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Register a new userCoupled-channel optical model potential for rare earth nuclei
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Inspired by the recent work by Dietrich et al., substantiating validity of the adiabatic assumption in coupled-channel calculations, we explore the possibility of generalizing a global spherical optical model potential (OMP) to make it usable in coupled-channel calculations on statically deformed nuclei. The generalization consists in adding the coupling of the ground state rotational band, deforming the potential by introducing appropriate quadrupole and hexadecupole deformation and correcting the OMP radius to preserve volume integral of the spherical OMP. We choose isotopes of three rare-earth elements (W, Ho, Gd), which are known to be nearly perfect rotors, to perform a consistent test of our conjecture on integrated cross sections as well as on angular distributions for elastic and inelastic neutron scattering. When doing this we employ the well-established Koning-Delaroche global spherical potential and experimentally determined deformations without any adjustments. We observe a dramatically improved agreement with experimental data compared to spherical optical model calculations. The effect of changing the OMP radius to preserve volume integral is moderate but visibly improves agreement at lower incident energies. We find that seven collective states need to be considered for the coupled-channel calculations to converge. Our results for total, elastic, inelastic, and capture cross sections, as well as elastic and inelastic angular distributions are in remarkable agreement with experimental data. This result confirms that the adiabatic assumption holds and can extend applicability of the global spherical OMP to rotational nuclei in the rare-earth region, essentially without any free parameter. Thus, quite reliable coupled-channel calculations can be performed on such nuclei even when the experimental data, and consequently a specific coupled-channel potential, are not available.
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We present an outline of an extensive study of the effects of collective couplings and nuclear deformations on integrated cross sections as well as on angular distributions in a consistent manner for neutron-induced reactions on nuclei in the rare-earth region. This specific subset of the nuclide chart was chosen precisely because of a clear static deformation pattern. We analyze the convergence of the coupled-channel calculations regarding the number of states being explicitly coupled. A model for deforming the spherical Koning-Delaroche optical potential as function of quadrupole and hexadecupole deformations is also proposed, inspired by previous works. We demonstrate that the obtained results of calculations for total, elastic, inelastic, and capture cross sections, as well as elastic and inelastic angular distributions are in remarkably good agreement with experimental data for scattering energies around a few MeV.
The coupled-channel theory is a natural way of treating nonelastic channels, in particular those arising from collective excitations characterized by nuclear deformations. A proper treatment of such excitations is often essential to the accurate description of experimental nuclear-reaction data and to the prediction of a wide variety of scattering observables. Stimulated by recent work substantiating the near validity of the adiabatic approximation in coupled-channel calculations for scattering on statically deformed nuclei, we explore the possibility of generalizing a global spherical optical model potential (OMP) to make it usable in coupled-channel calculations on this class of nuclei. To do this, we have deformed the Koning-Delaroche global spherical potential for neutrons, coupling a sufficient number of states of the ground state band to ensure convergence. We present an extensive study of the effects of collective couplings and nuclear deformations on integrated cross sections as well as on angular distributions for neutron-induced reactions on statically deformed nuclei in the rare-earth region. We choose isotopes of three rare-earth elements (Gd, Ho, W), which are known to be nearly perfect rotors, to exemplify the results of the proposed method. Predictions from our model for total, elastic and inelastic cross sections, as well as for elastic and inelastic angular distributions, are in reasonable agreement with measured experimental data. These results suggest that the deformed Koning-Delaroche potential provides a useful regional neutron optical potential for the statically deformed rare earth nuclei.
The coupled-channel theory is a natural way of treating nonelastic channels, in particular those arising from collective excitations, defined by nuclear deformations. Proper treatment of such excitations is often essential to the accurate description of reaction experimental data. Previous works have applied different models to specific nuclei with the purpose of determining angular-integrated cross sections. In this work, we present an extensive study of the effects of collective couplings and nuclear deformations on integrated cross sections as well as on angular distributions in a consistent manner for neutron-induced reactions on nuclei in the rare-earth region. This specific subset of the nuclide chart was chosen precisely because of a clear static deformation pattern. We analyze the convergence of the coupled-channel calculations regarding the number of states being explicitly coupled. Inspired by the work done by Dietrich emph{et al.}, a model for deforming the spherical Koning-Delaroche optical potential as function of quadrupole and hexadecupole deformations is also proposed. We demonstrate that the obtained results of calculations for total, elastic and inelastic cross sections, as well as elastic and inelastic angular distributions correspond to a remarkably good agreement with experimental data for scattering energies above around a few MeV.
The experimental $E1$ strength distribution below 4 MeV in rare-earth nuclei suggests a local breaking of isospin symmetry. In addition to the octupole states, additional $1^-$ states with enhanced E1 strength have been observed in rare-earth nuclei by means of ($gamma,gamma$) experiments. By reproducing the experimental results, the spdf interacting boson model calculations provide further evidence for the formation of an $alpha$ cluster in medium-mass nuclei and might provide a new understanding of the origin of low-lying E1 strength.
Given the established 2 alpha structure of 8Be, a realistic model of 4 interacting alpha clusters must be used to obtain a 8Be+8Be interaction potential. Such a four-body problem poses a challenge for the determination of the 8Be+8Be optical potential (OP) that is still unknown due to the lack of the elastic 8Be+8Be scattering data. The main goal of the present study is to probe the complex 8Be+8Be optical potential in the coupled reaction channel (CRC) study of the alpha transfer 12C(alpha,8Be) reaction measured at 65 MeV, and to obtain the spectroscopic information on the alpha+8Be cluster configuration of 12C. The 3- and 4-body Continuum-Discretized Coupled Channel (CDCC) methods are used to calculate the elastic alpha+8Be and 8Be+8Be scattering at the energy around 16 MeV/nucleon, with the breakup effect taken into account explicitly. Using the CDCC-based OP and alpha spectroscopic factors given by the cluster model calculation, a good CRC description of the alpha transfer data without any adjustment of the (complex) potential strength.
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