Coincidence Cross Sections Research Articles

Pre-emission ofαParticles in Deep-Inelastic Reactions

In-plane angular and energy correlations between $\ensuremath{\alpha}$ particles and heavy ejectiles have been measured for the reaction $^{14}\mathrm{N}$ + $^{58}\mathrm{Ni}$ at 148 MeV. The coincidence cross sections may be parametrized as a product of singles cross sections for the detection of $\ensuremath{\alpha}$ particles and heavy ejectiles. The observed correlations indicate that the $\ensuremath{\alpha}$ particles are emitted at an early stage, prior to the formation of the deep-inelastic fragments.

Electrodisintegration of deuterium including nucleon detection in coincidence

A consistent nonrelativistic treatment of deuteron electrodisintegration is presented including effects from meson exchange currents and isobar configurations. The 2H(e, e′) cross section for an oriented and an unoriented deuteron target is given in terms of form factors while the 2H(e, e′p) and 2H(e, e′ p ) coincidence cross sections are described by proper structure functions. The T-matrix is calculated by a multipole expansion up to L = 6 for inclusion of the final state interaction while for all higher multipoles the Born approximation for the final state has been used and very good convergence is achieved. We find good agreement between theory and experiment for 0 ≦ q 2 ≦ 20 fm −2 and excitation energies up to π-threshold. Coincidence experiments at low q but higher excitation energies turn out to be particularly sensitive to interaction effects from virtual isobar excitation.

Multiple scattering theory. II. Collision induced dissociation in first order

Computationally tractable formulae for one particle differential cross sections and for coincidence cross sections for atom— diatom collision induced dissociation (CID) are obtained within the framework of first order multiple scattering theory. The first order formulation is then used to analyze the simple “knockout circle” model for CID and to derive a more reliable multiple scattering spectator model. Finally, differential and coincidence cross sections are computed for Li + + H 2 at 2O eV and are compared with experiment. The qualitative insight afforded by coincidence studies of CID is clearly demonstrated.

Angular correlations from 6Li break-up near the Coulomb barrier of 118Sn and 208Pb

Absolute coincidence cross sections for three-particle final states have been measured inplane in the 6Li + 118Sn and 6Li + 208Pb reactions at incident energies of 22.2 and 23.0 MeV, respectively. Most strongly populated is the α + d branch, proceeding sequentially through the first excited state ( E x = 2.18 MeV, J π = 3 +) of 6Li. The angular distributions are fitted by DWBA calculations including Coulomb interaction in the excitation of the projectile. The main competing reaction channels above and at the Coulomb barrier ( 118Sn: E/ E c ≈ 1.3; 208Pb: E/ E c ≈ 0.9) are: neutron transfer ( 6Li, αp) and the non-sequential α + d break-up of 6Li. The latter spectra are consistent with a quasi-free break-up mechanism. No 3He or tritons have been found in the coincidence spectra, as well as no evidence for a three-particle dissociation of 6Li into α + p + n.

Three-body final states of the 3He+ 7Li reaction and clustering in 7Li

Absolute coincidence cross sections for five three-body final states of the 3He+ 7Li reaction have been measured with 37.5 MeV incident 3He ++ ions at geometries where quasi-elastic scattering could occur. The spectra were fitted with plane wave (PWIA) and/or modified plane wave impulse approximation (MPWIA) calculations. Data from the 7Li( 3He, 3He t)α reaction were consistent with strong α-t clustering in 7Li. The yield from the reaction 7Li( 3He, 3He d) 5He was equally large but inconsistent with the existence of deuteron clusters when interpreted by the MPWIA. Momentum distributions of spectator α and 5He particles from these reactions were consistent with l = 1 and l = 0, respectively. Cross sections for the 3He+ 6Li+n, 3He+ 6He+p and t+ 6Li+p final states were small, inconsistent with PWIA predictions for l = 1, and hence indicate very small 6Li and 6He cluster probabilities in 7Li.

Investigations of the deuteron break-up on heavy nuclei above the Coulomb barrier

The deuteron break-up on heavy nuclei is studied for deuteron energies above the Coulomb barrier in the post form of the DWBA. The “region of formation” of the DWBA integral is found to be located mainly outside the nuclear force range. Finite-range, non-locality and virtual break-up effects are carefully considered. A comparison of our theoretical calculations with the available experimental coincidence cross sections shows good agreement. This supports strongly the validity of the direct break-up model assumed here.

Initial-state distortion and final-state interactions in the 2H( 3He, 3He p)n and 2H( 3He, 3H p)p reactions

The predictions of two fully antisymmetrized reaction theories (DWBA and PWBA-FSI) are compared with absolute coincidence cross sections for the 2H( 3He, 3He p)n and 2H( 3He, 3H p)p reactions exhibiting final-state interactions (FSI) and quasi-elastic scattering (QES) both with and without charge exchange. The DWBA theory takes into account both the initial 3He-d and the final N-N interactions, while the PWBA-FSI theory includes only the latter. New QES data at E He = 35.9 MeV, as well as previously reported 26.8 and 35.9 MeV data, are fitted. The DWBA theory gives good fits, both in shape and magnitude, to spectra showing N-N final-state interactions but gives somewhat poorer fits to QES spectra whose predicted magnitudes are two to ten times too large. The PWBA-FSI theory always predicts cross sections that are too large; however the predicted shapes are about as good as those from the DWBA. The initial-state interaction is shown to affect both the width and position of QES peaks from these reactions.

Final-state interactions in the 2H(d, pp)nn reaction

Absolute coincidence cross sections for the 2H(d, pp)nn reaction were measured at E d = 23.15 MeV by detecting both protons at a small included angle to observe events with small p-p and n-n relative energies (ε pp and ε nn). Evidence for a double final-state interaction was obtained at( θ 1 = 18 δ, θ 2 = 36°) and (25°, 43°) where the yields were elevated above phase space at low ε nnand depressed below phase space at low ε pp. Watson-Migdal predictions, using accepted values of the effective range parameters for the singlet p-p and n-n interactions, gave reasonably good fits to the data except for the ε nn spectrum at (25°, 43°) which required an n-n scattering length a nn < −50 fm. Acceptable fits were also obtained with a double distorted-wave theory using computed p-p and n-n scattering wave functions, a Gaussian transition potential and Slaus-Van Oers deuteron wave functions.

Generalized nuclear polarizabilities in (e, e'γ) coincidence experiments

The (e, e'γ) coincidence cross section is expressed in terms of the nuclear polarizabilities as a generalization of the standard (γ, γ') formalism for polarized photons. This formalism is well suited to determine nuclear spins in a model-independent way. Due to the presence of virtual photons of longitudinal and transverse polarization and variable momentum transfer, electroexcitation gives more complete information than scattering of real photons and allows one to study the polarizabilities as function of excitation energy and momentum transfer.

Quasi-elastic electron scattering (e, e′p) and (e, e′d) from 6Li in a coincidence experiment

Coincidence cross sections for the reactions 6Li(e, e′p) and 6Li(e, e′d) have been measured in the region of quasi-elastic scattering. Using incident electrons of 2.5 and 2.7 GeV, the four-momentum transfers to the proton were 6.6 fm −2, 10.0 fm −2 and 11.6 fm −2. The proton coincidence data agree with shell-model distributions assuming a Woods-Saxon potential and including short-range nucleon-nucleon correlations. The best fit to the deuteron coincidence data is obtained with a cluster wave function for the p-nucleons and a harmonic oscillator wave function for the s-nucleons taking into account the deuteron yield from the s-shell. The ratio of the deuteron cross section from 6Li divided by the elastic e-d scattering cross section depends only slightly on the four-momentum transfer and has a value of ≈ 2.

Effects of exchange and final-state interactions in the reactions 2H( 3He, 3H p)p and 2H( 3He, 3He p)n

Absolute coincidence cross sections for the 2H( 3He, 3He p)n and 2H( 3He, 3H p)p reactions were measured at E He = 35.9 MeV. Spectra dominated by the nucleon-nucleon final-state interaction (FSI) are fitted by a fully antisymmetrized PWBA theory which includes the effects of FSI in all its matrix elements. Previously reported 26.8 MeV data showing both FSI and quasi-elastic scattering (both with and without charge exchange) are also fitted by the theory, which qualitatively describes the shapes of all these spectra and the ratios of the cross sections for the various processes. Predictions of Watson-Migdal theory are fitted to the FSI spectra and differences between the two theories are analyzed.

Distorted-Wave Theory of Deuteron Breakup

Deuteron-breakup coincidence cross sections are calculated in the prior-interaction formulation of distorted-wave Born approximation (DWBA); both nuclear and Coulomb interactions are included. The results disagree with experiment. This is attributed to incorrect treatment of Coulomb distortion in the prior form of the outgoing wave function. Nuclear contributions to breakup are found to be as important as Coulomb contributions. Numerical procedures are developed that can also be used to include Coulomb excitation in DWBA calculations of inelastic scattering.

Effects of short-range correlations on the quasielastic scattering of electrons

Coincidence cross sections for (e, e'p) reactions are evaluated within the framework of a single-particle model modified by two-particle short-range correlations. It turns out that correlations start to become important in the region of high recoil momenta (q R ⪆ 200 MeV/c ) of the residual nucleus.

The Coulomb break-up of the deuteron

A DWBA treatment of the break-up of a deuteron in the Coulomb field of a nucleus is given. A Hulthén wave function is used for the deuteron. There are no free parameters in the theory; therefore, a measurement of this process would give a test of the accuracy of the DWBA. The integral over the continuum wave functions can be reduced to a bremsstrahlung integral given by Sommerfeld and Nordsiek. Numerical calculations for various deuteron energies and targets Z have been performed in order to understand the main features of the process. Coincidence cross sections, cross sections integrated over proton or neutron angles and finally total cross sections are given, along with a discussion of the results.

Collisional ionization of helium by slow electrons

For single ionization of helium by electron impact the energies and scattering angles of the scattered and ejected electrons have been measured in a coincident experiment at primary energies E0 between 30 and 80 eV. Two types of collision are found, those in which the momentum transfer to the ion produced is small (binary encounter) and those in which the momentum transfer is large (recoil encounter). The maximum of the coincidence rate measured due to collisions of the binary encounter type is located in forward direction. Its angular position is varying with the collision parameters, whereas its angular half width is approximately 60 degrees for all data obtained. The recoil collisions cause a maximum of the coincidence cross section at about 160 degrees with a half width larger than 90 degrees . The relative intensity of the binary encounter peak and the recoil peak as well as the total number of ionizing transitions depend strongly on the energies and angles of the two outgoing electrons. Binary peak and recoil peak do not have a common symmetry axis, probably due to the interaction between the two ionization electrons.

Quasifree scattering of electrons from 12C

The scattering of high-energy electrons from 12C, accompanied by the knock-out of one proton, is studied using the Born approximation. The effects of using distorted waves for the outgoing proton and realistic wave functions for the bound states of 12C on the coincidence cross section are studied. The results are compared with those of simpler models and also with experiment.

Coincidence study of the reaction 2H(d, dp)n

Absolute coincidence cross sections were measured for the reaction 2H(d, dp)n at E d = 20.7 MeV. Strong peaks were observed centered at the minimum neutron laboratory energies. Their shapes were well fitted by PWBA calculations using both zero- and finite-range transition potentials, and by the PWBA modified by including the final p-n interaction. These calculations suggested the importance of both the simple spectator process and more complex mechanisms. DWBA calculations gave poorer fits. No conclusive evidence for unbound 3He levels was obtained.

Electron-Excitation—Gamma-Decay Reactions in Heavy Nuclei

The feasibility of using the reactions ${e+N({\ensuremath{\epsilon}}_{i},{J}_{i})\ensuremath{\rightarrow}{e}^{\ensuremath{'}}+,N({\ensuremath{\epsilon}}_{f},{J}_{f})}{\ensuremath{\searrow}N({\ensuremath{\epsilon}}_{\mathrm{ff}},{J}_{\mathrm{ff}})+\ensuremath{\gamma}}$ to investigate low-lying states of heavy nuclei is discussed. By detecting the decay photon, the problem of poor energy resolution for high-energy electrons can be circumvented. The formalism for the ${e}^{\ensuremath{'}}\ensuremath{-}\ensuremath{\gamma}$ coincidence cross section is given. The Coulomb distortion of the electron wave functions, which is important for heavy nuclei, is taken into account. Results for the ${e}^{\ensuremath{'}}\ensuremath{-}\ensuremath{\gamma}$ coincidence cross section and the $\ensuremath{\gamma}$-detection cross section for several nuclei are given. The $e\ensuremath{-}\ensuremath{\gamma}$ coincidence cross section appears to be feasible when superconducting accelerators became operational. The $\ensuremath{\gamma}$-detection cross section offers a method for investigating low-lying states with present-day accelerators.

P-p and p-t final state interactions in the reaction 3He(d, tp)p

Absolute coincidence cross sections were measured for the reaction 3He(d, tp)p at E d = 20.7 MeV. Deep minima were observed in the cross sections when the relative energy of either p+p or t+p was below ≈ 20 keV. Predictions of the Watson-Migdal theory and of the PWBA and DWBA theories of Henley, Richards and Yu gave good agreement with the shapes of the spectra near these minima, but the required normalization factors varied widely from one geometry to another. Decay of the 21.2 MeV 4He state, but not the 20.0 MeV state, was observed.

Production of pi-mesons by inelastic electron scattering from nuclei

The pi-meson contribution to the inelastic electron scattering has been investigated. Starting from the general form of the production amplitude, making no specific assumptions about nuclear states, but using the impulse approximation and neglecting final state interactions, we derive a formula for the double coincidence cross section, in which nuclear structure and the emission mechanism are conveniently separated. For numerical calculations the production amplitude for a single nucleon derived in a dispersion approach is used, and an example involving in the final system the collective vibrational states of 16N, which have been the subject of many recent studies, is considered.