuremath{\gamma},p) decay channel is dominantly E1. The (\ensuremath{\gamma},2p) channel is much smaller than the (\ensuremath{\gamma},2n) channel but the E2 contribution to this decay mode is of the same magnitude of the E1.

Electromagnetic dissociation of 28Si at Elab/A=14.6 GeV by nucleon emission.

Electromagnetic dissociation cross sections for one, two, and three nucleon removal were measured for an Elab/A=14.6 GeV Si28 beam impinging on Al27, Sn120, and Pb208 targets. The measured cross sections exhibit an approximate ZT2 dependence and are well reproduced by calculations convoluting the virtual photon spectrum with the experimental σ(γ,N) photonuclear cross sections. Comparison with other experimental results and energy dependence of the cross sections are discussed.Received 20 November 1989DOI:https://doi.org/10.1103/PhysRevC.41.1512©1990 American Physical Society

Real and virtual radiation

Electrodisintegration cross sections are related to the corresponding photonuclear processes through virtual-photon spectra. A brief review of virtual-photon theory is presented. Calculations of DWBA virtual-photon spectra for finite nuclei are compared with experimental results. The multipole decomposition of electrodisintegration cross sections using these spectra is discussed and several experimental results are presented. A brief review for the bremsstrahlung cross section is also presented.

Fragmentation cross sections of 28Si at 14.5 GeV/nucleon.

We used CR39 plastic nuclear track detectors (C12H18O7) in combination with automatic track measurement techniques to determine total charge changing and partial cross sections for the production of fragments of charge ZF = 6 to ZF = 13 in collisions of 28Si beam nuclei at 14.5 GeV/nucleon in targets H, C, CR39, (C18H38O), Al, Cu, Ag, and Pb. By application of factorization rules, measured partial cross sections are separated into pure nuclear and electromagnetic components. The cross sections for electromagnetic dissociation agree with theoretical models. The results are consistent with a Z2 dependence of virtual photon spectra.

Two-neutron emission from electromagnetic dissociation of 59Co and 197Au targets by relativistic heavy ions.

Electromagnetic dissociation of /sup 59/Co and /sup 197/Au target nuclei and their subsequent deexcitation by two-neutron emission was observed. Beams of relativistic /sup 12/C, /sup 20/Ne, /sup 40/Ar, /sup 56/Fe, and /sup 139/La ions were used. The measured electromagnetic dissociation cross sections become large for high-Z targets and projectiles, reaching 335 mb for the /sup 197/Au(/sup 139/La,X)/sup 195/Au reaction with 1.26 GeV/nucleon /sup 139/La projectiles. The experimental cross sections in excess of the estimated nuclear contributions are in reasonable agreement with a calculation of the electromagnetic dissociation contribution using the Weizsaecker-Williams method for estimating the virtual photon spectrum.

M1 strength in197Au

The electrodisintegration of 197Au was measured by residual activity from threshold to 23 MeV. The results are analysed with DWBA virtual photon spectra for finite nuclei (E1 and E2 multipoles, point DWBA for M1) to obtain M1 and E2 strengths.

Electrodisintegration of208Pb,209Bi and181Ta

The electrodisintegration cross section has been measured for 208Pb, 209Bi and 181Ta, from threshold to 22 MeV, by detecting the emitted neutrons. The quantity measured is sigma e,Tn= sigma e,n+2 sigma e,2n. The results are analysed with DWBA virtual photon spectra for finite nuclei to obtain M1 and E2 strengths.

Calculation of the virtual photon spectrum for a finite nucleus in distorted wave methods

The electron virtual photon spectrum is calculated for a finite nucleus in distorted wave methods for E1, E2, E3 and M1 transitions. Evaluation of the external radial integrals is made in terms of a series of incomplete gamma functions. Internal radial integrals are evaluated using charge and current distributions which are model independent up to an incident electron energy of about 200 MeV.

An algorithm for a semiempirical nuclear fragmentation model

In the present paper, an algorithm for HZE (High Charge and Energy) fragmentation based upon a combination of a two step abrasion/ablation model and electromagnetic dissociation is presented. Development of the model and detailed comparison with available experimental data are given elsewhere. The abrasion process accounts for the removal of nuclear matter in the overlap region of the colliding ions. An average transmission factor is used for the projectile and target nuclei at a given impact parameter to account for the finite mean free path in nuclear matter. The ions are treated otherwise on a geometric basis assuming uniform spheres. The ablation process is treated as a single nucleon-evaporation for every 10 MeV of excitation energy as used by Bowman in the original form of the model. The charge distribution of final fragments are calculated according to the Rudstam formula, except for some correction in mass 5, 8 and 9 fragments which show strong structure effects and correspondingly significant deviation from Rudstam's values. The nuclear electromagnetic dissociation is based on the Weizsacker-Williams (WW) method of virtual quanta where due to its simplicity, the virtual photon spectrum for individual multipoles, and finite extent of the charge distribution are not included. Comparisons of the model are made with the available experimental data here and more extensively elsewhere.