Phase-shift analysis in heavy-ion scattering

The application of inversion to nuclear scattering

“…[ [184][185][186][187][188] for details). Both formalisms can be applied with almost any inversion approach and there have been several successful applications in the context of optical model fits to experimental data.…”

“…the constrained χ 2 exp which takes also into consideration a priori information about the expected form of solution [187]. For various values of the regularization parameter γ , the minimum of the total χ 2 = χ 2 apr + χ 2 exp is determined by a nonlinear search of the parameters {b n } and the optimal value of γ is found [188]. It can be proved that in this constrained fit, if γ is sufficiently large, the small eigenvalues of the error matrix disappear and the error matrix becomes well conditioned.…”

“…It can be proved that in this constrained fit, if γ is sufficiently large, the small eigenvalues of the error matrix disappear and the error matrix becomes well conditioned. The details can be found, for example, in [188,193] in which the MSR was applied to α- 40 Ca elastic scattering at E α = 104 MeV, fitting the high-precision data of Gils et al [194]. In [188] the data were first roughly fitted with a conventional WS potential which becomes the a priori input potential with a definite b (0) .…”

“…The details can be found, for example, in [188,193] in which the MSR was applied to α- 40 Ca elastic scattering at E α = 104 MeV, fitting the high-precision data of Gils et al [194]. In [188] the data were first roughly fitted with a conventional WS potential which becomes the a priori input potential with a definite b (0) . Then using the a posteriori χ 2 apost with an optimal choice for γ , the effective number of fitting parameters was reduced from 32 to 20.…”