Plane Wave Impulse Approximation Research Articles

Influence of single-particle energy on inclusive electron scattering

Extensive studies have been carried out over the past decades to explore the impacts of nucleon momentum distributions (NMDs) on the inclusive electron scattering process. Nevertheless, there remains limited research about the effects of the single-particle energy level distributions E s.p.(β) on reaction. For a given nucleus, the E s.p.(β) of different deformations exhibits distinct changes. In this paper, we investigate the influences of the E s.p.(β) of distinct deformations on process. Using the plane-wave impulse approximation method, we calculate the cross sections of different deformed configurations. The corresponding E s.p.(β) and NMDs are obtained from the deformed relativistic mean-field model. It is found that the theoretical cross sections show moderate dependence on the E s.p.(β) of distinct deformations. This is due to the conservation of energy, which restricts the number of nucleons participating in the process of diverse deformed configurations. The studies in this paper can provide useful guides for future lepton-nucleus scattering experiments.

Full [formula omitted]-space analysis of molecular dynamics effect on electron momentum profile of outer-valence orbitals of oxetane

The molecular dynamics effect on electron momentum profiles (EMPs) of outer-valence orbitals of oxetane was investigated theoretically by using the thermal sampling molecular dynamics (TSMD) method to prepare the initial condition of molecules at a certain temperature. A full Q-space sampling is achieved including both harmonic and anharmonic vibrations, particularly the ring-puckering vibration. The sampled conditions were testified by comparing the simulated electron binding spectrum with the photoelectron spectrum. The plane wave impulse approximation (PWIA) is adopted to calculate the EMPs. The results of outer valence orbitals of oxetane are compared with experiments adopting the asymmetric noncoplanar kinematics and theoretical results by ring-puckering model and the harmonic analytical quantum mechanical (HAQM) model. For 3b1 orbital, where the vibrational excitation and anharmonicity of ring-puckering mode cannot be ignored, the present model gives an improved description. For the other orbitals, the present results are similar to the predictions by the HAQM model.

Experimental and Theoretical Study on Electron Momentum Spectroscopy of SF6: Distorted-Wave and Vibrational Motion.

The vibrational and distorted-wave effects are usually invoked to explain the measured electron momentum profiles for molecular orbitals. The vibrational effect can be accounted for quantitatively by a harmonic analytical quantum mechanical approach within the plane-wave impulse approximation (PWIA). On the other hand, quantitative calculation considering the distorted-wave effect was available only recently by a multicenter-three-distorted-wave (MCTDW) method (Phys. Rev. A2022, 105, 042805). Here, we report a joint experimental and theoretical investigation on electron momentum spectroscopy of SF6. The experiments were performed using a high-sensitivity (e, 2e) spectrometer employing non-coplanar symmetric geometry with incident electron energy equal to 1200 eV + binding energy. The experimental electron momentum profiles are compared with theoretical calculations by the MCTDW method at equilibrium geometry and by the PWIA method both at equilibrium geometry and considering vibrational motions. For all the measured orbitals, large discrepancies were observed between the experiments and the PWIA calculations at equilibrium geometry. For the highest occupied molecular orbital 1t1g, the vibrational effect can partly explain the high intensity of the experimental momentum profile at low momenta. For the other orbitals, the influence of the vibrational effect is negligible. On the other hand, the MCTDW calculations improve the agreement with the experiments for all the observed orbitals, indicating that the distorted-wave effect plays an important role in reproducing the measured momentum profiles of SF6.

Effects of nucleon-nucleon short-range correlations on inclusive electron scattering

The nucleon-nucleon short-range correlation (NN-SRC) is one of the key issues of nuclear physics, which typically manifest themselves in high-momentum components of the nuclear momentum distributions. In this paper, the nuclear spectral functions based on the axially deformed relativistic mean-field model are developed to involve the NN-SRC. With the spectral functions, the inclusive electron scattering $(e,{e}^{\ensuremath{'}})$ cross sections are calculated within the plane-wave impulse approximation (PWIA) framework, including the quasielastic (QE) part and $\mathrm{\ensuremath{\Delta}}$ production part. Especially in the $\mathrm{\ensuremath{\Delta}}$ production region, we reconsider the electromagnetic structures of the nucleon resonance $\mathrm{\ensuremath{\Delta}}$(1232) and the scattering mechanisms, and thereby the theoretical calculations are improved effectively and the cross sections are well consistent with the experimental data. The theoretical $(e,{e}^{\ensuremath{'}})$ cross sections are further divided into NN-SRC and mean-field contributions. It is found that, at the kinematics $0.5\phantom{\rule{0.16em}{0ex}}{\mathrm{GeV}}^{2}<{Q}^{2}<1\phantom{\rule{0.16em}{0ex}}{\mathrm{GeV}}^{2}$, the QE peak and $\mathrm{\ensuremath{\Delta}}$ production peak not only reflect the mean-field structure but also are sensitive to the NN-SRC information. Finally, we provide another method to extract the strengths of NN-SRC from experimental cross sections for selected nuclei at the suitable kinematics.

Asymptotic behavior of the electron-atom Compton profile due to the intramolecular H-atom motion in H2.

We report the asymptotic behavior of the electron-atom Compton profile due to the intramolecular H-atom motion in H2. The experiment has been performed at a scattering angle of 135° and at incident electron energies from 1.0 to 2.2 keV, thus covering a momentum transfer (K) range from 15.8 to 23.5 a.u. It is shown that with the increase in K, the Compton profile changes in shape and becomes more symmetric. Furthermore, it is found that the experiment reaches the limit of sufficiently large K at an incident electron energy of 2.0 keV, where the plane-wave impulse approximation is applicable to directly relate the Compton profile to the momentum distribution of the H atom.

Theoretical description of semi-inclusive T2K, MINERνA and MicroBooNE neutrino-nucleus data in the relativistic plane wave impulse approximation

We present the results of semi-inclusive neutrino-nucleus cross sections within the plane wave impulse approximation (PWIA) for three nuclear models: relativistic Fermi gas, independent-particle shell model, and natural orbital shell model in comparison with the available $\mathrm{CC}0\ensuremath{\pi}$ measurements from the T2K, $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$, and MicroBooNE collaborations where a muon and at least one proton are detected in the final state. Results are presented as a function of the momenta and angles of the final particles, as well as in terms of the imbalances between proton and muon kinematics. The present semi-inclusive formalism is based on fully relativistic microscopic calculations and numerical integrations to produce both lepton and hadron kinematics without relying on further approximations. The analysis reveals that contributions beyond PWIA are crucial to explain the experimental measurements and that the study of correlations between final-state proton and muon kinematics can provide valuable information on relevant nuclear effects such as the Fermi motion and final-state interactions.

Ruling out Color Transparency in Quasielastic ^{12}C(e,e^{'}p) up to Q^{2} of 14.2 (GeV/c)^{2}.

Quasielastic ^{12}C(e,e^{'}p) scattering was measured at spacelike 4-momentum transfer squared Q^{2}=8, 9.4, 11.4, and 14.2 (GeV/c)^{2}, the highest ever achieved to date. Nuclear transparency for this reaction was extracted by comparing the measured yield to that expected from a plane-wave impulse approximation calculation without any final state interactions. The measured transparency was consistent with no Q^{2} dependence, up to proton momenta of 8.5 GeV/c, ruling out the quantum chromodynamics effect of color transparency at the measured Q^{2} scales in exclusive (e,e^{'}p) reactions. These results impose strict constraints on models of color transparency for protons.

Probing the Deuteron at Very Large Internal Momenta.

We measure ^{2}H(e,e^{'}p)n cross sections at 4-momentum transfers of Q^{2}=4.5±0.5 (GeV/c)^{2} over a range of neutron recoil momenta p_{r}, reaching up to ∼1.0 GeV/c. We obtain data at fixed neutron recoil angles θ_{nq}=35°, 45°, and 75° with respect to the 3-momentum transfer q[over →]. The new data agree well with previous data, which reached p_{r}∼500 MeV/c. At θ_{nq}=35° and 45°, final state interactions, meson exchange currents, and isobar currents are suppressed and the plane wave impulse approximation provides the dominant cross section contribution. We compare the new data to recent theoretical calculations, where we observe a significant discrepancy for recoil momenta p_{r}>700 MeV/c.

Semi-inclusive charged-current neutrino-nucleus cross sections in the relativistic plane-wave impulse approximation

Neutrino-nucleus quasielastic scattering is studied in the plane wave impulse approximation for three nuclear models: the relativistic Fermi gas (RFG), the independent-particle shell model (IPSM) and the natural orbitals (NO) model with Lorentzian dependence of the excitation energy. A complete study of the kinematics of the semi-inclusive process and the associated cross sections are presented and discussed for 40 Ar and 12 C. Inclusive cross sections are also obtained by integrating the semi-inclusive expressions over the outgoing hadron. Results are consistent with previous studies restricted to the inclusive channel. In particular, a comparison with the analytical results for the RFG model is performed. Explicit expressions for the hadronic tensor and the 10 semi-inclusive nuclear responses are given. Theoretical predictions are compared with semi-inclusive experimental data from T2K experiment.

Clusters and their fundamental role for Trojan Horse Method

The Trojan Horse Method (THM) lays its foundations on the cluster structure of light nuclei which are usually used as “Trojan horses”. Many of them were successfully employed in the last decades to shed light to numerous astrophysical problems. Cluster structure and dynamics also suggest a series of tests which may be performed in order to strengthen the basis of the method. Among them pole invariance was investigated for three different situations. In fact, the cross sections for the $$^6$$ Li(d, $$\alpha )^4$$ He, $$^2$$ H(d,p) $$^3$$ H and $$^7$$ Li(p, $$\alpha )^4$$ He binary reactions were measured for several break-up schemes and analyzed within the framework of the Plane Wave Impulse Approximation (PWIA). The indirect results extracted by using different Trojan Horse nuclei (e.g. $$^2$$ H, $$^3$$ He, $$^6$$ Li) were compared with each other as well as with direct measurements of the corresponding astrophysical reactions. The very good agreement obtained confirms the applicability of the pole approximation and of the pole invariance method, namely the independence of binary indirect cross section on the chosen Trojan Horse nucleus, at least for the cases investigated. Moreover, we can verify that the effect of using a charged or a neutral particle as a spectator implies negligible corrections consistent with the experimental errors. In addition, the dynamics of clusters inside the Trojan Horse nucleus and their fingerprints on the measured momentum distribution play a key role for THM applications. In this article we will therefore discuss also these assertions studied in different systems( $$^2$$ H, $$^3$$ He, $$^6$$ Li, $$^9$$ Be, $$^{14}$$ N) and in particular for the deuteron case the relative impact of s and d waves in the momentum distribution will also be examined.

Probing short-range correlations in the deuteron via incoherent diffractive J/ψ production with spectator tagging at the EIC

Understanding the role of Quantum Chromodynamics in generating nuclear forces is important for uncovering the mechanism of short-ranged nuclear interactions and their manifestation in short range correlations (SRC). The future Electron-Ion-Collider (EIC) at Brookhaven National Laboratory in the US will provide an unprecedented opportunity to systematically investigate the underlying physics of SRC for energies and kinematic regions that are otherwise impossible to reach. We study SRCs in electron-deuteron scattering events using the Monte Carlo event generator BeAGLE. Specifically, we investigate the sensitivity of observables to high internal nucleon momentum in incoherent diffractive J/ψ vector meson production. In a plane wave impulse approximation, the initial state deuteron wave function can be accessed directly from the four-momentum of the spectator nucleon. We use realistic physics estimates and a conceptual far-forward detector simulations of the EIC to fully reveal the potential of this exclusive process. In particular, we provide the luminosity and detector requirements necessary to study SRCs in the deuteron at an EIC.

Total cross section of the reaction <i>γd → π<sup>–</sup>pp</i> in the threshold energy region

In the framework of the diagrammatic approach, the total cross section of near-threshold π– photoproduction on the deuteron is calculated. Contributions of the diagrams corresponding to the plane wave impulse approximation as well as to NN- and πN-interactions in the final state have been taken into account. We have compared the theoretical predictions with the results of the recent measurements performed at the MAX IV laboratory of the Lund University. There is good agreement with the data at photon energies from 147 to 155 MeV. However, at 158 and 160 MeV, the theoretical predictions significantly overestimate the measured cross sections.

Vibrational and distorted-wave effects on the highest occupied molecular orbital electronics structure of tetrachloromethane

In this work, we study the valence orbital momentum profiles of tetrachloromethane (CCl4) performed with binary (e, 2e) measurements at the impact energies of about 600 and 1200 eV with higher energy-resolution of Δε∼0.7 eV. The experimental momentum profiles for the molecular orbitals 2t1,7t2,2e,6t2, and 6a1 are obtained and compared with calculations under the plane-wave impulse approximation. The calculations at the equilibrium geometry of CCl4 show generally good agreement with the experimental momentum profiles except for the low momentum range of 2t1 and 2e which is considerable lower than the experiment. The experimental momentum profile shows dynamic dependencies on the impact energies which is ascribed to the distorted-wave effects. Further calculation considering molecular vibrations for the 2t1 highest occupied molecular orbital (HOMO) shows a better agreement with experiment than the equilibrium calculation, indicating the important role of nuclear motions on the HOMO electronic structure of CCl4.

Relative probability of recoilless Λ-production in nuclei in the plane-wave impulse approximation

The problem of estimating the relative probability Ρ of recoilless Λ production in nuclei by means of the (K-,π-) reaction is investigated in the plane-wave impulse approximation, which leads to approximate expressions of the "Debye-Waller type". The values of the relevant average overlap integrals between Λ and neutron normalized harmonic oscillator wave func­ tions are close to 1.

Charge exchange reactions on medium and heavy mass targets at intermediate energies

The nuclear isotopic structure can be understood easily via the intermediate-energy charge exchange reactions of (p, n) and [Formula: see text]He, [Formula: see text] type. In the current contribution, we present some results for charge exchange reactions induced by 3He on targets lying in mass region [Formula: see text] within the theoretical framework of plane wave impulse approximation (PWIA) and distorted wave impulse approximation (DWIA). Here, the recoil effects in PWIA have also been considered. Particularly, the angular distributions and the unit cross-sections have been calculated and compared with the available data. Further, the importance of inclusion of the exchange contribution in these reactions is also considered, which eventually enhance the matching with data.

Comparing proton momentum distributions in A = 2 and 3 nuclei via 2H 3H and 3He (e,e′p) measurements

We report the first measurement of the (e,e′p) reaction cross-section ratios for Helium-3 (He3), Tritium (H3), and Deuterium (d). The measurement covered a missing momentum range of 40≤pmiss≤550MeV/c, at large momentum transfer (〈Q2〉≈1.9 (GeV/c)2) and xB>1, which minimized contributions from non quasi-elastic (QE) reaction mechanisms. The data is compared with plane-wave impulse approximation (PWIA) calculations using realistic spectral functions and momentum distributions. The measured and PWIA-calculated cross-section ratios for He3/d and H3/d extend to just above the typical nucleon Fermi-momentum (kF≈250 MeV/c) and differ from each other by ∼20%, while for He3/H3 they agree within the measurement accuracy of about 3%. At momenta above kF, the measured He3/H3 ratios differ from the calculation by 20%−50%. Final state interaction (FSI) calculations using the generalized Eikonal Approximation indicate that FSI should change the He3/H3 cross-section ratio for this measurement by less than 5%. If these calculations are correct, then the differences at large missing momenta between the He3/H3 experimental and calculated ratios could be due to the underlying NN interaction, and thus could provide new constraints on the previously loosely-constrained short-distance parts of the NN interaction.

Measurement of the single-spin asymmetry [formula omitted] in quasi-elastic 3He↑(e,e′n) scattering at 0.4 < Q2 < 1.0 GeV/c2

Due to the lack of free neutron targets, studies of the structure of the neutron are typically made by scattering electrons from either 2H or 3He targets. In order to extract useful neutron information from a 3He target, one must understand how the neutron in a 3He system differs from a free neutron by taking into account nuclear effects such as final state interactions and meson exchange currents. The target single spin asymmetry Ay0 is an ideal probe of such effects, as any deviation from zero indicates effects beyond plane wave impulse approximation. New measurements of the target single spin asymmetry Ay0 at Q2 of 0.46 and 0.96 (GeV/c)2 were made at Jefferson Lab using the quasi-elastic He↑3(e,e′n) reaction. Our measured asymmetry decreases rapidly, from >20% at Q2=0.46 (GeV/c)2 to nearly zero at Q2=0.96 (GeV/c)2, demonstrating the fall-off of the reaction mechanism effects as Q2 increases. We also observed a small ϵ-dependent increase in Ay0 compared to previous measurements, particularly at moderate Q2. This indicates that upcoming high Q2 measurements from the Jefferson Lab 12 GeV program can cleanly probe neutron structure from polarized 3He using plane wave impulse approximation.

Experimental and theoretical study of valence electronic structure of tetrabromomethane by (e,2e) electron momentum spectroscopy

We report a measurement of the valence orbital momentum profiles of tetrabromomethane (${\mathrm{CBr}}_{4}$) using symmetric noncoplanar $(e,2e)$ experiments at the impact energies of about 600 and 1200 eV. The experimental momentum profiles for the individual orbitals $5{t}_{1}, 13{t}_{2}, 5e, 12{t}_{2}$, and $9{a}_{1}$ and the branching ratio of $5{t}_{1}$ to $13{t}_{2}$ and $5e$ to $13{t}_{2}$ are obtained and compared with two kinds of calculations under the plane-wave impulse approximation. One is theoretical momentum profiles that have been calculated at the equilibrium geometry, the other is those that involve vibrational effects using a thermal sampling molecular dynamics method. The calculations considering molecular vibrations are in better agreement with experiment than the equilibrium geometry calculations, indicating the important role of nuclear motions on the valence orbital electronic structures of ${\mathrm{CBr}}_{4}$. The distorted-wave effects are observed in the experimental momentum profiles of $5{t}_{1}, 5e$, and $12{t}_{2}$ which display dynamic dependencies on the impact energies. A multicenter interference or bond oscillation effect has been observed from the momentum profile ratios of $5{t}_{1}$ to $13{t}_{2}$ and $5e$ to $13{t}_{2}$ which has direct information about the bond length of a molecule.

Experimental and theoretical investigations on the valence orbitals of fluorobenzene by electron momentum spectroscopy

We report here an electron momentum spectroscopy study on the valence orbitals of fluorobenzene. The experiments are performed by a binary (e, 2e) spectrometer employing symmetric non-coplanar geometry at impact electron energies of 1200 and 800 eV plus binding energy. The experimental momentum distributions are compared with the theoretical calculations using Hartree–Fock and density functional theory methods within the framework of plane wave impulse approximation (PWIA). It is shown that the calculations are in generally good agreement with the measured electron momentum profiles, while the discrepancies can be mostly attributed to the distorted-wave effect. It is interesting to find that for the inner-valence orbitals, the pole strengths (PSs) obtained by comparing the experimental data with the theoretical calculations are different for different impact electron energies. This indicates that the PS can properly be determined only when the PWIA is fulfilled.

Observation of strong relativistic and distorted-wave effects in (e,2e) electron-momentum spectroscopy of mercury

We report a measurement of the valence orbital-momentum profiles of mercury (Hg) using a high-sensitivity binary $(e,2e)$ electron-momentum spectrometer at incident energies of 600 and 1200 eV plus the binding energy. The $6{s}_{1/2}$ orbital and the spin-orbit components of $5{d}_{5/2}$ and $5{d}_{3/2}$ orbitals are well separated in the measured binding-energy spectra. The experimental momentum distributions for the individual orbitals and the branching ratio of $5{d}_{5/2}$ to $5{d}_{3/2}$ are obtained and compared with predictions from a plane-wave impulse approximation (PWIA) in which the orbital wave functions are calculated using the nonrelativistic (NR) and spin-orbital (SO) relativistic theories. The SO relativistic calculations are in better agreement with experiment than the NR, indicating clearly the importance of relativistic effects in the electronic structure of Hg. We also observe some discrepancies between experiment and PWIA calculations in the high-momentum region of $6{s}_{1/2}$ and the low-momentum region of $5d$ orbitals which display a dynamic dependence on the impact energy. These discrepancies become smaller at a higher energy of about 1200 eV and thus can be qualitatively assigned to the distorted-wave effect in the $(e,2e)$ reaction of Hg.