Backward elastic electron scattering from odd-A nuclear targets is characterized by magnetic form factors containing precise information on the nuclear structure. We study the sensitivity of the magnetic form factors to structural effects related to the evolution and shape transitions in both isotopic and isotonic chains. Calculations of magnetic form factors are performed in the plane-wave Born approximation. The nuclear structure is obtained from a deformed self-consistent mean-field calculation based on a Skyrme HF+BCS formalism. Collective effects are included in the cranking approximation, whereas nucleon-nucleon correlations are taken into account in the coherent density fluctuation model. The evolution of the magnetic form factors is found to exhibit signatures of shape transitions that show up in selected isotopic and isotonic chains involving both stable and unstable nuclei. Several cases are identified as suitable candidates for showing such fingerprints of shape transitions. A new generation of electron scattering experiments involving electron-radioactive beam colliders will be available in the near future, leading to a renewed interest in this field.
Quasi-elastic responses in nuclear matter and in $^{12}$C and $^{40}$Ca nuclei are calculated in ring approximation to investigate the finite size effects on the electromagnetic quasi-elastic responses. A method to simulate these effects in infinite systems calculations is proposed. The sensitivity of the results to the various terms of the residual interaction is studied. The results of nuclear matter RPA calculations are compared with those obtained in ring approximation to evidence the importance of the exchange terms.
The elastic properties of neutron star crusts are relevant for a variety of currently observable or near-future electromagnetic and gravitational wave phenomena. These phenomena may depend on the elastic properties of nuclear pasta found in the inner crust. We present large scale classical molecular dynamics simulations where we deform nuclear pasta. We simulate idealized samples of nuclear pasta and describe their breaking mechanism. We also deform nuclear pasta that is arranged into many domains, similar to what is known for the ions in neutron star crusts. Our results show that nuclear past…
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.
The effects of nuclear re-interactions in the quasi-elastic neutrino-nucleus scattering are investigated with a phenomenological model. We found that the nuclear responses are lowered and their maxima are shifted towards higher excitation energies. This is reflected on the total neutrino-nucleus cross section in a general reduction of about 15% for neutrino energies above 300 MeV.
The problem of discontinuous functions and their representations in the form of Legendre polynomial series in quantum nuclear scattering theory is presented briefly. The problem is quite old yet not adequately explained in numerous Quantum Theory textbooks and sometimes not correctly understood by physicists. This problem might be quite important in interpretation and analyses of nuclear elastic scattering data and so requires to be stated in a more detailed and clear way.
A nuclear-elastic $^9$Be+$^4$He reaction is investigated. A tangential literature overview of the proximity potential is presented, necessitated by an approximate method for calculating $l\text{-values}$. The model is surveyed intensively, from classical conception (liquid drop model) to physical implication (fusion barrier height), leading to a second-part calculation of the $^9$Be+$^4$He angular distribution. The results obtained are limited by the exclusion of phase variation, but provide enough accuracy to give order-of-magnitude estimates for nuclei interacting peripherally, in agreement …
The quasi-elastic neutrino-nucleus cross section has been calculated by using a Fermi gas model corrected to consider the re-scattering between the emitted nucleon and the rest nucleus. As an example of the relevance of this effect we show results for the muon production cross section on 16O target.
A systematic study of the in-medium correction factor ($F$) on nucleon-nucleon elastic cross section is performed within the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. The effects of the beam energy dependence of $F$ on the directed, elliptic flow and nuclear stopping in $^{197}$Au+$^{197}$Au collisions with energy ranging from $0.09$ to $0.8A$ GeV are explored. It is found that the directed, elliptic flow and nuclear stopping at relatively low energies are very sensitive to $F$, and the sensitivity gradually weakens with increasing beam energy. The beam energy dependent in-m…
The elastic scattering of the halo nucleus $^6$He from heavy targets at incident energies near the Coulomb barrier displays a marked deviation from the standard Fresnel-type diffraction behavior. This deviation is due to the strong Coulomb dipole breakup coupling produced by the Coulomb field of the heavy target, a specific feature of the nuclear structure of $^6$He. We have performed Continuum Discretized Coupled Channels calculations for the elastic scattering of $^{6}$He and $^6$Li from $^{58}$Ni, $^{120}$Sn, $^{144}$Sm, $^{181}$Ta and $^{208}$Pb targets in order to determine the range of $…
We explore the nuclear responses at intermediate energies, particularly in the spin longitudinal and spin transverse isovector channels, within the continuum random phase approximation framework. We also employ an extension of the standard random phase approximation to account for the spreading width of the single particle states through the inclusion of a complex and energy-dependent nucleon self-energy. The nuclear responses are then used as the basic ingredient to calculate hadronic reactions in the Glauber theory framework. Here both one and two-step contributions to the multiple scatterin…
Elastic electron scattering from oriented odd-Aaxially deformed nuclei is studied in the plane-wave Born approximation. The nuclear structure is described within a microscopic selfconsistent Skyrme deformed Hartree-Fock approximation with pairing correlations. The interference form factors between monopole and quadrupole Coulomb terms that characterize the nuclear response with aligned nuclear targets are shown to increase or decrease the unpolarized cross-section, depending on the sign of the quadrupole deformation. This feature provides valuable information on the nuclear deformation that ca…
Motivated by arguments of the nuclear core-layer model formulated in [S.I. Bastrukov, J.A. Maruhn, Z.Phys. A 335 (1990) 139], the macroscopic excitation mechanism of electric pygmy dipole resonance (PDR) is considered as owing its origin to perturbation-induced effective decomposition of nucleus into two spherical domains - undisturbed inner region treated as static core and dynamical layer undergoing elastic shear vibrations. The focus is placed on the imprinted in the core-layer model mechanism of emergence of the low-energy dipole electric resonant excitation as Goldstone soft mode of trans…
Elastic $^{16}$O+$^{12}$C scattering is known to exhibit the nuclear rainbow pattern at incident energies $E_\text{lab}\gtrsim 200$ MeV, with the Airy structure of the far-side scattering cross section clearly seen at medium and large angles. Such a rainbow pattern is well described by the deep real optical potential (OP) given by the double-folding model (DFM). At lower energies, the extensive elastic $^{16}$O+$^{12}$C scattering data show consistently that the nuclear rainbow pattern at backward angles is deteriorated by an oscillating enhancement of elastic cross section that is difficult t…
I investigate the elastic electron scattering off nuclei far from the stability line. The effects of the neutron and proton skins and halos on the differential cross sections are explored. Examples are given for the charge distribution in Sn isotopes and its relation to the neutron skin. The neutron halo in $^{11}$Li and the proton halo in $^{8}$B are also investigated. Particular interest is paid to the inverse scattering problem and its dependence on the experimental precision. These studies are of particular interest for the upcoming electron ion colliders at the GSI and RIKEN facilities.
We formulate microscopic optical potentials for nucleon-nucleus scattering from chiral two- and three-nucleon forces. The real and imaginary central terms of the optical potentials are obtained from the nucleon self energy in infinite nuclear matter at a given density and isospin asymmetry, calculated self-consistently to second order in many-body perturbation theory. The real spin-orbit term is extracted from the same chiral potential using an improved density matrix expansion. The density-dependent optical potential is then folded with the nuclear density distributions of 40Ca, 42Ca, 44Ca, a…
The model independent procedure of extracting charge density distributions from elastic electron scattering data is investigated. The charge density distributions are expanded on an orthonormal basis and the parameters of the expansions are fixed by the comparison with the experimental data. Two bases with different analytical properties (Fourier-Bessel and Hermite) are used. This allows us to disentangle the uncertainties coming from the choice of the expansion basis from those intrinsic to the extraction procedure. We design a set of tests to select the number of the expansion coefficients a…
The effects of the nuclear structure uncertainties on the description of processes induced by coherent scattering of neutrinos on nuclei are investigated. A reference calculation based on a specific nuclear model is defined and the cross sections and also the expected number of events produced by neutrinos generated by the explosion of a supernova in our galaxy, and by a spallation neutron source are evaluated. By changing the input parameters of the reference calculation their relevance on cross sections and on the number of the detected events is estimated. Seven spherical nuclei with differ…
In order to clear up the sensitivity of the nucleus-nucleus scattering to the nuclear matter distributions of exotic halo nuclei, we have calculated differential cross sections for elastic scattering of the $^6$He and $^{11}$Li nuclei on several nuclear targets at the energy of 0.8 GeV/nucleon with different assumed nuclear density distributions in $^6$He and $^{11}$Li.
We formulate microscopic neutron-nucleus optical potentials from many-body perturbation theory based on chiral two- and three-body forces. The neutron self energy is first calculated in homogeneous matter to second order in perturbation theory, which gives the central real and imaginary terms of the optical potential. The real spin-orbit term is calculated separately from the density matrix expansion using the same chiral interaction as in the self energy. Finally, the full neutron-nucleus optical potential is derived within the improved local density approximation utilizing mean field models …
The driving terms in three-body theories of elastic and inelastic scattering of a charged particle off a bound state of two other charged particles contain the fully off-shell two-body Coulomb T-matrix describing the intermediate-state Coulomb scattering of the projectile with each of the charged target particles. Up to now the latter is usually replaced by the Coulomb potential, either when using the multiple-scattering approach or when solving three-body integral equations. General properties of the exact and the approximate on-shell driving terms are discussed, and the accuracy of this appr…
The last few years activity of the Italian community concerning nuclear physics with electroweak probes is reviewed.Inclusive quasi-elastic electron-scattering, photon end electron induced one- and two-nucleon emission are considered. The scattering of neutrinos off nuclei in the quasi-elastic region is also discussed.
We investigate the screening effects on the nucleon-nucleon elastic cross section inside nuclear matter at zero and finite temperature. The N-N interaction is described phenomenologically via meson exchanges ($σ$, $π$ and $ω$) in the framework of a relativistic lagrangian model. The expressions for the in-medium meson propagators, which take into account the effects of matter polarization and renormalized vacuum polarization, are used in the calculation of the various meson contributions to the total cross section in the one-boson exchange approximation. The final expressions allow a satisfact…
The optical model potentials for nucleon-nucleus elastic scattering at $65$~MeV are calculated for $^{12}$C, $^{16}$O, $^{28}$Si, $^{40}$Ca, $^{56}$Fe, $^{90}$Zr and $^{208}$Pb in first order multiple scattering theory, following the prescription of the spectator expansion, where the only inputs are the free NN potentials, the nuclear densities and the nuclear mean field as derived from microscopic nuclear structure calculations. These potentials are used to predict differential cross sections, analyzing powers and spin rotation functions for neutron and proton scattering at 65 MeV projectile …
The Coulomb-nuclear interference (CNI) has recently been used by the TOTEM Collaboration to analyse proton-proton elastic-scattering data from the LHC and to draw physics conclusions. This paper will present an eikonal calculation of the CNI effects performed to all orders of the fine structure constant, $α$. This calculation will be used as a reference to benchmark several widely-used CNI formulae and to verify several recent claims by other authors.
Elastic proton scattering on ${}^{3}{H}$ nucleus is studied inbetween p-% ${}^{3}{H}$ and n-${}^{3}{He}$ thresholds, in the energy region where $α$-particles first excited state is inbeded in the continuum. For this aim Faddeev-Yakubovski equations are solved in configuration space, fully considering effects due to the isospin breaking as well as rigorously treating Coulomb interaction. Different realistic nuclear Hamiltonians are tested, elucidating open problems in nuclear interaction description.
A new non-relativistic expansion in terms of the nucleon's momentum inside nuclear matter of the current for isobar electro-excitation from the nucleon is performed. Being exact with respect to the transferred energy and momentum, this yields new current operators which retain important aspects of relativity not taken into account in the traditional non-relativistic reductions. The transition current thus obtained differs from the leading order of the traditional expansion by simple multiplicative factors. These depend on the momentum and energy transfer and can be easily included together wit…
The Quasi-Elastic contribution of the nuclear inclusive electron scattering model developed in Nucl. Phys. A 627 (1997) 543 is extended to the study of electroweak Charged Current induced nuclear reactions, at intermediate energies of interest for future neutrino oscillation experiments. The model accounts for long range nuclear (RPA) correlations, Final State Interaction and Coulomb corrections. RPA correlations are shown to play a crucial role in the whole range of neutrino energies, up to 500 MeV, studied in this work. Predictions for inclusive muon capture for different nuclei, and for the…
We consider $K^-$ nucleon elastic and inelastic scattering in isospin symmetric nuclear matter. It is found that the proper description of the $Λ(1405)$ resonance structure in nuclear matter requires a self-consistent approach. Then the $Λ(1405) $ resonance mass remains basically unchanged, however, the resonance acquires an increased decay width as nuclear matter is compressed. The elastic and inelastic scattering amplitudes show important medium modifications close to the kaon nucleon threshold. We also construct the $K^-$-nuclear optical potential appropriate for $K^-$ atoms. Our microscopi…
Realistic nuclear structure calculations are presented for the event rates due to coherent elastic neutrino-nucleus scattering (CE$ν$NS), assuming neutrinos from pion-decay at-rest, from nuclear reactors and from Earth's interior. We focus on the currently interesting Germanium isotopes, $^{70,73,76}$Ge, which constitute detector materials of the recently planned CE$ν$NS experiments. We study in addition the potential use of $^{64,70}$Zn and $^{28}$Si isotopes as promising CE$ν$NS detectors. From nuclear physics perspectives, recently, calculations have been carried out within the framework of…
We calculate differential cross sections for proton-nucleus elastic scattering by using a Glauber theory in the optical limit approximation and nucleon distributions that can be obtained in the framework of macroscopic nuclear models in a way dependent on the equation of state of uniform nuclear matter near the saturation density. We find that the peak angle calculated for unstable neutron-rich nuclei in the small momentum transfer regime increases as the parameter L characterizing the density dependence of the symmetry energy decreases. This is a feature associated with the L dependence of th…
Parameterizations of Electron Scattering Form Factors for Elastic Scattering and Electro-Excitation of Nuclear States for $\rm ^{27}Al$ and $\rm ^{40}Ca$
The structure of the exotic $^{8}$B nucleus is studied by means of elastic scattering, as well as its breakup on nuclear targets. We present microscopic calculations of the optical potentials (OPs) and cross sections of elastic scattering of $^{8}$B on $^{12}$C, $^{58}$Ni, and $^{208}$Pb targets at energies $20<E<170$ MeV. The density distributions of $^{8}$B obtained within the variational Monte Carlo (VMC) model and the three-cluster model (3CM) are used to construct the potentials. The real part of the hybrid OP is calculated using the folding model with the direct and exchange terms includ…
The influence of nuclear isospin mixing on parity-violating elastic electron scattering is studied for the even-even, N=Z nuclei 12C, 24Mg, 28Si, and 32S. Their ground-state wave functions have been obtained using a self-consistent axially-symmetric mean-field approximation with density-dependent effective two-body Skyrme interactions. Some differences from previous shell-model calculations appear for the isovector Coulomb form factors which play a role in determining the parity-violating asymmetry. To gain an understanding of how these differences arise, the results have been expanded in a sp…
We investigate the possible disappearance of Mott oscillations in the scattering of bosonic nuclei at sub-barrier energies. This effect is universal and happens at a critical value of the Sommerfeld parameter. It is also found that the inclusion of the short-range nuclear interaction has a profound influence on this phenomenon. Thus we suggest that the study of this lack of Mott oscillation, which we call, ``transverse isotropy" is a potentially useful mean to study the nuclear interaction.
The feasibility of a model-independent extraction of the forward strong amplitude from elastic nuclear cross section data in the Coulomb-nuclear interference region is assessed for $π$ and $K^+$ scattering at intermediate energies. Theoretically-generated "data" are analyzed to provide criteria for optimally designing experiments to measure these amplitudes, whose energy dependence (particularly that of the real parts) is needed for disentangling various sources of medium modifications of the projectile-nucleon interaction. The issues considered include determining the angular region over whic…
We exhibit a wide variety of the nuclear shape phases over the nuclear chart along with a shell model scheme. Various nuclear shapes are demonstrated within the framework of proton-neutron spin-orbital interactions; ferro-deformed, sub-ferro-deformed, and spherical shapes. The spherical shape is classified into the three magic-number categories in view of a large shell gap mechanism; double-magic nuclei I, double magic nuclei II, and double magic nuclei III. We discuss nuclear shape coexistence in the space Z = 76 to 84 as providing a new way to understanding the dynamical shape phases.
We investigate the use of proton-nucleus elastic scattering experiments using secondary beams of 6He and 8He to determine the physical structure of these nuclei. The sensitivity of these experiments to nuclear structure is examined by using four different nuclear structure models with different spatial features using a full-folding optical potential model. The results show that elastic scattering at intermediate energies (<100 MeV per nucleon) is not a good constraint to be used to determine features of structure. Therefore researchers should look elsewhere to put constraints on the ground sta…
We investigate the possible disappearance of Mott oscillations in the scattering of bosonic nuclei at sub-barrier energies. This effect is universal and happens at a critical value of the Sommerfeld parameter. It is also found that the inclusion of the short-range nuclear interaction has a profound influence on this phenomenon. Thus we suggest that the study of this lack of Mott oscillation, which we call, "transverse isotropy" is a potentially useful mean to study the nuclear interaction.
The availability of the double-differential charged-current neutrino cross section, measured by the MiniBooNE collaboration using a carbon target, allows for a systematic comparison of nuclear effects in quasi-elastic electron and neutrino scattering. The results of our study, based on the impulse approximation scheme and a state-of-the-art model of the nuclear spectral functions, suggest that the electron cross section and the flux averaged neutrino cross sections, corresponding to the same target and comparable kinematical conditions, cannot be described within the same theoretical approach …
We discuss the role of channel coupling in the surface properties of an inter-nuclear potential for heavy-ion reactions. To this end, we analyze the experimental quasi-elastic cross sections for the $^{12}$C + $^{105,106}$Pd and $^{13}$C + $^{105,106}$Pd systems using the coupled-channels approach by including the vibrational excitations in the target nuclei. While earlier studies have reported a negligible influence of vibrational excitation on the surface diffuseness parameter for spherical systems, we find a significant effect for the C+Pd systems. Our systematic study also reveals influenc…
How does nature hold together protons and neutrons to form the wide variety of complex nuclei in the universe? Describing many-nucleon systems from the fundamental theory of quantum chromodynamics has been the greatest challenge in answering this question. The chiral effective field theory description of the nuclear force now makes this possible but requires certain parameters that are not uniquely determined. Defining the nuclear force needs identification of observables sensitive to the different parametrizations. From a measurement of proton elastic scattering on $^{10}$C at TRIUMF and ab i…
Based on the isospin-dependent Boltzmann-Uehling-Uhlenbeck(IBUU04) transport model, we explored effects of in-medium $NN$ elastic scattering cross section and nuclear symmetry energy on the sub-threshold pion production in $^{132}Sn+^{124}Sn$ reaction. We find that with decrease of incident beam energy, effects of in-medium $NN$ elastic scattering cross section on the $π^{-}/π^{+}$ ratio are larger than that of the symmetry energy although the latter may be also larger. While keeping the effect of symmetry energy, the double ratio of $π^{-}/π^{+}$ from neutron-rich and neutron-poor reaction sy…
A quantitative analysis of the evolution of nuclear shapes and shape phase transitions, including regions of short-lived nuclei that are becoming accessible in experiments at radioactive-beam facilities, necessitate accurate modeling of the underlying nucleonic dynamics. Important theoretical advances have recently been made in studies of complex shapes and the corresponding excitation spectra and electromagnetic decay patterns, especially in the "beyond mean-field" framework based on nuclear density functionals. Interesting applications include studies of shape evolution and coexistence in N …
We investigate the property of the high-density nuclear matter probed by the nucleus-nucleus elastic scattering in the framework of the double-folding (DF) model with the complex $G$-matrix interaction. The medium effect including three-body-force (TBF) effect is investigated with present two methods based on the frozen density approximation (FDA). The medium effect is clearly seen on the potential and the elastic cross section for the $^{16}$O + $^{16}$O system at $E/A =$ 70 MeV. The crucial role of the medium effect is also confirmed with other effective nucleon-nucleon ($NN$) interactions. …
We evaluate nuclear effects in neutrino reactions in a framework based on a model proposed by Marteau with quasi-elastic and $Δ$ production processes treated together. Nuclear effects include RPA corrections and $Δ$ width modification in nuclear matter.
To extract structure information from proton elastic scattering off S isotopes at 320 MeV and Ni isotopes at $E_p=180$ MeV, this study proposes isotopic analyses combining nuclear structure and reaction calculations. The isotonic analysis was repeated on $^{48}$Ca and $^{50}$Ti. The structure calculations were performed by using the spherical and deformed Relativistic Hartree--Bogoliubov (RHB) calculations, and the spherical nonrelativistic Skyrme Hartree--Fock--Bogoliubov calculations. The $(p,p)$ reactions were calculated using the relativistic impulse approximation (RIA) assuming the theore…
The role played by the effective residual interaction in the transverse nuclear response for quasi-free electron scattering is discussed. The analysis is done by comparing different calculations performed in the Random--Phase Approximation and Ring Approximation frameworks. The importance of the exchange terms in this energy region is investigated and the changes on the nuclear responses due to the modification of the interaction are evaluated. The calculated quasi-elastic responses show clear indication of their sensibility to the details of the interaction and this imposes the necessity of a…
Using a new approximate analytic parameter-free proxy-SU(3) scheme, we make simple predictions of shape observables for deformed nuclei, namely gamma and beta deformation variables, the global feature of prolate dominance and the locus of the prolate-oblate shape transition. The predictions are compared with empirical results.
We intend to provide a consistent description of the even-even Hg isotopes, 172-200Hg, using the interacting boson model including configuration mixing. We pay special attention to the description of the shape of the nuclei and to its connection with the shape coexistence phenomenon.
We consider the analyzing power on a spin-0 nuclear target. This observable is related to the imaginary part of the two-photon-exchange (box) diagram. We consider the contributions of elastic and inelastic intermediate states. The former requires knowledge of the elastic nuclear form factor, while the latter uses the optical theorem as input. The elastic contribution scales as the nuclear charge $Z$, while the inelastic contribution as the ratio of the atomic number and nuclear charge, $A/Z$. We provide estimates for $^4$He and $^{208}$Pb, in the kinematics of existing or upcoming experiments.…
The interpretation of the charged (CCQE) and neutral (NCE) current quasi elastic events collected by the MiniBooNE collaboration involves a number of unresolved issues. While it has been suggested that the data can be explained in terms of an effective nucleon axial mass, $M_A$, the results of our theoretical calculations suggest that the CCQE and NCE samples cannot be described by the same value of $M_A$. We argue that the disagreement between theory and data may arise from the uncertainties associated with the flux average procedure. We also analyze the role of the strange quark in NCE inter…
Large-angle elastic scattering of alpha-particle and strongly-bound light nuclei at a few tens MeV/nucleon has shown the pattern of rainbow scattering. This interesting process was shown to involve a significant overlap of the two colliding nuclei, with the total nuclear density well above the saturation density of normal nuclear matter (NM). For a microscopic calculation of the nucleus-nucleus potential within the folding model, we have developed a density dependent nucleon-nucleon (NN) interaction based on the G-matrix interaction M3Y. Our folding analysis of the refractive 4He, 12C, and 16O…
The Glauber model analysis of the elastic $^{6,8}$He+$p$ scattering data at energies around 700 MeV/nucleon, measured in two separate experiments at GSI-Darmstadt, has been done using several phenomenological parametrizations of the nuclear matter density. By taking into account the new data points measured at the high momentum transfer, the nuclear matter radii of $^{6,8}$He were accurately determined from the Glauber model analysis of the data, with the spin-orbital interaction explicitly taken into account. The well-known geometry for the core and dineutron halo has been used with the new p…
