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Register a new userAnalysis of a low-energy correction to the eikonal approximation
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Extensions of the eikonal approximation to low energy (20MeV/nucleon typically) are studied. The relation between the dynamical eikonal approximation (DEA) and the continuum-discretized coupled-channels method with the eikonal approximation (E-CDCC) is discussed. When Coulomb interaction is artificially turned off, DEA and E-CDCC are shown to give the same breakup cross section, within 3% error, of $^{15}$C on $^{208}$Pb at 20MeV/nucleon. When the Coulomb interaction is included, the difference is appreciable and none of these models agrees with full CDCC calculations. An empirical correction significantly reduces this difference. In addition, E-CDCC has a convergence problem. By including a quantum-mechanical correction to E-CDCC for lower partial waves between $^{15}$C and $^{208}$Pb, this problem is resolved and the result perfectly reproduces full CDCC calculations at a lower computational cost.
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E-CDCC and DEA, two eikonal-based reaction models are compared to CDCC at low energy (e.g. 20AMeV) to study their behaviour in the regime at which the eikonal approximation is supposed to fail. We confirm that these models lack the Coulomb deflection of the projectile by the target. We show that a hybrid model, built on the CDCC framework at low angular momenta and the eikonal approximation at larger angular momenta gives a perfect agreement with CDCC. An empirical shift in impact parameter can also be used reliably to simulate this missing Coulomb deflection.
The new data of the elastic scattering of $^{6}$He+$^{12}$C at about 40 MeV/nucleon are analyzed in the eikonal approximation. The $^{6}$He+$^{12}$C phase-shift function is evaluated completely without any {it ad hoc} assumption by a Monte Carlo integration, which makes it possible to use a realistic 6-nucleon wave function for a halo nucleus $^{6}$He. The effect of the breakup of $^6$He on the elastic differential cross sections as well as the optical potential is studied at different energies from 40 to 800 MeV/nucleon. PACS number(s): 24.10.-i; 21.60.Ka; 25.60.Bx; 25.10.+s Keywords: Eikonal; Glauber; Monte Carlo; Halo; Breakup
The adiabatic distorted wave approximation (ADWA) is widely used by the nuclear community to analyse deuteron stripping ($d$,$p$) experiments. It provides a quick way to take into account an important property of the reaction mechanism: deuteron breakup. In this work we provide a numerical quantification of a perturbative correction to this theory, recently proposed in [R.C. Johnson, J. Phys. G: Nucl. Part. Phys. 41 (2014) 094005] for separable rank-one nucleon-proton potentials. The correction involves an additional, nonlocal, term in the effective deuteron-target ADWA potential in the entrance channel. We test the calculations with perturbative corrections against continuum-discretized coupled channel predictions which treat deuteron breakup exactly.
We explore the eikonal approximation to graviton exchange in AdS_5 space, as relevant to scattering in gauge theories. We restrict ourselves to the regime where conformal invariance of the dual gauge theory holds, and to large t Hooft coupling where the computation involves pure gravity. We give a heuristic argument, a direct loop computation, and a shock wave derivation. The scalar propagator in AdS_3 plays a key role, indicating that even at strong coupling, two-dimensional conformal invariance controls high-energy four-dimensional gauge-theory scattering.
An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order $1/k^2$, where $k$ is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. A form of effective-momentum approximation is obtained using trajectory-dependent eikonal phases and focusing factors. Fixing the Coulomb distortion effects at the center of the nucleus, the often-used ema approximation is recovered. Comparisons of these approximations are made with full calculations using the electron eikonal wave functions. The ema results are found to agree well with the full calculations.
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