Microscopic Optical Potential Research Articles

The folding deuteron optical model potentials

For 52 target nuclei with deuteron as projectile, we calculate the reaction cross sections and elastic scattering angular distributions, as well as the $\chi^2$ values for 11 kinds of deuteron optical model potentials: our global deuteron optical potentials and 10 folding optical potentials calculated with 2 phenomenological global nucleon optical potentials given by Koning \textit{et al}(KD) and by Varner\textit{et al}(CH89), and 8 microscopic nucleon optical potentials with the generalized Skyrme force parameters(GS1-6) and modified Skyrme force parameters(SKa, SKb). We find that for constructing the folding deuteron optical potential, both SKa and SKb are the best Skyrme force parameters of the microscopic nucleon optical potential proposed by Q. Shen \textit{et al}.

Microscopic optical potential forα-nucleus elastic scattering in a Dirac-Brueckner-Hartree-Fock approach

The microscopic optical model potential (OMP) of $\ensuremath{\alpha}$-nucleus elastic scattering based on a double-folding model (DFM) is studied. The nucleon OMPs in nuclear matter as well as the nucleon-nucleon ($\mathit{NN}$) effective interaction are calculated in the framework of the Dirac-Brueckner-Hartree-Fock (DBHF) approach, in which the density and energy dependence is parametrized by polynomial expansions. The microscopic OMP of nucleus-nucleus scattering is obtained by doubly folding the complex $\mathit{NN}$ effective interaction with respect to the densities of both projectile and target nuclei. An improved local-density approximation is adopted to take account of the finite-range correction. Renormalization factors on the real and imaginary OMP are introduced to obtain the best fit to the experimental data. A systematic analysis of $^{4}\mathrm{He}$ elastic scattering off $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{28}\mathrm{Si}$, and $^{40}\mathrm{Ca}$ is performed. The calculated cross sections over a wide range of incident energies and scattering angles are in good agreement with the experimental data, which confirms the applicability of this model. Moreover, for the same projectile and target, the renormalization factors are found to be almost constant at various incident energies.

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.

Calculation of the 6He + p elastic scattering cross sections within the folding approach and the high-energy approximation for the optical potential

Data on cross sections for the 6He + p elastic scattering at energies of tens of MeV/nucleon are analyzed by calculating the microscopic optical potential (OP) (its real and imaginary parts). The effect produced on the cross section by the dependence of the nucleon-nucleon potential on the nuclear matter density, the role of the spin-orbit interaction, and the role of nonlinearity and renormalization of the microscopic OP are studied. A comparison with the experimental data allows sensitivity of cross sections to these effects to be tested.

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.

核子-核子散乱から核子-核散乱へ : 光学模型と媒質効果

核子-核子散乱から核子-核散乱へ : 光学模型と媒質効果

Inelastic scattering of heavy ions at intermediate energies with excitations of nuclear collective states

Excitation of low-lying nuclear collective states upon scattering of heavy ions with energies of several tens of MeV/nucleon has been studied. The interaction potential leading to excitation is chosen in the form of a derivative of the microscopic (or semimicroscopic) nucleus-nucleus double-folding optical potential. Elastic and inelastic scattering cross sections have been calculated within the high-energy approximation; the inelastic scattering amplitude was obtained in the first order in the deformation parameter. The cross sections are compared with the experimental data on scattering of 17O from a series of nuclei with excitation of the 2+ level.

Microscopic optical potentials in 6Li scattering by nuclei

A parameter-independent microscopic optical potential of nucleus-nucleus interaction is presented by a folding model with the isospin dependent complex nucleon-nuclear potential, which is calculated in the framework of the Dirac-Bruecker-Hartree-Fock approach. Investigations on 6Li scattering by 12C, 28Si, 40Ca, 58Ni, 90Zr, and 208Pb over a wide range of incident energy and scattering angle with the microscopic nucleus-nucleus optical potential is presented. To take account of the breakup effect of 6Li and the high order dynamic effect in the reaction a modification factor NR in the real part and an enhancing factor NI in the imaginary part of the microscopic optical potential are introduced. We take the imaginary part enhancing factor NI=3.0, which has been obtained in the previous study on 6He scattering by 12C. The modification factor NR is found to be almost constant with respect to the incident energy and target mass number. The calculations with NR≈0.5—0.6 and NI=3.0 well reproduce the experimental elastic scattering data for all targets and incident energies investigated. Our parameter-independent model should be of value in the description of the nucleus-nucleus scattering of many-body systems, especially unstable nucleus-nucleus systems.

Virtual coupling potential for elastic scattering of 10,11Be on proton and carbon targets

The 10,11Be(p, p) and (12C, 12C) reactions were analyzed to determine the influence of the weak binding energies of exotic nuclei on their interaction potential. The elastic cross sections were measured at GANIL in inverse kinematics using radioactive 10,11Be beams produced at energies of 39.1A and 38.4A MeV. The elastic proton scattering data were analyzed within the framework of the microscopic Jeukenne–Lejeune–Mahaux (JLM) nucleon–nucleus potential. The angular distributions are found to be best reproduced by reducing the real part of the microscopic optical potential, as a consequence of the coupling to the continuum. These effects modify deeply the elastic potential. Including the Virtual Coupling Potential (VCP), we show the ability of the general optical potentials to reproduce the data for scattering of unstable nuclei, using realistic densities. Finally, the concepts needed to develop a more general and microscopic approach of the VCP are discussed.

Calculations of 6He + p elastic-scattering cross-sections using folding approach and high-energy approximation for the optical potential

Calculations of microscopic optical potentials (OPs) (their real and imaginary parts) are performed to analyze the 6 He + p elastic-scattering data at a few tens of MeV/nucleon (MeV/N). The OPs and the cross-sections are calculated using three model densities of 6He . Effects of the regularization of the NN forces and their dependence on nuclear density are investigated. Also, the role of the spin-orbit terms and of the non-linearity in the calculations of the OPs, as well as effects of their renormalization are studied. The sensitivity of the cross-sections to the nuclear densities was tested and one of them that gives a better agreement with the data was chosen.

The isovector imaginary neutron potential: A key ingredient for the r-process nucleosynthesis

The isovector contribution to the imaginary component of the microscopic optical model potential is adjusted on experimental neutron strength function data. Within the Brückner–Hartree–Fock approximation of Jeukenne–Lejeune–Mahaux, it is shown that experimental data favours a strong isovector component that can have a drastic impact on the radiative neutron capture cross section for neutron-rich nuclei. If confirmed, this result strongly inhibits the resonant capture by exotic nuclei, so that the traditional r-process picture of the fast neutron captures during the nucleosynthesis r-process needs to be revisited in depth.

Nucleon–nucleus scattering as a test of shell structure of some light mass exotic nuclei

Shell model wave functions have been used to form microscopic g-folding optical potentials with which elastic scattering data from 8He, 10,11C, and 18,20,22O scattering on hydrogen have been analyzed. Those potentials, the effective two-nucleon interaction used in their formation, and the shell model details, then have been used in distorted wave approximation calculations of differential cross sections from inelastic scattering to the first excited states of five of those radioactive ions.

Charged current neutrino-induced coherent pion production

We analyze the neutrino induced charged current coherent pion production at the energies of interest for recent experiments like K2K and MiniBooNE. Medium effects in the production mechanism and the distortion of the pion wave function, obtained solving the Klein Gordon equation with a microscopic optical potential, are included in the calculation. We find a strong reduction of the cross section due to these effects and also substantial modifications of the energy distributions of the final lepton and pion.

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.

A study of the cross sections and the spin observables for proton-12C elastic scattering in momentum space in the intermediate energy region

The differential cross sections and the spin observables of p-12C elastic scattering in the whole intermediate energy region are calculated using the KMT multiple scattering theory with microscopic momentum space optical potential which incorporates the spin dependence of the NN and p-12C interactions. The theory takes into consideration the antisymmetrized NN amplitudes, nucleon recoil and binding energy shifts, Lorentz invariant angle transformations, t matrices with on-shell behavior from NN phase shifts,and off-shell behavior from a realistic separable potential model. Qualitative agreement is found in differential cross sections and polarization data for 200Ep&lt;1000 MeV.

Isospin-dependent optical potentials in Dirac-Brueckner-Hartree-Fock approach

The relativistic microscopic optical potential (RMOP) is studied within the framework of the Dirac-Brueckner-Hartree-Fock (DBHF) approach. A new decomposition of the Dirac structure of nuclear self-energy in the DBHF is extended to asymmetric nuclear matter calculations. A nucleon effective interaction is introduced to reproduce the results of the G matrix. The real part of nucleon self-energy in asymmetric nuclear matter is calculated with the G matrix in the Hartree-Fock approach, while the imaginary part is obtained from the polarization diagram. Nuclear optical potentials in finite nuclei are derived from the self-energies in asymmetric matter through a local-density approximation. The differential cross sections and the analyzing powers in p+Ca-40 and p+Pb-208 elastic scattering at E-p<= 200 MeV are studied with these RMOPs. A satisfactory agreement with the experimental data is found. This is achieved without readjusting phenomenologically the RMOP derived from the DBHF plus polarization diagram.

Correlations in microscopic optical model for nucleon elastic scattering off doubly closed-shell nuclei

The random phase approximation (RPA) long-range correlations are known to play a significant role in understanding the depletion of single particle-hole states observed in ($e,{e}^{'}$) and ($e,{e}^{'}p$) measurements. Here the RPA theory, implemented using the D1S force is considered for the specific purpose of building correlated ground states and related one-body density matrix elements. These may be implemented and tested in a fully microscopic optical model for NA scattering off doubly closed-shell nuclei. A method is presented to correct for the correlations overcounting inherent to the RPA formalism. One-body density matrix elements in the uncorrelated (i.e., Hartree-Fock) and correlated (i.e., RPA) ground states are then challenged in proton scattering studies based on the Melbourne microscopic optical model to highlight the role played by the RPA correlations. Agreement between the parameter free scattering predictions and measurements is good for incident proton energies ranging from 200 MeV down to approximately 60 MeV and becomes gradually worse in the lower energy range. Those features point unambiguously to the relevance of the g-matrix method to build microscopic optical model potentials at medium energies, and emphasize the need to include nucleon-phonon coupling, that is, a second-order component of the Feshbach type in the potential at lower energies. Illustrations are given for proton scattering observables measured up to 201 MeV for the $^{16}\mathrm{O}$, $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ target nuclei.

Analysis of nucleon-nucleus scattering in terms of a microscopic optical potential based on effective Skyrme forces

On the basis of a microscopic optical potential calculated by using effective Skyrme type forces with allowance for the rearrangement potential, nucleon scattering on even-even nuclei is analyzed in the region of intermediate energies. The volume integrals and root-mean-square radii of nucleon-nucleus optical potentials are calculated along with the energy dependences of the total reaction cross sections for neutron-and proton-nucleus interaction and of the differential cross sections for elastic neutron scattering at several energy values for various target nuclei. The results of these calculations are compared with experimental data, and it is shown that a resonable description of these data can in principle be obtained within the model being considered.

Excitation of nuclear collective states by heavy ions within the model of semimicroscopic optical potential

The (semi)microscopic double-folding nucleusAnucleus optical potentials are suggested for consid- eration of inelastic scattering with excitation of collective nuclear states by using the adiabatic approach and the elastic scattering amplitude in the high-energy approximation. The analytical expression for inelastic scattering amplitude is obtained keeping therst-order terms in the deformation parameter of a potential. Calculations of inelastic cross sections for the 17 O heavy ions scattered on different nuclei at about hundred MeV/nucleon are made, and the acceptable qualitative agreement with the experimental data is obtained without introducing free parameters. The prospect of the method for further applications is discussed. ²O · ¸¸³μE·¥´¨O ´¥E¶·E£μ£μ · ¸¸¥O´¨O ¸ ¢μ§iE|¤¥´¨¥³ ±μ²²¥±E¨¢´OI ¸μ¸EμO´¨° O¤¥· ¶·¥¤² - £ ¥E¸O ¨¸¶μ²O§μ¢ EO (¶μ²E)³¨±·μ¸±μ¶¨I¥¸±¨° O¤·μ-O¤¥·´O° μ¶E¨I¥¸±¨° ¶μE¥´I¨ ², ¤¨ i E¨I¥¸±¨° ¶μ¤Iμ¤ ¨ ³¶²¨EE¤E E¶·E£μ£μ · ¸¸¥O´¨O ¢ ¢O¸μ±μO´¥·£¥E¨I¥¸±μ³ ¶·¨i²¨|¥´¨¨. �μ²EI¥´μ ´ ²¨E¨- I¥¸±μ¥ ¢O· |¥´¨¥ ¤²O ³¶²¨EE¤O ´¥E¶·E£μ£μ · ¸¸¥O´¨O, £¤¥ E¤¥·|¨¢ OE¸O I²¥´O ¶¥·¢μ£μ ¶μ·O¤± ¢ · §²μ|¥´¨¨ ¶μE¥´I¨ ² ¶μ ¶ · ³¥E·E ¤¥Eμ·³ I¨¨. ‚O¶μ²´¥´O · ¸I¥EO ´¥E¶·E£¨I ¸¥I¥´¨° · ¸- ¸¥O´¨O EO|¥²OI ¨μ´μ¢ 17 O · §´O³¨ O¤· ³¨ ¶·¨ O´¥·£¨OI μ±μ²μ 100 ŒO‚/´E±²μ´, ¨ ¶μ²EI¥´μ E¤μ¢²¥E¢μ·¨E¥²O´μ¥ ¸μ£² ¸¨¥ ¸ O±¸¶¥·¨³¥´E ²O´O³¨ ¤ ´´O³¨ i¥§ ¢¢¥¤¥´¨O ¸¢μiμ¤´OI ¶ · ³¥E·μ¢. �i¸E|¤ OE¸O ¢μ§³μ|´μ¸E¨ ¶·¥¤²μ|¥´´μ£μ ¶μ¤Iμ¤ ¤²O ¤ ²O´¥°I¨I ¶·¨²μ|¥´¨°.

Nucleon-nucleus optical potential at finite temperatures within a semimicroscopic approach for the case of Skyrme forces

Within the nuclear-matter approximation, the local-density approximation, and perturbation theory, an approach to constructing a microscopic nucleon-nucleus optical potential at finite nuclear temperatures is developed on the basis of effective density-dependent nucleon-nucleon forces. The real and the imaginary part of the neutron-nucleus optical potential and the mean free paths of neutrons in nuclear matter are calculated at various neutron energies and various nuclear temperatures. The effect of the inclusion of the rearrangement potential on the quantities under consideration is studied, and its importance is demonstrated.