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Register a new userFull-folding optical potential for preequilibrium nucleon scattering at low energies
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The real part of the optical potential for the nucleon-nucleus scattering at lower energies (E_i<100MeV) has been calculated including nucleonic and mesonic form factors by a double folding approach. Realistic density- and energy-dependent effective NN-interactions DDM3Y, BDM3Y and HLM3Y based on the Reid and Paris potentials are used in this respect. The effects of the nucleon density distribution and the average relative momentum on the folded potential have been analysed. A good agreement with the phenomenological potential of Lagrange-Lejeune, as well as with the parametrization of Jeukenne-Lejeune-Mahaux for both neutron and proton double-folded potentials is obtained. The results indicate that the strongly simplified model interactions used in preequilibrium reaction theory neglect important dynamical details of such processes.
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Optical model potentials for elastic nucleon nucleus scattering are calculated for a number of target nuclides from a full-folding integral of two different realistic target density matrices together with full off-shell nucleon-nucleon t-matrices derived from two different Bonn meson exchange models. Elastic proton and neutron scattering observables calculated from these full-folding optical potentials are compared to those obtained from `optimum factorized approximations in the energy regime between 65 and 400 MeV projectile energy. The optimum factorized form is found to provide a good approximation to elastic scattering observables obtained from the full-folding optical potentials, although the potentials differ somewhat in the structure of their nonlocality.
Simultaneous $chi^{2}$ analyses previously made for elastic scattering and fusion cross section data for the $^{6}$Li+$^{208}$Pb system is extended to the $^{7}$Li+$^{208}$Pb system at near-Coulomb-barrier energies based on the extended optical model approach, in which the polarization potential is decomposed into direct reaction (DR) and fusion parts. Use is made of the double folding potential as a bare potential. It is found that the experimental elastic scattering and fusion data are well reproduced without introducing any normalization factor for the double folding potential and that both the DR and fusion parts of the polarization potential determined from the $chi^{2}$ analyses satisfy separately the dispersion relation. Further, we find that the real part of the fusion portion of the polarization potential is attractive while that of the DR part is repulsive except at energies far below the Coulomb barrier energy. A comparison is made of the present results with those obtained from the Continuum Discretized Coupled Channel (CDCC) calculations and a previous study based on the conventional optical model with a double folding potential. We also compare the present results for the $^7$Li+$^{208}$Pb system with the analysis previously made for the $^{6}$Li+$^{208}$Pb system.
We apply the low-energy theorems to analyze the recent lattice QCD results for the two-nucleon system at a pion mass of $M_pisimeq 450$ MeV obtained by the NPLQCD collaboration. We find that the binding energies of the deuteron and dineutron are inconsistent with the low-energy behavior of the corresponding phase shifts within the quoted uncertainties and vice versa. Using the binding energies of the deuteron and dineutron as input, we employ the low-energy theorems to predict the phase shifts and extract the scattering length and the effective range in the $^3S_1$ and $^1S_0$ channels. Our results for these quantities are consistent with those obtained by the NPLQCD collaboration from effective field theory analyses but are in conflict with their determination based on the effective-range approximation.
Nuclear fusion reactions, at energies, far below the Coulomb barrier play a significant role in the synthesis of light elements in the primordial nucleosynthesis as well as in the interior of compact stellar objects. Many different kinds of nuclear reactions are occurring simultaneously inside the stellar core depending upon the density and temperature conditions of the nuclear plasma along with other relevant parameters of these stars. Nuclear fusion reactions in the energy range ($Esim$ 1 eV to few keV) can be explained successfully by quantum mechanical tunneling through the mutual Coulomb barrier of interacting nuclei. The measurement of the cross-sections at extremely low energy is quite difficult because of the larger width of the Coulomb barrier, which results in a very small value of the reaction cross-section. Hence, any improvement in the data on astrophysical S-factors for the light nuclei fusion may give a better picture of the elemental abundance in nucleosynthesis. In this work, we have theoretically investigated the energy dependence of fusion cross-sections and astrophysical S-factors for fusion reaction of light nuclei like D-D and p-$^{11}$B using complex Gaussian nuclear potential with adjustable depth and range parameters plus the mutual Coulomb interaction of the interacting nuclei. Numerical computation of the observables is done in the framework of the selective resonant tunneling model approach. The results of our calculation are compared with those found in the literature.
The discrete energy-eigenvalues of two nucleons interacting with a finite-range nuclear force and confined to a harmonic potential are used to numerically reconstruct the free-space scattering phase shifts. The extracted phase shifts are compared to those obtained from the exact continuum scattering solution and agree within the uncertainties of the calculations. Our results suggest that it might be possible to determine the amplitudes for the scattering of complex systems, such as n-d, n-t or n-alpha, from the energy-eigenvalues confined to finite volumes using ab-initio bound-state techniques.
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