Virtual Photon Spectrum Research Articles

Electron induced fission of the 238U, 237Np, 239Pu and 243Am nuclei in the energy region 100–1000 MeV

Electrofission cross sections for 238U, 237Np, 239Pu and 243Am have been measured over the energy range 100–1000 MeV. Relative flssilities are evaluated. Analysis in terms of the virtual photon spectra technique involving a nuclear size effect is made. Contributions of various electronuclear excitation mechanisms in the large-energy region are discussed.

Virtual photons in pion electroproduction

We examine the applicability of the virtual photon spectrum to pion production experiments by using an exact calculation of pion electroproduction from the proton and from 3He. After deriving a new virtual spectrum formula which takes into account the recoil of light target nuclei and the proper electron kinematics near the endpoint, we find that the concept of a virtual photon spectrum in such experiments is very good.

Absolute cross sections for electron- and positron-induced fission of 238U and tests of DWGA virtual-photon spectra

Absolute cross sections for electron- and positron-induced fission of 238U have been measured in the energy range 10–35 MeV. The cross sections were compared with the corresponding photo-fission cross sections using DWBA virtual-photon spectra. The reliability of the virtual-photon formalism to extract E2 strength from inclusive electrodisintegration experiments is critically discussed.

Fission decay of the giant quadrupole resonance forU234

The electrofission cross section for $^{234}\mathrm{U}$ from 5.5 to 25.4 MeV has been measured. From a combined analysis of it and the previously measured photofission cross section, using virtual-photon spectra calculated in the distorted-wave Born approximation, the $E2$ photofission cross section has been determined. Parameters of the fission-decay branch of the giant quadrupole resonance for this nucleus have been obtained. A comparison of the $E2$ and $E1$ integrated photofission cross sections for the even uranium isotopes shows that the $E1$ fission channel increases in strength more rapidly with fissility than does the $E2$ channel.NUCLEAR REACTIONS Measured $\ensuremath{\sigma}(e,f)$ for $^{234}\mathrm{U}$; deduced ${\ensuremath{\sigma}}^{E2}(\ensuremath{\gamma},f)$.

Calculation of the virtual photon spectrum in distorted wave analysis

Calculation of the virtual photon spectrum in distorted wave analysis

E2giant resonances and anM1component in the photofission ofU236

Electrofission and photofission yields and electrofission-fragment angular distributions for /sup 236/U have been measured with fission-track detectors for incident electron energies from 5.5 to 33.0 MeV. Analysis of these data with the use of virtual-photon spectra calculated in distorted-wave Born approximation, combined with the known photofission cross section, results in the simultaneous determination for this nucleus of (a) a giant isoscalar E2 resonance located at 10.8 +- 0.4 MeV, having a width of 6 +- 1 MeV, and exhausting approx.70% of the isoscalar energy-weighted sum rule, and (b) a small M1 component located at 5.8 +- 0.2 MeV whose strength is <2% of that of the giant isoscalar E2 resonance. No evidence is seen for a giant isovector E2 resonance between 22 and 30 MeV.

Test ofE2virtual-photon spectra calculated in the distorted-wave Born approximation

From a joint analysis of electrofission- and photofission-fragment angular distribution data for $^{236}\mathrm{U}$ and $^{238}\mathrm{U}$, limits can be set on the uncertainties of the $E2$ virtual-photon spectra calculated in the distorted-wave Born approximation that are no larger than \ifmmode\pm\else\textpm\fi{}20%.NUCLEAR REACTIONS $^{236,238}\mathrm{U}(e, f)$ angular distributions; virtual-photon spectra; distorted-wave Born approximation.

Experimental test of virtual photon theory for pion electroproduction on light nuclei

The virtual photon spectrum shape and intensity within several MeV of the kinematic limit was measured for $^{9}\mathrm{Be}(e, {\ensuremath{\pi}}^{+})^{9}\mathrm{Li}, {e}^{\ensuremath{'}}$ and $^{16}\mathrm{O}(e, {\ensuremath{\pi}}^{+})^{16}\mathrm{N}, {e}^{\ensuremath{'}}({T}_{\ensuremath{\pi}}=28 \mathrm{MeV}, {\ensuremath{\theta}}_{\ensuremath{\pi}}=90\ifmmode^\circ\else\textdegree\fi{})$. The intensity over this interval is 1.25\ifmmode\pm\else\textpm\fi{}0.10 times plane-wave virtual photon theory predictions; the shape agrees with theory within errors. Measurements on the proton 30 to 55 MeV below the end point agree with the intensity predictions of virtual photon theory within the errors (\ifmmode\pm\else\textpm\fi{}8%).NUCLEAR REACTIONS $^{16}\mathrm{O}(e, {\ensuremath{\pi}}^{+})$, $E=180.4$ MeV; $^{9}\mathrm{Be}(e, {\ensuremath{\pi}}^{+})$, $E=184.8$ MeV; measured $\ensuremath{\sigma}({E}_{\ensuremath{\pi}}, {90\ifmmode^\circ\else\textdegree\fi{}}_{\mathrm{lab}})$ relative to ($\ensuremath{\gamma}, {\ensuremath{\pi}}^{+}$), near ${E}_{\ensuremath{\pi}}=28$ MeV. $^{1}\mathrm{H}(e, {\ensuremath{\pi}}^{+})$, $E=230$ MeV; measured $\ensuremath{\sigma}({E}_{\ensuremath{\pi}}, {90\ifmmode^\circ\else\textdegree\fi{}}_{\mathrm{lab}})$ relative to ($\ensuremath{\gamma}, {\ensuremath{\pi}}^{+}$), near ${E}_{\ensuremath{\pi}}=18, 30$ MeV. Compared to PWBA virtual photon theory.

Statistical and pre-equilibrium (γ,α) cross sections ofZr90and their multipolarities via theZr90(e,α) reaction

The (e,..cap alpha..) cross section in /sup 90/Zr has been measured at incident electron energies from 13.5 MeV to 66.5 MeV for ..cap alpha.. particles between 6.9 and 16.8 MeV. The (..gamma..,..cap alpha..) cross section was deduced from it assuming both E1 interaction and E2 interaction. The angular distribution of the (..gamma..,..cap alpha../sub 0/) cross section and an experiment using the bremsstrahlung plus electron beam make it clear that the E1 interaction is dominant over all the present energy range. The (..gamma..,..cap alpha..) cross section extracted by using E1 virtual photon spectra has a large bump above the excitation energy of 30 MeV in addition to a bump in the giant dipole resonance region. The (..gamma..,..cap alpha../sub 0/) cross section also has a bump at the giant dipole resonance which exhausts most of the (..gamma..,..cap alpha..) cross section in that region. The compound nucleus model was used successfully to explain the bump at the giant dipole resonance. The cross section above 30 MeV is discussed in terms of the pre-equilibrium ..cap alpha.. emission process combined with the quasi-deuteron model.

Fe56(e,α) reaction and its relevance to theE2isoscalar sum rule

The cross section $^{56}\mathrm{Fe}$($e$,$\ensuremath{\alpha}$) has been measured as a function of $\ensuremath{\alpha}$ energy, lab angle, and incident electron energy. The analyses of these data using distorted-wave Born approximation virtual photon spectra have been performed in the framework of models suggested by the data. We find that the ($e$,$\ensuremath{\alpha}$) channel exhausts a sizable percentage of the $E2$ isoscalar sum rule.NUCLEAR REACTIONS $^{56}\mathrm{Fe}$($e$,$\ensuremath{\alpha}$,) measured $\ensuremath{\sigma}({E}_{0},{E}_{\ensuremath{\alpha}},{\ensuremath{\theta}}_{\ensuremath{\alpha}})$, obtained $\ensuremath{\sigma}(e,\ensuremath{\alpha})$ and determined ${\ensuremath{\sigma}}^{E1}(\ensuremath{\gamma},\ensuremath{\alpha})$ and ${\ensuremath{\sigma}}^{E2}(\ensuremath{\gamma},\ensuremath{\alpha})$.

Electrodisintegration of 197Au

Cross sections for the (e, xn) reaction on 197Au have been measured for 1 ≦ x ≦ 12 at 37, 72, 124 and 147 MeV bombarding energies using activation methods. Data for x ≦ 2 are compared with cross sections estimated from published (γ, n) and (γ, 2n) data integrated over the virtual photon spectrum. Theoretical cross sections for x ≧ 4 were calculated by means of an intranuclear cascade model. Good agreement is found for x ≦ 7. The increasing discrepancy between experimental and theoretical cross sections for x ≧ 7 is discussed. No evidence is found for giant resonances in regions above the giant dipole resonance.

Decay Modes of Giant Resonances inNi58,Ni60, andNi62

The ($e$,$p$) and ($e$,$\ensuremath{\alpha}$) cross sections for targets of $^{58}\mathrm{Ni}$, $^{60}\mathrm{Ni}$, and $^{62}\mathrm{Ni}$ have been measured in the electron energy range 16-50 MeV. They have been analyzed using the distorted-wave Born-approximation $E1$ and $E2$ virtual-photon spectra. Protons are emitted primarily following $E1$ absorption but $\ensuremath{\alpha}$ emission results from a combination of $E1$ and $E2$ absorption. The $E2$ isoscalar giant resonance decays predominantly by $\ensuremath{\alpha}$ emission for these nuclei.

Improved Weizsäcker-Williams method

In the spirit of the Weizs\"acker-Williams method virtual-photon spectra are derived which have the Weizs\"acker-Williams form for low frequencies. It is shown for the cases of pair production of fermions and single-boson production that the photon spectra give remarkably accurate results for one- and two-virtual-photon processes.

Electrodisintegration ofC12

The cross section for the production of the /sup 1/1C activity by bombarding /sup 1/2C with 30 MeV electrons has been measured absolutely. The result, 11.9 +- 0.2 ..mu..b, has a smaller absolute error than any previous measurement. This value corresponds to a (..gamma..,n) cross section integrated to 30 MeV of 41.0 +- 0.6 MeV mb, based on a distorted-wave Born-approximation electric dipole virtual photon spectrum.

A new technique for calculating virtual photon spectra

A first-order matrix differential equation in energy is used to propagate radial matrix elements arising in DWBA of relativistic electron scattering from nuclei. Given an initial set of matrix elements at some value of the energy, this equation permits the evaluation of the radial matrix elements over the complete energy transfer range. A computer code has been written for this new procedure and the virtual photon spectra accompanying electron scattering from a point nucleus is calculated as a function of photon energy for various multipoles, nuclear charges, and incident electron energies.

A comparison of absolute cross sections for electro- and photo-induced reactions

Absolute cross sections for electron and positron induced reactions on12C,63Cu and107Ag are compared with cross sections for the corresponding photo-induced reactions in order to test DWBA calculations of the virtual photon spectra. A good agreement is found between the experimental cross sections for the electrodisintegration and those calculated with DWBA spectra and photonuclear cross sections.

Radial integrals with finite energy loss for Dirac–Coulomb functions

Analytic results for radial integrals over products of Dirac–Coulomb functions and the radial part of the electromagnetic Green’s function are expressed in terms of a matrix generalization of the gamma function. This matrix gamma function has many useful properties, including a recurrence relation similar to that of the gamma function, and provides a compact easily manipulated method of evaluating the Dirac–Coulomb radial integrals. These results can be used to calculate the virtual and real photon spectra associated with electron scattering from the nucleus.

Electrofission and photofission ofU238in the energy range 6-60 MeV

Experimental results are presented for the electrofission and photofission of $^{238}\mathrm{U}$ in the energy range 6 to 60 MeV. The importance of the inclusion of the Coulomb corrections in the calculation of the virtual photon spectrum is emphasized and the relative $E1$ contribution to the electrofission process has been evaluated using the distorted-wave Born-approximation analysis of the experimental data.NUCLEAR REACTIONS, FISSION Measured electrofission and photofission cross sections of $^{238}\mathrm{U}$ in the energy range 6-60 MeV. Deduced relative $E1$ contribution to the electrofission process using DWBA analysis of the experimental data.

Electro- and photoinduced spallation reactions on27Al and51V at intermediate energies

Cross sections for some electro- and photoinduced spallation reactions on27Al and51V have been measured in the energy region 130–580 MeV with the activation method. The cross sections per photon are compared to Monte-Carlo calculations based on a cascade-evaporation model. The electrodisintegration cross sections are compared to calculations based on the Dalitz formalism for virtual photon spectra.

Photoproton Cross Section for 19F

Proton energy spectra have been measured at 90° for the 19 F(e, e'p) 18 O reaction in the giant resonance region. The (γ, p 0 ) and (γ, p 1 ) differential cross sections are extracted from the proton energy spectra by using virtual-photon spectra. The integrated differential cross section of the (γ, p 0 ) and (γ, p 1 ) reactions are 1.80±0.27 and 0.50±0.45 MeV-mb/sr, respectively. The results are discussed with the shell model theory by comparing with the (γ, p 0 ) cross section of the neighboring 4 n -nucleus 20 Ne. A significant increase of the proton yield leaving the non-ground states is found at 25 MeV of the incident electron energy. This is discussed in terms of the core excitation effect.