Spin Rotation Functions Research Articles

Elastic scattering based on energy-dependent relativistic Love-Franey model at energies between 20 and 800 MeV* *Supported by the National Natural Science Foundation of China (12175072, 11722546, 12147106)

In order to investigate the elastic scattering, we fit scattering observables of the weighted fits (WF16) with the relativistic Love-Franey (RLF) model. The masses, cutoff parameters, and initial coupling strengths of RLF are assumed to be independent of energy. Because the energy boundary between low energy and high energy is around 200 MeV, the masses, cutoff parameters, and initial coupling strengths of RLF are obtained by fitting scattering observables of WF16 at an incident energy of 200 MeV. With the masses, cutoff parameters, and initial coupling strengths as the input, the energy-dependent RLF model is constructed over the laboratory energy range of 20 to 800 MeV within a unified fit. To examine the validity of this fit, we investigate p+ elastic scattering for various energies. Although the scattering observables of pp and pn of 200 MeV best fit the values of WF16, the RLF model of 200 MeV without the Pauli blocking (PB) corrections fails to describe the experimental differential cross sections, analyzing powers, and spinrotation functions. When the PB corrections are taken into account for various energies, the RLF model can well describe the experimental data of p+ elastic scattering.

SIDES: Nucleon–nucleus elastic scattering code for nonlocal potential

We introduce the package SIDES (Schrödinger Integro-Differential Equation Solver) that solves the integro-differential Schrödinger equation for elastic scattering of a nonlocal optical potential in coordinate space. The code is capable of treating the Coulomb interaction without restrictions. The method is based on previous developments by Jacques Raynal in the DWBA07 code. Elastic scattering observables such as differential and integral cross sections, as well as analyzing power and spin rotation functions for both neutron and proton projectiles are evaluated, with no restriction on the type of nonlocality of the potential nor on the beam energy. The corresponding distorted wavefunctions are calculated as well. The SIDES package includes a Perey–Buck potential generator with two parametrizations. It includes as well local potential parametrizations and allows for mixing local and nonlocal contributions. Benchmarks are performed and discussed. Program summaryProgram Title: SIDESProgram Files doi:http://dx.doi.org/10.17632/cmpjgyrngr.1Licensing provisions: GNU General Public License, Version 2Programming language: FORTRAN-90Nature of problem: The description of nucleon elastic scattering off a target nucleus involves solving the Schrödinger’s wave equation for positive incident energy. The determination of scattering observables calls for accurate treatments of the continuum. The effective coupling between the projectile and the target is accounted for by an optical potential, an operator which is by nature complex, energy-dependent and nonlocal. The coupling becomes long-range in the case of charged projectiles. In a general scenario under nonlocal potentials, Schrödinger’s equation becomes an integro-differential equation.Solution method: SIDES solves the Schrödinger integro-differential equation numerically by matrix inversion using Gibbs, Numerov or a modified Numerov method with a uniform radial mesh in a box. The solution is refined by an iterative procedure until a specified precision is achieved. To obtain elastic scattering observables, the associated phase-shifts are calculated via matching of the numerical solution with its analytic asymptotic behavior.

The proton microscopic optical potential based on Skyrme interaction

The proton microscopic optical potential (MOP) based on Skyrme interaction has been achieved by the Green function method in the nuclear matter, and given by the local density approximation (LDA) for finite nuclei. The reaction cross-sections, elastic scattering angular distributions, analyzing powers, and spin-rotation functions are predicted by the obtained proton MOP with Skyrme interaction SkC in the mass range of target nuclei 24[Formula: see text][Formula: see text][Formula: see text]A[Formula: see text][Formula: see text][Formula: see text]209 with incident proton energy below 100[Formula: see text]MeV. These observables are further predicted for some light nuclei and actinide nuclei below 100[Formula: see text]MeV. The prediction is compared with existing experimental data. It is revealed that the obtained proton MOP based on Skyrme interaction SkC can satisfactorily describe the proton–nucleus elastic scattering.

Microscopic optical potential with two and three body forces for nucleon–nucleus scattering

The proton - nucleus optical potentials generated by folding the calculated complex, density and energy dependent g- matrices (with and without three-body forces (TBF): Urbana IX (UVIX) and TNI) over the target nucleon density distributions obtained from the relativistic mean field theory, are used for the calculation of the differential cross section dσ / dθ , polarization Ay , spin rotation function (Q). for 65 and 200 MeV polarized proton incident on 40 Ca and 208 Pb . The agreement with the experiment is rather impressive. It is found that the inclusion of TBF (Urbana IX )UVIX) and TNI) reduces the strength of the central part of the optical potential in the nuclear interior and affects the calculated spin-orbit potential only marginally and leads to an improvement in the agreement with the corresponding experimental results.

A theoretical study of halo structure using elastic proton-nucleus scattering

Elastic proton scattering from Be, C, and O isotopes has been investigated in the relativistic impulse approximation (RIA). In the calculations, the nucleon-nucleus optical potentials are obtained using ground state nuclear matter densities, which are computed using the relativistic mean field model with the FSU parameter set. The scattering observables, including differential cross section, analyzing power, and spin-rotation function, are analyzed. It is found that the scattering observables for O isotopic chains display a clear mass dependence, for instance, the minimum analyzing power shifts to a low scattering angle with increasing mass number. While for the Be isotopic chain, the emergence of a neutron halo in 14Be breaks this trend, i.e., the minimum analyzing powers for 12Be and 14Be are almost the same as each other.

Microscopic optical potentials for nucleon–nucleus scattering at 65 MeV

Microscopic optical potentials for nucleon–nucleus scattering obtained from folding the calculated G-matrices with RMF densities of the target have been used to analyze the 65 MeV proton and neutron–nucleus scattering data over a wide mass region. The soft-core Argonne AV14, AV18 and the old hard-core Hamada–Johnston inter-nucleon potentials have been used to calculate the G-matrices in the Brueckner–Hartree–Fock approach. The calculated potentials have been used to analyze the differential elastic cross-section, analyzing power and spin-rotation function for neutron and proton scattering at 65 MeV from 12C to 208Pb. Our results are in satisfactory agreement with the experimental data. Comparison of our results with phenomenological optical model analyses is also presented. Mass number dependence of the mean square radii of real central optical potential 〈r2〉 pot. for the microscopic potentials used here is found to be in close agreement with each other as well as with empirical results. We also present our results for proton reaction cross-section from 12C to 90Zr in the energy region 20–200 MeV.

Interaction of intermediate-energy protons with 20Ne and 24Mg nuclei within the multiple-scattering model

Observables of the elastic and inelastic scattering of 800- and 250-MeV protons on 20Ne and 24Mg nuclei were calculated on the basis of the theory of multiple diffractive scattering and the dispersive α-cluster model. The 20Ne and 24Mg nuclei were assumed to consist of a core (16O nucleus) and additional alpha-particle clusters, which could be situated with the highest probability both in the vicinity of the center of mass of the core and outside the core. The multiparticle densities of these nuclei and single-particle nucleon-distribution densities as obtained from the dispersive α-cluster model were used in the calculations. The differential cross sections and polarizations for elastic and inelastic p 20Ne and p 24Mg scattering at the energy of 800 MeV are in better agreement with experimental data than the analogous calculations at the energy of 250 MeV. The spin-rotation functions calculated in the singleparticle approximation for elastic p 20Ne and p 24Mg scattering at these two energy values differ qualitatively from their counterparts calculated on the basis of the dispersive α-cluster model.

Validity of the relativistic impulse approximation for elastic proton-nucleus scattering at energies lower than 200 MeV

We present the first study to examine the validity of the relativistic impulse approximation (RIA) for describing elastic proton-nucleus scattering at incident laboratory kinetic energies lower than 200 MeV. For simplicity we choose a (208)Pb target, which is a spin-saturated spherical nucleus for which reliable nuclear structure models exist. Microscopic scalar and vector optical potentials are generated by folding invariant scalar and vector scattering nucleon-nucleon (NN) amplitudes, based on our recently developed relativistic meson-exchange model, with Lorentz scalar and vector densities resulting from the accurately calibrated PK1 relativistic mean field model of nuclear structure. It is seen that phenomenological Pauli blocking (PB) effects and density-dependent corrections to sigma N and omega N meson-nucleon coupling constants modify the RIA microscopic scalar and vector optical potentials so as to provide a consistent and quantitative description of all elastic scattering observables, namely, total reaction cross sections, differential cross sections, analyzing powers and spin rotation functions. In particular, the effect of PB becomes more significant at energies lower than 200 MeV, whereas phenomenological density-dependent corrections to the NN interaction also play an increasingly important role at energies lower than 100 MeV.

Microscopic optical model potentials forp-nucleus scattering at intermediate energies

A comparative study of the microscopic optical potentials viz., semimicroscopic with extended Jeukenne-Lejeune-Mahaux interaction and microscopic Brueckner theory using Hamada-Johnston as well as Urbana V14 soft-core internucleon interactions, has been carried out. These microscopic optical potentials are compared with that of Dirac phenomenology (DP) for the polarized proton-$^{40}\mathrm{Ca}$ elastic scattering at 35 MeV and 200 MeV. These potentials have different shapes for 200 MeV below 4 fm. In particular, for the real part of the central potential, only the Dirac phenomenology and the microscopic optical potential calculated with the Hamada-Johnston interaction exhibit the well known wine-bottle-bottom shape. It is found that the calculated observables (cross section, analyzing power and spin rotation function) using these potentials having different shapes, compare well with the experiment.

Effects of Distorted Wave on Proton Elastic Scattering fromLight Nuclei at 200 MeV

The distorted wave is introduced into the relativistic impulseapproximation to generate the Dirac optical potentials for protonelastic scattering. Those potentials, produced by folding the targetground state wavefunction with the free nucleon-nucleon interactions,are used to reevaluate scattering observables, such as differentialcross section, analysing power and spin rotation function, for protonelastic scattering from 12C and 16O at Elab = 200 MeV, respectively. The inclusion of the distorted wave in theoriginal relativistic impulse approximation has brought out betterresults of the observables, especially at small scattering angles.

PROTON–4He ELASTIC SCATTERING AT ~ 1 GeV

Based on the (spin-independent) Sugar–Blanckenbecler eikonal expansion for the T-matrix, we parametrize the (spin-dependent) NN amplitude (SNN) which successfully describes the pp and pn elastic scattering observables at ~ 1 GeV up to the available momentum transfers. Using SNN, we calculate the differential cross-section, polarization, and spin-rotation function of ~ 1 GeV protons on 4 He within the framework of the Glauber model. The analysis also includes the phase variation in the NN amplitude. It is found that the use of SNN, in comparision with the usually parametrized one-term amplitude, improves the agreement with the experimental data. The introduction of a global phase variation provides only a slight improvement over the results with a constant phase. However, if we allow different phases in the central- and spin-dependent parts of the NN amplitude, the agreement with the polarization data improves further without affecting the differential cross-section results.

Elastic and inelastic scattering of 800-MeV protons on 16O and 20Ne nuclei

Differential cross sections and polarization observables for the elastic and inelastic scattering of 800-MeV protons on 16O and 20Ne nuclei are calculated on the basis of the theory of multiple diffractive scattering and the α-cluster model involving dispersion. The single-particle nucleon-density distributions obtained within the α-cluster model involving dispersion are used in the calculations. The differential cross sections and polarization calculated for elastic and inelastic p16O and p20Ne scattering are compatible with available experimental data. The spin-rotation functions calculated for elastic p16O and p20Ne scattering within the independent-nucleon model differ qualitatively from their counterparts calculated within the α-cluster model involving dispersion.

Relevance of pseudospin symmetry in proton-nucleus scattering

The manifestation of pseudospin symmetry in proton-nucleus scattering is discussed. Constraints on the pseudospin-symmetry violating scattering amplitude are given, which require as input cross section and polarization data, but no measurements of the spin-rotation function. Application of these constraints to $p\text{\ensuremath{-}}^{58}\mathrm{Ni}$ and $p\text{\ensuremath{-}}^{208}\mathrm{Pb}$ scattering data in the laboratory energy range of $200\phantom{\rule{0.3em}{0ex}}\text{MeV}--800\phantom{\rule{0.3em}{0ex}}\text{MeV}$ reveals a significant violation of the symmetry at lower energies and a weak one at higher energies. Using a schematic model within the Dirac phenomenology, the role of the Coulomb potential in proton-nucleus scattering with regard to pseudospin symmetry is studied. Our results indicate that the existence of pseudospin symmetry in proton-nucleus scattering is questionable in the whole energy region considered and that the violation of this symmetry stems from the long range nature of the Coulomb interaction.

Semimicroscopic nucleon-nucleus spherical optical model for nuclei withA>~40at energies up to 200 MeV

A nucleon-nucleus optical model potential (OMP) is built from the nuclear matter (NM) approach of Jeukenne, Lejeune, and Mahaux (JLM). The imaginary component of the on-shell NM mass operator, originally parametrized by these authors as a function of matter density and energy, is given a new representation suitable for energies from 1 to 200 MeV. The JLM model extended in this manner is then applied through an improved local density approximation (LDA) to treat nucleon scattering from closed- and near closed-shell nuclei with masses $40<~A<~209$. For proton, neutron, and charge radial densities, we use those obtained from Hartree-Fock-Bogoliubov calculations based on the finite range, density dependent Gogny force. Several LDA and spin-orbit potential prescriptions are tested to select those which provide the best overall description of elastic scattering and reaction measurements. Over three hundred datasets including differential cross sections, analyzing powers, spin rotation functions, and reaction cross sections are considered in the present analyses. The OMP components include normalization factors which are optimized for each incident energy, probe, and for most target nuclei. We give close forms which represent the energy variation of these factors for the $n+X$ and $p+X$ systems. The global OMPs built in this manner produce a good overall description of the neutron and proton scattering and reaction measurements available up to 200 MeV.

Isotope and temperature effects on nuclear magnetic shieldings and spin-rotation constants calculated at the coupled-cluster level

The temperature dependence of nuclear shieldings as well as isotope effects on shieldings and spin-rotation constants have been computationally investigated for H2, HF, F2, CO, and N2 employing the coupled-cluster singles and doubles (CCSD) method augmented by a perturbative treatment of triple excitations (CCSD(T)) for the calculation of potential curves, shieldings and spin–rotation functions together with finite-element techniques for the solution of the rovibrational problem. Calculated and measured temperature dependence of the isotropic shieldings agrees for N2, while for CO and F2 the computed temperature dependence is smaller than the experimental result. Isotropic shieldings have been deduced on the basis of our calculations from the measured spin-rotation constants for four isotopomers of H2 and agree, as required by theory. However, calculated and measured temperature dependence of the isotope shifts between HD and D2 differ by up to 10% which is larger than the estimated error bars for the exp...

Isotope and temperature effects on nuclear magnetic shieldings and spin-rotation constants calculated at the coupled-cluster level

The temperature dependence of nuclear shieldings as well as isotope effects on shieldings and spin-rotation constants have been computationally investigated for H2, HF, F2, CO, and N2 employing the coupled-cluster singles and doubles (CCSD) method augmented by a perturbative treatment of triple excitations (CCSD(T)) for the calculation of potential curves, shieldings and spin–rotation functions together with finite-element techniques for the solution of the rovibrational problem. Calculated and measured temperature dependence of the isotropic shieldings agrees for N2, while for CO and F2 the computed temperature dependence is smaller than the experimental result. Isotropic shieldings have been deduced on the basis of our calculations from the measured spin-rotation constants for four isotopomers of H2 and agree, as required by theory. However, calculated and measured temperature dependence of the isotope shifts between HD and D2 differ by up to 10% which is larger than the estimated error bars for the experimental values. For HF and CO, calculated and measured isotope shifts agree, while for N2 no experimental data for comparison are available. In case of spin–rotation constants, the calculated dependence on the rotational angular momentum quantum number are for both H2 and F2 in good agreement with the dependence deduced from measurements, while for HF not enough experimental data are available for a comparison.

Dirac phenomenology for p-40Ca at intermediate energies

We have analysed p-40Ca differential elastic scattering, analysing power and spin-rotation function data at 200 and 500 MeV using Dirac optional potential and various prescriptions for nucleon density in the target. Our results show that the predictions of the spin-rotation function are in good agreement with data only at 500 MeV with all target densities used here. However, at 200 MeV the spin-rotation function data seems to be more sensitive to minor differences in the target densities. Our results show that the spin observables are better reproduced by the wine-bottle-bottom shape of the real Schrodinger equivalent potential. We have found that the shape of the real potential has an important effect on the prediction of spin observables especially in the transition region.

Proton-nucleus scattering based on the relativistic Brueckner-Hartree-Fock model.

Nucleon-nucleus scattering is studied with optical potentials derived from solutions of the relativistic Brueckner-Bethe-Goldstone (RBBG) equation using the Bonn interaction. The complex effective mass is determined phenomenologically by a fit to 200 MeV proton-nucleus scattering data. Calculations with this effective mass are made and compared with elastic scattering data for p${\mathrm{\ensuremath{-}}}^{16}$O, $^{40}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, $^{208}\mathrm{Pb}$ in the energy range from 160 to 500 MeV. Predictions for the differential scattering cross section, analyzing power, and spin rotation functions are compared with elastic proton-nucleus scattering data over a wide range of projectile energies and target mass number.

Phase variation in the NN amplitude and proton-nucleus scattering at 800 MeV

The differential cross section, analysing power and spin rotation function of proton elastic scattering from 16O and 40Ca are calculated within the Glauber diffractive model. The effects of the NN phase are discussed in detail. It is found the introduction of a global phase greatly improved the calculations with the NN amplitude obtained through phaseshift analysis.

Application of multiple scattering theory to lower-energy elastic nucleon-nucleus scattering.

The optical model potentials for nucleon-nucleus elastic scattering at 65 meV are calculated for $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{28}\mathrm{Si}$, $^{40}\mathrm{Ca}$, $^{56}\mathrm{Fe}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$ in first-order multiple scattering theory, following the prescription of the spectator expansion, where the only inputs are the free nucleon-nucleon (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 energy and compared with available experimental data. The theoretical curves are in very good agreement with the data. The modification of the propagator due to the coupling of the struck nucleon to the residual nucleus is seen to be significant at this energy and invariably improves the congruence of theoretical prediction and measurement.