Refractive elastic scattering of carbon and oxygen nuclei: The mean field analysis and Airy structures

The experimental data on the $^{16}$O$+^{12}$C and $^{18}$O$+^{12}$C elastic scatterings and their optical model analysis are presented. Detailed and complete elastic angular distributions have been measured at the Strasbourg Vivitron accelerator at several energies covering the energy range between 5 and 10 MeV per nucleon. The elastic scattering angular distributions show the usual diffraction pattern and also, at larger angles, refractive effects in the form of nuclear rainbow and associated Airy structures. The optical model analysis unambiguously shows the evolution of the refractive scattering pattern. The observed structure, namely the Airy minima, can be consistently described by a nucleus-nucleus potential with a deep real part and a weakly absorptive imaginary part. The difference in absorption in the two systems is explained by an increased imaginary (mostly surface) part of the potential in the $^{18}$O$+^{12}$C system. The relation between the obtained potentials and those reported for the symmetrical $^{16}$O$+^{16}$O and $^{12}$C$+^{12}$C systems is drawn.Comment: 10 pages, 9 figures, Phys. rev. C in pres

A Systematic Investigation of Light Heavy-Ion Reactions

We introduce a novel coupling potential for the scattering of deformed light heavy-ion reactions. This new approach is based on replacing the usual first-derivative coupling potential by a new, second derivative coupling potential in the coupled-channels formalism. The new approach has been successfully applied to the study of the $^{12}$C+$^{12}$C, $^{12}$C+$^{24}$Mg, $^{16}$O+$^{28}$Si and $^{16}$O+$^{24}$Mg systems and made major improvements over all the previous coupled-channels calculations for these systems. This paper also shows the limitations of the standard coupled-channels theory and presents a global solution to the problems faced in the previous theoretical accounts of these reactions.Comment: 7 pages with 4 figure

Barrier and internal wave contributions to the quantum probability density and flux in light heavy-ion elastic scattering

We investigate the properties of the optical model wave function for light heavy-ion systems where absorption is incomplete, such as $\alpha + ^{40}$Ca and $\alpha + ^{16}$O around 30 MeV incident energy. Strong focusing effects are predicted to occur well inside the nucleus, where the probability density can reach values much higher than that of the incident wave. This focusing is shown to be correlated with the presence at back angles of a strong enhancement in the elastic cross section, the so-called ALAS (anomalous large angle scattering) phenomenon; this is substantiated by calculations of the quantum probability flux and of classical trajectories. To clarify this mechanism, we decompose the scattering wave function and the associated probability flux into their barrier and internal wave contributions within a fully quantal calculation. Finally, a calculation of the divergence of the quantum flux shows that when absorption is incomplete, the focal region gives a sizeable contribution to nonelastic processes.Comment: 16 pages, 15 figures. RevTeX file. To appear in Phys. Rev. C. The figures are only available via anonynous FTP on ftp://umhsp02.umh.ac.be/pub/ftp_pnt/figscat

Application of Absorbing Boundary Condition to Nuclear Breakup Reactions

Absorbing boundary condition approach to nuclear breakup reactions is investigated. A key ingredient of the method is an absorbing potential outside the physical area, which simulates the outgoing boundary condition for scattered waves. After discretizing the radial variables, the problem results in a linear algebraic equation with a sparse coefficient matrix, to which efficient iterative methods can be applicable. No virtual state such as discretized continuum channel needs to be introduced in the method. Basic aspects of the method are discussed by considering a nuclear two-body scattering problem described with an optical potential. We then apply the method to the breakup reactions of deuterons described in a three-body direct reaction model. Results employing the absorbing boundary condition are found to accurately coincide with those of the existing method which utilizes discretized continuum channels.Comment: 21 pages, 5 figures, RevTeX

A Global Potential Analysis of the 16^{16}O+28^{28}Si Reaction Using a New Type of Coupling Potential

A new approach has been used to explain the experimental data for the $^{16}$O+$^{28}$Si system over a wide energy range in the laboratory system from 29.0 to 142.5 MeV. A number of serious problems has continued to plague the study of this system for a couple of decades. The explanation of anomalous large angle scattering data; the reproduction of the oscillatory structure near the Coulomb barrier; the out-of-phase problem between theoretical predictions and experimental data; the consistent description of angular distributions together with excitation functions data are just some of these problems. These are long standing problems that have persisted over the years and do represent a challenge calling for a consistent framework to resolve these difficulties within a unified approach. Traditional frameworks have failed to describe these phenomena within a single model and have so far only offered different approaches where these difficulties are investigated separately from one another. The present work offers a plausible framework where all these difficulties are investigated and answered. Not only it improves the simultaneous fits to the data of these diverse observables, achieving this within a unified approach over a wide energy range, but it departs for its coupling potential from the standard formulation. This new feature is shown to improve consistently the agreement with the experimental data and has made major improvement on all the previous coupled-channels calculations for this system.Comment: 21 pages with 12 figure

Total Reaction Cross Section in an Isospin-Dependent Quantum Molecular Dynamics (IDQMD) Model

The isospin-dependent quantum molecular dynamics (IDQMD) model is used to study the total reaction cross section $\sigma_R$. The energy-dependent Pauli volumes of neutrons and protons have been discussed and introduced into the IDQMD calculation to replace the widely used energy-independent Pauli volumes. The modified IDQMD calculation can reproduce the experimental $\sigma_R$ well for both stable and exotic nuclei induced reactions. Comparisons of the calculated $\sigma_R$ induced by $^{11}Li$ with different initial density distributions have been performed. It is shown that the calculation by using the experimentally deduced density distribution with a long tail can fit the experimental excitation function better than that by using the Skyrme-Hartree-Fock calculated density without long tails. It is also found that $\sigma_R$ at high energy is sensitive to the long tail of density distribution.Comment: 4 page, 4 fig

Toward a global description of the nucleus-nucleus interaction

Extensive systematization of theoretical and experimental nuclear densities and of optical potential strengths exctracted from heavy-ion elastic scattering data analyses at low and intermediate energies are presented.The energy-dependence of the nuclear potential is accounted for within a model based on the nonlocal nature of the interaction.The systematics indicate that the heavy-ion nuclear potential can be described in a simple global way through a double-folding shape,which basically depends only on the density of nucleons of the partners in the collision.The poissibility of extracting information about the nucleon-nucleon interaction from the heavy-ion potential is investigated.Comment: 12 pages,12 figure

Quantum Tunneling in Nuclear Fusion

Recent theoretical advances in the study of heavy ion fusion reactions below the Coulomb barrier are reviewed. Particular emphasis is given to new ways of analyzing data, such as studying barrier distributions; new approaches to channel coupling, such as the path integral and Green function formalisms; and alternative methods to describe nuclear structure effects, such as those using the Interacting Boson Model. The roles of nucleon transfer, asymmetry effects, higher-order couplings, and shape-phase transitions are elucidated. The current status of the fusion of unstable nuclei and very massive systems are briefly discussed.Comment: To appear in the January 1998 issue of Reviews of Modern Physics. 13 Figures (postscript file for Figure 6 is not available; a hard copy can be requested from the authors). Full text and figures are also available at http://nucth.physics.wisc.edu/preprints

Age Differences in Marriage: Exploring Predictors of Marital Quality in Husband-Older, Wife-Older, and Same-Age Marriages

Using data from a nationally representative sample of 723 married adults, this study explored the association of age differences between spouses at the time of marriage on various aspects of marital quality years into the marriage. Four groups (full sample, husband-older, wife-older, and same-age marriages) were compared to see how marital quality was affected by age difference and several other moderating variables. Spousal interactions increased among wife-older marriages, but not among the other groups. An increased level of husband participation in household labor was linked with an increase in marital happiness and a decrease in marital problems for wife-older marriages. It also was related to a decrease in marital happiness for husband-older marriages as well as a decrease in spousal interaction for all groups except wife-older marriages, which showed no significant association to the division of household labor. Finally, a more traditional approach to gender roles among the same-age marriages was associated with a decrease in marital problems and a decrease in spousal interaction

Optical model potentials involving loosely bound p-shell nuclei around 10 MeV/A

We present the results of a search for optical model potentials for use in the description of elastic scattering and transfer reactions involving stable and radioactive p-shell nuclei. This was done in connection with our program to use transfer reactions to obtain data for nuclear astrophysics, in particular for the determination of the astrophysical S_17 factor for 7Be(p,\gamma)8B using two (7Be,8B) proton transfer reactions. Elastic scattering was measured using 7Li, 10B, 13C and 14N projectiles on 9Be and 13C targets at or about E/A=10 MeV/nucleon. Woods-Saxon type optical model potentials were extracted and are compared with potentials obtained from a microscopic double folding model. We use these results to find optical model potentials for unstable nuclei with emphasis on the reliability of the description they provide for peripheral proton transfer reactions. We discuss the uncertainty introduced by the procedure in the prediction of the DWBA cross sections for the (7Be,8B) reactions used in extracting the astrophysical factor S_17(0).Comment: 16 pages, LaTEX file, 9 figures (PostScript files