Continuum Random Phase Approximation Research Articles

Application of relativistic continuum random phase approximation to giant dipole resonance of $$^{208}$$Pb and $$^{132}$$Sn

Application of relativistic continuum random phase approximation to giant dipole resonance of $$^{208}$$Pb and $$^{132}$$Sn

Continuum random-phase approximation for (n,γ) reactions on neutron-rich nuclei: Collective effects and resonances

We formulate a microscopic theory to calculate cross section of the radiative neutron capture reaction on neutron-rich nuclei using the continuum random-phase approximation (cRPA) to the time-dependent density functional theory (TDDFT). With an intention of applying to the $r$ process, for which the statistical reaction model may not be appropriate, we describe the transition between a initial state of incident neutron and a final state of the $\ensuremath{\gamma}$ decay by means of a single many-body framework of the cRPA-TDDFT. With the cRPA approach, it is possible to describe various excitation modes present in the $(n,\ensuremath{\gamma})$ reaction, including soft dipole excitation, the giant resonances, as well as noncollective excitations and the single-particle resonances. Furthermore, it enables us to describe the $(n,\ensuremath{\gamma})$ reaction where the the final states of the $\ensuremath{\gamma}$ transition are low-lying surface vibrational states. We demonstrate the theory by performing numerical calculation for the reaction $^{139}\mathrm{Sn}(n,\ensuremath{\gamma})^{140}\mathrm{Sn}$. We discuss various new features which are beyond the single-particle model: the presence of narrow and wide resonances originating from noncollective and collective excitations and roles of low-lying quadrupole and octupole vibrational states.

Cross Sections for Coherent Elastic and Inelastic Neutrino-Nucleus Scattering

The prospects of extracting new physics signals in coherent elastic neutrino–nucleus scattering (CEνNS) processes are limited by the precision with which the underlying nuclear structure physics, embedded in the weak nuclear form factor, is known. We present calculations of charge and weak nuclear form factors and CEνNS cross sections on 12C, 16O, 40Ar, 56Fe and 208Pb nuclei. We obtain the proton and neutron densities, and charge and weak form factors by solving Hartree–Fock (HF) equations with a Skyrme (SkE2) nuclear potential. We validate our approach by comparing 208Pb and 40Ar charge form factor predictions with available elastic electron scattering data. Since CEνNS experiments at stopped-pion sources are also well suited to measure inelastic charged–current and neutral–current neutrino–nucleus cross sections, we also present calculations for these processes, incorporating a continuum Random Phase Approximation (CRPA) description on top of the HF–SkE2 picture of the nucleus. Providing both coherent as well as inelastic cross sections in a consistent framework, we aim at obtaining a reliable and detailed comparison of the strength of these processes in the energy region below 100 MeV. Furthermore, we attempt to gauge the level of theoretical uncertainty pertaining to the description of the 40Ar form factor and CEνNS cross sections by comparing relative differences between recent microscopic nuclear theory and widely-used phenomenological form factor predictions. Future precision measurements of CEνNS will potentially help in constraining these nuclear structure details that will in turn improve prospects of extracting new physics.

Implementation of the continuum random phase approximation model in the GENIE generator and an analysis of nuclear effects in low-energy transfer neutrino interactions

We present the implementation and validation of the Hartree-Fock continuum random phase approximation (HF-CRPA) model in the GENIE neutrino-nucleus interaction event generator and a comparison of the subsequent predictions to experimental measurements of lepton kinematics from interactions with no mesons in the final state. These predictions are also compared to those of other models available in GENIE. It is shown that, with respect to these models, HF-CRPA predicts a significantly different evolution of the cross section when moving between different interaction targets, when considering incoming anti-neutrinos compared to neutrinos and when changing neutrino energies. These differences are most apparent for interactions with low energy and momentum transfer. It is also clear that the impact of nucleon correlations within the HF-CRPA framework is very different than in GENIE's standard implementation of RPA corrections. Since many neutrino oscillation experiments rely on their input model to extrapolate between targets, flavours, and neutrino energies, the newly implemented HF-CRPA model provides a useful means to verify that such differences between models are appropriately covered in oscillation analysis systematic error budgets.

Continuum random-phase approximation for γ transitions between excited states in neutron-rich nuclei

A characteristic feature of collective and particle-hole excitations in neutron-rich nuclei is that many of them couple to unbound neutron in continuum single-particle orbits. The continuum random phase approximation (cRPA) is a powerful many-body method that describes such excitations, and it provides a scheme to evaluate transition strengths from the ground state. In an attempt to apply cRPA to the radiative neutron capture reaction, we formulate in the present study an extended scheme of cRPA that describes gamma-transitions from the excited states under consideration, which decay to low-lying excited states as well as the ground state. This is achieved by introducing a non-local one-body operator which causes transitions to a low-lying excited state, and describing a density-matrix response against this operator. As a demonstration of this new scheme, we perform numerical calculation for dipole, quadrupole, and octupole excitations in $^{140}$Sn, and discuss E1 and E2 transitions decaying to low-lying $2^{+}_{1,2}$ and $3^{-}_{1}$ states. The results point to cases where the branching ratio to the low-lying states is larger than or comparable with that to the ground state. We discuss key roles of collectivity and continuum orbits in both initial and final states.

Modeling quasielastic interactions of monoenergetic kaon decay-at-rest neutrinos

Monoenergetic muon neutrinos at 236 MeV are readily produced in intense medium-energy proton facilities ($\gtrsim$2-3~GeV) when a positive kaon decays at rest (KDAR; $K^+ \rightarrow \mu^+ \nu_\mu$). These neutrinos provide a unique opportunity to both study the neutrino interaction and probe the nucleus with a monoenergetic weak-interaction-only tool. We present cross section calculations for quasielastic scattering of these 236~MeV neutrinos off $^{12}$C and $^{40}$Ar, paying special attention to low-energy aspects of the scattering process. Our model takes the description of the nucleus in a mean-field (MF) approach as the starting point, where we solve Hartree-Fock (HF) equations using a Skyrme type nucleon-nucleon interaction. Thereby, we introduce long-range nuclear correlations by means of a continuum random phase approximation (CRPA) framework where we solve the CRPA equations using a Green's function method. The model successfully describes ($e,e'$) data on $^{12}$C and $^{40}$Ca in the kinematic region that overlaps with the KDAR $\nu_\mu$ phase space. In addition to these results, we present future prospects for precision KDAR cross section measurements and applications of our calculations in current and future experiments that will utilize these neutrinos.

Lepton kinematics in low-energy neutrino-argon interactions

Background: Neutrinos in the low-energy regime provide a gateway to a wealth of interesting physics. While plenty of literature exists on detailing the calculation and measurement of total reaction strengths, relatively little attention is paid to the measurement and modeling of the final lepton through differential cross sections at low energies, despite the experimental importance. Purpose: We calculate differential cross sections for low-energy neutrino-nucleus scattering. We examine the role played by forbidden transitions in these distributions and how this differs across different energies and nuclear target masses. Attention is also paid to predictions for typical experimental neutrino spectra. Method: The differential cross sections are calculated within a Continuum Random Phase Approximation framework, which allows us to include collective excitations induced by long-range correlations. The Coulomb interaction of the final lepton in charged current events is treated in an effective way. Results: Kinematic distributions are calculated for $^{16}$O, $^{40}$Ar and $^{208}$Pb. $^{40}$Ar model results are compared for CC ($\nu_e,e^-$) reactions to events generated by the MARLEY event generator, with noticeable discrepancies. Conclusion: Forbidden transitions have a marked effect on the kinematic distributions of the final lepton at low-energy kinematics, such as for DAR neutrinos or for a Fermi-Dirac spectrum at low temperature. This could introduce biases in experimental analyses. Backwards scattering is noticeably more prominent than with MARLEY.

Constraints in modeling the quasielastic response in inclusive lepton-nucleus scattering

We show that the quasielastic (QE) response calculated with the SuSAv2 (superscaling approach) model, that relies on the scaling phenomenon observed in the analysis of (e,e') data and on the relativistic mean-field theory, is very similar to that from a relativistic distorted wave impulse approximation model when only the real part of the optical potentials is employed. The coincidence between the results from these two completely independent approaches, which satisfactorily agree with the inclusive data, reinforces the reliability of the quasielastic predictions stemming from both models and sets constraints for the QE response. We also study the low energy and momentum transfer region of the inclusive response by confronting the results of the relativistic mean-field model with those of the Hartree-Fock continuum random-phase approximation model, which accounts for nuclear long-range correlations. Finally, we present a comparison of our results with the recent JLab (e,e') data for argon, titanium and carbon, finding good agreement with the three data sets.

Low-energy neutrino scattering in experiment and astrophysics

We review the relevance of neutrino-nucleus interactions at energy transfers below 100 MeV for accelerator-based experiments, experiments at lower energies and for astrophysical neutrinos. The impact of low-energy scattering processes in the energy reconstruction analysis of oscillation experiments is investigated. We discuss the modeling of coherent scattering processes and compare its strength to that of inelastic interactions. The presented results are obtained within a continuum random phase approximation approach.

Mean-field approach to reconstructed neutrino energy distributions in accelerator-based experiments

The reconstruction of the neutrino energy is crucial in oscillation experiments that use interactions with nuclei to detect the neutrino. The common reconstruction procedure is based on the kinematics of the final-state lepton. The interpretation of the reconstructed energy in terms of the real neutrino energy must rely on a model for the neutrino-nucleus interaction. The Relativistic Fermi Gas (RFG) model is frequently used in these analyses. In the Hartree-Fock (HF) model for quasielastic nucleon knockout, the bound nucleon wave functions are obtained using an effective nucleon-nucleon force. The final-state wave function is constructed from continuum states in the same potential which have the correct asymptotic behavior. The Continuum Random Phase Approximation (CRPA) model extends the HF approach taking long range correlations into account in a self-consistent way. Considering only single-nucleon processes, the distributions of reconstructed neutrino energies obtained within the HF-CRPA approach are compared with the results of the RFG, an RPWIA calculation, and the RPA+np-nh model of Martini et al. We find that the distributions of reconstructed energies for a fixed incoming energy in the HF-CRPA display additional strength in the low reconstructed energy tails compared to models without elastic distortion of the outgoing nucleon. This asymmetry redistributes strength from higher to lower values of the reconstructed energy. The mean field description of the nuclear dynamics results in a reshaping of the reconstructed energy distribution that cannot be accounted for in a plane wave impulse approximation model, even by modifying ad hoc parameters such as the binding energy. In particular it is shown that in the RFG calculations there is no value of the binding energy which is able to reproduce the entire T2K $\nu_\mu$ oscillated spectrum as calculated in HF-CRPA.

Neutrino-nucleus reactions on O16 based on new shell-model Hamiltonians

Neutrino-induced reactions on $^{16}\mathrm{O}$ are investigated by shell-model calculations with new shell-model Hamiltonians, which can describe well the structure of $p$-shell and $p\ensuremath{-}sd$-shell nuclei. The distribution of the spin-dipole strengths in $^{16}\mathrm{O}$, which give major contributions to the $\ensuremath{\nu}\ensuremath{-}^{16}\mathrm{O}$ reaction cross sections, is studied with the new Hamiltonians. Muon-capture reaction rates on $^{16}\mathrm{O}$ are also studied to discuss the quenching of the axial-vector coupling in the nuclear medium. Charged-current and neutral-current reaction cross sections are evaluated in various particle and $\ensuremath{\gamma}$ emission channels as well as the total ones at neutrino energies up to ${E}_{\ensuremath{\nu}}\ensuremath{\approx}100$ MeV. Branching ratios for the various channels are obtained by the Hauser-Feshbach statistical model calculations, and partial cross sections for single- and multiparticle emission channels are evaluated. The cross sections updated are compared with previous continuum random phase approximation calculations. Effects of multiparticle emission channels on nucleosynthesis in core-collapse supernova explosions are investigated. Inclusion of $\ensuremath{\alpha}p$ emission channels is found to lead to an enhancement of production yields of $^{11}\mathrm{B}$ and $^{11}\mathrm{C}$ through $^{16}\mathrm{O}(\ensuremath{\nu},{\ensuremath{\nu}}^{\ensuremath{'}}\ensuremath{\alpha}p)^{11}\mathrm{B}$ and $^{16}\mathrm{O}({\ensuremath{\nu}}_{e},{e}^{\ensuremath{-}}\ensuremath{\alpha}p)^{11}\mathrm{C}$ reactions, respectively.

A dependence of quasielastic charged-current neutrino-nucleus cross sections

Background: 12C has been and is still widely used in neutrino-nucleus scattering and oscillation experiments. More recently, 40Ar has emerged as an important nuclear target for current and future experiments. Liquid argon time projection chambers (LArTPCs) possess various advantages in measuring electroweak neutrino-nucleus cross sections. Concurrent theoretical research is an evident necessity. Purpose: 40Ar is larger than 12C, and one expects nuclear effects to play a bigger role in reactions. We present inclusive differential and total cross section results for charged-current neutrino scattering on 40Ar and perform a comparison with 12C, 16O and 56Fe targets, to find out about the A-dependent behavior of model predictions. Method: Our model starts off with a Hartree-Fock description of the nucleus, with the nucleons interacting through a mean field generated by an effective Skyrme force. Long-range correlations are introduced by means of a continuum random phase approximation (CRPA) approach. Further methods to improve the accuracy of model predictions are also incorporated in the calculations. Results: We present calculations for 12C, 16O, 40Ar and 56Fe, showcasing differential cross sections over a broad range of kinematic values in the quasielastic regime. We furthermore show flux-folded results for 40Ar and we discuss the differences between nuclear responses. Conclusions: At low incoming energies and forward scattering we identify an enhancement in the 40Ar cross section compared to 12C, as well as in the high $\omega$ (low $T_\mu$ ) region across the entire studied $E_\nu$ range. The contribution to the folded cross section of the reaction strength at values of $\omega$ lower than 50 MeV for forward scattering is sizeable.

Impact of low-energy nuclear excitations on neutrino-nucleus scattering at MiniBooNE and T2K kinematics

[Background] Meticulous modeling of neutrino-nucleus interactions is essential to achieve the unprecedented precision goals of present and future accelerator-based neutrino-oscillation experiments. [Purpose] Confront our calculations of charged-current quasielastic cross section with the measurements of MiniBooNE and T2K, and to quantitatively investigate the role of nuclear-structure effects, in particular, low-energy nuclear excitations in forward muon scattering. [Method] The model takes the mean-field (MF) approach as the starting point, and solves Hartree-Fock (HF) equations using a Skyrme (SkE2) nucleon-nucleon interaction. Long-range nuclear correlations are taken into account by means of the continuum random-phase approximation (CRPA) framework. [Results] We present our calculations on flux-folded double differential, and flux-unfolded total cross sections off $^{12}$C and compare them with MiniBooNE and (off-axis) T2K measurements. We discuss the importance of low-energy nuclear excitations for the forward bins. [Conclusions] The CRPA predictions describe the gross features of the measured cross sections. They underpredict the data (more in the neutrino than in the antineutrino case) because of the absence of processes beyond pure quasielastic scattering in our model. At very forward muon scattering, low-energy nuclear excitations ($\omega < $ 50 MeV) account for nearly 50% of the flux-folded cross section.

Electron-neutrino scattering off nuclei from two different theoretical perspectives

We analyze charged-current electron-neutrino cross sections on Carbon. We consider two different theoretical approaches, on one hand the Continuum Random Phase Approximation (CRPA) which allows a description of giant resonances and quasielastic excitations, on the other hand the RPA-based calculations which are able to describe multinucleon emission and coherent and incoherent pion production as well as quasielastic excitations. We compare the two approaches in the genuine quasielastic channel, and find a satisfactory agreement between them at large energies while at low energies the collective giant resonances show up only in the CRPA approach. We also compare electron-neutrino cross sections with the corresponding muon-neutrino ones in order to investigate the impact of the different charged-lepton masses. Finally, restricting to the RPA-based approach we compare the sum of quasielastic, multinucleon emission, coherent and incoherent one-pion production cross sections (folded with the electron-neutrino T2K flux) with the charged-current inclusive electron-neutrino differential cross sections on Carbon measured by T2K. We find a good agreement with the data. The multinucleon component is needed in order to reproduce the T2K electron-neutrino inclusive cross sections.

Proton pygmy resonances: Predictions for N = 20 isotones

We study theoretically the low-energy electric-dipole response of N=20 isotones. We present results from a quasiparticle random-phase approximation (QRPA) and a continuum random-phase approximation (CRPA), and we compare them with results for the mirror Z=20 nuclei. According to our analysis, enhanced E1 strength is expected energetically well below the giant dipole resonance in the proton-rich isotones. Large amounts of E1 strength in the asymmetric N=20 isotones are predicted, unlike their equally asymmetric Z=20 mirror nuclei, pointing unambiguously to the role of structural effects such as loose binding. A proton-skin oscillation could develop especially in 46Fe. The proper description of non localized threshold transitions and the nucleon effective mass in mean-field treatments may affect theoretical predictions. We call for systematic theoretical investigations to quantify the role bulk-matter properties, in anticipation of measurements of E1 transitions in proton-rich nuclei.

Continuum Random Phase Approximation with finite-range interactions

We rewrite the Random Phase Approximation secular equations in a form which allows the treatment of the continuum part of the single-particle spectrum without approximations. Within this formalism finite-range interactions can be used without restrictions. We present some results, obtained with Gogny interactions, where the role of the continuum is relevant.

Self-consistent continuum random-phase approximation with finite-range interactions for charge-exchange excitations

The formalism of the continuum random-phase approximation theory which treats, without ap- proximations, the continuum part of the single-particle spectrum, is extended to describe charge- exchange excitations. Our approach is self-consistent, meaning that we use a unique, finite-range, interaction in the Hartree-Fock calculations which generate the single-particle basis and in the con- tinuum random-phase approximation which describes the excitation. We study excitations induced by the Fermi, Gamow-Teller and spin-dipole operators in doubly magic nuclei by using four Gogny- like finite-range interactions, two of them containing tensor forces. We focus our attention on the importance of the correct treatment of the continuum configuration space and on the effects of the tensor terms of the force.1

Low-energy excitations and quasielastic contribution to electron-nucleus and neutrino-nucleus scattering in the continuum random-phase approximation

We present a detailed study of a continuum random phase approximation approach to quasielastic electron-nucleus and neutrino-nucleus scattering. The formalism is validated by confronting ($e,e'$) cross-section predictions with electron scattering data for the nuclear targets $^{12}$C, $^{16}$O, and $^{40}$Ca, in the kinematic region where quasielastic scattering is expected to dominate. We examine the longitudinal and transverse contributions to $^{12}$C($e,e'$) and compare them with the available data. Further, we study the $^{12}$C($\nu_{\mu},\mu^{-}$) cross sections relevant for accelerator-based neutrino-oscillation experiments. We pay special attention to low-energy excitations which can account for non-negligible contributions in measurements, and require a beyond-Fermi-gas formalism.

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.

Relation between isospin-symmetry-breaking correction to superallowedβdecay and the energy of the charge-exchange giant monopole resonance

After application of an analytical transformation, a new exact representation for the nuclear isospin-symmetry breaking correction $\delta_C$ to superallowed beta decay is obtained. The correction is shown to be essentially the reciprocal of the square of an energy parameter $\Omega_M$ which characterizes the charge-exchange monopole strength distribution. The proportionality coefficient in this relation is determined by basic properties of the ground state of the even-even parent nucleus, and should be reliably calculable in any realistic nuclear model. Therefore, the single parameter $\Omega_M$ contains all the information about the properties of excited $0^+$ states needed to describe $\delta_C$. This parameter can possibly be determined experimentally by charge-exchange reactions. Basic quantities of interest are calculated within the isospin-consistent continuum random phase approximation, and the values of $\delta_C$ are compared with the corresponding results from other approaches.