Nucleus Optical Potential Research Articles

Low-energyω(→π0γ)meson photoproduction in the nucleus

The ${\ensuremath{\pi}}^{0}\ensuremath{\gamma}$ invariant mass distribution spectra in the $(\ensuremath{\gamma},{\ensuremath{\pi}}^{0}\ensuremath{\gamma})$ reaction were measured by the TAPS/ELSA Collaboration to look for the hadron parameters of the $\ensuremath{\omega}$ meson in the Nb nucleus. We study the mechanism for this reaction, where we consider that the elementary reaction in the Nb nucleus proceeds as $\ensuremath{\gamma}N\ensuremath{\rightarrow}\ensuremath{\omega}N;\ensuremath{\omega}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}$. The $\ensuremath{\omega}$-meson photoproduction amplitude for this reaction is extracted from the measured four-momentum transfer distribution in the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\omega}p$ reaction. The propagation of the $\ensuremath{\omega}$ meson and the distorted wave function for the ${\ensuremath{\pi}}^{0}$ meson in the final state are described by the eikonal form. The $\ensuremath{\omega}$ and ${\ensuremath{\pi}}^{0}$ mesons' nucleus optical potentials, appearing in the $\ensuremath{\omega}$ meson propagator and ${\ensuremath{\pi}}^{0}$ meson distorted wave function respectively, are estimated using the $t\ensuremath{\varrho}$ approximation. The effects of pair correlation and color transparency are also studied. The calculated results do not show medium modification for the $\ensuremath{\omega}$ meson produced in the nucleus for momentum greater than 200 MeV. It occurs because the $\ensuremath{\omega}$ meson predominantly decays outside the nucleus. The dependence of the cross section on the final-state interaction is also investigated. The broadening of the $\ensuremath{\omega}$-meson mass distribution spectra is shown to occur due to the large resolution width associated with the detector used in the experiment.

Proton scattering observables from Skyrme–Hartree–Fock densities

Proton and neutron densities from Skyrme–Hartree–Fock (SHF) calculations are used to generate non-local ( g-folding) proton–nucleus optical potentials. They are formed by folding the densities with realistic nucleon–nucleon interactions. The potentials are then used to calculate differential cross sections and spin observables for proton scattering. Good agreement with data has been found, supporting those found previously when using SHF charge densities in analyses of electron scattering data. That agreement was improved by use of (shell model) occupation numbers to constrain the HF iterations. That, in part, is also the case with analyses of proton scattering data. The g-folding method is extended to exotic nuclei by including data for neutron-rich sd-shell nuclei from the inverse kinematics of scattering from hydrogen.

Microscopic K +-nucleus optical potential and calculations of differential elastic-scattering cross sections and total reaction cross sections

The differential elastic-scattering cross sections and the total reaction cross sections for the interaction of K+ mesons with 12C and 40Ca nuclei at beam momenta of 0.635, 0.715, and 0.8 GeV/c are calculated. The microscopic optical potential derived in the high-energy approximation is used in these calculations. It is determined by the amplitude for kaon-nucleon scattering and the density distribution of pointlike nucleons of the target nucleus. In the high-energy approximation, the Klein-Gordon-Fock equation reduces to the form of the Schrodinger equation. It is shown that small distinctions between the reduction methods do not lead to significant changes in differential elastic-scattering cross sections, but the effects of relativization as such are quite large. Good agreement with experimental data on elastic K+A scattering is attained. The total reaction cross sections can be described upon adding, to the volume potential, a term that takes the form of its derivative and which has a maximum at the periphery, its contribution being fitted to experimental data.

Brieva–Rook localization of the microscopic nucleon–nucleus potential

The nonlocality of the microscopic nucleon–nucleus optical potential is commonly localized by the Brieva–Rook approximation. The validity of the localization is tested for the proton+90Zr scattering at incident energies from 65 MeV to 800 MeV. The localization is valid in a wide incident-energy range.

Proton emission off nuclei induced by kaons in flight

We study the (K-,p) reaction on nuclei with a 1 GeV/c momentum kaon beam, paying a special attention at the region of emitted protons having kinetic energy above 600 MeV, which was used to claim a deeply attractive kaon nucleus optical potential. Our model describes the nuclear reaction in the framework of a local density approach and the calculations are performed following two different procedures: one is based on a many-body method using the Lindhard function and the other one is based on a Monte Carlo simulation. While both procedures coincide when it comes to consider the contribution of kaon quasi-elastic scattering, the simulation method offers more flexibility since it allows us to account for other processes which also contribute to the proton spectra, such as K- absorption by one and two nucleons producing hyperons. The simulation also considers final state interactions in terms of multiple scattering of the K-, p and all other primary and secondary particles on their way out of the nucleus, as well as the weak decay of the produced hyperons into (pi N). We find that this kaon in-flight reaction is not well suited to determine the kaon optical potential due, essentially, to the limited sensitivity of the cross section to its strength, but also to unavoidable uncertainties in the contribution from other processes. We also simulate the experimental requirement of having, together with the energetic proton, at least one charged particle detected in the decay counter surrounding the target, and find that the shape of the original cross section is appreciably distorted. We conclude that the new mechanisms, not considered in the analysis of the original experiment, allow us to explain the observed spectrum with the shallow kaon nucleus optical potential obtained in chiral models.

MICROSCOPIC NUCLEON–NUCLEUS OPTICAL POTENTIAL WITH REARRANGEMENT EFFECTS BASED ON THE EFFECTIVE SKYRME FORCES

The nucleon scattering on even–even nuclei in the medium-energy region has been analyzed on the basis of microscopic optical potential (OP) obtained from nuclear-matter calculations with using effective density-dependent nucleon–nucleon interaction of Skyrme type with taking account of the rearrangement potential. Calculations have been performed for volume integrals and rms radii of nucleon–nucleus OP, for energy dependencies of total and total reaction cross sections of neutron– and proton–nucleus scattering and for differential cross sections of the elastic neutron scattering at several energies on various target nuclei. Comparison of the calculation results for the mentioned quantities with corresponding experimental data has been carried out, which has shown a principal possibility of their reasonable description in the framework of the model under consideration.

Predicted weakening of the spin-orbit interaction with the addition of neutrons

The fully microscopic $p$-nucleus optical potential has been calculated in the framework of the first order Brueckner theory employing Urbana V14, soft-core internucleon interaction along with the relativistic mean field densities both for protons and neutrons. It is observed that the volume integral per nucleon, of the real part of the spin-orbit interaction calculated for Zr ($A=76\text{\ensuremath{-}}110$) and Sn ($A=96\text{\ensuremath{-}}136$) isotopes, decreases with the increase in neutron number. The present optical model calculation satisfactorily reproduces the experimental (where available) cross sections and analyzing power. Further the magnitude of the first maximum (minimum) in the calculated analyzing power decreases (increases) with the addition of neutrons both for Zr and Sn isotopes reflecting the weakening of the spin-orbit interaction.

AstrophysicalSfactor forαcapture onSn117

The cross sections of the $^{117}\mathrm{Sn}$($\ensuremath{\alpha},\ensuremath{\gamma}$) $^{121}\mathrm{Te}$ and $^{117}\mathrm{Sn}$($\ensuremath{\alpha},p$) $^{120}\mathrm{Sb}$ reactions have been measured in the effective center of mass energy from 11.5 to 14.6 MeV. Highly enriched self-supporting $^{117}\mathrm{Sn}$ (90%) foils were bombarded with an $\ensuremath{\alpha}$ beam delivered by the Bucharest IFIN-HH tandem accelerator. The induced activity of $^{121}\mathrm{Te}$ and $^{120}\mathrm{Sb}$ was measured with two large-volume high-purity Ge detectors in close geometry to maximize the detector efficiency. The experimental cross section and astrophysical $S$ factor are compared with statistical model predictions for different global $\ensuremath{\alpha}$-nucleus optical potentials.

Microscopic optical potential of nucleus–nucleus elastic scattering

Microscopic optical potential of nucleus–nucleus interaction is presented by a folding method with the isospin-dependent complex nucleon–nucleus optical potential, which is calculated in the framework of the Dirac–Bruecker–Hartree–Fock approach. A local density and improved local density approximations are adopted to make the potentials in nuclear matter relevant to finite nuclei. The 4He scattering off 12C at various energies E< 200 MeV are studied first. Then the elastic scattering data of 6He at 229.8 MeV on 12C target are analyzed within the standard optical model. To take account of the breakup effect of 6He in the reaction a phenomenological, large enhancing factor on the imaginary potential is introduced by hand. The calculated 6He+12C elastic scattering differential cross section is in reasonable agreement with the experimental data. Meanwhile comparisons with results in the double-folded model based on M3Y nucleon–nucleon effective interaction and the few body Glauber-model calculations are discussed. Our model should be of value in the description of the nucleus–nucleus scattering, especially unstable nucleus–nucleus systems.

Unbound excited states in 19,17C

The neutron-rich carbon isotopes 19,17C have been investigated via proton inelastic scattering on a liquid hydrogen target at 70 MeV/nucleon. The invariant mass method in inverse kinematics was employed to reconstruct the energy spectrum, in which fast neutrons and charged fragments were detected in coincidence using a neutron hodoscope and a dipole magnet system. A peak has been observed with an excitation energy of 1.46(10) MeV in 19C, while three peaks with energies of 2.20(3), 3.05(3), and 6.13(9) MeV have been observed in 17C. Deduced cross sections are compared with microscopic DWBA calculations based on p-sd shell model wave functions and modern nucleon–nucleus optical potentials. Jπ assignments are made for the four observed states as well as the ground states of both nuclei.

Momentum dependence ofK−-nuclear potentials

The momentum dependent K--nucleus optical potentials are obtained based on the relativistic mean-field theory. By considering the quarks coordinates of K- meson, we introduced a momentum-dependent factor to modify the coupling vertexes. The parameters in the form factors are determined by fitting the experimental K--nucleus scattering data. It is found that the real part of the optical potentials decrease with increasing K- momenta, however the imaginary potentials increase at first with increasing momenta up to P-k=450 similar to 550 MeV and then decrease. By comparing the calculated K- mean free paths with those from K(-)n/K(-)p scattering data, we suggested that the real potential depth is V-0 similar to 80 MeV, and the imaginary potential parameter is W-0 similar to 65 MeV.

Radial sensitivity of kaonic atoms and strongly boundK¯states

The strength of the low-energy ${K}^{\ensuremath{-}}$-nucleus real potential has recently received renewed attention in view of experimental evidence for the possible existence of strongly bound ${K}^{\ensuremath{-}}$ states. Previous fits to kaonic atom data led to either ``shallow'' or ``deep'' potentials, where only the former are in agreement with chiral approaches but only the latter can produce strongly bound states. Here we explore the uncertainties of the ${K}^{\ensuremath{-}}$-nucleus optical potentials, obtained from fits to kaonic atom data, using the functional derivatives of the best-fit ${\ensuremath{\chi}}^{2}$ values with respect to the potential. We find that only the deep type of potential provides information that is applicable to the ${K}^{\ensuremath{-}}$ interaction in the nuclear interior.

Folding model analysis of proton scattering from [formula omitted] nuclei

The elastic and inelastic proton scattering on O 18 , 20 , 22 nuclei are studied in a folding model formalism of nucleon–nucleus optical potential and inelastic form factor. The DDM3Y effective interaction is used and the ground state densities are obtained in continuum Skyrme-HFB approach. A semi-microscopic approach of collective form factors is done to extract the deformation parameters from inelastic scattering analysis while the microscopic approach uses the continuum QRPA form factors. Implications of the values of the deformation parameters, neutron and proton transition moments for the nuclei are discussed. The p-analyzing powers on O 18 , 20 , 22 nuclei are also predicted in the same framework.

NUCLEON–NUCLEUS OPTICAL POTENTIAL FROM HARD- AND SOFT-CORE INTERNUCLEON POTENTIALS

We have compared the binding energy of nuclear matter and the nucleon–nucleus optical potential, calculated in Brueckner theory starting from both the soft-core Urbana V-14 and the hard-core Hamada–Johnston internucleon potentials. Our results show that the real central part of the optical potential calculated from V-14 is about 10 MeV deeper than from the hard-core potential in the energy region 1–200 MeV. This greater depth mainly comes from the internucleon S- and D-states. In these states, the V-14 and Hamada–Johnston potentials give different phase shifts, the V-14 being in better agreement with experimental data. This difference is further enhanced by the Pauli principle in the calculation of the optical potential. Our analysis of proton–40 Ca differential cross-section and polarization data, in the energy region 30–200 MeV, shows that the optical potential calculated using V-14 is in better agreement with the data as compared with the Hamada–Johnston potential.

Production of [formula omitted] hypernuclei with the [formula omitted] reaction

We present results on the production of bound states of Θ+ in nuclei using the (K+,π+) reaction. By taking into account the states obtained within a wide range of strength of the Θ+ nucleus optical potential, plus the possibility to replace different nucleons of the nucleus, we obtain an excitation spectra with clearly differentiated peaks. The magnitude of the calculated cross sections is well within reachable range.

The π-nucleus optical potential to O( p5) in Chiral Perturbation Theory

We describe the calculation of the π -nucleus optical potential to NLO in Chiral Perturbation Theory (ChPT) within a new formulation of the effective theory in the presence of a nuclear background, characterized by a static, non-uniform distribution of the baryon number, describing the finite nucleus. This formulation reduces to the conventional Inmedium ChPT in the case of a uniform distribution. In this way we are able to identify unambiguously the nuclear finite size effects and disentangle the S -, P - and D -wave contributions to the optical potential without invoking the local density approximation.

Is the Σ–nucleus potential for [formula omitted] atoms consistent with the [formula omitted] data?

In order to examine whether the Σ–nucleus potential for Σ − atoms can explain the experimental ( π − , K + ) data or not, we evaluate Σ − hypernuclear production by the ( π − , K + ) reaction on a 28Si target, in the framework of a distorted-wave impulse approximation with an optimal Fermi-averaging for the elementary π − + p → K + + Σ − t-matrix. Inclusive K + spectra of the Si 28 ( π − , K + ) reaction are calculated with several Σ–nucleus (optical) potentials for Σ − – Al 27 which are determined by fits to the Σ − atomic X-ray data, and the properties of these potentials are tested in detail by comparing the calculated spectra with the ( π − , K + ) experimental data at KEK. The results show that the potentials having a repulsion inside the nuclear surface and an attraction outside the nucleus with a sizable absorption, can reproduce the Si 28 ( π − , K + ) data very well; the optimal Fermi-averaging for the π − + p → K + + Σ − reaction also gives a good description of the energy-dependence in the Σ − quasi-free spectrum. This is the first successful attempt to explain simultaneously the Σ − atomic X-ray data and the ( π − , K + ) reaction.

Different Methods for Pion-nucleus Optical Potential

Elastic and inelastic cross-sections for pion scat tering on 12 C at pion kinetic energy ranging from 50 to 260 MeV are computed using three independent methods of π ± -nucleus optical potential, the 3 α-particle model of the nucleus, the equivalent loca l Kisslinger potential and the Laplacian one. Reasonable fits to the measured values are obtained for 12 C without adjusting free parameters. The ability of these methods to account for elastic, in elastic, total and reaction cross-section data are somewhat similar. The Kisslinger-based local potent ial is the more suitable for describing the elastic and inelastic cross-sections of π ± -nucleus scattering . It seems that the 3 α -particle model of 12 C is not useful in the description of pion scattering on 12 C at least in the ∆-resonance region.

Chiral perturbation theory in a nuclear background

We propose a novel way to formulate chiral perturbation theory (ChPT) in a nuclear background, characterized by a static, non-uniform distribution of the baryon number that describes the finite nucleus. In the limiting case of a uniform distribution, the theory reduces to the well-known zero-temperature in-medium ChPT. The proposed approach is used to calculate the self-energy of the charged pion in the background of the heavy nucleus at O( p 5) in the chiral expansion, and to derive the leading terms of the pion–nucleus optical potential.

Low energyK + scattering onN =Z nuclei

The data for the total cross-section ofK + scattering on various nuclei have been analysed in the Glauber multiple scattering theory. Energy-dependentK + -nucleus optical potential is generated using the forwardK + -nucleon scattering amplitude and the nuclear density distribution. Along with this, the calculated totalK + -nucleus cross-sections using the effectiveK + -nucleon crosssection inside the nucleus are also presented.