Impulse Approximation Calculations Research Articles

Projectile-charge-state dependence of 0 degrees binary-encounter electron production in 30-MeV Oq++O2 collisions.

Double-differential cross sections (DDCS's) for the production of binary-encounter electrons (BEE's) are reported for 30-MeV ${\mathrm{O}}^{\mathit{q}+}$+${\mathrm{O}}_{2}$ collisions. The BEE DDCS's were measured at \ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{} with respect to the beam direction for projectile charge states q=4--8. The measured BEE DDCS's were found to increase with decreasing charge state in agreement with other recent BEE results employing simpler ${\mathrm{H}}_{2}$ and He targets. Impulse-approximation calculations of BEE production for \ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{}--45\ifmmode^\circ\else\textdegree\fi{} are also presented, in which it is assumed that target electrons undergo elastic scattering in the screened Coulomb field of the projectile ion. These calculations are shown to be in agreement with our data at \ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{} where only 2s and 2p target electrons are considered.

Comparison of the quasielastic (e,e'p) and the ( gamma,p) reactions.

Recent data obtained with the quasielastic (e,e'p) reaction, and the (\ensuremath{\gamma},p) reaction at photon energies of about 60 MeV, on $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{27}\mathrm{Al}$, $^{40}\mathrm{Ca}$, and $^{51}\mathrm{V}$ are examined. Comparisons are made using disorted-wave impulse-approximation calculations. The (e,e'p) data are used to determined the values of spectroscopic factors and root-mean-square radii of the overlap wave function for each transition considered. These parameters constrain the direct-knockout (DKO) calculations for the (\ensuremath{\gamma},p) reactions which have been performed within the same framework. While the calculations give a very good description of the (e,e'p) data, a discrepancy of typically a factor of six is observed between the DKO calculations and the (\ensuremath{\gamma},p) data. The discrepancy is largely removed when meson exchange current contributions in the (\ensuremath{\gamma},p) reaction are estimated on the basis of the Siegert theorem.

Radiative electron capture by high-energy oxygen ions in hydrogen and helium.

X rays produced in the collisions of 94--222-MeV ${\mathrm{O}}^{8+}$ ions with ${\mathrm{H}}_{2}$ and He targets have been measured. Resulting spectra have been analyzed to determine absolute yields, profile widths, and energies for x rays emitted in the process of radiative electron capture (REC). These measurements are compared with predictions based on impulse-approximation calculations, using differential cross sections for radiative recombination (RR) folded with target Compton profiles. Measured absolute peak energy positions and profiles are found to be in good agreement with these simple theoretical estimates. Cross sections derived from REC yields are compared with other measurements and with theoretical RR values. A small systematic discrepancy between experimental and theoretical cross sections is noted.

Ionic charge dependence of the zero degree binary encounter peak for partially stripped heavy ions

We report on the measurements of double differential cross sections, at zero degree, for the production of secondary electrons from the collision of 0.6 MeV amu-1 Cu5+, I7+, Au11+, U13+, Cu19+ I23+ and Au29+ projectiles with H2 and He. The shapes and positions of the observed binary encounter electron peaks are compared with continuum distorted wave-eikonal initial state (CDW-EIS), impulse approximation and classical trajectory Monte Carlo calculations, as well as with predictions from an adiabatic resonant tunnelling model proposed by Fainstein and co-workers (1992). The experimentally observed binary peak positions were essentially determined by the projectile's ionic charge q and were independent of the projectile's nuclear charge Zp. Although the experimental conditions correspond to the strong perturbation regime. i.e. 1.0<or=q/VP<or=5.9 (VP being the projectile velocity), the CDW-EIS approach accounts well for the position and shape of the binary peak.

Transition from quantum to quasi-classical behaviour of the binary encounter peak in collisions of 0.6 to 3.6 MeV amu-1 I23+ and Xe21+ with He and Ar

Double differential cross sections are reported for the production of binary encounter electrons in collisions of 0.6 MeV amu-1 I23+ and 1.4, 2.4, and 3.6 MeV amu-1 Xe21+ projectiles incident on He and Ar targets. Electron energy spectra were measured between 0 degrees and 45 degrees in the case of the two lower projectile energies, and between 17.5 degrees and 60 degrees for the two higher projectile energies. The data are compared with quantum mechanical impulse approximation and classical trajectory Monte Carlo calculations. While the quantum model calculation predicts a rapid disappearance of diffraction effects in the binary encounter peak with increasing projectile energy, these remain visible in the experimental results up to the highest energy measured. The necessity of including multiple target ionization involving inner shell electrons in the theoretical description of the collision process is demonstrated by the classical trajectory Monte Carlo calculation, which accounts well for the shape of the 2.4 and 3.6 MeV amu-1 cross sections, except at angles where diffraction effects are manifest. Systematic shifts of the binary encounter peak position towards lower energies with increasing emission angle were observed for all projectile energies.

Dipole and spin-dipole resonances in charge-exchange reactions on 12C.

The $^{12}\mathrm{C}$(n,p${)}^{12}$B reaction was studied using the white neutron source at the Los Alamos Meson Physics Facility/Weapon Neutron Research Center with a continuous incident neutron energy from 60 to 260 MeV. Double differential cross sections were measured in the angular range 11\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}${\mathrm{\ensuremath{\theta}}}_{\mathrm{lab}}$\ensuremath{\le}37\ifmmode^\circ\else\textdegree\fi{}. Using the neutron time-of-flight facility at the Indiana University Cyclotron Facility, we also studied the $^{12}\mathrm{C}$(p,n${)}^{12}$N reaction at ${\mathit{E}}_{\mathit{p}}$=186 MeV and the $^{12}\mathrm{C}$(p\ensuremath{\rightarrow},n\ensuremath{\rightarrow}${)}^{12}$N reaction at ${\mathit{E}}_{\mathit{p}\ensuremath{\rightarrow}}$=160 and 186 MeV. Double differential cross sections were measured between ${\mathrm{\ensuremath{\theta}}}_{\mathrm{lab}}$=0\ifmmode^\circ\else\textdegree\fi{} and ${\mathrm{\ensuremath{\theta}}}_{\mathrm{lab}}$=50\ifmmode^\circ\else\textdegree\fi{} in 5\ifmmode^\circ\else\textdegree\fi{} steps. Spin observables ${\mathit{D}}_{\mathit{N}\mathit{N}}$, ${\mathit{A}}_{\mathit{Y}}$, and P were measured at ${\mathrm{\ensuremath{\theta}}}_{\mathrm{lab}}$=5\ifmmode^\circ\else\textdegree\fi{},9\ifmmode^\circ\else\textdegree\fi{},13\ifmmode^\circ\else\textdegree\fi{} with ${\mathit{E}}_{\mathit{p}\ensuremath{\rightarrow}}$=160 MeV and ${\mathrm{\ensuremath{\theta}}}_{\mathrm{lab}}$=15\ifmmode^\circ\else\textdegree\fi{},20\ifmmode^\circ\else\textdegree\fi{} with ${\mathit{E}}_{\mathit{p}\ensuremath{\rightarrow}}$=186 MeV. Angular distributions of differential cross section and spin observables for low-lying transitions in the residual nuclei are compared with disorted-wave impulse approximation (DWIA) calculations. A multipole decomposition analysis was performed to study the giant dipole and giant spin-dipole resonances. The contributions of the quasifree reaction in the giant resonance region was subtracted. The empirical results of energy distributions for dipole (\ensuremath{\Delta}L=1) transition are compared with DWIA calculations using nuclear structure information obtained with a conventional shell model and also with a random phase approximation.

Separation of Delta S=0 and Delta S=1 in the response of 12C to 318 MeV protons.

Angular distributions of the double-differential cross section ${\mathit{d}}^{2}$\ensuremath{\sigma}/d\ensuremath{\Omega} dE (\ensuremath{\sigma}) and the spin-flip probability ${\mathit{S}}_{\mathit{n}\mathit{n}}$ have been measured for inclusive inelastic proton scattering from $^{12}\mathrm{C}$ at ${\mathit{E}}_{\mathit{p}}$=318 MeV. Data have been obtained over an excitation energy range 9 MeV \ensuremath{\le}${\mathit{E}}_{\mathit{x}}$\ensuremath{\le}42 MeV for laboratory scattering angles of 3\ifmmode^\circ\else\textdegree\fi{}, 5\ifmmode^\circ\else\textdegree\fi{}, 7\ifmmode^\circ\else\textdegree\fi{}, 9\ifmmode^\circ\else\textdegree\fi{}, 12\ifmmode^\circ\else\textdegree\fi{}, 15\ifmmode^\circ\else\textdegree\fi{}, and 18\ifmmode^\circ\else\textdegree\fi{}. Multipole decompositions of angular distributions of both the spin-flip cross section ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{SF}}$=\ensuremath{\sigma}${\mathit{S}}_{\mathit{n}\mathit{n}}$ and the estimated cross section for \ensuremath{\Delta}S=0 transitions have been performed. The distribution of deduced \ensuremath{\Delta}L=1, \ensuremath{\Delta}S=0 (the giant-dipole resonance) strength peaks near ${\mathit{E}}_{\mathit{x}}$=22 MeV; although there is apparently much more strength relative to the energy-weighted sum rule (EWSR) than expected, this appears to be an artifact of instrumental background at small angles. Approximately 55% of the EWSR for \ensuremath{\Delta}L=2, \ensuremath{\Delta}S=0 was observed spread uniformly across the spectrum with no evidence for a giant-quadrupole resonance. Angular distributions for ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{SF}}$ were analyzed using the predictions from random-phase approximation calculations for the nuclear structure and distorted-wave impulse approximation calculations for the scattering. These predictions are found to provide a good description of the ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{SF}}$ data above ${\mathit{E}}_{\mathit{x}}$=25 MeV; values of ${\mathit{S}}_{\mathit{n}\mathit{n}}$ are predicted somewhat too low in this region.

Proton-induced nucleon knockout from polarized 3He at 220 MeV.

A high pressure polarized $^{3}\mathrm{He}$ gas target has been used to measure spin observables and absolute cross sections for (p\ensuremath{\rightarrow},2p) and (p\ensuremath{\rightarrow},pn) nucleon knockout in quasielastic kinematics at 220 MeV. The neutron knockout spin observables exhibit large deviations from plane wave impulse approximation (PWIA) calculations and show the importance of rescattering corrections. At this energy, the proton knockout spin observables differ slightly from PWIA calculations, especially at low energy transfers (\ensuremath{\omega}), but this discrepancy may be resolved when final state interactions between nucleons of the two-body recoil scattering state are included. The large rescattering effects observed in the (p\ensuremath{\rightarrow},pn) results may have implications for experiments which consider polarized $^{3}\mathrm{He}$ as a polarized neutron.

Cross section and deuteron analysing powers of the 1H(d, 2p)n reaction at 200 and 350 MeV

The cross section and analysing powers A y , A xx and A yy of the charge-exchange reaction 1 H( d , 2 p) n have been measured at E d = 200 and 350 MeV up to excitation energies ( E x) of 8 MeV in the final pp system. The good agreement observed between the experimental dependence of the cross section and analysing powers upon E x and the predictions of an impulse approximation calculation improves with increasing beam energy. The large experimental figures of merit found for A xx and A yy demonstrate that this reaction can be used as the basis of a new deuteron tensor polarimeter in the 200–400 MeV energy range.

Search for Gamow-Teller strength in the continuum via the 3He(n,p)3H reaction at 288 MeV.

Cross sections for the $^{3}\mathrm{He}$(n,p) reaction were measured at angles of 2.7\ifmmode^\circ\else\textdegree\fi{}, 7.5\ifmmode^\circ\else\textdegree\fi{}, 14.4\ifmmode^\circ\else\textdegree\fi{}, 28.2\ifmmode^\circ\else\textdegree\fi{}, and 34.9\ifmmode^\circ\else\textdegree\fi{} (c.m.) at an incident beam energy of 288 MeV. Outgoing protons were observed to energies corresponding to a Q value of -40 MeV. The reduced cross section for the Gamow-Teller component of the ground-state isobaric-analog transition was determined to be \ensuremath{\sigma}^=\ensuremath{\sigma}(q=0)/${\mathit{B}}_{\mathrm{GT}}$=6.9\ifmmode\pm\else\textpm\fi{}0.2 mb/sr. This value is significantly smaller than that observed for nuclei in the mass range 6\ensuremath{\le}A\ensuremath{\le}13. A multipole analysis of the data indicates that the cross section of the continuum up to a Q value of -20 MeV involves mainly \ensuremath{\Delta}L=1 spin dipole transitions. The analysis determines an upper limit of 0.06 units of Gamow-Teller strength in transitions to excited states between 7 and 16 MeV, but is consistent with no Gamow-Teller strength in this region. Distorted wave impulse approximation calculations using transition amplitudes from a large-scale shell model calculation provide a good fit to the measured ground-state cross section, but fail to account for the magnitude of the measured cross sections to the continuum below 30 MeV excitation.

Energy dependence of two-nucleon pion absorption on 16O.

Inclusive [sup 16]O([pi][sup +],[ital p]) and exclusive [sup 16]O([pi][sup +],2[ital p]) data are presented for 115 MeV and 165 MeV pions. Using a combination of distorted-wave impulse approximation (DWIA) calculations for two-nucleon absorption and phase space simulations for more complicated processes, the data are fit and the total direct two-nucleon absorption cross sections are extracted. These cross sections fall faster with energy than [pi][sup +][ital d][r arrow][ital pp]. The DWIA calculations were used to calculate the effects of final state interactions (FSI). After correcting for FSI, the two-nucleon absorption process is found to dominate at 115 MeV, becoming less important as the incident energy increases to 165 MeV. The decrease with energy in the two-nucleon fraction of the total absorption cross section is found to be in remarkably good agreement with theoretical predictions.

Quasi-elastic electron scattering off nuclei

A survey is given of results of electron-induced quasi-elastic proton knockout experiments. We present results of experimental investigations of the (e,e′p) reaction-mechanism, among which are a separation of three of the four structure functions, and the determination of the momentum-transfer dependence of the cross section. Furthermore, the experimental momentum distributions are compared to Distorted Wave Impulse Approximation calculations that employ bound-state wave functions evaluated in a mean-field potential. The mass- and energy-dependence of the deduced spectroscopic strengths are discussed on the basis of modern calculations of the nuclear response that include short-range correlations.

Spin-longitudinal and spin-tranverse response ofCa40to 500 MeV protons at low momentum transfer

A complete set of diagonal spin-transfer observables has been measured at excitation energies between 30 and 40 MeV for inelastic proton scattering from $^{40}\mathrm{Ca}$ at 497 and 581 MeV at a momentum transfer of 0.56 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. The longitudinal and transverse spin-flip probabilities are deduced. Their unequal enhancements relative to free nucleon-nucleon scattering values are explained by a distorted-wave impulse approximation calculation in which the finite nucleus random-phase approximation is used to describe the nuclear respose.

N* electroproduction and propagation in nuclei.

We have measured the C12(γ*,π−p)11Cg.s. cross section using virtual bremsstrahlung at three points at invariant masses of 1444 and 1530 MeV. At low neutron initial momentum (pm≊60 MeV/c) and large N* momentum (pN*≊750 MeV/c) the measured cross section is at or below the distorted wave impulse approximation (DWIA) calculation. At larger initial momentum (pm≊220 MeV/c) and smaller N* momentum (pN*≊500 MeV/c), the measured cross section is almost twice as large as the DWIA calculation. This discrepancy might be due to N*-nucleus interactions.Received 10 August 1992DOI:https://doi.org/10.1103/PhysRevC.47.225©1993 American Physical Society

Pion absorption on polarized nuclear targets.

The availability of polarized nuclear targets for nuclear reaction studies offers new research directions. In this paper we present the distorted wave impulse approximation formalism and calculations for two-nucleon pion absorption on polarized nuclear targets. We assume that the pion absorbs on a $^{3}$${\mathit{S}}_{1}$ n-p pair and use phenomenological amplitudes to describe the \ensuremath{\pi}NN vertex. The effects of the distortions on the incoming pion and outgoing protons, in contrast to the elementary \ensuremath{\pi}NN vertex, are delineated for certain special cases in which the formalism simplifies. Predictions of cross sections and vector and tensor analyzing powers are made for polarized target nuclei $^{6}\mathrm{Li}$, $^{7}\mathrm{Li}$, $^{13}\mathrm{C}$, and $^{14}\mathrm{N}$ at pion incident energies of 115, 165, and 255 MeV.

Nuclear compton scattering from pion threshold to the delta

The first measurements of elastic photon scattering on complex nuclei from 150 MeV to the Δ(1232) ( E γ = 300 MeV) are compared with theoretical calculations. Data on 4 He at the Δ peak are in agreement with a Δh calculation, but substantial disagreement occurs at lower energies that is at least partly due to the approximate treatment of non-resonant parts of the elementary nucleon amplitude. An impulse approximation calculation which includes meson exchange provides an adequate description of the data at 187 MeV on 4 He. Improved data on the proton at 20–30° and 120–140° at a range of energies are in agreement with a recent dispersion relation calculation. Data taken on 12 C are still too preliminary to report, due to the difficulty of eliminating inelastic contributions.

Exclusive 16O( gamma, pi -p) reaction in the Delta resonance region.

We report the first exclusive (\ensuremath{\gamma},${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$p) measurements on a complex nucleus. The $^{16}\mathrm{O}$(\ensuremath{\gamma},${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$p) reaction was measured at pion laboratory angles of 64\ifmmode^\circ\else\textdegree\fi{} and 120\ifmmode^\circ\else\textdegree\fi{}. Coincident protons were detected over the quasifree angular correlation range using a vertical array of seven plastic scintillator detectors spanning \ifmmode\pm\else\textpm\fi{}33\ifmmode^\circ\else\textdegree\fi{} about the scattering plane. The cross sections are compared to factorized distorted-wave impulse approximation calculations; these provide a good description of the backward angle data, but are in serious disagreement with the forward angle data.

7Li( alpha,2 alpha )3H reaction from 77 to 119 MeV.

Absolute cross sections for the $^{7}\mathrm{Li}$(\ensuremath{\alpha},2\ensuremath{\alpha}${)}^{3}$H reaction, measured at 77, 99, and 119 MeV, show features expected for \ensuremath{\alpha}-\ensuremath{\alpha} quasielastic scattering from \ensuremath{\alpha} clusters bound in an l=1 state: minima and maxima for triton momenta of 0 and 55\ifmmode\pm\else\textpm\fi{}4 MeV/c, respectively. The magnitudes and energy dependence of the cross sections, and the most probable spectator momenta, were reproduced with distorted-wave impulse approximation calculations when the volume integrals of the optical-model central potentials and ground-state interactions were adjusted to currently accepted values.

Alpha-particle scattering from 6Li near the alpha -d breakup threshold.

The $^{6}\mathrm{Li}$(\ensuremath{\alpha},\ensuremath{\alpha}') reaction was studied at ${\mathit{E}}_{\mathrm{\ensuremath{\alpha}}}$=50 MeV. The angular distribution of the continuum region near the $^{6}\mathrm{\ensuremath{\alpha}}$+d breakup threshold (1.475 MeV) was measured for ${\mathrm{\ensuremath{\theta}}}_{\mathrm{lab}}$=7\ifmmode^\circ\else\textdegree\fi{}--40\ifmmode^\circ\else\textdegree\fi{}. The data were analyzed in terms of plane-wave and distorted-wave impulse approximation calculations. To study the possible effects of recombination of the breakup clusters in the exit channel, distorted-wave Born approximation calculations were also performed.

Dominance of the two-nucleon mechanism in 16O( pi +,pp) at 115 MeV.

Singles $^{16}\mathrm{O}$(${\mathrm{\ensuremath{\pi}}}^{+}$,p) and coincidence $^{16}\mathrm{O}$(${\mathrm{\ensuremath{\pi}}}^{+}$,2p${)}^{14}$N measurements have been made at ${\mathit{T}}_{\mathrm{\ensuremath{\pi}}}$=115 MeV over an extended range of the phase space of the two final-state protons. The coincidence measurements have a missing-mass resolution of 4 MeV. The direct two-nucleon absorption cross section extracted from the data is 58\ifmmode\pm\else\textpm\fi{}8 mb. After corrections for final-state interactions, it was found that the two-nucleon ${\mathrm{\ensuremath{\pi}}}^{+}$+np\ensuremath{\rightarrow}pp process accounts for about 76% of the total absorption cross section, and thus is the dominant absorption mechanism. Evidence for absorption on s-p pairs is seen as a broad bump near 32 MeV of excitation. At backward angles the inclusive $^{16}\mathrm{O}$(${\mathrm{\ensuremath{\pi}}}^{+}$,p) spectra show a distinct absorption peak, an important feature not previously observed. Comparisons of distorted wave impulse approximation calculations to both the coincidence data and inclusive data are presented.