Coupled-channel Optical Model Research Articles

Unified description of the coupled-channels and statistical Hauser-Feshbach nuclear reaction theories for low energy neutron incident reactions

We incorporate the coupled-channels optical model into the statistical Hauser-Feshbach nuclear reaction theory, where the scattering matrix is diagonalized by performing the Engelbrecht-Weidenmüller transformation. This technique has been implemented in the coupled-channels optical model code ECIS by J. Raynal, and we extend this method so that all the open channels in a nucleon-induced reaction on a deformed nucleus can be calculated consistently.

Multiband coupling and nuclear softness in optical model calculations for even-even and odd-A actinides

A new dispersive multiband coupled channels optical model with soft-rotator “effective” deformations is proposed to describe nucleon scattering on even-even and odd-A actinides. The impact of the introduction of axial and non-axial dynamical deformations that describe nuclear softness is discussed. Softness and multiband coupling are shown to change compound-nucleus formation cross section by up to ≈ 10% for incident neutron energies below 1 MeV.

Coupled-channel analysis of deuteron scattering on 56Fe

The deuteron elastic and inelastic scattering on 56Fe is calculated by using the coupled-channel method and the collective motion models. Based on the experimental angular distributions of scattering processes, an optimal set of parameters are obtained for the deuteron's coupled-channel optical model potential and 56Fe's deformation including first ten low-lying excited states. The calculation results are in good agreement with the experimental data at low incident energies (Ed < 30 MeV), except for 41+(2.085 MeV) and 23+(2.960 MeV), and the deviation is found for several states at 56 MeV. That indicates further analyses and discussions are necessary.

The neutron transmission of natFe, 197Au and natW

Neutron total cross sections of natFe, 197Au and natW have been measured at the n ELBE neutron time-of-flight facility in the energy range 0.15-8MeV with an uncertainty due to counting statistics of up to 2% and a total uncertainty due to systematic effects of 1%. The neutrons are produced with the superconducting electron accelerator ELBE using a liquid lead circuit as photo-neutron target. By periodical sample-in-sample-out measurements the transmission of the sample materials has been determined using a low-threshold plastic scintillation detector. The resulting effective total cross sections show good agreement with previously measured data that cover only part of the energy range available at n ELBE. The results have also been compared to evaluated library files and recent calculations based on a dispersive coupled channel optical model potential.

Evaluation of cross sections for neutron interactions with 238U in the energy region between 5 keV and 150 keV

.Cross sections for neutron interactions with 238U in the energy region from 5keV to 150keV have been evaluated. Average total and capture cross sections have been derived from a least squares analysis using experimental data reported in the literature. The resulting cross sections have been parameterised in terms of average resonance parameters maintaining full consistency with results of optical model calculations by using a dispersive coupled channel optical model potential. The average compound partial cross sections have been expressed in terms of transmission coefficients by applying the Hauser-Feshbach statistical reaction theory including width-fluctuations. A generalized single-level representation compatible with the energy-dependent options of the ENDF-6 format has been applied using standard boundary conditions. The results have been transferred into a full ENDF-6 compatible data file.

Predicting the optical observables for nucleon scattering on even-even actinides**Supported by International Atomic Energy Agency, through the IAEA Research Contract 19263, by the Spanish Ministry of Economy and Competitivity under Contracts FPA2014-53290-C2-2-P and FPA2016-77689-C2-1-R.

The previously derived Lane consistent dispersive coupled-channel optical model for nucleon scattering on 232Th and 238U nuclei is extended to describe scattering on even-even actinides with Z = 90–98. A soft-rotator-model (SRM) description of the low-lying nuclear structure is used, where the SRM Hamiltonian parameters are adjusted to the observed collective levels of the target nucleus. SRM nuclear wave functions (mixed in K quantum number) have been used to calculate the coupling matrix elements of the generalized optical model. The “effective” deformations that define inter-band couplings are derived from the SRM Hamiltonian parameters. Conservation of nuclear volume is enforced by introducing a dynamic monopolar term to the deformed potential, leading to additional couplings between rotational bands. The fitted static deformation parameters are in very good agreement with those derived by Wang and collaborators using the Weizsäcker-Skyrme global mass model (WS4), allowing use of the latter to predict cross sections for nuclei without experimental data. A good description of the scarce “optical” experimental database is achieved. SRM couplings and volume conservation allow a precise calculation of the compound-nucleus formation cross sections, which is significantly different from that calculated with rigid-rotor potentials coupling the ground-state rotational band. The derived parameters can be used to describe both neutron- and proton-induced reactions.

Evaluation of neutron total and capture cross sections on99Tc in the unresolved resonance region

Long-lived fission product Technetium-99 is one of the most important radioisotopes for nuclear transmutation. The reliable nuclear data are indispensable for a wide energy range up to a few MeV, in order to develop environmental load reducing technology. The statistical analyses of resolved resonances were performed by using the truncated Porter-Thomas distribution, coupled-channels optical model, nuclear level density model and Bayes' theorem on conditional probability. The total and capture cross sections were calculated by a nuclear reaction model code CCONE. The resulting cross sections have statistical consistency between the resolved and unresolved resonance regions. The evaluated capture data reproduce those recently measured at ANNRI of J-PARC/MLF above resolved resonance region up to 800 keV.

Optical model with multiple band couplings using soft rotator structure

A new dispersive coupled-channel optical model (DCCOM) is derived that describes nucleon scattering on 238 U and 232 Th targets using a soft-rotator-model (SRM) description of the collective levels of the target nucleus. SRM Hamiltonian parameters are adjusted to the observed collective levels of the target nucleus. SRM nuclear wave functions (mixed in K quantum number) have been used to calculate coupling matrix elements of the generalized optical model. Five rotational bands are coupled: the ground-state band, β-, γ-, non-axial- bands, and a negative parity band. Such coupling scheme includes almost all levels below 1.2 MeV of excitation energy of targets. The “effective” deformations that define inter-band couplings are derived from SRM Hamiltonian parameters. Conservation of nuclear volume is enforced by introducing a monopolar deformed potential leading to additional couplings between rotational bands. The present DCCOM describes the total cross section differences between 238 U and 232 Th targets within experimental uncertainty from 50 keV up to 200 MeV of neutron incident energy. SRM couplings and volume conservation allow a precise calculation of the compound-nucleus (CN) formation cross sections, which is significantly different from the one calculated with rigid-rotor potentials with any number of coupled levels.

Nucleon scattering on actinides using a dispersive optical model with extended couplings

Tamura coupling model has been extended to consider the coupling of additional low-lying rotational bands to the ground state band. Rotational bands are built on vibrational bandheads (even-even targets) or single particle bandheads (odd-$A$ targets) including both axial and non-axial deformations. These additional excitations are introduced as a perturbation to the underlying axially-symmetric rigid rotor structure of the ground state rotational band. Coupling matrix elements of the generalized optical model are derived for extended multi-band transitions in even-even and odd-$A$ nuclei. Isospin symmetric formulation of the optical model is employed. A coupled-channels optical model potential (OMP) containing a dispersive contribution is used to fit simultaneously all available optical experimental databases including neutron strength functions for nucleon scattering on $^{232}$Th, $^{233,235,238}$U and $^{239}$Pu nuclei and quasi-elastic ($p$,$n$) scattering data on $^{232}$Th and $^{238}$U. Lane consistent OMP is derived for all actinides if corresponding multi-band coupling schemes are defined. Calculations using the derived OMP potential reproduce measured total cross-section differences between several actinide pairs within experimental uncertainty for incident neutron energies from 50 keV up to 150MeV. Multi-band coupling is stronger in even-even targets due to the collective nature of the coupling; the impact of extended coupling on predicted compound-nucleus formation cross section reaches 5% below 3 MeV of incident neutron energy. Coupling of ground-state rotational band levels in odd-$A$ nuclei is sufficient for a good description of the compound-nucleus formation cross sections as long as the coupling is saturated (a minimum of 7 coupled levels are typically needed).

Evaluation of neutron nuclear data on platinum isotopes

ABSTRACTNeutron nuclear data on 10 isotopes of platinum have been evaluated for the next version of Japanese Evaluated Nuclear Data Library general-purpose file in the energy region from 10−5 eV to 20 MeV. Resolved resonance parameters of naturally occurring isotopes were taken from a compilation work, while unresolved resonance parameters were obtained by fitting to the total and capture cross sections calculated from nuclear models. A statistical model code was applied to evaluate cross sections above the resolved resonance region. Compound, pre-equilibrium and direct-reaction processes were considered for cross-section calculation. Coupled-channel optical model parameters were employed for the interaction between neutrons and nuclei. Giant-dipole and pygmy resonance parameters for E1 γ-ray transition from platinum isotopes were determined so as to reproduce measured γ-ray spectrum. The present results reproduce experimental data very well. The evaluated data are compiled into Evaluated Nuclear Data File formatted data files.

Statistical Hauser-Feshbach theory with width-fluctuation correction including direct reaction channels for neutron-induced reactions at low energies

A model to calculate particle-induced reaction cross sections with statistical Hauser-Feshbach theory including direct reactions is given. The energy average of the scattering matrix from the coupled-channels optical model is diagonalized by the transformation proposed by Engelbrecht and Weidenm\"uller [C. A. Engelbrecht and H. A. Weidenm\"uller, Phys. Rev. C 8, 859 (1973)]. The ensemble average of $S$-matrix elements in the diagonalized channel space is approximated by a model of Moldauer [P. A. Moldauer, Phys. Rev. C 12, 744 (1975)] using the newly parametrized channel degree-of-freedom ${\ensuremath{\nu}}_{a}$ to better describe the Gaussian orthogonal ensemble (GOE) reference calculations. The Moldauer approximation is confirmed by a Monte Carlo study using a randomly generated $S$ matrix, as well as the GOE threefold integration formula. The method proposed is applied to the $^{238}\mathrm{U}(n,{n}^{\ensuremath{'}})$ cross-section calculation in the fast-energy range, showing an enhancement in the inelastic scattering cross sections.

Evaluation of neutron nuclear data on mercury isotopes

ABSTRACTNeutron nuclear data on 10 isotopes of mercury have been evaluated for the next version of Japanese evaluated nuclear data library (JENDL) general-purpose file in the energy region from 10−5 eV to 20 MeV. Resolved resonance parameters (RRPs) for 200, 202Hg were supplemented with the data which had not been considered in the previous library. Unresolved resonance parameters (URPs) were obtained by fitting to the total and capture cross sections calculated from nuclear models. A statistical model code was applied to evaluate cross sections above the resolved resonance region. Coupled-channel optical model parameters were employed for the interaction between neutrons and nuclei except 203Hg. Compound, pre-equilibrium, and direct-reaction processes were considered for cross-section calculation in the high energy region. The present results reproduce experimental data very well. The evaluated data are compiled into evaluated nuclear data file (ENDF) formatted data files.

A Lane consistent optical model potential for nucleon scattering on actinide nuclei with extended coupling

An extension for odd-A actinides of a previously derived dispersive coupledchannel optical model potential (OMP) for 238 U and 232 Th nuclei is presented. It is used to fit simultaneously all the available experimental databases including neutron strength functions for nucleon scattering on 232 Th, 233,235,238 U and 239 Pu nuclei. Quasi-elastic (p,n) scattering data on 232 Th and 238 U to the isobaric analogue states of the target nucleus are also used to constrain the isovector part of the optical potential. For even-even (odd) actinides almost all low-lying collective levels below 1 MeV (0.5 MeV) of excitation energy are coupled. OMP parameters show a smooth energy dependence and energy independent geometry.

Evaluation of neutron nuclear data on iodine isotopes

Neutron nuclear data on six isotopes of iodine have been evaluated for the next version of Japanese Evaluated Nuclear Data Library (JENDL) general-purpose file in the energy region from 10−5 eV to 20 MeV. Unresolved resonance parameters were obtained by fitting to the total and capture cross sections calculated from nuclear models, while resolved resonance parameters remain unchanged from JENDL-4.0. A statistical model code was applied to evaluate the cross sections above the resolved resonance region. Coupled-channel optical model parameters were employed for the interaction between neutrons and nuclei. Compound, pre-equilibrium and direct-reaction processes were considered for cross-section calculation in high-energy region. Giant-dipole resonance parameters for γ-ray transition from iodine isotopes were determined so as to reproduce measured γ-ray spectrum for 127I. The present results reproduce experimental data very well. The evaluated data are compiled into ENDF-formatted data files.

Evaluation of neutron nuclear data on tellurium isotopes

Neutron nuclear data on 13 Te isotopes have been evaluated for the next release of Japanese Evaluated Nuclear Data Library (JENDL) general purpose file in the energy region from 10− 5 eV to 20 MeV. Thermal capture cross sections of 120, 121m, 127m, 129m, 131m, 132Te were determined from the latest measurements or from a simplified formula, although the resolved resonance parameters, which describe the low-energy behavior of cross sections, remain unchanged from JENDL-4.0 for 122, 123, 124, 125, 126, 128, 130Te. A statistical model code was applied to evaluate the cross sections above the resolved resonance region. Coupled-channel optical model parameters were employed for the interaction between neutrons and nuclei. Compound, pre-equilibrium, and direct-reaction processes were considered for cross-section calculation in high-energy region. The present results reproduce experimental data very well, and are found to be much better than the JENDL-4.0 data. The evaluated data are compiled into evaluated nuclear data file (ENDF)-formatted data files.

Isotopic features of the N p N n function for even-even isotope chains of Ni and Zn

Low-energy (0.04–3.0 MeV) neutron data for even-even 58–64Ni and 64–70Zn isotopes are analyzed in terms of the coupled channel optical model (CCOM) as a function of NpNn, where Np(Nn) are the numbers of valent nucleons (particles or holes), and consider the relationship between the diffuseness parameter obtained from CCOM calculations and the value of the NpNn function. Considering the Ni and Zn isotope chains with the traditional magic number Z = 28 and the nontraditional N = 38 proves the existence of N = 28–38 subshells. The results from our analysis indicate the possible existence of the nontraditional magic nucleus 3068Zn38.

Rotational-vibrational Description of Nucleon Scattering on Actinide Nuclei Using a Dispersive Coupled-channel Optical Model

Tamura's coupling formalism has been extended to consider low-lying rotational bands built on vibrational (single-particle) band heads in well-deformed even-even (odd) actinides. These additional excitations are introduced as a perturbation to the underlying rigid rotor structure that is known to describe well the ground state rotational band of major actinides. Coupling matrix elements needed in extended Tamura's formalism are derived for both even-even and odd actinides. Employed dispersive optical model (DCCOMP) replaces the incident proton energy Ep (for proton induced reactions) by the equivalent Coulomb subtracted energy in all potential terms including both the imaginary and real potentials with the corresponding dispersive corrections. Therefore, the optical potential becomes fully symmetric for protons and neutrons. This potential is used to fit simultaneously all the available optical experimental databases (including neutron strength functions) for nucleon scattering on 238U and 232Th (even even) nuclei. Quasi-elastic (p,n) scattering data to the isobaric analogue states of the target nuclei are also used to constrain the isovector part of the optical potential. Derived Lane-consistent DCCOMP is based on coupling of almost all levels below 1 MeV of excitation energy. The ground state, octupole, beta, gamma and non-axial rotational bands are considered for even nuclei, and rotational bands built on single-particle levels – for odd nuclei. Application of derived potential to odd targets based on a new coupling scheme is foreseen.

A Fully Lane-consistent Dispersive Optical Model Potential for Even Fe Isotopes Based on a Soft-rotator Model

A fully Lane-consistent dispersive coupled-channel optical model (DCCOM) potential is derived that describes nucleon induced reactions on even iron isotopes. Low-lying structure of excited levels in iron even-even isotopes is described by a soft-rotator model that allows for dynamical deformation around the spherical shape. Soft-rotator Hamiltonian parameters are adjusted to reproduce the experimental energies of the low-lying collective levels of these isotopes. The comprehensive experimental database used in the fitting process included all scattering data for neutron and proton scattering up to 200 MeV. Employed Lane-consistent formalism allows deriving a potential fully symmetric for neutrons and protons. Lane consistency of the derived potential was validated by describing the quasi-elastic (p,n) scattering with excitation of IAS states. An exact approach for calculation of inelastic analyzing powers is derived. Calculated elastic and inelastic analyzing powers both for neutron and proton induced reactions were shown to be in good agreement with experimental data demonstrating the reliability of dispersive spin-orbit potential.

Evaluation of neutron nuclear data on antimony isotopes

Neutron nuclear data on 121,123,124,125,126Sb have been evaluated for the next version of JENDL general purpose file in the energy region from 10− 5 eV to 20 MeV. In the low-energy region, the latest resolved resonance parameters were taken into account for 121, 123Sb. The thermal capture cross sections of 125, 126Sb, for which no measurements exist, were determined by using a simplified formula. The statistical model was applied to calculate the cross sections above the resolved resonance region. In the calculations, coupled-channel optical model parameters were used for the interaction between neutrons and odd-mass targets. Preequilibrium and direct-reaction processes were considered in addition to the compound process. The present evaluation is consistent with available experimental data. The evaluated data are compiled into an ENDF-formatted data file.

Coupled channels optical model potential for rare earth nuclei

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.