Distorted-wave Impulse Approximation Calculations Research Articles

Distorted-wave impulse approximation and coupled-channels analysis of inelastic pion scattering from 18O.

Data for inelastic pion scattering from $^{18}\mathrm{O}$ at ${T}_{\ensuremath{\pi}}$=164 MeV, exciting the lowest ${2}^{+}$, ${3}^{\mathrm{\ensuremath{-}}}$, and ${1}^{\mathrm{\ensuremath{-}}}$ states, were analyzed by distorted-wave impulse approximation and coupled-channel calculations using transition densities derived from shell model calculations. Coupled-channels effects were found to be relatively unimportant for the ${2}^{+}$ and ${3}^{\mathrm{\ensuremath{-}}}$ states, but non-negligible for the excitation of the ${1}^{\mathrm{\ensuremath{-}}}$ state. Nevertheless, the inclusion of multistep excitation paths is not sufficient to generate a fit to the ${1}^{\mathrm{\ensuremath{-}}}$ data with the shell model wave functions. Major modifications are needed in the radial dependence of the neutron and proton parts of the transition density for the ${0}^{+}$\ensuremath{\rightarrow}${1}^{\mathrm{\ensuremath{-}}}$ one-step process.

Multipole decomposition of Gamow–Teller strength

Doubly differential continuum cross sections from the 90Zr(p, n)90Nb reaction have been analyzed via a multipoledecomposition technique. No quasi-free charge-exchange background has been subtracted, following the assumption that the observed cross sections are primarily due to one-step charge-exchange leading to 1p–1h states of all multipolarities to all excitations. The theoretical shapes of the differential cross sections for each Jπ multipole have been taken from random-phase approximation (RPA)–distorted-wave impulse approximation (DWIA) calculations. The experimental dσ/dΩ, for each 1 MeV excitation-energy bin have been decomposed into different multipole components by a least squares fit. This RPA-based analysis should determine the Jπ = 1+ cross sections with different, and also fewer, assumptions than usual for describing the underlying background. It can be of general importance in determining the extent of possible quenching of Gamow–Teller (GT) strength. The present decomposition accounts for all the theoretically predicted GT strength. The purpose of the present report is to illustrate an analysis based on RPA–DWIA shapes rather than to present final-decomposition results.

Observation of eta -meson production in the reaction pi -+3He--> eta

Pion-induced $\ensuremath{\eta}$-meson production populating a discrete nuclear state is observed for the first time in the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}+^{3}\mathrm{He}\ensuremath{\rightarrow}\ensuremath{\eta}+t$. At 680 MeV/c ${\ensuremath{\pi}}^{\ensuremath{-}}$ momentum, this reaction is identified by measurement of the recoiling tritons. The measured cross sections are approximately 3 orders of magnitude greater than the $p+d\ensuremath{\rightarrow}\ensuremath{\eta}+^{3}\mathrm{He}$ and the $d+d\ensuremath{\rightarrow}\ensuremath{\eta}+^{4}\mathrm{He}$ cross sections. Distorted-wave impulse-approximation calculations underpredict the observed cross sections by a factor of 2-4.

Pion elastic and inelastic scattering from 48,50Ti, 52Cr, and 54,56Fe at 180 MeV: Determination of neutron and proton multipole matrix elements.

Differential cross sections were measured for pion elastic and inelastic scattering from /sup 48,50/Ti, /sup 52/Cr, and /sup 54,56/Fe at T/sub ..pi../ = 180 MeV. Elastic scattering data were analyzed using a standard Kisslinger potential. Inelastic scattering data were analyzed using distorted-wave impulse-approximation calculations with collective-model transition densities. Ground-state neutron density parameters and matrix elements for some of the transitions were extracted and ..pi../sup +//..pi../sup -/ differences investigated.

16O( gamma, pi +)16N reaction at 320 MeV photon energy.

The pion angular distribution for the /sup 16/O(..gamma..,..pi../sup +/) /sup 16/N reaction leading to the lowest quartet of states in /sup 16/N has been measured at 320 MeV photon energy. The results are compared with a distorted-wave impulse approximation calculation.

16O( alpha, alpha p) and 40Ca( alpha, alpha p) reactions at 139.2 MeV incident energy.

The (\ensuremath{\alpha},\ensuremath{\alpha}p) reactions on $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$ targets have been measured in a quasifree geometry using a 139.2 MeV \ensuremath{\alpha} particle beam. In general, the shape of the experimental distributions are well described by distorted-wave impulse approximation calculations. Relative spectroscopic factors are consistent with (p,2p) studies. However, discrepancies in absolute magnitude exist and are discussed.

Excitation of isovector giant resonances in pion single-charge exchange at 120, 165, and 230 MeV.

We have measured doubly differential cross sections for the (${\ensuremath{\pi}}^{+}$,${\ensuremath{\pi}}^{0}$) and (${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$,${\ensuremath{\pi}}^{0}$) reactions at 120- and 230-MeV kinetic energies for $^{40}\mathrm{Ca}$, $^{60}\mathrm{Ni}$, and $^{120}\mathrm{Sn}$. Nuclear-excitation energies up to 60 MeV were observed. We have extracted excitation energies, widths, and maximum cross sections for the isospin components of the isovector monopole resonance and the isovector dipole resonance. The excitation energies and widths from the present data and from earlier measurements at 165 MeV are compared and found to be in agreement. The cross sections for the isovector monopole and isovector dipole resonances show the same increase with bombarding energy in all targets. No isovector quadrupole strength is required to fit the experimental data. We compare the energy dependences of the isovector-resonance cross sections with those of isobaric-analog states, and to distorted-wave impulse approximation calculations.

Tests of the factorized distorted wave impulse approximation for (p,2p) reactions.

Cross sections for the $^{40}\mathrm{Ca}$(p,2p) reactions at 101.3 and 76.1 MeV and the $^{16}\mathrm{O}$(p,2p) reaction at 101.3 MeV have been measured and analyzed using distorted-wave impulse approximation calculations. The sensitivity to the choice of distortion parameters, nonlocality corrections, and spin-orbit terms in the optical potentials have been studied. For the region of phase space studied, the factorization approximation is found to be valid even at energies as low as 76.1 MeV. Extracted spectroscopic factors are compatible with shell model estimates.

Comprehensive calculations of the ( pi +,K+) reaction on 12C.

The results of comprehensive distorted-wave impulse-approximation calculations are presented for the reaction /sup 12/C(..pi../sup +/,K/sup +/) /sub //sub <1/ /sup 12/C and compared to recent experimental data. The calculation includes scattering from bound states and resonances plus quasifree scattering in one consistent formalism. The features of the data are reproduced by the calculation, and these features are identified with underlying shell-model configurations.

Analyzing-power measurements in the 48Ca(p,n)48Sc reaction at 134 MeV.

Analyzing-power measurements were performed for the $^{48}\mathrm{Ca}$(p,n${)}^{48}$Sc reaction at 134 MeV in about 6\ifmmode^\circ\else\textdegree\fi{} steps from 0\ifmmode^\circ\else\textdegree\fi{} to 60\ifmmode^\circ\else\textdegree\fi{}. The overall neutron energy resolution varied from about 400 keV for angles out to 42\ifmmode^\circ\else\textdegree\fi{} to about 700 keV at wider angles. Analyzing-power angular distributions were extracted for the (\ensuremath{\pi}${f}_{7/2}$,\ensuremath{\nu}${f}_{7/2}^{\mathrm{\ensuremath{-}}1}$) octet of states, the ${1}^{+}$ Gamow-Teller giant resonance, and the T=4, ${1}^{+}$ state at ${E}_{x}$=16.8 MeV. All of these angular distributions are described reasonably well by ``standard'' distorted-wave impulse approximation calculations. A qualitative difference is observed in the analyzing power between the transitions to the low-lying ${0}^{+}$ and ${1}^{+}$ states compared to the transition to the high-lying ${1}^{+}$ state. This difference appears to be associated with a sensitivity to the predominant particle-hole structure of the final states, viz., (\ensuremath{\pi}${f}_{7/2}$,\ensuremath{\nu}${f}_{7/2}^{\mathrm{\ensuremath{-}}1}$) versus (\ensuremath{\pi}${f}_{5/2}$,\ensuremath{\nu}${f}_{7/2}^{\mathrm{\ensuremath{-}}1}$). This sensitivity is ascribed to the difference in nonlocality contributions to the two different 1p1h excitations. Excitation-energy plots of the analyzing power were extracted at each angle. No characteristic signature of spin-transfer strength is observed in the region of the Gamow-Teller giant resonance.

Cross section and analyzing powers for the reaction p 3H → γ4He at Ep = 227, 300 and 375 MeV

Cross sections and analyzing powers for the radiative capture of polarized protons by tritium have been measured at energies of 227, 300, and 375 MeV. The cross-section results are in good accord with data taken for the inverse photodisintegration reaction assuming detailed balance which indicates there is no violation of time-reversal invariance. The experimental results are compared with distorted wave impulse approximation calculation and it is found that the inclusion of meson exchange current effects is important in this energy range.

Particle-hole strength excited in theCa40(p,n)40Sc reaction at 134 MeV

The $^{40}\mathrm{Ca}$(p,n${)}^{40}$Sc reaction was studied at 134 MeV. Neutron energy spectra were measured by the time-of-flight technique with resolutions of 220 keV at angles from 0\ifmmode^\circ\else\textdegree\fi{} to 41\ifmmode^\circ\else\textdegree\fi{} and 415 keV out to 62\ifmmode^\circ\else\textdegree\fi{}. The ${2}^{\mathrm{\ensuremath{-}}}$,${3}^{\mathrm{\ensuremath{-}}}$,${4}^{\mathrm{\ensuremath{-}}}$,${5}^{\mathrm{\ensuremath{-}}}$ band of states based on the (${f}_{7/2}$,${d}_{3/2}^{\mathrm{\ensuremath{-}}1}$) 1p1h structure was observed at low excitation energies, in good agreement with known analog states in $^{40}\mathrm{Ca}$ and $^{40}\mathrm{K}$. The shapes of the cross-section and analyzing-power angular distributions are in good agreement with distorted-wave impulse-approximation calculations using simple 1p1h (Tamm-Dancoff approximation) shell-model wave functions. A relatively strong transition to a state at ${E}_{x}$=2.3 MeV with L=3 is identified tentatively as a ${4}^{\mathrm{\ensuremath{-}}}$ state with the predominant 1p1h structure (1${f}_{7/2}$,2${s}_{1/2}^{\mathrm{\ensuremath{-}}1}$).The excitation of the (T=1) ${6}^{\mathrm{\ensuremath{-}}}$ (${f}_{7/2}$,${d}_{5/2}^{\mathrm{\ensuremath{-}}1}$) stretched state is observed near ${E}_{x}$=7 MeV, fragmented over approximately 3 MeV. The normalization factor required to make a distorted-wave impulse-approximation calculation agree in magnitude with the ${6}^{\mathrm{\ensuremath{-}}}$ excitation is 0.35, which is larger than the normalization factor for this excitation in mass 28, analyzed in a similar manner. The L=1 giant resonance is observed to be centered near ${E}_{x}$=10 MeV with a width (full width at half maximum) of about 5 MeV, and a distorted-wave impulse-approximation normalization factor of 0.16. Two ${1}^{+}$ excitations are observed at ${E}_{x}$=2.7 and 4.3 MeV which indicate directly the presence of ground-state correlations in the $^{40}\mathrm{Ca}$ target. The fact that the analog of the higher ${1}^{+}$ excitation is not seen in inelastic electron scattering indicates strong interference between spin and orbital current contributions. The effect of ground-state correlations on the 1p1h wave functions was investigated by performing calculations which allowed multiparticle-multihole correlations in the ${d}_{3/2}$ and ${f}_{7/2}$ orbitals. The distorted-wave impulse-approximation normalization factors obtained with these wave functions were found to increase by a factor of about 2 relative to those obtained with $^{40}\mathrm{Ca}$ assumed to be a closed core.

Medium effects in photopion reactions.

After discussing the status of distorted wave impulse approximation approaches to the photoproduction of pions from nuclear targets, it is shown that medium effects due to the excitation of particle-hole states by pion propagation are quite significant and serve to improve agreement between coordinate space distorted-wave impulse-approximation calculations and recent data on the reaction $^{14}(\ensuremath{\gamma}$,${\ensuremath{\pi}}^{+}$${)}^{14}$C. The need to include such medium effects in distorted-wave impulse-approximation photopion calculations is demonstrated, but evidence is given that one must go beyond the local density approximation for evaluating medium effects. The role of recent nuclear structure information and of pion distorted waves on photopion production calculations are also examined.

40Ca( gamma,p0)39K reaction for E gamma =100-300 MeV.

The differential cross section for the /sup 40/Ca(..gamma..,p/sub 0/) /sup 39/K process has been measured in the energy range E/sub ..gamma../ = 100-300 MeV at laboratory angles of 45/sup 0/, 90/sup 0/, and 135/sup 0/. The cross section for the (..gamma..,p) reaction leaving /sup 39/K in its ground state was extracted from the tip region of the proton spectra measured at a series of bremsstrahlung endpoint energies. The data are compared with a distorted-wave impulse-approximation calculation based on a direct, single-particle knockout mechanism.

Electron momentum spectroscopy of xenon: A detailed analysis.

Accurate measurements of the 1000-eV noncoplanar symmetric (e,2e) reaction on xenon are reported. Cross-section calculations are carried out with the use of both the plane-wave and distorted-wave impulse approximations. The distorted-wave impulse approximation accurately describes both the 5${p}^{\mathrm{\ensuremath{-}}1}$ and 5${s}^{\mathrm{\ensuremath{-}}1}$ angular correlations and their relative cross sections. It also describes accurately the 5${p}_{3/2}^{\mathrm{\ensuremath{-}}1}$:5${p}_{1/2}^{\mathrm{\ensuremath{-}}1}$ branching ratios if Dirac-Fock target wave functions are used. The branching ratios show the inadequacy of Hartree-Fock wave functions for xenon. The plane-wave impulse-approximation overestimates the 5${s}^{\mathrm{\ensuremath{-}}1}$ cross section relative to the 5${p}^{\mathrm{\ensuremath{-}}1}$ and underestimates the cross section at large angles. The 5${s}^{\mathrm{\ensuremath{-}}1}$ spectroscopic factors are assigned up to a separation energy of 45 eV, and the distorted-wave impulse-approximation calculation verifies that all the 5${s}^{\mathrm{\ensuremath{-}}1}$ strength has been found. The spectroscopic factors for the 5${s}^{\mathrm{\ensuremath{-}}1}$ manifold are obtained at 1000 and 1200 eV at a number of angles and are found to be independent of incident energy and ion recoil momentum. The spectroscopic factor for the lowest 5${s}^{\mathrm{\ensuremath{-}}1}$ transition at 23.4 eV is 0.37\ifmmode\pm\else\textpm\fi{}0.01, whereas that for the ground-state 5${p}^{\mathrm{\ensuremath{-}}1}$ transition is greater than or equal to 0.98.

2H, 3,4He(p

The continuum cross sections and analyzing powers from the $^{2}\mathrm{H}$, $^{3}$,4He(p\ensuremath{\rightarrow},p') and $^{3}$,4He(p\ensuremath{\rightarrow},d') reactions were measured for 98.7 and 149.3 MeV polarized protons in the angular range 17.5\ifmmode^\circ\else\textdegree\fi{} to 60\ifmmode^\circ\else\textdegree\fi{}. The $^{2}\mathrm{H}$ and $^{3}\mathrm{He}$ data show strong quasifree contributions with more ambiguous results for $^{4}\mathrm{He}$. These data are compared with distorted-wave impulse approximation calculations based on quasifree nucleon and deuteron knockout. Overall, the agreement between theory and experiment is moderately good. However, some significant discrepancies are observed and corrections to the simple model are discussed.

Reply to "Role of pion absorption on quasi-deuterons in sup12C( pi sup+,2p)"

An attempt is made to clarify some of the areas of disagreement concerning recent distorted-wave impulse approximation calculations of the sup12C(..pi..sup+,2p) reaction. In the absence of detailed exclusive data, it is argued that the identification of the broad ''background'' reported remains uncertain.

Role of pion absorption on quasi-deuterons in sup12C( pi sup+,2p).

It is argued that the conclusions drawn from recent distorted-wave impulse approximation calculations of the sup12C(\ensuremath{\pi}sup+,2p) reaction should be based on results of calculations which include distortions. Such results support the interpretation given in the paper describing the experimental study of this reaction.

Cross sections and analyzing powers for quenched spin excitations in 40,48Ca at Ep

The inelastic cross sections and analyzing powers for spin excitations in /sup 40,48/Ca have been measured at E/sub p/ = 334 MeV. The data for excited states in /sup 40/Ca at 8.424 MeV (2/sup -/) and 10.31 MeV (1/sup +/) and the 10.22-MeV (1/sup +/) state in /sup 48/Ca are fairly well described by microscopic distorted-wave impulse approximation calculations. Normalizations of the calculated cross sections to the experimental data show that these spin excitations are quenched. We deduce B(M2)up-arrow = 281 ..mu../sub N//sup 2/fm/sup 2/ for the 8.42-MeV 2/sup -/ state in /sup 40/Ca.

9Be(p,p alpha ) 5He cluster knockout reaction with 150 MeV polarized protons.

The (p,p\ensuremath{\alpha}) cluster knockout reaction on $^{9}\mathrm{Be}$ was investigated using polarized incident protons. Coincident data for eight quasifree angle pairs were obtained at a bombarding energy of 150 MeV. Both differential cross sections and analyzing powers were measured for the energy-sharing distribution. Distorted wave impulse approximation calculations indicate that the reaction is dominated by a quasifree knockout process, and that a D-state component of the cluster-core wave function is important for larger momentum transfer. Extracted absolute spectroscopic factors for both S- and D-state knockout are in good agreement with theoretical predictions. The analyzing power follows the trend of free p${\mathrm{\ensuremath{-}}}^{4}$He scattering and agrees with the distorted wave impulse approximation calculation reasonably well. Near zero recoil momentum, the spin-orbit interaction in the distorted waves plays little role.