Impulse Approximation Calculations Research Articles

Polarization transfer and spin response functions of theH2(p⃗,n⃗)reaction at345MeV

Differential cross sections and a complete set of polarization observables have been measured in the quasielastic $^{2}\mathrm{H}(p,n)$ reaction at a bombarding energy of $345\phantom{\rule{0.3em}{0ex}}\text{MeV}$ and laboratory scattering angles of $16\ifmmode^\circ\else\textdegree\fi{}$, $22\ifmmode^\circ\else\textdegree\fi{}$, and $27\ifmmode^\circ\else\textdegree\fi{}$. The data are compared with plane-wave impulse approximation calculations employing an optimal factorization approximation. The agreement between the experimental and theoretical results validates these approximations in the present momentum- and energy-transfer regions. The experimental spin-longitudinal and spin-transverse response functions, ${R}_{L}$ and ${R}_{T}$, respectively, are deduced from the data. The obtained ${R}_{T}$ is consistent with that obtained from the quasielastic electron scattering. The theoretical calculations with the Reid soft core potential give good descriptions for ${R}_{L}$ and ${R}_{T}$, whereas the latter is slightly underestimated around the quasielastic peak.

Three-body dN interaction in the analysis of the 12C[formula omitted] reaction at 270 MeV

We have measured the cross sections and analyzing powers Ay and Ayy for the elastic and inelastic scattering of deuterons from the 0+(g.s.), 2+(4.44 MeV), 3−(9.64 MeV), 1+(12.71 MeV), and 2−(18.3 MeV) states in 12C at an incident energy of 270 MeV. The data are compared with microscopic distorted-wave impulse approximation calculations where the projectile-nucleon effective interaction is taken from the three-nucleon t-matrix given by rigorous Faddeev calculations presently available at intermediate energies. The agreement between theory and data compares well with that for the (p,p′) reactions at comparable incident energies/nucleon.

Analyzing power and cross section distributions of the knockout reaction208Pb(p→,2p)207Tlat an incident energy of 202 MeV

Exclusive measurements of the cross section and analyzing power for the ${}^{208}\mathrm{Pb}(\stackrel{\ensuremath{\rightarrow}}{p}{,2p)}^{207}\mathrm{Tl}$ proton knockout reaction at 202 MeV are presented for three quasifree angle pairs. Energy-sharing cross section distributions are found to be in excellent agreement with distorted wave impulse approximation (DWIA) calculations, yielding spectroscopic factors that are in reasonable agreement with ${(e,e}^{\ensuremath{'}}p)$ studies and theoretical expectations. The measured analyzing powers are, however, in significant disagreement with results of standard DWIA calculations that utilize the free nucleon-nucleon interaction. Analyzing power calculations are furthermore found to be insensitive to variations in the distorting potentials, different descriptions of the bound state, different energy prescriptions of the two-body interaction, and nonlocality effects. Agreement between theory and experiment is shown to improve only when the density dependence of the nucleon-nucleon interaction is incorporated within the DWIA.

Polarization transfer measurements for the13C(p→,n→)13Nreaction at 197 MeV and empirical isovector spin-longitudinal response for the(1/2)g.s.−→(1/2)1+transition

We present differential cross sections and complete sets of polarization-transfer coefficients, ${D}_{\mathrm{ij}},$ obtained in the ${}^{13}\mathrm{C}(\stackrel{\ensuremath{\rightarrow}}{p},\stackrel{\ensuremath{\rightarrow}}{n}{)}^{13}\mathrm{N}$ reaction studied at 197 MeV incident proton energy and laboratory angles between $0\ifmmode^\circ\else\textdegree\fi{}$ and $33\ifmmode^\circ\else\textdegree\fi{}.$ These complete sets of polarization observables are used to obtain spin-longitudinal and spin-transverse components for transitions to the ground state, to the first, and to the unresolved second and third excited states in ${}^{13}\mathrm{N}$ at 2.36 MeV and $(3.50+3.55) \mathrm{MeV},$ respectively. The results are used to obtain the two $\ensuremath{\Delta}{J}^{\ensuremath{\pi}}$ contributions for the ground and first excited state transitions and are compared with corresponding distorted-wave impulse approximation (DWIA) calculations. In particular, empirical angular distribution values for the unique spin-longitudinal $\ensuremath{\Delta}{J=0}^{\ensuremath{-}}$ transition to the first excited state in ${}^{13}\mathrm{N}$ are obtained and compared with DWIA calculations.

Polarization transfer in the16O(p,p′)reaction at forward angles and structure of the spin-dipole resonances

Cross sections and polarization transfer observables in the $^{16}$O$(p,p')$ reactions at 392 MeV were measured at several angles between $\theta_{lab}=$ 0$^\circ$ and 14$^\circ$. The non-spin-flip (${\Delta}S=0$) and spin-flip (${\Delta}S=1$) strengths in transitions to several discrete states and broad resonances in $^{16}$O were extracted using a model-independent method. The giant resonances in the energy region of $E_x=19-$27 MeV were found to be predominantly excited by ${\Delta}L=1$ transitions. The strength distribution of spin-dipole transitions with ${\Delta}S=1$ and ${\Delta}L=1$ were deduced. The obtained distribution was compared with a recent shell model calculation. Experimental results are reasonably explained by distorted-wave impulse approximation calculations with the shell model wave functions.

Spin Transfer Measurements in $(\vec{p},\vec{n})$ Reactions

The measurement of complete sets of spin transfer coefficients in nuclear transitions, induced via charge-exchange (\((\vec p, \vec n)\)) reactions at intermediate energies, is a unique form of separating the spin-dependent and spin-independent contributions to the differential cross section. The two components of the spin-dependent contribution, the spin-longitudinal and spin-transverse components may equally be separated. This is extremely important in cases where the target nuclei has a non-integer ground state spin. In this study and as an example of the above, we present differential cross section and complete set of polarization transfer coefficients obtained in the (\(^{13} C(\vec p, \vec n)\)) 13N reaction studied at angles between 0° and 33° and at 197 MeV incident proton energy. Polarization transfer coefficients are used to obtain the fraction of the Gamow-Teller (GT) component in the mirror ground state transition, which is a combination of the spin-independent Fermi (F) and spin-dependent GT components. Data are also presented for the transition to the first excited state in 13N at 2.34 MeV. This is a (1/2)− → (1/2)+ transition and the cross section is an incoherent admixture of ΔJ π = 1− and ΔJ π = 0− components. The complete set of polarization transfer coefficients are used to obtain differential cross section data for both components. The empirical results are compared with Distorted Wave Impulse Approximation calculations, DWIA.

New distorted-wave impulse approximation calculation for inelastic scattering of deuterons at intermediate energies with the sudden approximation approach

We perform a distorted-wave impulse approximation calculation of inelastic scattering of deuterons by nuclei using effective interactions in the framework of the sudden approximation at ${E}_{d}=400$ MeV. Cross sections and spin observables are expressed in terms of amplitudes for the corresponding nucleon-nucleus scattering. The calculation is examined for the excitation of ${}^{12}\mathrm{C}$ to the ${2}^{+}$ (2.44 MeV), ${3}^{\ensuremath{-}}$ (9.64 MeV), and ${1}^{+}$ (12.71 MeV) states and is found to give a reasonable description for most of the observables. Some discrepancies are found for the transition leading to the ${1}^{+}$ state, suggesting the limitation of the applicability of the effective interaction. Contributions of the deuteron D state are studied. Relations between the deuteron-nucleus and proton-nucleus scattering observables are found and are studied against existing data.

Electron- and photon-induced proton knockout from209Bi

Cross sections have been measured for the ${}^{209}\mathrm{Bi}{(e,e}^{\ensuremath{'}}{p)}^{208}\mathrm{Pb}$ and ${}^{209}\mathrm{Bi}(\ensuremath{\gamma}{,p)}^{208}\mathrm{Pb}$ reactions using electrons at ${E}_{e}=293$ and 412 MeV, and tagged photons at mean ${E}_{\ensuremath{\gamma}}\ensuremath{\sim}43.7$ and $\ensuremath{\sim}52.0$ MeV, respectively. The ${}^{209}\mathrm{Bi}{(e,e}^{\ensuremath{'}}{p)}^{208}\mathrm{Pb}$ results are compared to complete distorted wave impulse approximation calculations, from which it is deduced that a model of ${}^{209}\mathrm{Bi}$ based on a ${1h}_{9/2}$ proton orbiting an inert ${}^{208}\mathrm{Pb}$ core has a high degree of validity. The interpretation of the ${}^{209}\mathrm{Bi}(\ensuremath{\gamma}{,p)}^{208}\mathrm{Pb}$ results makes use of the ${(e,e}^{\ensuremath{'}}p)$ results to constrain the calculation of the direct knockout contribution. Using this approach, a comparison of the ${}^{209}\mathrm{Bi}(\ensuremath{\gamma}{,p)}^{208}\mathrm{Pb}$ data to various calculations with and without meson exchange contributions shows that the enhancement of the $(\ensuremath{\gamma},p)$ cross section due to meson exchange is small. This is in contrast to results obtained for light nuclei, but in agreement with results for heavier nuclei.

Dynamical relativistic effects in quasielastic 1p-shell proton knockout from 16O

We have measured the cross section for quasielastic 1p-shell proton knockout in the 16O(e,e(')p) reaction at omega = 0.439 GeV and Q2 = 0.8 (GeV/c)(2) for missing momentum P(miss)</=355 MeV/c. We have extracted the response functions R(L+TT), R(T), R(LT), and the left-right asymmetry, A(LT), for the 1p(1/2) and the 1p(3/2) states. The data are well described by relativistic distorted wave impulse approximation calculations. At large P(miss), the structure observed in A(LT) indicates the existence of dynamical relativistic effects.

Antisymmetric distorted wave impulse approximation calculations of spin transfer cross sections for(3He→,t→)reactions to the continuum

A formalism is presented for the calculation of spin transfer cross section for intermediate energy charge exchange ${(}^{3}\mathrm{He}\ensuremath{\rightarrow},\stackrel{\ensuremath{\rightarrow}}{t})$ [and $(\stackrel{\ensuremath{\rightarrow}}{p},\stackrel{\ensuremath{\rightarrow}}{n})]$ reactions to the continuum. The nuclear structure part of the formalism is based on the continuum Tamm-Dancoff method and the nuclear reaction part is treated within the distorted wave impulse approximation. In the nuclear structure part, we thus include particle-hole correlations and continuum effects on the excited particle. The knockon-exchange effect and the damping of the particle through an imaginary potential added to the single particle real potential are also taken into account. Results of numerical calculations are presented for the inclusive cross sections $\ensuremath{\sigma}(0\ifmmode^\circ\else\textdegree\fi{})$ and the spin transfer coefficients ${D}_{\mathrm{nn}}(0\ifmmode^\circ\else\textdegree\fi{})$ for forward scattering, for the intermediate energy ${(}^{3}\mathrm{He}\ensuremath{\rightarrow},\stackrel{\ensuremath{\rightarrow}}{t})$ and $(\stackrel{\ensuremath{\rightarrow}}{p},\stackrel{\ensuremath{\rightarrow}}{n})$ reactions on ${}^{12}\mathrm{C}$ and ${}^{90}\mathrm{Zr}$ targets leading to Gamow-Teller resonances in the continuum. It is shown that ${D}_{\mathrm{nn}}(0\ifmmode^\circ\else\textdegree\fi{})$ for this case takes a value of $\ensuremath{-}1/3,$ regardless of the details of nuclear structure and reaction mechanisms, if the reaction is assumed to proceed as an orbital angular momentum transfer ${l}_{t}=0$ process, and that deviations from $\ensuremath{-}1/3$ come from admixture of ${l}_{t}=2$ components. A simple closed form of the expression is derived which can be used to understand a subtle dependence of the ${D}_{\mathrm{nn}}$ values on nuclear structure and effective interaction.

Improving the convergence of NN effective field theory

We study a low-energy effective field theory (EFT) describing the NN system in which all exchanged particles are integrated out. We show that fitting the residue of the 3S 1 amplitude at the deuteron pole, rather than the 3S 1 effective range, dramatically improves the convergence of deuteron observables in this theory. Reproducing the residue ensures that the tail of the deuteron wave function, which is directly related to NN scattering data via analytic continuation, is correctly reproduced in the EFT at next-to-leading order. The role of multi-nucleon-electroweak operators which produce deviations from effective-range theory can then be explicitly separated from the physics of the wave function tail. Such an operator contributes to the deuteron quadrupole moment, μ Q , at low order, indicating a sensitivity to short-distance physics. This is consistent with the failure of impulse-approximation calculations in NN potential models to reproduce μ Q . The convergence of NN phase shifts in the EFT is unimpaired by the use of this new expansion.

Testing microscopic medium effects on nucleons and mesons using polarization observables in high-spin, unnatural-parity(p→,p′)reactions at 200 MeV

We compare measurements of the cross section, analyzing power, induced polarization, and polarization transfer coefficients for $(\stackrel{\ensuremath{\rightarrow}}{p},{p}^{\ensuremath{'}})$ reactions leading to unnatural-parity, high-spin states in ${}^{16}\mathrm{O}$ and ${}^{28}\mathrm{Si}$ with distorted wave impulse approximation calculations. We use an effective nucleon-nucleon (NN) interaction obtained from a microscopic treatment of nuclear medium effects. The NN potential is generated from a one-boson-exchange model of the nuclear force that reproduces NN scattering data well. Medium effects are incorporated through a G matrix obtained within a Dirac-Brueckner approach to nuclear matter. While agreement for some observables is good, differences for the polarization transfer coefficients indicate that systematic problems with the relative sizes of the spin-orbit and tensor interaction components exist. The differences are larger for ${}^{28}\mathrm{Si}$ than for ${}^{16}\mathrm{O}.$ A new model that incorporates density-dependent meson mass reductions produces only small effects that do not change the quality of the agreement. Connections to previous calculations are investigated.

Nuclear pion photoproduction in theΔresonance region

A measurement of the /sup 12/C( gamma , pi /sup +/n)/sup 11/B reaction in quasifree pi -production kinematic regimes has been performed using tagged photons in conjunction with large solid angle pi and n detectors. The aim of the experiment was to investigate predicted modifications to the Delta excitation of nucleons and their subsequent propagation and decay, brought about by the nuclear medium. Differential cross sections are presented for photon energies spanning the Delta (1232) excitation region. The measurements are consistent with distorted wave impulse approximation calculations in which the amplitude for proton Delta excitation, followed by Delta propagation and decay to pi /sup +/+n, is reduced compared to that for a free p. However, because of uncertainties in the magnitudes of the final state interactions, it is concluded that improved calculations are required to obtain a quantitative estimate of Delta - medium effects.

Lessons to be learned from the coherent photoproduction of pseudoscalar mesons

We study the coherent photoproduction of pseudoscalar mesons---particularly of neutral pions---placing special emphasis on the various sources that put into question earlier nonrelativistic-impulse-approximation calculations. These include: final-state interactions, relativistic effects, off-shell ambiguities, and violations to the impulse approximation. We establish that, while distortions play an essential role in the modification of the coherent cross section, the uncertainty in our results due to the various choices of optical-potential models is relatively small (of at most 30%). By far the largest uncertainty emerges from the ambiguity in extending the many on-shell-equivalent representations of the elementary amplitude off the mass shell. Indeed, relativistic impulse-approximation calculations that include the same pionic distortions, the same nuclear-structure model, and two sets of elementary amplitudes that are identical on-shell, lead to variations in the magnitude of the coherent cross section by up to factors of five. Finally, we address qualitatively the assumption of locality implicit in most impulse-approximation treatments, and suggest that the coherent reaction probes---in addition to the nuclear density---the polarization structure of the nucleus.

Polarization transfer observables for proton inelastic scattering from [formula omitted]C at 0°

Polarization transfer (PT) observables in the 12C(p,p′) reaction at 0° for 392 MeV protons have been measured. The excitation strengths are decomposed into the spin-flip part and the non-spin-flip part by using the obtained PT observables. The PT observables for excitation of the 1+, T=0 and 1+, T=1 states are compared with distorted wave impulse approximation calculations. The strength ratios of the isoscalar spin-dependent term to the isovector tensor term and the isovector tensor term to the isovector spin-dependent term are reasonably consistent with the Franey and Love interaction.

Spin-isospin flip giant resonances and shell dependence in7Liand9Bebyπ+photoproduction

The giant resonances of spin-isospin flip mode are studied by measuring the energy and angular distributions of ${\ensuremath{\pi}}^{+}$ electroproduced from ${}^{7}\mathrm{Li}$ and ${}^{9}\mathrm{Be}$ nuclei. Several strong ${\ensuremath{\pi}}^{+}$ groups are found and angular distributions of these groups are analyzed by distorted-wave impulse approximation calculations using the single particle shell model. The experimental cross section of the groups corresponds to an order of the charge exchange single particle transition strength, establishing them as spin-isospin flip giant resonances. The shell model nature of $(\ensuremath{\gamma},{\ensuremath{\pi}}^{+})$ results for ${1p}_{3/2}$ shell nuclei are summarized and presented together with previously published data. The obtained results are compared to previously published data for $({\ensuremath{\pi}}^{\ensuremath{-}},\ensuremath{\gamma}),$ (n,p), ${(e,e}^{\ensuremath{'}}p),$ and $(p,2p)$ reactions. Strong transitions consistent with the giant resonance excitations from the ${1s}_{1/2}$ shell in the core and from the ${1p}_{3/2}$ valence shell are observed.

Measurement of the6Li(γ,π0)reaction near threshold

Total and differential cross sections for the reaction ${}^{6}\mathrm{Li}(\ensuremath{\gamma},{\ensuremath{\pi}}^{0})$ have been measured within 23 MeV of threshold using the tagged photon facility at SAL in conjunction with the ${\ensuremath{\pi}}^{0}$ spectrometer IGLOO. The differential measurements are the first to be reported in the threshold region, while the quality of the total cross section far surpasses previous investigations. The electric dipole amplitude for ${\ensuremath{\pi}}^{0}$ photoproduction has been deduced at threshold, and the relation to the corresponding free-deuteron amplitude as recently measured is examined within the context of an $\ensuremath{\alpha}\ensuremath{-}d$ cluster model of ${}^{6}\mathrm{Li}.$ The reduced P-wave amplitude ${P}_{3}^{(+)}/kq$ is deduced at threshold and is consistent with previous estimates from both the nucleon and nuclear sectors. The apparent stability of this amplitude as a function of environment remains a puzzle. Finally, the present cross sections compare favorably with the recent distorted-wave impulse approximation calculations of Kamalov et al.

Quasifree inclusive and exclusive analyzing powers at 200 MeV

Analyzing power measurements for both inclusive (pW ,p8) and exclusive (pW ,2p) and (pW ,np) quasifree scattering at 200 MeV from H and C have been completed in the angular range from 27° to 34°. Previous experimental and theoretical work has indicated non-negligible suppression of the inclusive (pW ,p8) analyzing powers with respect to impulse approximation calculations. Conversely, both suppression and enhancement of the isovector (pW ,n) analyzing power data have been found depending on the mass number of the target. Both nonrelativistic and fully relativistic calculations have sought to explain these features. However to address such questions within the inclusive data, it is important to fully understand the makeup of the inclusive spectra. This ensures that any ‘‘nonconventional’’ aspects of the data do not arise from contamination of the quasifree scattering yield. @S0556-2813~99!01004-3#

α-clustering probabilities extracted from the12C(α,2α)8Bereaction at 200 MeV

The energy-sharing distribution at a coplanar symmetric quasifree angle pair has been measured for the ${}^{12}\mathrm{C}(\ensuremath{\alpha},2\ensuremath{\alpha}{)}^{8}\mathrm{Be}(\mathrm{g}.\mathrm{s}.)$ reaction at an incident energy of 200 MeV. The measured knockout cross sections are compared with distorted wave impulse approximation calculations. Extracted spectroscopic factors are found to be in reasonable agreement with a theoretical prediction and results from $(p,p\ensuremath{\alpha})$ studies. The present results indicate a transition in the dynamics of this reaction in the incident energy region 140--200 MeV.

(α,2α) cluster knockout reaction on9Beand12Cat 580 MeV

Cross-section measurements of the ${}^{9}\mathrm{Be}{,}^{12}\mathrm{C}(\ensuremath{\alpha},2\ensuremath{\alpha})$ reaction at 580 MeV bombarding energy are presented. The data are compared with distorted-wave impulse approximation calculations. The agreement between theory and experiment suggests a dominance of the quasifree knockout mechanism. The extracted $\ensuremath{\alpha}$-particle spectroscopic factors are in reasonable agreement with theory and proton-induced knockout reactions, unlike measurements for the $(\ensuremath{\alpha},2\ensuremath{\alpha})$ reaction at energies $l~140$ MeV, but still show significant angular dependence.