Two-nucleon Knockout Reactions Research Articles

Spectroscopy of the T=32 A=47 and A=45 mirror nuclei via one- and two-nucleon knockout reactions

Level schemes of the proton-rich nuclei, Mn47 (Z=25,N=22) and Cr45 (Z=24,N=21), have been established for the first time. The technique of mirrored one- and two-nucleon knockout reactions was applied to the secondary beams of V48/Mn48 and V47/Cr47 to populate states in Ti47/Mn47 and Sc45/Cr45, respectively. Mirror energy differences (MED) have been studied between the mirrored T=32 states for both mirror pairs and interpreted using both a shell-model approach and a density-functional-theory approach using the no-core configuration-interaction method. MED in this mass region provide a stringent test of the model prescriptions since both fp- and sd-shell orbitals are active and, in Cr45, spherical and well-deformed structures coexist near the ground state. The inclusive and exclusive one-nucleon removal cross sections have been determined for the populated states in Ti47/Mn47 and compared with results from reaction-model calculations.5 MoreReceived 28 April 2022Accepted 21 July 2022DOI:https://doi.org/10.1103/PhysRevC.106.024327Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCoulomb energies & analogue statesDirect reactionsElectromagnetic transitionsEnergy levels & level densitiesNuclear density functional theoryNucleon-nucleon interactionsRare & new isotopesShell modelProperties39 ≤ A ≤ 58TechniquesRadioactive beamsNuclear Physics

Two-neutron knockout as a probe of the composition of states in Mg22,Al23 , and Si24

Simpson and Tostevin proposed that the width and shape of exclusive parallel momentum distributions of the A-2 residue in direct two-nucleon knockout reactions carry a measurable sensitivity to the nucleon single-particle configurations and their couplings within the wave functions of exotic nuclei. We report here on the first benchmarks and use of this new spectroscopic tool. Exclusive parallel momentum distributions for states in the neutron-deficient nuclei $^{22}$Mg, $^{23}$Al, and $^{24}$Si populated in such direct two-neutron removal reactions were extracted and compared to predictions combining eikonal reaction theory and shell-model calculations. For the well-known $^{22}$Mg and $^{23}$Al nuclei, measurements and calculations were found to agree, supporting the dependence of the parallel momentum distribution width on the angular momentum composition of the shell-model two-neutron amplitudes. In $^{24}$Si, a level at 3439(9) keV, of relevance for the important $^{23}$Al(p,$\gamma$)$^{24}$Si astrophysical reaction rate, was confirmed to be the $2^+_2$ state, while the $4^+_1$ state, expected to be strongly populated in two-neutron knockout, was not observed. This puzzle is resolved by theoretical considerations of the Thomas-Ehrman shift, which also suggest that a previously reported 3471-keV state in $^{24}$Si is in fact the ($0^+_2$) level with one of the largest experimental mirror-energy shifts ever observed.

Energy and momentum dependence of nuclear short-range correlations - Spectral function, exclusive scattering experiments and the contact formalism

Results of electron-induced one- and two-nucleon hard knockout reactions, A(e,e′p) and A(e,e′pN), in kinematics sensitive to nuclear short-range correlations, are studied using the nuclear contact formalism. A relation between the spectral function and the nuclear contacts is derived and used to analyze the dependence of the data on the initial energy and momentum of the knocked-out proton. The ratio between the number of emitted proton-proton pairs and proton-neutron pairs is shown to depend predominantly on a single ratio of contacts. This ratio is expected to present deep minima in the initial energy and momentum plane, associated with the node in the proton-proton wave function.The formalism is applied to analyze data from recent 4He and 12C electron-scattering experiments performed at Jefferson laboratory. Different nucleon-nucleon potentials were used to assess the model-dependence of the results. For the ratio of proton-proton to proton-neutron pairs in 4He, a fair agreement with the experimental data is obtained using the two potentials, whereas for the ratio of proton-proton pairs to the total knocked-out protons in 12C, some of the features of the theory are not seen in the experimental data. Several possible explanations for this disagreement are discussed. It is also observed that the spectral function at specific domains of the momentum-energy plane is sensitive to the nucleon-nucleon interaction. Based on this sensitivity, it might be possible to constrain the short range part of the nuclear potential using such experimental data.

Probing short-range correlations in asymmetric nuclei with quasi-free pair knockout reactions

Short-range correlations (SRC) in asymmetric nuclei with an unusual neutron-to-proton ratio can be studied with quasi-free two-nucleon knockout processes following the collision between accelerated ions and a proton target. We derive an approximate factorized cross section for those SRC-driven p(A,p′N1N2) reactions. Our reaction model hinges on the factorization properties of SRC-driven A(e,e′N1N2) reactions for which strong indications are found in theory-experiment comparisons. In order to put our model to the test we compare its predictions with results of C12(p,p′pn) measurements conducted at Brookhaven National Laboratory (BNL) and find a fair agreement. The model can also reproduce characteristic features of SRC-driven two-nucleon knockout reactions, like back-to-back emission of the correlated nucleons. We study the asymmetry dependence of nuclear SRC by providing predictions for the ratio of proton–proton to proton–neutron knockout cross sections for the carbon isotopes 9−15C thereby covering neutron excess values (N−Z)/Z between −0.5 and +0.5.

Final-state interactions in two-nucleon knockout reactions

Background: Exclusive two-nucleon knockout after electroexcitation of nuclei ($A(e,e'NN)$ in brief) is considered to be a primary source of information about short-range correlations (SRC) in nuclei. For a proper interpretation of the data, final-state interactions (FSI) need to be theoretically controlled. Purpose: Our goal is to quantify the role of FSI effects in exclusive $A(e,e'pN)$ reactions for four target nuclei representative for the whole mass region. Our focus is on processes that are SRC driven. We investigate the role of FSI for two characteristic detector setups corresponding with a "small" and "large" coverage of the available phase space. Results: The transparency $T^{pN}_{A}$, defined as the ratio of exclusive $(e,e'pN)$ cross sections on nuclei to those on "free" nucleon pairs, drops from $ 0.2-0.3 $ for $^{12}$C to $0.04-0.07$ for $^{208}$Pb. For all considered kinematics, the mass dependence of the $T^{pN}_{A}$ can be captured by the power law $T^{pN}_{A} \propto A^{- \lambda}$ with $ 0.4 \lesssim \lambda \lesssim 0.5 $. Apart from an overall reduction factor, we find that FSI only modestly affects the distinct features of SRC-driven $A(e,e'pN)$ which are dictated by the c.m. distribution of close-proximity pairs. Conclusion: The SCX mechanisms represent a relatively small (order of a few percent) contribution of SRC-driven $A(e,e'pN)$ processes. The mass dependence of FSI effects in exclusive $A(e,e'pN)$ can be captured in a robust power law and is in agreement with the predictions obtained in a toy model.

Nucleus probing for short-range correlations using neutrino-nucleon interactions

Short-range nucleon-nucleon correlations (NN SRC) contain important information about nuclear structure and dynamics within the nuclei. It has been extensively studied through two-nucleon knockout reactions, in both pion and electron scattering experiments. A very recent approach is to probe NN SRC using neutrino scattering, however, with limited results due to the intrinsic uncertainty of the four-momentum transfer. Here, we present one of the latest attempts to reconstruct this information.

Spectroscopy and correlations probed in direct two-nucleon knockout reactions

Nucleon knockout reactions from fast radioactive secondary beams colliding with light nuclear targets provide a useful tool for studying structure away from the valley of (β-stability. An efficient means of producing specific exotic nuclei, the technique has been recently applied to study nuclear halos, isospin symmetry and cross-shell excitations, and in tracking the evolution of single-particle states, and probing the associated quenching (N=20, N=28) and emergence (N=16) of shell gaps. Recent theoretical work has demonstrated the sensitivity of residue momentum distributions following two-nucleon removal to the underlying structure. In particular, there is a sensitivity to the total orbital angular momentum of the removed pair, providing additional tests of (shell- or many-body-) structure-model two-nucleon overlaps. We illustrate the structural sensitivities in the context of nucleon knockout from 12C and 16O, and discuss the prospects for studying np-correlations along the N = Z line, highlighting the need for new final-state exclusive measurements, including those with stable beams.

Longitudinal momentum distributions of the reaction residues following fast two-nucleon knockout reactions

The longitudinal momentum distributions of the cross sections of heavy projectile-like residues after fast, direct two-like-nucleon knockout reactions are discussed. Both the two-nucleon inelastic breakup (stripping) and the stripping-diffraction removal events are considered. We show that, because the two mechanisms have a very similar nuclear surface localization, they generate essentially identical longitudinal momentum distributions. The approach used combines reaction dynamics, using the sudden, eikonal and spectator-core approximations, with structure wave functions from the many-body shell model. The sensitivities of the resulting longitudinal momentum distributions to the orbital angular momenta, the separation energies, and the angular momentum coupling of the two removed nucleons are clarified. In particular, the widths of these distributions are shown to provide a very clear signal of the total angular momentum of the removed-nucleon pair---pairs coupled to larger total angular momentum giving broader distributions. These now complete distributions, from correlated wave functions, are significantly different from earlier uncorrelated estimates. Confirmation of these theoretical expectations is presented, based on very recent intermediate-energy, residue final-state inclusive and exclusive two-nucleon removal measurements.

Center-of-mass effects in electromagnetic two-proton knockout reactions

The role of center-of mass (CM) effects in the one-body nuclear current in the description of electromagnetically induced two-nucleon knockout reactions is discussed in connection with the problem of the lack of orthogonality between initial bound states and final scattering states obtained by the use of an energy-dependent optical model potential. Results for the cross sections of the exclusive $^{16}$O(e,e$'$pp)$^{14}$C and $^{16}$O($\gamma$,pp)$^{14}$C knockout reactions in different kinematics are presented and discussed. In super-parallel kinematics CM effects produce a strong enhancement of the $^{16}$O(e,e$'$pp)$^{14}$C$_{\rm g.s.}$ cross section which strongly reduces the destructive interference between the one-body and $\Delta$-current and the sensitivity to the treatment of the $\Delta$-current found in previous work.

Diffraction dissociation contributions to two-nucleon knockout reactions and the suppression of shell-model strength

The contributions to the cross sections of intermediate energy two-nucleon knockout reactions from events in which one nucleon is removed by the stripping (inelastic breakup) mechanism and a second by the diffraction (elastic breakup) mechanism are discussed. The small additional contributions from two-nucleon diffraction events are also estimated. The approach used combines the eikonal reaction and shell model structure theory frameworks. For reactions involving the removal of two well-bound like nucleons, at incident energies of order 100 MeV per nucleon, the additional cross sections are shown to be of approximately the same size as those from events in which both nucleons are stripped in inelastic interactions. These more complete dynamical calculations now permit a quantitative comparison of the theoretical cross sections with recent partial cross-section measurements of the two-neutron (two-proton) removal reactions from neutron-deficient (neutron-rich) nuclei. As has been observed in both nuclear- and electron-induced single-nucleon knockout reaction analyses, the theoretical two-nucleon knockout cross sections overestimate the measured values, requiring a suppression of the two nucleon shell-model transition strengths. The deduced two-nucleon suppression factors, ${R}_{s}(2N)$, are consistent with a value of 0.5 for each of the five reactions considered.

Short-range correlations in two-nucleon knockout reactions

A theory of short-range correlations in two-nucleon removal due to elastic breakup (diffraction dissociation) on a light target is developed. Fingerprints of these correlations will appear in momentum distributions of back-to-back emission of the nucleon pair. Expressions for the momentum distributions are derived and calculations for reactions involving stable and unstable nuclear species are performed. The signature of short-range correlations in other reaction processes is also studied.

DIRECT REACTIONS WITH EXOTIC NUCLEI

▪ Abstract The identification of direct-reaction processes and their subsequent exploitation for the spectroscopy of weak radioactive beams of exotic nuclei are important problems in modern nuclear physics. One- and two-nucleon knockout reactions, studied using intermediate-energy radioactive beams, have been shown to be powerful tools for this purpose. This article discusses the current status of such investigations and reviews what has been learned to date from the experiments and analyses of the past five years. The techniques are still in their formative stages, and the open questions and challenges are outlined.

Theoretical aspects of (e, e'NN) reactions

Electromagnetically induced two-nucleon knockout reactions are considered. The theoretical framework is outlined and some results are presented for the exclusive 16O(e,e'pp)14C reaction. The possibility of obtaining in comparison with data direct and clear information on short-range correlations is discussed.

Final state interaction in exclusive(e,e′NN)reactions

Contributions of nucleon-nucleon (NN) correlations, meson exchange currents and the residual final state interactions (FSI) on exclusive two-nucleon knock-out reactions induced by electron scattering are investigated. All contributions are derived from the same realistic meson exchange model for the NN interaction. Effects of correlations and FSI are determined in a consistent way by solving the NN scattering equation, the Bethe-Goldstone equation, for two nucleons in nuclear matter. One finds that the FSI re-scattering terms are non-negligible even if the two nucleons are emitted back to back.

Nucleon-nucleon correlations and two-nucleon currents in exclusive(e,e′NN)reactions

The contributions of short-range nucleon-nucleon $(\mathrm{NN})$ correlations, meson exchange current (MEC) terms, and the influence of $\ensuremath{\Delta}$ isobar excitations (isobaric currents) on exclusive two-nucleon knockout reactions induced by electron scattering are investigated. The nuclear structure functions are evaluated for nuclear matter. Realistic $\mathrm{NN}$ interactions derived in the framework of a one-boson-exchange model are employed to evaluate the effects of correlations and MEC in a consistent way. The correlations are determined by solving the Bethe-Goldstone equation. This yields significant contributions to the structure functions ${W}_{L}$ and ${W}_{T}$ of the ${(e,e}^{\ensuremath{'}}pn)$ and ${(e,e}^{\ensuremath{'}}pp)$ reactions. These contributions compete with MEC corrections originating from the $\ensuremath{\pi}$ and $\ensuremath{\rho}$ exchange terms of the same interaction. Special attention is paid to the so-called ``superparallel'' kinematics at momentum transfers which can be measured, e.g., at MAMI in Mainz.

Using a genetic algorithm to investigate two-nucleon knockout reactions

The use of genetic algorithms as tools in nuclear physics problems is highlighted by examining the particular case of two-nucleon knockout reactions. The predictions of a factorized model of (e,e',pp) reactions are investigated by maximizing functions of the calculated cross sections within the phase space, to establish kinematics where particular effects will occur most strongly. In this first investigation we find that, contrary to received wisdom, the Gent factorized model predicts that the effect of short-range correlations can be seen most clearly in kinematics which are not in a so-called super-parallel configuration. Variants and extensions of this method are likely to be of benefit to both theorists and experimentalists who have to cope with multi-dimensional problems.

Short-range and tensor correlations in the16O(e,e′pn)reaction

The cross sections for electron-induced two-nucleon knockout reactions are evaluated for the example of the ${}^{16}\mathrm{O}{(e,e}^{\ensuremath{'}}{pn)}^{14}\mathrm{N}$ reaction leading to discrete states in the residual nucleus ${}^{14}\mathrm{N}.$ These calculations account for the effects of nucleon-nucleon correlations and include the contributions of two-body meson exchange currents as the pion seagull, pion in flight, and the isobar current contribution. The effects of short-range as well as tensor correlations are calculated within the framework of the coupled cluster method employing the Argonne V14 potential as a model for a realistic nucleon-nucleon interaction. The relative importance of correlation effects as compared to the contribution of the meson exchange currents depends on the final state of the residual nucleus. The cross section leading to specific states, such as, e.g., the ground state of ${}^{14}\mathrm{N},$ is rather sensitive to the details of the correlated wave function.

Electron-induced two-proton knockout from 3He

Electron-induced two-nucleon knockout reactions at intermediate electron energies are driven both by one-body currents (coupling of the virtual photon to correlated nucleon pairs) and two-body currents (intermediate Δ-excitation and meson exchange currents (MEC)). In addition, final state interactions (FSI) contribute to the cross section. Recent experiments [1] have shown that the 160(e, e’pp)14C reaction is dominated by the direct knockout of strongly correlated proton pairs via one-body currents.

Photon-induced two-nucleon knockout reactions to discrete final states

Cross sections and photon asymmetries of the 16O(γ, pn) 14N and 16O(γ, pp) 14C knockout reactions are calculated for transitions to the low-lying discrete final states of the residual nucleus in the photon-energy range between 100 and 400 MeV. Exclusive reactions may represent a test of reaction mechanisms and a promising tool for investigating the dynamics of nucleon pairs in different states. Cross sections and asymmetries for both (γ,pn) and (γ,pp) turn out to be only slightly affected by short-range correlations and dominated by two-body currents. Therefore, two-nucleon knockout reactions induced by real photons appear well suited to investigate the nuclear current and the selectivity of individual transitions to its different components.

Treatment of the Δ current in electromagnetic two-nucleon knockout reactions

The contribution of the $\Delta$(1232) isobar to the electromagnetic current of the two-nucleon system and its role in ($\gamma$,NN) processes is investigated. The difference between the genuine $\Delta$-excitation current and that part of the current connected to the deexcitation of a preformed $\Delta$ in the target nucleus is stressed. The latter cannot lead to a resonant behaviour of matrix elements for energies in the $\Delta$ region. The reaction $^{16}O(\gamma,pp)^{14}C$, where the $\Delta$ contribution is dominant at intermediate energies, is considered. The large variations found in the cross sections for different treatments stress the need for a proper treatment of the $\Delta$ current for a clear understanding of the reaction mechanism of two-nucleon emission processes.