Optical model with multiple band couplings using soft rotator structure

Abstract

Abstract.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. Coupled-channel optical model with soft-rotor couplingsTamura classical coupling model [1] has been recently extended to consider the coupling of collective rotational bands to the ground state band in even-even actinides including both axial and non-axial deformations [2][3][4]. These additional excitations were introduced as a perturbation to the underlying axial-symmetric rigid rotor structure of the ground state band (GSB) (i.e., K was considered a good quantum number characterizing all collective bands). However, it is well known that the rigid-rotor calculated energy of the levels overestimates the measured excitation energy with increasing excitation energy. For 238 U nucleus, the 10 + (12 + ) state is 6% (8.4%) higher in energy than predicted by the rigid-rotor model.A proper description of the energy of excited levels in actinides can be achieved by using a soft-rotator model (SRM) as demonstrated in Refs. [5,6]. SRM considers the stretching of the nucleus that lead to a higher momentum of inertia and lower excitation energies of high spin collective states in much better agreement with experimental data. Our goal is to use the SRM -reproducing the low-lying nuclear structure of even-even actinides with high accuracy -to predict coupling strengths and calculate corresponding matrix elements of the generalized dispersive optical model. The instant nuclear shape is described by small nonaxiality, and quadrupolar and octupolar departures a e-mail: dmart@sosny.bas-net.by from the axially symmetric equilibrium shape as follows λ=2,4,6,8 where R rr i is the rigid-rotor nuclear shape and δ R i -the shape perturbations, θ and ϕ are the angular coordinates in the body-fixed (intrin...

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

“…They indicate how nucleus shape changes upon transition between its states. Here we consider the following dynamic deformations of a nucleus shape: nonaxial quadrupole, axial octupole, and volume conservation correction (see [17,18]). This results in "effective" deformations: As discussed in Ref.…”

“…"Effective" deformations for interband coupling were treated as adjustable parameters for both even-even and odd-A nuclides, and for the later vibrational excitations were neglected. As a next step the SRM, describing low-energy collective excited states of a soft deformed even-even nucleus below 1 MeV, was used to compute "effective" deformations [18]. This allowed to perform more robust and reliable calculations with an account of multiband coupling and softness of target nucleus on even-even targets.…”

Predicting the optical observables for nucleon scattering on even-even actinides

“…Saturated couplings [13] were also shown to be important for an accurate prediction of the compound-nucleus formation cross sections, which is a key quantity (though not directly measurable) for statistical decay model calculations. Moreover, the total cross section differences of 232 Th and 238 U were well described [12], which is a very stringent test for the isovector component of the potential. Therefore, the same OMP can be used to describe nucleon-induced reactions on target nuclei with different numbers of neutrons and protons.…”

“…The soft rotator model (SRM) of nuclear structure has been successfully applied in coupled-channels optical model analyses for nucleon-induced reactions on many nuclei [9][10][11]. However, only recently were we able to derive a dispersive coupled-channels optical model potential for actinides based on soft-rotator couplings [12,13] with volume conservation and a saturated coupling scheme. The use of the SRM allows derivation of the inter-band coupling strengths from the low-lying nuclear structure of the even-even target nucleus, as shown for 232 Th and 238 U in Ref.…”

“…The use of the SRM allows derivation of the inter-band coupling strengths from the low-lying nuclear structure of the even-even target nucleus, as shown for 232 Th and 238 U in Ref. [12]. Saturated couplings [13] were also shown to be important for an accurate prediction of the compound-nucleus formation cross sections, which is a key quantity (though not directly measurable) for statistical decay model calculations.…”