Two-nucleon Emission Research Articles

Exploring Semi-Inclusive Two-Nucleon Emission in Neutrino Scattering: A Factorized Approximation Approach

The semi-inclusive cross-section of two-nucleon emission induced by neutrinos and antineutrinos is computed by employing the relativistic mean field model of nuclear matter and the dynamics of meson-exchange currents. Within this model, we explore a factorization approximation based on the product of an integrated two-hole spectral function and a two-nucleon cross-section averaged over hole pairs. We demonstrate that the integrated spectral function of the uncorrelated Fermi gas can be analytically computed, and we derive a simple, fully relativistic formula for this function, showcasing its dependency solely on both missing momentum and missing energy. A prescription for the average momenta of the two holes in the factorized two-nucleon cross-section is provided, assuming that these momenta are perpendicular to the missing momentum in the center-of-mass system. The validity of the factorized approach is assessed by comparing it with the unfactorized calculation. Our investigation includes the study of the semi-inclusive cross-section integrated over the energy of one of the emitted nucleons and the cross-section integrated over the emission angles of the two nucleons and the outgoing muon kinematics. A comparison is made with the pure phase-space model and other models from the literature. The results of this analysis offer valuable insights into the influence of the semi-inclusive hadronic tensor on the cross-section, providing a deeper understanding of the underlying nuclear processes.

Semi-inclusive two-nucleon emission in (anti) neutrino charged current scattering within the relativistic mean field framework

This paper delves into the distribution of semi-inclusive events involving the emission of two nucleons in (anti) neutrino charged-current scattering. The analysis is conducted within the framework of relativistic mean-field theory applied to nuclear matter. To quantify the likelihood of such semi-inclusive events occurring, we employ a relativistic model of meson-exchange currents that aligns with the 2p2h inclusive cross section. The outcomes are presented in terms of onefold and twofold integrated semi-inclusive cross sections. To highlight disparities among the various emission channels, including proton-proton, neutron-proton, and neutron-neutron, we compare them against a purely phase-space isotropic distribution within the center of mass of the two nucleons. These comparisons reveal significant differences in the event distributions, shedding light on the distinctive characteristics of each channel. Published by the American Physical Society 2024

Semiempirical formula for electroweak response functions in the two-nucleon emission channel in neutrino-nucleus scattering

A semi-empirical formula for the electroweak response functions in the two-nucleon emission channel is proposed. The method consists in expanding each one of the vector-vector, axial-axial and vector-axial responses as sums of six sub-responses. These corresponds to separating the meson-exchange currents as the sum of three currents of similar structure, and expanding the hadronic tensor, as the sum of the separate contributions from each current plus the interferences between them. For each sub-response we factorize the coupling constants, the electroweak form factors, the phase space and the delta propagator, for the delta forward current. The remaining spin-isospin contributions are encoded in coefficients for each value of the momentum transfer, $q$. The coefficients are fitted to the exact results in the relativistic mean field model of nuclear matter, for each value of $q$. The dependence on the energy transfer, $\omega$ is well described by the semi-empirical formula. The $q$-dependency of the coefficients of the sub-responses can be parameterized or can be interpolated from the provided tables. The description of the five theoretical responses is quite good. The parameters of the formula, the Fermi momentum, number of particles relativistic effective mass, vector energy the electroweak form factors and the coupling constants, can be modified easily. This semi-empirical formula can be applied to the cross-section of neutrinos, antineutrinos and electrons.

Meson-exchange currents and superscaling analysis with relativistic effective mass of quasielastic electron scattering from C12

We reanalyze the scaling properties of inclusive quasielastic electron scattering from $^{12}\mathrm{C}$ by subtracting from the data the effects of two-particle emission. A model of relativistic meson-exchange currents (MEC) is employed within the mean field theory of nuclear matter, with scalar and vector potentials that induce an effective mass and a vector energy to the nucleons. A new phenomenological quasielastic scaling function is extracted from a selection of the data after the subtraction of the 2p-2h contribution. The resulting superscaling approach with relativistic effective mass (SuSAM*) can be used to compute the genuine quasielastic cross section without contamination of the 2p-2h channel that can then be added separately to obtain the total quasielastic plus two-nucleon emission response.

Fermion Pair Dynamics in Open Quantum Systems.

Three-body decay is a rare decay mode observed in a handful of unbound rare isotopes. The angular and energy correlations between emitted nucleons are of particular interest, as they provide invaluable information on the interplay between structure and reaction aspects of the nuclear open quantum system. To study the mechanism of two-nucleon emission, we developed a time-dependent approach that allows us to probe emitted nucleons at long times and large distances. We successfully benchmarked the new method against the Green's function approach and applied it to low-energy two-proton and two-neutron decays. In particular, we studied the interplay between initial-state nucleon-nucleon correlations and final-state interaction. We demonstrated that the time evolution of the two-nucleon wave function is strongly impacted by the diproton/dineutron dynamics and that the correlations between emitted nucleons provide invaluable information on the dinucleon structure in the initial state.

Two-nucleon emitters within a pseudostate method: The case of Be6 and Be16

Background: Since the first experimental observation, two-nucleon radioactivity has gained renewed attention over the past fifteen years. The $^6$Be system is the lightest two-proton ground-state emitter, while $^{16}$Be has been recently proposed to be the first two-neutron ground-state emitter ever observed. A proper understanding of their properties and decay modes requires a reasonable description of the three-body continuum. Purpose: Study the ground-state properties of $^6$Be and $^{16}$Be within a general three-body model and investigate their nucleon-nucleon correlations in the continuum. Method: The pseudostate (PS) method in hyperspherical coordinates, using the analytical transformed harmonic oscillator (THO) basis for three-body systems, is used to construct the $^6$Be and $^{16}$Be ground-state wave functions. These resonances are approximated as a stable PS around the known two-nucleon separation energy. Effective core-$N$ potentials, constrained by the available experimental information on the binary subsystems $^5$Li and $^{15}$Be, are employed in the calculations. Results: The ground state of $^{16}$Be is found to present a strong dineutron configuration, with the valence neutrons occupying mostly an $l=2$ state relative to the core. The results are consistent with previous $R$-matrix calculations for the actual continuum. The case of $^6$Be shows a clear symmetry with respect to its mirror partner, the two-neutron halo $^6$He: The diproton configuration is dominant, and the valence protons occupy an $l=1$ orbit. Conclusions: The PS method is found to be a suitable tool in describing the properties of unbound $\text{core}+N+N$ ground states. For both $^{16}$Be and $^6$Be, the results are consistent with previous theoretical studies and confirm the dominant dinucleon configuration. This favors the picture of a correlated two-nucleon emission.

Time-dependent Method for Many-body Problems and Its Application to Nuclear Resonant Systems

The decay process of the schematic one-dimensional three-body system is considered. A time-dependent approach is used in combination with a one-dimensional three-body model, which is composed of a heavier core nucleus and two nucleons, with the aim of describing its evolution in two-nucleon emission. The process is calculated from the initial state, in which the three ingredient particles are confined. In this process, two different types of emission can be found: the earlier process includes the emission of spatially correlated two-nucleon pair, like a dinucleon, whereas, at a subsequent time, all the particles are separated from each other. The time-dependent method can be a suitable option to investigate the meta-stable and/or open-quantum systems, where the complicated many-body dynamics should necessarily be taken into account.

Two-nucleon emission in neutrino and electron scattering from nuclei: The modified convolution approximation

The theoretical formalism of inclusive lepton–nucleus scattering in the two-nucleon emission channel is discussed in the context of a simplified approach, the modified convolution approximation. This allows one to write the 2p2h responses of the relativistic Fermi gas as a folding integral of two 1p1h responses with the energies and momenta transferred to each nucleon. The idea behind this method is to introduce different average momenta for the two initial nucleons in the matrix elements of the two-body current, with the innovation that they depend on the transferred energies and momenta. This method treats exactly the two-body phase space kinematics, and reduces the formulae of the response functions from seven-dimensional integrals over momenta to much simpler three-dimensional ones. The applicability of the method is checked by comparing with the full results within a model of electroweak meson-exchange currents. The predictions are accurate enough, especially in the low-energy threshold region where the average momentum approximation works the best.

Pion photoproduction on nucleus with two-nucleon emission

A model for the pion photoproduction on nuclei in the $A\left({\gamma ,\, \pi NN} \right)B$ reaction is presented. This is an extension of our recent model for the $A\left({\gamma ,\, \pi N} \right)B$ reaction. In this approach we have moved beyond the standard shell-model considering $\Delta$\textit{N} correlations in the nuclear wave functions, which are caused by the virtual transitions $NN \to \Delta N \to NN$ in the ground state of the nucleus. The main ingredients of the model are the two- and three-particle density matrices and the transition operators $\gamma \Delta \to N\pi $ and $\gamma N \to N\pi $. The direct and exchange reaction mechanisms, which follow from the structure of the density matrices, are examined. The model is used to investigate the $^{12}$C$\left({\gamma ,\, \pi ^{+} p} \right)$ and $^{12}$C$\left({\gamma ,\, \pi ^{-} p} \right)$ reactions in the kinematic region of the large momentum transfers to the residual nuclear system, where the pion production occurs with the emission of two nucleons.

Two-nucleon emission experiments at MAMI Mainz

Thw series of two-nucleon removal experiments performed with real and virtual photons at the DC electron accelerator Mami in Mainz are described. As targets the nuclei 6Li, 12C and 16O have been used as well as the few body systems 3,4He. The role of the various competing reaction mechanisms has been clarified. Despite many technical improvements a satifying microscopic description of the data is missing.

Exclusive electrodisintegration ofHe3at highQ2. II. Decay function formalism

Based on the theoretical framework of generalized eikonal approximation we study the two-nucleon emission reactions in high $Q^2$ electro-disintegration of $^3He$. Main aim is to investigate those features of the reaction which can be unambiguously identified with the short range properties of the ground state nuclear wave function. To evaluate the differential cross section we work in the formalism of the decay function which characterizes the property of the ground state wave function as well as the decay properties of final two nucleon spectator system. Our main motivation here is to explore the accessibility of two-- and three--nucleon short range correlations in $^3$He as well as to isolate unambiguously single and double rescattering processes in the reaction dynamics. Our analysis allowed us also to identify new approaches for investigating the role of the practically unknown three-nucleon forces in the ground state wave function of $^3He$.

Role of 2p–2h MEC excitations in superscaling

Following recent studies of inclusive electron scattering from nuclei at high energies which focused on two-nucleon emission mediated by meson-exchange currents, in this work the superscaling behavior of such contributions is investigated. Comparisons are made with existing data below the quasielastic peak where at high momentum transfers scaling of the second kind is known to be excellent and scaling of the first kind is good, in the proximity of the peak where both 1p–1h and 2p–2h contributions come into play, and above the peak where inelasticity becomes important and one finds scaling violations of the two kinds.

Polarization in electromagnetic two-nucleon emission

Polarization in electromagnetic two-nucleon emission

Polarized photon measurements of the12C(γ→,pp)and12C(γ→,pn)reactions forEγ=160−350MeV

The ${}^{12}\mathrm{C}(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}},pp)$ and ${}^{12}\mathrm{C}(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}},pn)$ reactions have been studied for ${E}_{\ensuremath{\gamma}}=160\ensuremath{-}350$ MeV using linearly polarized photons from the Glasgow tagged photon spectrometer at the Mainz microtron MAMI. Both reaction channels show a negative photon asymmetry $\ensuremath{\Sigma}$ for missing energies ${E}_{m}$ below 70 MeV, where direct emission nucleon pairs is expected. A strong peak at low ${E}_{m}$ is observed in ${\ensuremath{\Sigma}}_{(\ensuremath{\gamma},pp)},$ but not in ${\ensuremath{\Sigma}}_{(\ensuremath{\gamma},pn)}.$ Further differences between the two reaction channels are observed in the ${E}_{\ensuremath{\gamma}}$ dependence of $\ensuremath{\Sigma}$ and in the angular distributions of differential cross sections for photons polarized parallel, or perpendicular, to the reaction plane. Theoretical calculations using an unfactorized distorted wave treatment of direct two-nucleon emission do not agree with the magnitude of the photon asymmetry or the angular dependence of the differential cross sections for either channel. For ${E}_{m}>70$ MeV and ${E}_{\ensuremath{\gamma}}>250$ MeV, $\ensuremath{\Sigma}$ has a substantial negative value which is similar for both reaction channels. This is attributed to two-step reactions following initial quasifree pion production.

Correlated Model for Quasi-Elastic Responses in Finite Nuclear Systems

A model to calculate nuclear responses considering short-range correlation effects is presented. The model is applied to the study of electromagnetic responses induced by one-body operators. We calculate one- and two-nucleon emission responses and cross sections of the 16O and 40Ca nuclei in the quasi-elastic region, and we compare them with experimental data.

Two-nucleon spectral function in infinite nuclear matter

The two-nucleon spectral function in nuclear matter is studied using Correlated Basis Function perturbation theory, including central and tensor correlations produceded by a realistic hamiltonian. The factorization property of the two-nucleon momentum distribution into the product of the two single nucleon distributions shows up in an analogous property of the spectral function. The correlated model yields a two-hole contribution quenched whith respect to Fermi gas model, while the peaks acquire a quasiparticle width that vanishes as the two momenta approach $k_F$. In addition, three-hole one-particle and more complicated intermediate states give rise to a background, spread out in energy and absent in the uncorrelated models. The possible connections with one- and two-nucleon emission processes are briefly discussed.

Formula omitted]C( [formula omitted],pn) photon asymmetry for Eγ=180–340 MeV

The photon asymmetry ( Σ) of the 12 C( γ → ,pn) reaction has been measured using linearly polarised tagged photons at the Mainz microtron MAMI for E γ =180–340 MeV. The data have been analysed in separate missing energy ( E m) regions corresponding to the ejection of nucleons from (1p) 2 and (1p)(1s) shells. The measured Σ values for both E m regions are smaller in magnitude than corresponding 2 H data, but the (1p) 2 results have a similar E γ dependence. Calculations of direct two-nucleon emission overestimate the magnitude of Σ at all photon energies.

Investigation of short-range nucleon-nucleon correlations using the reaction [formula omitted] in close to 4 π geometry

Two-proton correlations were studied in close to 4 π geometry using the reaction 12 C(e,e′pp) . The beam energy was 705 MeV, the energy transfer 225 MeV, and the three-momentum transfer 412 MeV/c. The electrons were observed in a large-acceptance magnetic spectrometer in coincidence with protons observed in a BGO crystal ball. Missing energy and momentum, relative momentum and angular distributions were derived and compared with a factorized two-nucleon emission model. Soft-core correlation functions are favoured by the data.

Polarization degrees of freedom in photoinduced two-nucleon knockout from finite nuclei

The polarization degrees of freedom in photoinduced two-nucleon knockout from finite nuclei are studied. It is pointed out that they open good perspectives to study the dynamics of dinucleons in the medium in detail. The $(\ensuremath{\gamma},pp)$ and $(\ensuremath{\gamma},pn)$ angular cross sections, photon asymmetries, and outgoing nucleon polarizations are calculated for the target nuclei ${}^{16}$O and ${}^{12}$C and photon energies ranging from 100 up to 500 MeV. It is investigated to which degree the two-nucleon emission reaction is dominated by photoabsorption on ${}^{3}{S}_{1}(T=0)$ proton-neutron and ${}^{1}{S}_{0}(T=1)$ proton-proton pairs in the nuclear medium. The calculations demonstrate that dominance of $S$-wave photoabsorption in the $(\ensuremath{\gamma},pn)$ channel does not necessarily imply that the reaction mechanism is similar to what is observed in deuteron photodisintegration.

Two-nucleon emission in the longitudinal response

The contribution of the two-nucleon emission in the longitudinal response for inclusive electron scattering reactions is studied. The model adopted to perform the calculations is based upon correlated basis function theory but it considers only first order terms in the correlation function. The proper normalization of the wave function is ensured by considering, in addition to the usually evaluated two-point diagrams, the three-point diagrams. Results for the {sup 12}C nucleus in the quasielastic region are presented. {copyright} {ital 1998} {ital The American Physical Society}