Two-nucleon Knockout Research Articles

Revealing the short-range structure of the mirror nuclei 3H and 3He

When protons and neutrons (nucleons) are bound into atomic nuclei, they are close enough to feel significant attraction, or repulsion, from the strong, short-distance part of the nucleon-nucleon interaction. These strong interactions lead to hard collisions between nucleons, generating pairs of highly energetic nucleons referred to as short-range correlations (SRCs). SRCs are an important but relatively poorly understood part of nuclear structure1-3, and mapping out the strength and the isospin structure (neutron-proton (np) versus proton-proton (pp) pairs) of these virtual excitations is thus critical input for modelling a range of nuclear, particle and astrophysics measurements3-5. Two-nucleon knockout or 'triple coincidence' reactions have been used to measure the relative contribution of np-SRCs and pp-SRCs by knocking out a proton from the SRC and detecting its partner nucleon (proton or neutron). These measurements6-8 have shown that SRCs are almost exclusively np pairs, but they had limited statistics and required large model-dependent final-state interaction corrections. Here we report on measurements using inclusive scattering from the mirror nuclei hydrogen-3 and helium-3 to extract the np/pp ratio of SRCs in systems with a mass number of three. We obtain a measure of the np/pp SRC ratio that is an order of magnitude more precise than previous experiments, and find a marked deviation from the near-total np dominance observed in heavy nuclei. This result implies an unexpected structure in the high-momentum wavefunction for hydrogen-3 and helium-3. Understanding these results will improve our understanding of the short-range part of the nucleon-nucleon interaction.

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

Isoscalar pairing correlations by the tensor force in the ground states of C12, O16, Ne20 , and S32 nuclei

We investigate roles of the tensor force (TF) on the pairing correlations in the ground-state structure of $^{12}\mathrm{C}, ^{16}\mathrm{O}, ^{20}\mathrm{Ne}$, and $^{32}\mathrm{S}$ nuclei within a deformed BCS model. For pairing matrix elements, we exploit the Brueckner $G$ matrix derived from the charge-dependent Bonn potential. In particular, the isoscalar (IS) neutron-proton ($np$) pairing is studied in detail in relation to spin-triplet even TF in the nucleon-nucleon interaction. Detailed analyses of the $np$ pairing and possible enhancement of the IS channel are performed by focusing on roles of attractive spin-triplet even and repulsive spin-triplet odd channels in the TF for the ground states of the nuclei with some deformation. It is also shown that the TF may play a crucial role of properly interpreting the experimental data of a two-nucleon knockout reaction from $^{12}\mathrm{C}$.

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.

Neutron measurements from antineutrino hydrocarbon reactions

Charged-current anti-neutrino interactions on hydrocarbon scintillator in the MINERvA detector are used to study activity from their final-state neutrons. To ensure that most of the neutrons are from the primary interaction, rather than hadronic reinteractions in the detector, the sample is limited to momentum transfers below 0.8 GeV/c. From 16,129 interactions, 15,246 neutral particle candidates are observed. The reference simulation predicts 64\% of these candidates are due to neutrons from the anti-neutrino interaction directly, but also overpredicts the number of candidates by 15\% overall, which is beyond the standard uncertainty estimates for models of neutrino interactions and neutron propagation in the detector. Using the measured distributions for energy deposition, time of flight, position, and speed, we explore the sensitivity to the details those two aspects of the models. We also use multiplicity distributions to evaluate the presence of a two-nucleon knockout process. These results provide critical new information toward a complete description of the hadronic final state of neutrino interactions, which is vital to neutrino oscillation experiments.

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.

Antineutrino Charged-Current Reactions on Hydrocarbon with Low Momentum Transfer.

We report on multinucleon effects in low momentum transfer (<0.8 GeV/c) antineutrino interactions on plastic (CH) scintillator. These data are from the 2010-2011 antineutrino phase of the MINERvA experiment at Fermilab. The hadronic energy spectrum of this inclusive sample is well described when a screening effect at a low energy transfer and a two-nucleon knockout process are added to a relativistic Fermi gas model of quasielastic, Δ resonance, and higher resonance processes. In this analysis, model elements introduced to describe previously published neutrino results have quantitatively similar benefits for this antineutrino sample. We present the results as a double-differential cross section to accelerate the investigation of alternate models for antineutrino scattering off nuclei.

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.

Seagull and pion-in-flight currents in neutrino-induced 1N and 2N knockout

[Background] The neutrino-nucleus ($\nu A$) cross section is a major source of systematic uncertainty in neutrino-oscillation studies. A precise $\nu A$ scattering model, in which multinucleon effects are incorporated, is pivotal for an accurate interpretation of the data. [Purpose] In $\nu A$ interactions, meson-exchange currents (MECs) can induce two-nucleon ($2N$) knockout from the target nucleus, resulting in a two-particle two-hole (2p2h) final state. They also affect single nucleon ($1N$) knockout reactions, yielding a one-particle one-hole (1p1h) final state. Both channels affect the inclusive strength. We present a study of axial and vector, seagull and pion-in-flight currents in muon-neutrino induced $1N$ and $2N$ knockout reactions on $^{12}$C. [Method] Bound and emitted nucleons are described as Hartree-Fock wave functions. For the vector MECs, the standard expressions are used. For the axial current, three parameterizations are considered. The framework developed here allows for a treatment of MECs and short-range correlations (SRCs). [Results] Results are compared with electron-scattering data and with literature. The strengths of the seagull, pion-in-flight and axial currents are studied separately and double differential cross sections including MECs are compared with results including SRCs. A comparison with MiniBooNE and T2K data is presented. [Conclusions] In the 1p1h channel, the effects of the MECs tend to cancel each other, resulting in a small effect on the double differential cross section. $2N$ knockout processes provide a small contribution to the inclusive double differential cross section, ranging from the $2N$ knockout threshold into the dip region. A fair agreement with the MiniBooNE and T2K data is reached.

Differential cross section measurement of the 12C(e,e’pp)10Beg.s. reaction

The differential cross section was measured for the 12C(e,e’pp)10Beg.s. reaction at energy and momentum transfers of 163MeV and 198MeV/c, respectively. The measurement was performed at the Mainz Microtron by using two high-resolution magnetic spectrometers of the A1 Collaboration and a newly developed silicon detector telescope. The overall resolution of the detector system was sufficient to distinguish the ground state from the first excited state in 10 Be. We chose a super-parallel geometry that minimizes the effect of two-body currents and emphasizes the effect of nucleon-nucleon correlations. The obtained differential cross section is compared to the theoretical results of the Pavia reaction code in which different processes leading to two-nucleon knockout are accounted for microscopically. The comparison shows a strong sensitivity to nuclear-structure input and the measured cross section is seen to be dominated by the interplay between long- and short-range nucleon-nucleon correlations. Microscopic calculations based on the ab initio self-consistent Green’s function method give a reasonable description of the experimental cross section.

Influence of short-range correlations in neutrino-nucleus scattering

Background: Nuclear short-range correlations (SRCs) are corrections to mean-field wave functions connected with the short-distance behavior of the nucleon-nucleon interaction. These SRCs provide corrections to lepton- nucleus cross sections as computed in the impulse approximation (IA). Purpose: We want to investigate the influence of SRCs on the one-nucleon (1N) and two-nucleon (2N) knockout channel for muon-neutrino induced processes on a $^{12}$C target at energies relevant for contemporary measurements. Method: The model adopted in this work, corrects the impulse approximation for SRCs by shifting the com- plexity induced by the SRCs from the wave functions to the operators. Due to the local character of the SRCs, it is argued that the expansion of these operators can be truncated at a low order. Results: The model is compared with electron-scattering data, and two-particle two-hole responses are presented for neutrino scattering. The contributions from the vector and axial-vector parts of the nuclear current as well as the central, tensor and spin-isospin part of the SRCs are studied. Conclusions: Nuclear SRCs affect the 1N knockout channel and give rise to 2N knockout. The exclusive neutrino-induced 2N knockout cross section of SRC pairs is shown and the 2N knockout contribution to the QE signal is calculated. The strength occurs as a broad background which extends into the dip region.

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.

Triplet energy differences and the low lying structure ofGa62

Author(s): Henry, TW; Bentley, MA; Clark, RM; Davies, PJ; Bader, VM; Baugher, T; Bazin, D; Beausang, CW; Berryman, JS; Bruce, AM; Campbell, CM; Crawford, HL; Cromaz, M; Fallon, P; Gade, A; Henderson, J; Iwasaki, H; Jenkins, DG; Lee, IY; Lemasson, A; Lenzi, SM; Macchiavelli, AO; Napoli, DR; Nichols, AJ; Paschalis, S; Petri, M; Recchia, F; Rissanen, J; Simpson, EC; Stroberg, SR; Wadsworth, R; Weisshaar, D; Wiens, A; Walz, C | Abstract: Background: Triplet energy differences (TED) can be studied to yield information on isospin-non-conserving interactions in nuclei. Purpose: The systematic behavior of triplet energy differences (TED) of T=1, Jπ=2+ states is examined. The A=62 isobar is identified as having a TED value that deviates significantly from an otherwise very consistent trend. This deviation can be attributed to the tentative assignments of the pertinent states in Ga62 and Ge62. Methods: An in-beam γ-ray spectroscopy experiment was performed to identify excited states in Ga62 using Gamma-Ray Energy Tracking In-Beam Nuclear Array with the S800 spectrometer at NSCL using a two-nucleon knockout approach. Cross-section calculations for the knockout process and shell-model calculations have been performed to interpret the population and decay properties observed. Results: Using the systematics as a guide, a candidate for the transition from the T=1, 2+ state is identified. However, previous work has identified similar states with different Jπ assignments. Cross-section calculations indicate that the relevant T=1, 2+ state should be one of the states directly populated in this reaction. Conclusions: As spins and parities were not measurable, it is concluded that an unambiguous identification of the first T=1, 2+ state is required to reconcile our understanding of TED systematics.

Factorization of exclusive electron-induced two-nucleon knockout

We investigate the factorization properties of the exclusive electroinduced two-nucleon knockout reaction $A(e,e'pN)$. A factorized expression for the cross section is derived and the conditions for factorization are studied. The $A(e,e'pN)$ cross section is shown to be proportional to the conditional center-of-mass (c.m.) momentum distribution for close-proximity pairs in a state with zero relative orbital momentum and zero radial quantum number. The width of this conditional c.m. momentum distribution is larger than the one corresponding with the full c.m. momentum distribution. It is shown that the final-state interactions (FSIs) only moderately affect the shape of the factorization function for the $A(e,e'pN)$ cross sections. Another prediction of the proposed factorization is that the mass dependence of the $A(e,e'pp)$ $[A(e,e'pn)]$ cross sections is much softer than $\frac{Z(Z-1)}{2}$ $[NZ]$.

Mass dependence of short-range correlations in nuclei and the EMC effect

We sketch an approximate method to quantify the number of correlated pairs in any nucleus $A$. It is based on counting independent-particle model (IPM) nucleon-nucleon pairs in a relative $S$-state with no radial excitation. We show that IPM pairs with those quantum numbers are most prone to short-range correlations and are at the origin of the high-momentum tail of the nuclear momentum distributions. Our method allows to compute the $a_2$ ratios extracted from inclusive electron scattering. Furthermore, our results reproduce the observed linear correlation between the number of correlated pairs and the magnitude of the EMC effect. We show that the width of the pair center-of-mass distribution in exclusive two-nucleon knockout yields information on the quantum numbers of the pairs.

Mirror Energy Differences at Large Isospin Studied through Direct Two-Nucleon Knockout

The first spectroscopy of excited states in 52Ni (T(z)=-2) and 51Co (T(z)=-3/2) has been obtained using the highly selective two-neutron knockout reaction. Mirror energy differences between isobaric analogue states in these nuclei and their mirror partners are interpreted in terms of isospin nonconserving effects. A comparison between large-scale shell-model calculations and data provides the most compelling evidence to date that both electromagnetic and an additional isospin nonconserving interactions for J=2 couplings, of unknown origin, are required to obtain good agreement.

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.

Role of short-range and tensor correlations in nuclei

The present theoretical understanding of the role of short-range correlations in nuclei near stability is reviewed. Two effects are identified in particular: first, the depletion of mean-field single-particle strength that is no longer available to participate in low-lying excitations. Second, the admixture of high-momentum nucleons in the ground state that is implied by the vanishing relative wave functions of pairs in the medium. The role of the tensor force will be further clarified by discussing isospin-polarized matter. It is demonstrated that the depletion of the proton and neutron Fermi seas depends strongly on the nuclear tensor force and appears to be determined by nucleon-nucleon scattering data. The increased role of short-range and tensor correlations for the minority species makes the case for further experimental scrutiny of nuclei with large neutron excess. Appropriate data of single- and two-nucleon knockout experiments are employed to illustrate the role of short-range and tensor correlations.

Experimental studies of few-body systems at MAMI

Few-body experiments at the Mainz Microtron were focused on a number of selected topics. Double-polarization experiments to determine the neutron electric form factor Gen have been performed using both deuterium and polarized helium-3 targets. The structure of 3He has been studied in the reactions 3H e e(ee,e′n) and 3H e e(ee,e′p) with large (transversal) missing momenta and in quasi-elastic electron scattering. Electromagnetically induced two-nucleon knockout has been investigated in order to study the role of correlated nucleon-nucleon motion in the nucleus. Measurements of the (e,e′pn) reaction on 3He and 16O were performed for the first time. A triple-polarization experiment of type 3H e e(ee,e′ep)d has been performed, where, in addition, the spin of the knocked out proton is analyzed. This measurement provides information on the spin-dependent momentum distribution of proton-deuteron clusters in the 3He nucleus. Hence, by tagging the outgoing deuteron spin-polarized 3He might also serve as an effective polarized proton target for electron scattering experiments. Moreover, in inclusive 3,4He(e,e′) measurements at low momentum transfer, the effect of 3-body-forces has been studied.