Virtual Photon Theory Research Articles

Systematic study on the role of various higher-order processes in the breakup of weakly-bound projectiles

Abstract The virtual photon theory (VPT), which is based on first-order Coulomb dissociation restricted to the electric dipole (E1), has been successfully used to explain the breakup data for several cases. Our aim is to study the role of various higher-order processes that are ignored in the VPT, such as the nuclear breakup, interference between nuclear and Coulomb amplitudes, and multistep breakup processes mainly due to strong continuum-continuum couplings in the breakup of two-body projectiles on a heavy target at both intermediate and higher incident energies. For the purpose of numerical calculations, we employed eikonal version of three-body continuum-discretized coupled-channels (CDCC) reaction model. Our results for the breakup of 11Be and 17F on 208Pb target at 100, 250, and 520 MeV/A, show the importance of nuclear breakup contribution, and its significant role in the multistep processes. The multistep effect on Coulomb breakup for core-neutron projectile was found to be negligible, whereas it was important for core-proton projectile. Coulomb-nuclear interference (CNI) effect was also found to be non-negligible. Qantitatively, the multistep effects due to the nuclear breakup was found to depend on the incident energy through the energy dependence of the core-target and nucleon-target nuclear potentials. The nuclear breakup component, the CNI effect, and the multistep breakup processes are all found to be non-negligible; hence, the assumptions adopted in the VPT for the accurate description of breakup cross sections are not valid.

Full coupled-channel description of three-body and four-body breakup reactions

Recent development of the continuum-discretized coupled-channels method (CDCC) is reported with introducing the eikonal CDCC method (E-CDCC) and four-body CDCC. The former is applied to analysis of 8B breakup by 208Pb at 52 A MeV and the astrophysical factor S 17 ( 0 ) for the 7Be( p , γ ) 8B reaction is extracted with the asymptotic normalization coefficient method. We obtain S 17 ( 0 ) = 20.9 −1.9 +2.0 eV b , which is significantly larger than the previous one, S 17 ( 0 ) = 18.9 ± 1.8 eV b , determined from an analysis with the virtual photon theory. The difference between the two values is found to be due to the contributions from nuclear breakup and higher-order processes. The latter, four-body CDCC, is applied to 6He+ 209Bi scattering near the Coulomb barrier energy and found to reproduce the elastic cross sections well, in contrast to the standard three-body CDCC. Accurate treatment of the three-body continuum states of 6He turns out to be essential to correctly describe the 6He+ 209Bi scattering.

Cross Sections and Angular Distributions for the10B(e,p) and10B(e,d) Reactions in the Giant Resonance Region

The cross sections and angular distributions of (γ,p) and (γ,d) reactions on 10 B have been measured in the giant resonance region by the (e,p) and (e,d) reactions applying the virtual photon theory. The E2 cross section of the (γ,p 0 ) reaction derived by a model dependent analysis of the angular distributions shows contributions of 26.5 ±4.5% to the E2 energy weighted sum rule. The (γ,p 0,2 ) integrated cross section up to 27 MeV is 6.1 ±0.2% of the E1 sum rule value which is smaller than 30% for 10 B(γ,n). This suggests that the (γ,p) reaction leaves high-lying residual states as the prediction of the shell model calculation. The E2 strength deduced from the 10 B(γ,d 0 ) reaction is 0.14 ±0.05% of the E2 energy weighted sum rule, which is one order of magnitude smaller than the case of neighboring odd–odd nuclei; 6 Li and 14 N. This may be suppressed by a competition with (γ,d 1 ).

Experimental test of virtual photon theory via electrodisintegration and photodisintegration of the deuteron

Virtual photon theory (VPT) has long been suggested as a means of extracting photoreaction cross sections from measurements of cross sections for equivalent electron-induced reactions. Experimental information on the validity of VPT is, however, extremely limited. A test of VPT is reported in this paper. Measurements of the cross section for the ${d(e,p)e}^{\ensuremath{'}}n$ reaction at energies between 165 and 365 MeV have been performed for outgoing proton angles of $40\ifmmode^\circ\else\textdegree\fi{},$ $90\ifmmode^\circ\else\textdegree\fi{},$ and $120\ifmmode^\circ\else\textdegree\fi{}.$ From these results, cross sections for the $d(\ensuremath{\gamma},p)n$ reaction have been extracted using VPT, and are compared with $d(\ensuremath{\gamma},p)n$ cross sections measured concurrently using a bremsstrahlung beam.

The [formula omitted] reaction in 197Au

Proton energy spectra of the 197Au (e,p) reaction were measured in the region between 17 and 30 MeV at three angles: 40°, 90° and 140°. Two prominent bumps were observed in the (γ,p) spectra converted using virtual photon theory. The higher-energy bump shifts with photon energies and the lower-energy one stays at 10.5 MeV. The higher-energy bump is much larger at 40° than at 140°; on the contrary the angular dependence of the lower-energy bump is small. Neither bump can be described by a statistical calculation. A calculation of a microscopic shell model shows that the lower-energy bump is attributed to the decay of proton-particle–neutron-hole pairs in the T > states, leaving a neutron hole around the Fermi surface. The higher-energy bump can be ascribed to the direct–semidirect mechanism. This paper gives the solution to a part of the long-standing question about the origin of photo-proton emission in heavy nuclei.

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.

Electroproduction of negative pions on 15N leading to the ground state of 15O

An angular distribution of negative pions produced on 15N, leading to the ground state of15O, has been measured via the (e, π−)-reaction at Ee ≈ 170 MeV. Using virtual photon theory, single-differential cross sections are extracted from the measured double-differential cross sections. The measured data is in good agreement with theoretical calculations in the DWIA model. A clear signature of nuclear EO excitation is found in contrast to previous experiments in a similar reaction on 13C.

Virtual photon analysis of the reaction181Ta(e,e' π+)181Hf

Previously reported data for the reaction 181Ta(e,e' pi +)181Hf have been analysed in terms of virtual photon theory. This analysis shows that a plane-wave (PW) calculation in the long-wavelength limit is consistent with the data whereas a calculation using the second-order Born approximation (SOBA) including finite-size effects gives results that are about 20% too low.

Measurement of positive pion production from 14N at low momentum transfer

Double differential cross sections of the reaction 14N(e, π +) have been measured at E 0 = 173.5 MeV for pion production angles of Θ π = 25° and 100° which correspond to momentum transfer values of q 2 = 0.22 and 1.14 fm 2. Using the virtual photon theory single differential cross sections of the reaction 14n( γ, π +) 14C g.s. are extracted from the measured data. The data are compared with recent DWIA calculations and indicate a larger nuclear spin-flip transition matrix element between 14N and 14C than that obtained from β-decay. Mixing parameters for shell model wave functions of 14N and 14C ground states are derived from the data.

Photoproduction of charged pions on 16O to bound states of the nuclei 16N and 16F

Abstract Positive and negative pions have been measured in an electroproduction experiment. Photoproduction cross sections have been extracted from the data via virtual photon theory. Angular distributions and energy dependencies of the photoproduction cross sections have been obtained in the energy range of 30 MeV ⩽ Tπ ⩽ 70 MeV. The data are compared with various calculations based on the DWIA approximation. The measured π − π + ratio as a function of the production angle agrees rather well with the ratio on the nucleon.

Nuclear size effects in virtual photon spectra

The (e,n) cross section has been measured for 181Ta from threshold to 30 MeV. The results are compared with the cross sections predicted by virtual photon theory using different corrections for nuclear size effects.

Virtual photon theory in electrofission.

The process of nuclear fission induced by electrons or other charged leptons is analyzed using distorted electron wave functions and interpreted in terms of virtual photon exchange, thus relating electrofission to photofission. Comparison of cross sections and fission fragment angular distributions for photofission, electrofission, and positrofission is shown to lead to reasonable conclusions in terms of the contributions of different multipoles and intermediate states. The effects of electron distortion are found to be considerable. As a method of analysis of fission, especially near threshold, inclusive and exclusive electrofission experiments and also the ratio of electron to positron cross sections promise good results.

Virtual photons in theory and experiment

Before the last decade nuclear electrodisintegration experiments in the region of the giant dipole resonance were carried out primarily as an expedient experimental alternative to photodisintegration experiments. Lack of an adequate treatment of Coulomb distortion of the incident and scattered electron's wavefunction in heavy nuclei and recoil in light nuclei when the momentum of the scattered electron was not much smaller than the momentum of the recoiling residual nucleus limited the establishment of the correspondence between photo- and electrodisintegration to roughly s-d shell nuclei. Distorted-wave Born approximation calculations have solved the former problem in virtual photon analysis of (e, X) total cross-section measurements and the effects of recoil on PWBA virtual photons have been recently investigated. In principle, an inclusive (e, X) experiment completely determines the (γ, X) cross-section. Besides those matrix elements present in the photodisintegration cross-section that are associated with the transverse form factor as q → w, other terms associated with the Coulomb, interference, and polarization terms of the (e, eX́) cross-section appear in the (e, X) cross-section. Inclusive (e, X) experiments done at NBS to test the limitations of E1 virtual photon theory are described. The proliferation of (e, eX́) experiments will intensify interest in (e, X) theory and experiments, with the X arm singles serving as an important check on the internal consistency of the (e, eX́) results.

Pion photoproduction on 14N at 173 MeV photon energy

The reaction 14 N(γ, π +) 14 C g.s. has been measured at a photon energy of 173 MeV and various pion angles at the Mainz microtron via the (e, π) reaction. Single differential cross sections were extracted using the virtual-photon theory. We have compared our data with momentum-space DWIA calculations using Blomqvist-Laget operators and pion wave functions distorted by an optical potential of Stricker, McManus and Carr. In a comparison with the Cohen-Kurath shell model and phenomenological A= 14 wave functions we show that the Cohen-Kurath wave functions overestimate the data up to a factor of 4, while a wave function recently proposed by Huffman et al. gives very good agreement. The analysis rise to new speculations on the forbidden 14C beta decay.

Experimental test of the bremsstrahlung cross section

The bremsstrahlung cross section has been studied by measuring the activity induced in $^{63}\mathrm{Cu}$ by electrodisintegration and when thin radiators of Cu, Mo, Ta, and Th were placed in the electron beam just ahead of the target. The electron energies were varied from 13.5 to 60 MeV for the electrodisintegration and from 20 to 60 MeV for the radiator-in measurements; the ($\ensuremath{\gamma}$,n) cross section for $^{63}\mathrm{Cu}$ was determined using virtual photon theory; the radiator data were fitted using various bremsstrahlung cross sections. The best fit is obtained using the synthesized spectrum of Seltzer which differs from the Davies-Bethe-Maximon cross section as given by equation (3CS) of Koch and Motz.

Electroproduction of low energy pions from deuterium

The inclusive electroproduction of 30 MeV ..pi../sup +/ and ..pi../sup -/ mesons has been observed at a laboratory angle of 90/sup 0/ for electron energies from 185 MeV (the kinematic threshold) to 235 MeV. Measurements of the yield were performed and double differential cross sections for photoproduction were obtained using virtual-photon theory. A significant discrepancy between experiment and distorted-wave impulse approximation calculations was found. This is particularly surprising since these calculations agree with the total cross sections for the /sup 2/H(..gamma..,..pi../sup +/)nn reaction from threshold to 20 MeV above threshold.

The pion electroproduction and the virtual-photon theory

The double differential cross-section for pion electroproduction was measured for the processes p(e,π+n and12C(e,π+)12B. The proton-induced cross-section was evaluated by using the virtual-photon concept. The experimental data were used to test different formulae for the virtual-photon spectrum. We found significant deviations to a generally used formula (Dalitz-Yennie) and good agreement with a new formula (Tiator-Wright). In addition, we have measured pion production crosssections with real photons under equal kinematic conditions. Electro-and photoproduction measurements give the same results.

Electroproduction of charged pions on 12C leading to discrete isobar analogue states

Angular distribution of pions from 12C, leading to the ground state of 12B and 12N and to the first excited state of 12B, have been measured via the (e, π) reaction at T π = 32 MeV. Using the virtual photon theory single differential cross sections are extracted from the measured data. The results are compared with data from other laboratories and with theoretical calculations. The theoretical description of the data is qualitatively very good. Quantitatively the measured data are only partially well described by the theoretical calculations of the different authors.

Experimental test of the virtual photon theory for pion electroproduction

The double differential cross section for pion electroproduction was measured for the processes p( e,π +) n and 12 C( e, π +) 12 B . The photon-induced cross section was evaluated using the virtual photon concept. The experimental data were used to test different formulas for the virtual photon spectrum. We found significant deviations from a generally used formula (Dalitz-Yennie) and good agreement with a new formula (Tiator-Wright). In addition, we have measured pion production cross sections with real photons under equal kinematic conditions. Electro- and photoproduction measurements give the same results.

A study of the decay modes of the [formula omitted] isobaric analog resonances in 209Bi using electrons and bremsstrahlung

Differential cross sections at several scattering angles and proton spectra around the g 9 2 spin-flip and i 11 2 non-spin-flip IAR in 209Bi were measured with the (e, p) reaction using a broad-range magnetic spectrometer and 100 solid-state detectors. Experiments on the (γ, p) reaction using bremsstrahlung were also performed on the same subjects using the same detector system and geometry as for the (e, p) reaction experiments. Both data agree well with each other when the virtual photon theory is used. Strengths deduced for the resonance at the g 9 2 IAS at θ lab = 125.3° are in basic agreement with previous data which are in contradiction with the results of the (p, γ 0) reaction and β-decay. Proton decay modes of these resonances were deduced by the photondifference method. Proton groups emitted through the i 11 2 IAR are found to have a decay mode typical of the IAS and leave the residual nucleus in neutron l p-1 h states. The decay mode at the g 9 2 IAR shows an anomalous reaction process as do previous data on the f 7 2 spin-flip IAR in 139La.