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Register a new userExtrapolation of scattering data to the negative-energy region
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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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The problem of analytic continuation of the scattering data to the negative-energy region to obtain information on asymptotic normalization coefficients (ANCs) of bound states is discussed. It is shown that a recently suggested $Delta$ method [O.L.Ram{i}rez Suarez and J.-M. Sparenberg, Phys. Rev. C {bf 96}, 034601 (2017)] is not strictly correct in the mathematical sense since it is not an analytic continuation of a partial-wave scattering amplitude to the region of negative energies. However, it can be used for practical purposes for sufficiently large charges and masses of colliding particles. Both the $Delta$ method and the standard method of continuing of the effective range function are applied to the $p-^{16}$O system which is of interest for nuclear astrophysics. The ANCs for the ground $5/2^+$ and excited $1/2^+$ states of $^{17}$F are determined.
A new method is proposed for extrapolation of elastic-scattering data to the negative-energy region for a short-range interaction. The method is based on the analytic approximation of the modulus-squared of the partial-wave scattering amplitude. It is shown that the proposed method has an advantage over the traditional one based on continuation of the effective-range function. The new method has been applied to determine the asymptotic normalization coefficients for the $^{17}$O and $^{13}$C nuclei in the $n+^{16}$O and $n+^{12}$C channels, respectively.
The energy variance extrapolation method consists in relating the approximate energies in many-body calculations to the corresponding energy variances and inferring eigenvalues by extrapolating to zero variance. The method needs a fast evaluation of the energy variances. For many-body methods that expand the nuclear wave functions in terms of deformed Slater determinants, the best available method for the evaluation of energy variances scales with the sixth power of the number of single-particle states. We propose a new method which depends on the number of single-particle orbits and the number of particles rather than the number of single-particle states. We discuss as an example the case of ${}^4He$ using the chiral N3LO interaction in a basis consisting up to 184 single-particle states.
A new analysis of the precise experimental astrophysical $S$-factors for the direct capture $^3He(alpha,gamma)^7{rm {Be}}$ reaction [B.S. Nara Singh et al., Phys.Rev.Lett. {bf 93} (2004) 262503; D. Bemmerer et al., Phys.Rev.Lett. {bf 97} (2006) 122502; F.Confortola et al., Phys.Rev. {bf C 75} (2007) 065803 and T.A.D.Brown et al., Phys.Rev. {bf C 76} (2007) 055801] populating to the ground and first excited states of $^7{rm Be}$ is carried out based on the modified two - body potential approach in which the direct astrophysical $S$-factor, $S_{34}(E)$, is expressed in terms of the asymptotic normalization constants for $^3{rm {He}}+alphato ^7{rm {Be}}$ and two additional conditions are involved to verify the peripheral character of the reaction under consideration. The Woods--Saxon potential form is used for the bound ($alpha+^3{rm {He}}$)- state and the $^3{rm {He}}alpha$- scattering wave functions. New estimates are obtained for the indirectly measured, values of the asymptotic normalization constants (the nuclear vertex constants) for $^3{rm {He}}+alphato^7{rm {Be}}(g.s.)$ and $^3{rm {He}}+alphato^7{rm {Be}}(0.429 MeV)$ as well as the astrophysical $S$-factors $S_{34}(E)$ at E$le$ 90 keV, including $E$=0. The values of asymptotic normalization constants have been used for getting information about the $alpha$-particle spectroscopic factors for the mirror ($^7Li^7{rm {Be}}$)-pair.
We present a model for electron- and neutrino-scattering off nucleons and nuclei focussing on the quasielastic and resonance region. The lepton-nucleon reaction is described within a relativistic formalism that includes, besides quasielastic scattering, the excitation of 13 N* and Delta resonances and a non-resonant single-pion background. Recent electron-scattering data is used for the state-of-the-art parametrizations of the vector form factors; the axial couplings are determined via PCAC and, in the case of the Delta resonance, the axial form factor is refitted using neutrino-scattering data. Scattering off nuclei is treated within the GiBUU framework that takes into account various nuclear effects: the local density approximation for the nuclear ground state, mean-field potentials and in-medium spectral functions. Results for inclusive scattering off Oxygen are presented and, in the case of electron-induced reactions, compared to experimental data and other models.
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