Extrapolation of scattering data to the negative-energy region

Abstract

Explicit analytic expressions are derived for the effective-range function for the case when the interaction is represented by a sum of the short-range square-well and long-range Coulomb potentials. These expressions are then transformed into forms convenient for extrapolating to the negative-energy region and obtaining the information about bound-state properties. Alternative ways of extrapolation are discussed. Analytic properties of separate terms entering these expressions for the effective-range function and the partial-wave scattering amplitude are investigated.

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Cited by in corpus (14)

• Connection formulas between Coulomb wave functions
• Elastic $\alpha$-${}^{12}$C scattering at low energies with the bound states of ${}^{16}$O in effective field theory
• Algorithm for the asymptotic nuclear coefficients calculations using phase shift data for charged particles scattering
• Extrapolation of scattering data to the negative-energy region II
• Theoretical study of the direct $\alpha +d$ $\to$ ${}^6$Li + $\gamma$ astrophysical capture process in a three-body model II. Reaction rates and primordial abundance
• Effective-range function methods for charged particle collisions
• Astrophysical ${}^3\mathrm{He}(\alpha ,\gamma {)}^7\mathrm{Be}$ and ${}^3\mathrm{H}(\alpha ,\gamma {)}^7\mathrm{Li}$ direct capture reactions in a potential model approach
• Extrapolation of scattering data to the negative-energy region. Application to the $p{-}^{16}$O system
• Determination of asymptotic normalization coefficients for the channel ${}^{16}$O$\to \alpha {+}^{12}$C. Excited state ${}^{16}$O($0^{+};6.05$ MeV)
• New method of analytic continuation of elastic-scattering data to the negative-energy region and asymptotic normalization coefficients for ${}^{17}$O and ${}^{13}$C
• Charged-particle bound states in periodic boxes
• Resonance properties including asymptotic normalization coefficients deduced from phase-shift data without the effective-range function
• An effective two-body model for spectra of clusters of ${}^2$H, ${}^3$H, ${}^3$He, and ${}^4$He with ${}^4$He, and ${}^2$H-${}^4$He scattering
• Complex-energy analysis of proton-proton fusion