Incoming Wave Boundary Condition Research Articles

Application of the incoming wave boundary condition to16O+16O and12C+12C elastic scattering

The elastic scattering of12C+12C and16O+16O has been studied in the framework of an incoming wave boundary condition model. Different logarithmic derivatives for the incoming waves have been tested and their effects investigated with the help of Fourier analyses. It is shown that a logarithmic derivative obtained from a JWKB approximation leads to strong absorption of the low partial waves while a logarithmic derivative constant for all partial waves causes reflections. These reflections are necessary to describe the high energy elastic scattering of12C+12C. The fits thus obtained with shallow real potentials are comparable to those obtained with deep folding potentials. It is shown that not the lowest partial waves, but those within a window just below the grazing angular momentum are most important for the higher energy12C+12C angular distributions.

14N+ 10B fusion and elastic scattering cross section measurements near the interaction barrier

The 14N+ 10B fusion reactions were studied at c.m. energies between 2.9 and 7.5 MeV by measuring the yields of γ-rays from the residual nuclei formed by particle evaporation from the compound system. Cross sections for formation of the evaporation residues 16O, 19F, 19Ne, 20Ne, 21Ne, 22Ne, 22Na, 23Na and 23Mg, as well as the total cross section, were deduced from these yields with the aid of statistical model calculations. The 14N+ 10B elastic scattering differential cross sections were measured from E c.m. = 4.3 to 9.1 MeV at θ c.m. = 74.4°, and from E c.m. = 3.3 to 8.3 MeV at θ c.m. = 90.0°. The elastic scattering cross sections were analyzed within the framework of the incoming-wave boundary condition (IWBC) model. The fusion cross sections calculated for the real ion-ion potential deduced from the IWBC model fit to the elastic scattering are in good agreement with the measured values.

9Be + 12C, 9Be + 16O, 9Be + 19F reactions at energies below the barrier

The 16O + 9Be reactions have been studied from E c.m. = 2.0 MeV to 5.1 MeV, an energy near the top of the Coulomb barrier. The cross section for the neutron transfer reaction 9Be( 16O, 17O ∗ (0.87 MeV)) 8Be has been measured over this range by detecting the prompt 0.87 MeV γ-rays. The total fusion cross section has been determined from E c.m. = 2.8 to 5.1 MeV by observing individual γ-ray transitions in the evaporation residues with a Ge(Li) detector, and then summing the separate yields. Direct processes are found to dominate the reaction yield below E c.m. = 4 MeV. A comparison of the energy dependence of the fusion cross section for this reaction and the 12C + 13C reaction, which proceeds via the formation of the same compound nucleus, 25Mg, reveals differences at sub-barrier energies. Optical model and incoming-wave boundary condition calculations are presented. Data have also been obtained for the near optimum Q-value neutron-transfer reactions 9Be( 12C, 13C ∗) 8Be and 9Be( 19F, 20F) 8Be, and these are discussed in terms of a simple model of sub-barrier direct reactions.

Low energy muonic hydrogen reactions with heavy atoms

Average s-wave cross-sections appropriate for liquid hydrogen temperatures are calculated with the aid of an in-coming wave boundary condition for the muon transfer process μ -p + Z → (μ - Z) ∗ + p on heavy atoms. The surface-correlated nature of the heavy atom X-rays is emphasized.

IWB analysis of scattering and fusion cross sections for the 12C+ 12C, 13C+ 16O and 16O+ 16O reactions for energies near and below the Coulomb barrier

Calculations are presented of the elastic scattering and fusion cross sections for the astrophysically interesting reactions 12C+ 12C, 12C+ 16O and 16O+ 16O. The calculations are performed using the incoming wave boundary condition (IWB) and a real ion-ion interaction potential. The results are compared with the available experimental data for the energy region near and below the Coulomb barrier. With values of two adjustable potential parameters (the radial position of the l = 0 barrier and the diffuseness) determined by fitting elastic scattering data, good agreement is obtained for the average energy dependence of the 12C+ 12C and 12C+ 16O fusion cross sections. In the case of 16O+ 16O, both the calculated absolute magnitude and the energy dependence of the fusion cross section are inconsistent with the data and this discrepancy is discussed.

Measurement of fusion cross sections for 14N + 14N and 12C + 16O at low energles

Total fusion cross sections for 14N + 14N and 12C + 16O have been measured for bombarding energies extending from the Coulomb barrier down to E c.m. ≈ 4.6 MeV. Absolute cross sections were deduced from the yields of individual γ-ray transitions observed with a Ge(Li) detector and a statistical-model calculation of the decay modes of the compound nucleus. This technique was checked by a detailed comparison of the present results for 12C + 16O with the earlier results of Patterson et al. for charged particle decay, with the study of Spinka and Winkler of activation following neutron emission, and with the measurements of Čujec and Barnes on total γ-ray emission. The present method for determination of the total fusion cross section was found to compare very favourably with other methods. The gross energy dependence of the fusion cross section for 14N + 14N was observed to be similar to that of 12C + 16O. In contrast to 12C + 16O, however, the cross section does not exhibit any resonant-like structure. A simple barrier-penetration model employing the incoming-wave boundary condition is able to reproduce the observed fusion cross section for 14N + 14N. An analysis of the transfer reaction 14N( 14N, 13N) 15N at sub-barrier energies is also presented and a comparison is made between the direct and compound reactions.

Interaction sizes of the even neodymium isotopes from elasticαscattering

Differential cross sections for $\ensuremath{\alpha}$ particles elastically scattered from $^{142,144,146,148,150}\mathrm{Nd}$ have been measured at six angles over the energy region 11-19 MeV. The cross sections were analyzed using the optical model, the incoming-wave boundary condition model, and the coupled-channels model. The radius at which the real nuclear potential is 2% of the Coulomb potential was found to be effectively independent of the ambiguities in the optical potential. In the coupled-channels analysis, the radius at which the spherically averaged real nuclear potential is 2% of the spherically averaged Coulomb potential is almost identical, for a given nucleus, to the corresponding quantity determined using the spherical optical model. The absolute increase in the "2% radius" over the neodymium isotopes is about 2 times larger than the increase in the charge distribution as observed in muonicatom and electron-scattering studies.NUCLEAR REACTIONS $^{142,144,146,148,150}\mathrm{Nd}(\ensuremath{\alpha},\ensuremath{\alpha})$; $E=11\ensuremath{-}19$ MeV; measured $\ensuremath{\sigma}(E,\ensuremath{\theta})$. Deduced nuclear interaction size. Enriched targets.

The incoming wave boundary condition for elastic scattering of heavy particles at incident energies near the coulomb barrier

An incoming wave boundary condition (IWB) approach is used to calculate differential cross sections for 16O + Ca and α + Pb elastic scattering, at incident energies near the Coulomb barrier. A comparison is made to optical model (OM) calculations and it is shown that the present method is competitive with the OM method in the energy region mentioned above.