Impulse Approximation Research Articles

Momentum-space approach to nuclear reaction studies: opportunities and perspectives

The application of momentum-space three- and four-body scattering equations to the description of nuclear reactions involving systems of three and four nucleons is reviewed, and major achievements and challenges are identified. The calculations include realistic state-of-the-art interactions between nucleon pairs, together with the Coulomb interaction between protons. The effect of including three- and four-nucleon forces is discussed. Further calculations are shown involving the study of nuclear reactions where three-body degrees of freedom play a significant role. These studies involve not just an attempt to describe data in terms of a full three-body model that is solved numerically in a converged way, but also to use this exact framework to validade and test the accuracy of approximate reaction methods such as continuum discretized coupled channel (CDCC), distorted wave impulse approximation (DWIA), plane-wave impulse approximation (PWIA) and the Glauber multiple scattering approach. These comparisons are able to teach researchers under which conditions approximate methods can be used to extract important structural information about exotic nuclei. Prospects and challenges are discussed.

Nuclear effects and neutron structure in deeply virtual Compton scattering off 3He

The study of nuclear generalized parton distributions (GPDs) could be a crucial achievement of hadronic physics since they open new ways to obtain new information on the structure of bound nucleons, in particular, to access the neutron GPDs. Here, the results of calculations of 3He GPDs in Impulse Approximation (IA) are presented. The calculation of the sum of GPDs H + E, and , with the correct limits, will be shown. These quantities, at low momentum transfer, are largely dominated by the neutron contribution so that 3He is an ideal target for these kind of studies. Nevertheless the extraction of neutron information from future 3He data could be non trivial. A procedure, which takes into account nuclear effects encoded in IA, is presented. The calculation of H, E and allows also to evaluate the cross section asymmetries for deeply virtual compton scattering (DVCS) at Jefferson Lab kinematics. Thanks to these observations, DVCS off 3He could be an ideal process to access the neutron information in the next future.

Comparing spin observables in the reaction $^{12} C(\vec p,\vec p')^{12} C$ at 100–500 MeV with various distorted-wave impulse approximations

Spin observables in the process \((\vec p,\vec p')\) are analyzed at intermediate energies in the range 100–500 MeV. Experimental and theoretical data are compared for the reaction \(^{12} C(\vec p,\vec p')^{12} C\) involving excitation of states 1+, T = 0 (12.71 MeV) and 1+, T = 1 (15.11 MeV). Two varieties of DWIA-type calculations are mainly used, allowing the role of isospin effects to be distinguished.

Similarity between positronium-atom and electron-atom scattering.

We employ the impulse approximation for a description of positronium-atom scattering. Our analysis and calculations of Ps-Kr and Ps-Ar collisions provide a theoretical explanation of the similarity between the cross sections for positronium scattering and electron scattering for a range of atomic and molecular targets observed by S. J. Brawley et al. [Science 330, 789 (2010)].

Quasielastic electron-deuteron scattering in the weak-binding approximation

We perform a global analysis of all available electron-deuteron quasielastic scattering data using Q^2-dependent smearing functions that describe inclusive inelastic e-d scattering within the weak binding approximation. We study the dependence of the cross sections on the deuteron wave function and the off-shell extrapolation of the elastic electron-nucleon cross sections, which show particular sensitivity at x >> 1. The excellent overall agreement with data over a large range of Q^2 and x suggests a limited need for effects beyond the impulse approximation, with the possible exception of the very high-x or very low-Q^2 regions, where short-distance effects or scattering from non-nucleonic constituents in the deuteron become more relevant.

Erratum: Relativistic impulse approximation analysis of elastic proton scattering from He isotopes [Phys. Rev. C89, 014620 (2014)

Erratum: Relativistic impulse approximation analysis of elastic proton scattering from He isotopes [Phys. Rev. C<b>89</b>, 014620 (2014)

ΣNNquasibound states inHe3(K−,π∓) reactions at 600 MeV/c

We theoretically demonstrate the inclusive and semiexclusive spectra in the $^{3}\mathrm{He}$(${K}^{\ensuremath{-}}$, ${\ensuremath{\pi}}^{\ensuremath{\mp}}$) reactions at 600 MeV/$c$ (4${}^{\ensuremath{\circ}}$) within a distorted-wave impulse approximation, using a coupled ($2N\ensuremath{-}\ensuremath{\Lambda})+(2N\ensuremath{-}\ensuremath{\Sigma}$) model with a spreading potential. We present the possible existence of the $\ensuremath{\Sigma}\mathit{NN}$ quasibound state with ${J}^{\ensuremath{\pi}}=$ 1/2${}^{+}$, $T\ensuremath{\simeq}$ 1 near the $\ensuremath{\Sigma}$ threshold, predicted by a $2N\ensuremath{-}Y$ folding-model potential derived from $\mathit{YN}$ $g$-matrices. The result shows that a signal of the ${}_{\ensuremath{\Sigma}}^{3}$He quasibound state is clearly confirmed near the $\ensuremath{\Sigma}$ threshold in the ${\ensuremath{\pi}}^{\ensuremath{-}}$ spectrum, whereas a peak of the ${}_{\ensuremath{\Sigma}}^{3}n$ quasibound state is rather reduced in the ${\ensuremath{\pi}}^{+}$ spectrum owing to the interference effects caused by the ${}^{3}{S}_{1}$-${}^{1}{S}_{0}$ admixture in the $\mathit{NN}$ pair. The mechanism of $\ensuremath{\Sigma}$ production for these spectra and charge symmetry breaking effects are also discussed.

A Monte Carlo code to get response spectrum of ions for Neutron Depth Profiling

This paper presents a Monte Carlo code to get response spectrum of ions for the Neutron Depth Profiling (NDP) technique called Monte Carlo NDP (MC-NDP) that simulates the behavior of ions transmitted through a sample matrix and generates the energy spectrum for a specified detector. The MC-NDP model is based on the Ziegler-Bier- sack-Littmark Model, but incorporates the advantages of TRIM and CORTEO. The Impulse Approximation method is used to determine the flight length with the indexical inter- polation method rather than the Magic algorithm for the scattering angle between ions and nucleus. This makes MC- NDP more efficient and convenient to simulate entire ion histories by a Monte Carlo approach. MC-NDP's results agree well with both TRIM results and the experimental data.

State-selective electron capture in collisions of C6+, N7+ with Hydrogen at intermediate energies

We present a joint study of the electron capture process in multicharged ions on atomic Hydrogen at intermediate energies. We have applied two methods, the Eikonal Impulse Approximation (EIA) and the hydrogenic-Classical Trajectory Monte Carlo (CTMC) method. Good agreement is found in both total and state-selective electron capture cross sections.

Intramolecular diffraction in (e, 2e) reactions of CX4 (X=F, Cl, Br)

The remarkable discrepancies between the experimental momentum distributions and the calculated distributions within the plane wave impulse approximation (PWIA) were observed in (e, 2e) reaction of CF4, CCl4, and CBr4. The discrepancies evidently depend on the impact energy of electrons. One possible explanation is the intramolecular diffraction.

Nuclearσterms and scalar-isoscalar WIMP-nucleus interactions from lattice QCD

It has been argued that the leading scalar-isoscalar WIMP-nucleus interactions receive parametrically enhanced contributions in the context of nuclear effective field theories. These contributions arise from meson-exchange currents (MECs) and potentially modify the impulse approximation estimates of these interactions by 10--60%. We point out that these MECs also contribute to the quark mass dependence of nuclear binding energies, that is, nuclear \sigma-terms. In this work, we use recent lattice QCD calculations of the binding energies of the deuteron, He-3 and He-4 at pion masses near 500 MeV and 800 MeV, combined with the experimentally determined binding energies at the physical point, to provide approximate determinations of the \sigma-terms for these light nuclei. For each nucleus, we find that the deviation of the corresponding nuclear \sigma-term from the single-nucleon estimate is at the few percent level, in conflict with the conjectured enhancement. As a consequence, lattice QCD calculations currently indicate that the cross sections for scalar-isoscalar WIMP-nucleus interactions arising from fundamental WIMP interactions with quarks do not suffer from significant uncertainties due to enhanced meson-exchange currents.

Cluster knockout reactions

Cluster knockout reactions are expected to reveal the amount of clustering (such as that of α, d and even of heavier clusters such as12C, 16O etc.) in the target nucleus. In simple terms, incident medium high-energy nuclear projectile interacts strongly with the cluster (present in the target nucleus) as if it were existing as a free entity. Theoretically, the relatively softer interactions of the two outgoing particles with the residual nucleus lead to optical distortions and are treated in terms of distorted wave (DW) formalism. The long-range projectile–cluster interaction is accounted for, in terms of the finite range (FR) direct reaction formalism, as against the more commonly adopted zero-range (ZR) distorted wave impulse approximation (DWIA) formalism. Comparison of the DWIA calculations with the observed data provide information about the momentum distribution and the clustering spectroscopic factor of the target nucleus. Interesting results and some recent advancements in the area of (α, 2 α) reactions and heavy cluster knockout reactions are discussed. Importance of the finite-range vertex and the final-state interactions are brought out.

Distorted spin-dependent spectral function of anA=3nucleus and semi-inclusive deep-inelastic scattering processes

The distorted spin-dependent spectral function of a nucleon inside an A=3 nucleus is introduced as a novel tool for investigating the polarized electron scattering off polarized $^3$He in semi-inclusive DIS regime (SiDIS), going beyond the standard plane wave impulse approximation. This distribution function is applied to the study of the spectator SiDIS, $\vec{^3{\rm He}}(\vec e, e' ~{^2}{\rm H})X$, in order to properly take into account the final state interaction between the hadronizing quark and the detected deuteron, with the final goal of a more reliable extraction of the polarized parton-distribution $g_1(x)$ inside a bound proton. Our analysis allows to single out two well-defined kinematical regions where the experimental asymmetries could yield very interesting information: the region where the final state effects can be minimized, and therefore the direct access to the parton distributions in the proton is feasible, and the one where the final state interaction dominates, and the spectator SiDIS reactions can elucidate the mechanism of the quark hadronization itself. The perspectives of extending our approach i) to the mirror nucleus, $^3$H, for achieving a less model-dependent flavor decomposition, and ii) to the asymmetries measured in the standard SiDIS reactions, $\vec e + \vec{^3 {\rm He}} \to e' + h+X$ with $h$ a detected fast hadron, with the aim of extracting the neutron transversity, are discussed.

Determination of the axial nucleon form factor from the MiniBooNE data

Both neutrino and antineutrino charged-current quasielastic scattering on a carbon target are studied to investigate the nuclear effect on the determination of the axial form factor ${F}_{A}({Q}^{2})$. A method for extraction of ${F}_{A}({Q}^{2})$ from the flux-integrated $d\ensuremath{\sigma}/d{Q}^{2}$ cross section of (anti)neutrino scattering on nuclei is presented. Data from the MiniBooNE experiment are analyzed in the relativistic distorted-wave impulse approximation, the Fermi gas model, and the Fermi gas model with enhancements in the transverse cross section. We found that the values of the axial form factor, extracted in the impulse approximation and predicted by the dipole approximation with the axial mass ${M}_{A}\ensuremath{\approx}1.37\text{ }\mathrm{GeV}$, are in good agreement. The agreement between the extracted form factor and meson-dominance ansatz also is good. On the other hand, the ${Q}^{2}$ dependence of ${F}_{A}$ extracted in the approach with the transverse enhancement is found to differ significantly from the dipole approximation.

Quark Mass Functions and Pion Structure in Minkowski Space

We present a study of the dressed quark mass function and the pion structure in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. We use an interaction kernel in momentum space that is a relativistic generalization of the linear confining q-qbar potential and a constant potential shift that defines the energy scale. The confining interaction has a Lorentz scalar part that is not chirally invariant by itself but decouples from the equations in the chiral limit and therefore allows the Nambu-Jona-Lasinio mechanism to work. We adjust the parameters of our quark mass function calculated in Minkowski-space to agree with Lattice QCD data obtained in Euclidean space. Results of a calculation of the pion electromagnetic form factor in the relativistic impulse approximation using the same mass function are presented and compared with experimental data.

Quasielastic contribution to antineutrino-nucleus scattering

We report on a calculation of cross sections for charged-current quasielastic antineutrino scattering off ${}^{12}$C in the energy range of interest for the MiniBooNE experiment. We adopt the impulse approximation (IA) and use the nonrelativistic continuum random phase approximation (CRPA) to model the nuclear dynamics. An effective nucleon-nucleon interaction of the Skyrme type is used. We compare our results with the recent MiniBooNE antineutrino cross-section data and confront them with alternate calculations. The CRPA predictions reproduce the gross features of the shape of the measured double-differential cross sections. The CRPA cross sections are typically larger than those of other reported IA calculations but tend to underestimate the magnitude of the MiniBooNE data. We observe that an enhancement of the nucleon axial mass in CRPA calculations is an effective way of improving on the description of the shape and magnitude of the double-differential cross sections. The rescaling of ${M}_{A}$ is illustrated to affect the shape of the double-differential cross sections differently than multinucleon effects beyond the IA.

Relativistic impulse approximation analysis of elastic proton scattering from He isotopes

Recent relativistic mean field (RMF) calculations have provided nuclear distributions of some isotopes whose mass numbers are much larger than atomic numbers. For helium isotopes, the RMF calculation seems to be inappropriate because of the small mass numbers; however, applicable results are obtained for ${}^{6,8}$He nuclei. The author calculates observables of proton elastic scattering from the helium isotopes and discusses relations between observables and nuclear distributions of the isotopes by comparison of the calculated results with experimental data. The calculations are based on relativistic impulse approximation (RIA) at incident proton energy: 71 MeV for ${}^{4,6,8}$He, 300 and 500 MeV for ${}^{4}$He, and 0.7 GeV for ${}^{6}$He. Scattering observables are predicted for ${}^{6,8}$He at 200 MeV.

Theoretical Description of Deeply Virtual Compton Scattering off 3He

Recently, coherent deeply virtual Compton scattering (DVCS) off $^3$He nuclei has been proposed to access the neutron generalized parton distributions (GPDs). In Impulse Approximation (IA) studies, it has been shown, in particular, that the sum of the two leading twist, quark helicity conserving GPDs of $^3$He, $H$ and $E$, at low momentum transfer, is dominated by the neutron contribution, so that $^3$He is very promising for the extraction of the neutron information. Nevertheless, such an extraction could be not trivial. A technique, able to take into account the nuclear effects included in the IA analysis in the extraction procedure, has been therefore developed. In this work, the IA calculation of the spin dependent GPD $\tilde H$ of $^3$He is presented for the first time. This quantity is found to be largely dominated, at low momentum transfer, by the neutron contribution, which could be extracted using arguments similar to the ones previously proposed for the other GPDs. The known forward limit of the IA calculation of $\tilde H$, yielding the polarized parton distributions of $^3$He, is correctly recovered. The knowledge of the GPDs $H, E$ and $\tilde H$ of $^3$He will allow now the evaluation of the cross section asymmetries which are relevant for coherent DVCS off $^3$He at Jefferson Lab kinematics, an important step towards the planning of possible experiments.

Charged-current quasielastic neutrino scattering cross sections on12C with realistic spectral and scaling functions

Charge-current quasielastic (CCQE) (anti)neutrino scattering cross sections on a $^{12}$C target are analyzed using a spectral function $S(p,{\cal E})$ that gives a scaling function in accordance with the ($e,e'$) scattering data. The spectral function accounts for the nucleon-nucleon (NN) correlations, it has a realistic energy dependence and natural orbitals (NO's) from the Jastrow correlation method are used in its construction. In all calculations the standard value of the axial mass $M_A= 1.032$ GeV/c$^2$ is used. The results are compared with those when NN correlations are not included, as in the Relativistic Fermi Gas (RFG) model, or when harmonic-oscillator (HO) single-particle wave functions are used instead of NO's. The role of the final-state interactions (FSI) on the theoretical spectral and scaling functions, as well as on the cross sections is accounted for. A comparison of the results for the cases with and without FSI, as well as to results from the phenomenological scaling function obtained from the superscaling analysis (SuSA) is carried out. Our calculations based on the impulse approximation (IA) underpredict the MiniBooNE data, but agree with the data from the NOMAD experiment. The possible missing ingredients in the considered theoretical models are discussed.

Pion electromagnetic form factor in the covariant spectator theory

The pion electromagnetic form factor at spacelike momentum transfer is calculated in relativistic impulse approximation using the Covariant Spectator Theory. The same dressed quark mass function and the equation for the pion bound-state vertex function as discussed in the companion paper are used for the calculation, together with a dressed quark current that satisfies the Ward-Takahashi identity. The results obtained for the pion form factor are in agreement with experimental data, they exhibit the typical monopole behavior at high-momentum transfer, and they satisfy some remarkable scaling relations.