Double-folding Potential Research Articles

Elastic scattering of 318 MeV 6Li from 12C and 28Si: Unique phenomenological and folding-model potentials.

The cross sections for elastic scattering of 318 MeV [sup 6]Li from [sup 12]C and [sup 28]Si were measured. The data extend well beyond the rainbow angle into the region where the far-side scattering dominates, and thus define unique [sup 6]Li phenomenological potentials. These complement earlier unique [sup 6]Li potentials derived at an energy of 210 MeV. Double-folded real potentials also were generated using effective nucleon-nucleon interactions. The M3Y and Franey-Love 50 MeV nucleon-nucleon interactions gave similar potentials. A Woods-Saxon form was used for the imaginary potential. The experimental cross-section data were reasonably well reproduced without renormalization of the folded potentials.

On Fusion Reactions Induced by 11Li via Soft Dipole Mode and Static Deformation

The numerical calculations for fusion reactions of a halo nucleus 11Li with deformed target nuclei at low energies have been carried out under the sudden limit for rotational excitation combined with a double folding potential of ion-ion interaction. The properties of fusion cross section involving the combined effects both from projectiles and target nuclei in such systems are investigated in detail.

Elastic scattering of alpha particles from 209Bi at 24.8, 28.5, 34.7, 38.8, and 69.5 MeV.

Differential cross sections for the elastic scattering of alpha particles from $^{209}\mathrm{Bi}$ have been measured over a wide angular range at a number of energies between 24 and 70 MeV. The present data along with existing data in this energy range have been analyzed using the optical model with both phenomenological and double-folded potentials. The application of the dispersion relation of Mahaux, Ng\^o, and Satchler allows a reproduction of the observed energy dependence of the real part of the potential. A nearside-farside decomposition of the data clearly reveals large-angle Fraunh\ofer oscillations. The inelastic cross sections at 69.5 MeV have also been measured and the deformation lengths obtained from a distorted-wave Born analysis are consistent with values reported in the literature.

Analysis of the quasielastic scattering of polarised 23Na from 90Zr

Angular distributions of the differential cross section for quasielastic scattering and the tensor analysing powers TT10, TT20, TT30, T20 and T21 for elastic and quasielastic scattering of polarised 23Na from 90Zr at ELab=110 MeV have been measured. The structure of the polarisation data indicates the usefulness of the isocentrifugal approximation which leads to relations between the second-rank tensor analysing powers (shape-effect relations). Details of deriving a double-folding potential are given. This enables one to describe the complete data set by fitting to the data in a coupled-channel calculation only one complex strength parameter. Coupling to the lowest two excited states of the projectile is shown to be essential.

Coupled-channel analysis of elastic and inelastic alpha scattering on 24Mg in the energy range 28-120 MeV.

The elastic and inelastic \ensuremath{\alpha} scattering to states of the ground state and \ensuremath{\gamma} band in $^{24}\mathrm{Mg}$ has been measured at 54 MeV. The data have been analyzed with the coupled-channel method based both on conventional Saxon-Woods type potentials and double-folding potentials. Coupled-channel calculations utilizing the results of this analysis give a good overall agreement with existing data in the energy range 28--120 MeV. The deduced isoscalar transition strengths compare very favorably with corresponding electromagnetic properties as well as with phenomenological interacting boson-model and microscopic shell-model calculations. The only serious discrepancy between isoscalar and electromagnetic properties, the ${2}_{2}^{+}$\ensuremath{\rightarrow}${2}_{1}^{+}$ transition strength, persists further on. The shell-model calculations have been carried out based upon the Wildenthal interaction. They account very well for both the energies and the dynamic properties of the ground state and \ensuremath{\gamma} band of $^{24}\mathrm{Mg}$.

Elastic and quasielastic scattering of 110-MeV polarized 23Na from 90Zr.

Angular distributions of the analyzing powers /sup T/T/sub k0/ (k = 1,2,3), T/sub 20/, and T/sub 21/ for elastic and quasielastic scattering of 110-MeV polarized /sup 23/Na from /sup 90/Zr and the cross section for quasielastic scattering have been measured. Vanishing odd-rank tensor analyzing powers and the validity of the shape-effect relations indicate the importance of the projectile deformation for the interaction potential. The data are well explained by coupled-channel calculations using realistic double-folding potentials and taking into account projectile deformation and excitation.

Projectile breakup effect in elastic scattering of 9Be

The projectile breakup effect on the elastic scattering of 9Be has been studied by coupled-channel calculations based on the microscopic cluster-model wave functions for 9Be. It is found that the effect is quite significant and essential to reproduce the elastic scattering at E lab = 158 MeV without introducing any renormalisation factor to the double-folding potential. The dynamical polarisation potential derived clearly shows the repulsive nature of the breakup effect.

Comparison of woods-saxon and double-folding potentials forα-particle scattering from54Fe at 24.5 MeV

Inelastic-scattering data are presented forα-particles of 24.5 MeV from54Fe over the range 15° to 175° in the centre-of-mass system. The real part of the optical potential is calculated microscopically using the M3Y effective interaction of Bertschet al. and the DDM3Y density-dependent interaction. Elastic scattering has been analysed by using as real part of the optical potential M3Y, DDM3Y and Woods-Saxon forms (WS), taking in all three cases as imaginary part a WS potential. To fit the data the double-folding potential needs to be normalized by a factor of ⋍1.6 for the M3Y interaction and of ⋍1.13 for the DDM3Y interaction. By the study of the invariant-point ambiguity it has been observed that there exists a zone near the strong-absorption radius in which the real potential is well defined. Inelastic scattering has been analysed by coupled-channel calculations. The transition form factors for WS and DDM3Y obtained in the framework of vibrational model have been compared.

Absolute magnitude of (p,α) and (α, p) cross sections-new results concerning a long-standing problem

Recent microscopic finite-range DWBA analyses of (p, alpha ) and ( alpha , p) reactions based on Saxon-Woods optical potentials underestimate the absolute values of the cross section by about two orders of magnitude. Therefore, the authors have re-analysed reaction data using double-folded alpha potentials. It was possible to obtain almost the correct magnitude of the cross sections. Simultaneously, the angular distributions of the elastic and reaction cross sections and the analysing powers could be reproduced.

Elastic scattering and single nucleon transfer reactions for 7+ 11B and 7Li+ 13C at 34MeV

Elastic scattering cross sections for 10–170° c.m. have been measured for 7Li+ 11B and 7Li + 13C at 34 MeV. These data have been analyzed with the optical model using Woods-Saxon potentials, or potentials with a double-folded real part. The double-folded potentials were found to fit the data better, and quadrupole contributions were required to fit the large angle 7Li+ 11B data. In addition angular distributions for the ( 7Li, 8Li), ( 7Li, 6Li) and ( 7Li, 6He) reactions were measured. The transfer data were analyzed with finite-range DWBA calculations which were able to describe the shape of the data well and produced spectroscopic factors in agreement with theoretical and other experimental values. A phase shift of about 3° between the calculations and the data was found for the ( 7Li, 6Li) and ( 7Li, 6He) reactions.

16O + 28Si elastic scattering at E L=94 MeV/nucleon

16O + 28Si elastic scattering has been measured at E Lab=94 MeV/nucleon. The angular distribution is sensitive to the real part of the ion-ion potential over a broad domain extending from 5 to 8 fm. i.e. well inside the strong absorption radius (7.3 fm) and overlapping the sum of the nuclear radii (5.7 fm). The data are not well described by a standard double-folded potential based on the M3Y interaction. A good fit is obtained when using a density-dependent generalization of this interaction.

Detailed test of distorting potentials for the transfer reactions 40Ca( 7Li, 6Li/ 6He)

Angular distributions for the transfer reactions 40Ca( 7Li, 6Li) 41Ca and 40Ca( 7Li, 6He) 41Sc have been measured at 34 MeV, in small angular increments out to angles where the cross section has fallen by four orders of magnitude. Finite range DWBA calculations show a high sensitivity to different distorting potentials at the largest angle cross sections. It is found that a combination of Woods-Saxon and double-folded potentials does the best job of reproducing the data over the whole angular range.

Microscopic Derivation of the Spin-Orbit Potential of Mass-Three Nucleus

16 0 and 40C a are analysed. Various exchange components and their energy-dependences are discussed. The renormalization of the kinetic exchange potential and central-interaction exchange potential into the spin-orbit potential is found to be large, which makes the total spin-orbit potential larger even three times than the double-folding spin-orbit potential in the tail region for the low incident energy.

Potential model representation of channel coupling and the Coulomb barrier anomaly

We show directly that the large renormalization of the double-folded potential for 16O elastic scattering from 208Pb at 80 MeV is due to channel coupling, including transfer coupling. The demonstration involves applying perturbative-iterative S-matrix to potential inversion to the elastic S-matrix elements of the coupled channel calculations of Thompson et al. This attractive polarization potential fits naturally into systematics in which the polarization potential is, in other cases, often repulsive.

Potential sensitivity in projectile excitation for 7Li

Detailed angular distributions have been measured for /sup 7/Li elastic and inelastic scattering to the first 1/2/sup -/ state in /sup 7/Li (projectile excitation) and the first 2/sup +/, 3/sup -/, and 5/sup -/ states in /sup 40/Ca at E( /sup 7/Li) = 34 MeV. Distorted-wave Born approximation and coupled-channels calculations of the inelastic processes were carried out with both Woods-Saxon and microscopic double-folded real optical potentials. No renormalization of the real double-folded potential is needed to fit the elastic data when the contribution from the ground state quadrupole moment of /sup 7/Li is accounted for in coupled-channels calculations, otherwise a renormalization of 0.6 is required. Moreover, these coupled-channels calculations matched the phase of the oscillations in the projectile excitation data, while calculations employing a Woods-Saxon real potential did not. The calculations for the excitation of states in /sup 40/Ca were insensitive to the form of real potential chosen.

Inelastic scattering and excitation of 6Li.

Differential cross sections for elastic and inelastic $^{6}\mathrm{Li}$ scattering from $^{12}\mathrm{C}$ at ${E}_{\mathrm{c}.\mathrm{m}.=16}$ and 20 MeV, and scattering from $^{16}\mathrm{O}$ at 18.7 MeV were measured out to ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.\mathrm{\ensuremath{\approxeq}}170}$\ifmmode^\circ\else\textdegree\fi{}. Also by scattering $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ from $^{6}\mathrm{Li}$, the inelastic cross sections for the excitation of the ${3}^{+}$ (2.18 MeV) and the ${2}^{+}$ (4.31 MeV) states of $^{6}\mathrm{Li}$ and an estimate of the continuum inelastic cross sections of $^{6}\mathrm{Li}$ were determined. The inelastic data were analyzed using the distorted-wave Born approximation and coupled-channels techniques with folded real and phenomenological imaginary form factors, with the deformations derived from electron scattering. The inelastic data are well described. Coupled-channels effects due to the ${3}^{+}$ state of $^{6}\mathrm{Li}$ were found to play an important role in the scattering. The inclusion of the ${3}^{+}$ state in the coupled-channels calculations reduced the discrepancy in the normalization of the real double-folded potential between $^{6}\mathrm{Li}$ and other heavy-ion projectiles, and the imaginary potential became weaker in the surface region. The present results show that L=2 coupling in the elastic scattering is very important and that the source can be a state in either the projectile, the target, or both.

Energy-dependent renormalization coefficients of folding-model description of 32S+ 40Ca elastic scattering

Angular distributions for the elastic scattering of 32S on 40Ca have been measured at 32S bombarding energies of 100, 120 and 151.5 MeV. Optical model analyses were performed using Woods-Saxon and double-folding potentials which yield a good description of the angular distributions. The energy dependence of the phenomenological optical potentials and renormal- ization coefficients of the double-folded potential were found. These results are anomalous in comparison with the elastic scattering of heavy projectiles (with A > 12) on the same target nucleus.

Test of the proximity theorem for deformed nuclei

We compare a proximity-type potential for two interacting nuclei with the double-folding method. Both spherical and deformed systems are considered. Special orientation windows are found for two deformed nuclei giving rise to nuclear cohesion. If the same nucleon-nucleon interaction is utilized, the proximity and the double-folding potentials agree fairly well for a spherical + deformed system. However, deviations are found in the case of two deformed nuclei.

Microscopic optical potential analyses of carbon–carbon elastic scattering

Utilizing eikonal phase shifts determined from a microscopic double-folding optical potential, marked improvement in the agreement between theory and experiment, for elastic carbon–carbon scattering between 200 and 300 MeV, is obtained when only those values for the nucleon–nucleon slope parameter, appropriate for diffractive scattering, are used. The appropriateness of the perturbative eikonal expansion is discussed by comparison with recent results, obtained for the same potentials, using a more exact complex Wentzell–Kramers–Brillouin (WKB) formalism.

Eikonal phase shift analyses of carbon–carbon scattering

A high-energy double-folding optical potential approximation to the exact nucleus–nucleus multiple-scattering series is used to determine eikonal phase shifts for carbon –carbon scattering at 204.2, 242.7, and 288.6 MeV. The double-folding potentials are obtained by folding the energy-dependent free nucleon–nucleon interaction with densities for the projectile and target obtained by unfolding the finite nucleon charge density from harmonic-well carbon charge distributions. The charge parameters for the latter are taken from the results of electron scattering experiments. Predictions for total, reaction, and elastic differential cross sections, using standard partial wave analysis for the scattering of identical particles, are made and compared with recent experimental results. Excellent agreement is obtained although there are no arbitrarily adjusted parameters in the theory.