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Register a new userExtrapolation of scattering data to the negative-energy region. Application to the $p-^{16}$O system
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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.
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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.
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 structures of excited states in $^{34}$S are investigated using the antisymmetrized molecular dynamics and generator coordinate method (GCM). The GCM basis wave functions are calculated via energy variation with a constraint on the quadrupole deformation parameter $beta$. By applying the GCM after parity and angular momentum projections, the coexistence of two positive- and one negative-parity superdeformed (SD) bands are predicted, and low-lying states and other deformed bands are obtained. The SD bands have structures of $^{16}$O + $^{16}$O + two valence neutrons in molecular orbitals around the two $^{16}$O cores in a cluster picture. The configurations of the two valence neutrons are $delta^2$ and $pi^2$ for the positive-parity SD bands and $pi^1delta^1$ for the negative-parity SD band. The structural changes of the yrast states are also discussed.
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.
The optical model potentials for nucleon-nucleus elastic scattering at $65$~MeV are calculated for $^{12}$C, $^{16}$O, $^{28}$Si, $^{40}$Ca, $^{56}$Fe, $^{90}$Zr and $^{208}$Pb in first order multiple scattering theory, following the prescription of the spectator expansion, where the only inputs are the free NN potentials, the nuclear densities and the nuclear mean field as derived from microscopic nuclear structure calculations. These potentials are used to predict differential cross sections, analyzing powers and spin rotation functions for neutron and proton scattering at 65 MeV projectile energy and compared with available experimental data.
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