Nuclear Optical Potential Research Articles

Peripheral reactions and elastic scattering induced by strongly bound, weakly bound and exotic nuclei

A phenomenological study of peripheral reactions induced by strongly bound, weakly bound and exotic projectiles on different targets is presented. A large number of experimental elastic scattering differential cross sections at energies close to the Coulomb barrier is studied on the basis of a simple nuclear optical model potential that depends on a small number of parameters. The derived wave functions, together with the imaginary component of the optical potential, allow the analysis of the radial peripheral absorption density distributions for the different kind of projectiles. These distributions, when appropriately normalized, show a clear correlation with the type of projectile regardless of the involved target and indicate that projectiles more prone to break up show a more peripheral absorption density distribution. This manifests in their magnitude, location and width. The relationship of these variables in the strongly bound group and the weakly bound group are described with a simple exponential function, while the exotic projectiles show two distinct groups, namely the neutron-halo and the proton-halo. For the neutron-halo projectiles such as He6, Li11 and Be11 there is a notable increment of the radial peripheral absorption density peak and the total reaction cross section as the breakup separation energy decreases. The same relationship is established for the proton-halo projectiles B8 and F17 but their reduced effective dipole charge leads to a lower probability of dipole Coulomb breakup that results in a substantial reduction in the extent of their peripheral absorption.

Optical potentials for the rare-isotope beam era

We review recent progress and motivate the need for further developments in nuclear optical potentials that are widely used in the theoretical analysis of nucleon elastic scattering and reaction cross sections. In regions of the nuclear chart away from stability, which represent a frontier in nuclear science over the coming decade and which will be probed at new rare-isotope beam facilities worldwide, there is a targeted need to quantify and reduce theoretical reaction model uncertainties, especially with respect to nuclear optical potentials. We first describe the primary physics motivations for an improved description of nuclear reactions involving short-lived isotopes, focusing on its benefits for fundamental science discoveries and applications to medicine, energy, and security. We then outline the various methods in use today to build optical potentials starting from phenomenological, microscopic, and ab initio methods, highlighting in particular, the strengths and weaknesses of each approach. We then discuss publicly-available tools and resources facilitating the propagation of recent progresses in the field to practitioners. Finally, we provide a set of open challenges and recommendations for the field to advance the fundamental science goals of nuclear reaction studies in the rare-isotope beam era. This paper is the outcome of the Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program ‘Optical Potentials in Nuclear Physics’ held in March 2022 at FRIB. Its content is non-exhaustive, was chosen by the participants and reflects their efforts related to optical potentials.

Cluster folding model analysis of the 7Be+28Si elastic scattering in the near-barrier

In the framework of the optical model, the elastic scattering of the radioactive projectile 7Be on the 28Si target at four energies near the Coulomb barrier has been analyzed. The cluster folding model is used to determine the real part of the nuclear optical potential. For comparison, two microscopic optical potentials have been generated using the DDM3Y effective NN interaction based upon two different forms for 7Be density distribution. All the obtained real potentials, in conjunction with phenomenological Woods-Saxon imaginary parts, have successfully reproduced the elastic scattering angular distributions over the measured angular range. The energy dependence of the real and imaginary strengths that are produced by the best-fit of the experimental data was examined. Neither the usual threshold anomaly nor the breakup threshold anomaly can be observed at the considered energy range. The obtained cross sections have been reduced and compared with earlier theoretical and experimental data of 7Li on the same target near the Coulomb barrier.

On the width of the K−D atom ground state

Experiments at DAΦNE-Frascati and at J-PARC are scheduled to produce K−D atoms and observe their X-ray cascade down to the 1S ground state (g.s.), thereby measuring its strong-interaction width and shift away from a purely Coulomb state. A width Γ1S≲1 keV will ensure good resolution of the X-ray transitions feeding the 1S g.s. Here we study the expected K−D 1S g.s. width from the perspective of global fits to level shifts and widths in heavier kaonic atoms across the periodic table, using K− nuclear optical potentials constructed from K¯N chiral interaction models. Special attention is paid to the subthreshold energy at which the K¯N subsystem interacts in the K−D atom g.s. Within this approach we predict strong-interaction upward level shift of close to 700 eV and width of about 1.2 to 1.3 keV for the K−D atom 1S g.s., in fair agreement with genuinely three-body K−D atom calculations. Comparison is made with π−D atom phenomenology.

Different folding models for 6Li+28Si elastic scattering

In this work, the elastic scattering of 6Li+[Formula: see text]Si system at wide range energies from 76 to 318[Formula: see text]MeV is analyzed. The analysis is carried out in the framework of the optical model (OM). Two different methods are adopted for nuclear optical potential of this system. The first method is the double folding cluster (DFC) for the real part supplied with an imaginary part in the Woods–Saxon (WS) form. In the second one, the double folding (DF) model based upon São Paulo potential (SPP) is used as real and imaginary parts each multiplied by a corresponding normalization factor. For [Formula: see text]Si, the full [Formula: see text]-cluster density is considered while the [Formula: see text]-deuteron ([Formula: see text]–[Formula: see text]) structure is considered for 6Li. Therefore, the DFC real central part is calculated by folding both [Formula: see text]–[Formula: see text] and [Formula: see text]–[Formula: see text] effective interaction between target and nuclei over the cluster densities of the target and projectile. The derived renormalized potentials give a successful description of the data. The present results are in good agreement with the previous work. This agreement confirms the validity of the present methods to generate nucleus–nucleus optical potentials.

Comparison of optical potential for nucleons and varDelta resonances

Precise modeling of neutrino interactions on nuclear targets is essential for neutrino oscillations experiments. The modeling of the energy of final state particles in quasielastic (QE) scattering and resonance production on bound nucleons requires knowledge of both the removal energy of the initial state bound nucleon as well as the average Coulomb and nuclear optical potentials for final state leptons and hadrons. We extract the average values of the real part of the nuclear optical potential for final state nucleons (U_{opt}^{QE}) as a function of the nucleon kinetic energy from inclusive electron scattering data on nuclear targets (_mathbf{6 }^mathbf{12 }{} mathbf{C} +_mathbf{8 }^mathbf{16 }{} mathbf{O} , _mathbf{20 }^mathbf{40 }{} mathbf{Ca} +_mathbf{18 }^mathbf{40 }{} mathbf{Ar} , _mathbf{3 }^mathbf{6 }{} mathbf{Li} , _mathbf{18 }^mathbf{27 }{} mathbf{Al} , _mathbf{26 }^mathbf{56 }{} mathbf{Fe} , _mathbf{82 }^mathbf{208 }{} mathbf{Pb} ) in the QE region and compare to calculations. We also extract values of the average of the real part of the nuclear optical potential for a varDelta (1232) resonance in the final state (U^varDelta _{opt}) within the impulse approximation. We find that U^varDelta _{opt} is more negative than U_{opt}^{QE} with U^varDelta _{opt}approx 1.5 U_{opt}^{QE} for _mathbf{6 }^mathbf{12 }{} mathbf{C} .

Neutron elastic scattering on calcium isotopes from chiral nuclear optical potentials

We formulate microscopic neutron-nucleus optical potentials from many-body perturbation theory based on chiral two- and three-body forces. The neutron self energy is first calculated in homogeneous matter to second order in perturbation theory, which gives the central real and imaginary terms of the optical potential. The real spin-orbit term is calculated separately from the density matrix expansion using the same chiral interaction as in the self energy. Finally, the full neutron-nucleus optical potential is derived within the improved local density approximation utilizing mean field models consistent with the chiral nuclear force employed. We compare the results of the microscopic calculations to phenomenological models and experimental data up to projectile energies of $E = 200$ MeV. Experimental elastic differential scattering cross sections and vector analyzing powers are generally well reproduced by the chiral optical potential, but we find that total cross sections are overestimated at high energies.

Systematic analysis of elastic α scattering on [formula omitted] nuclei around the Coulomb barrier

Alpha elastic scattering angular distributions on target nuclei 118, 124Sn and 120-130Te at energies near the Coulomb barrier are analyzed. We used three versions of the nuclear optical model potentials (OMP) to analyze twenty-nine data sets. JLM and the density and energy-dependent DDM3Y1 with finite range exchange term effective interactions were used to generate these potentials. Two real folded potentials based on JLM and DDM3Y1 effective interactions supplied with the conventional Wood–Saxon (WS) imaginary potential are used in the cross sections calculations. These potentials are denoted as JLM-R and DDM3Y1-FR, respectively. In addition, we used the full complex folded OMP, denoted as JLM-RI, to analyze the same data. These potentials successfully predict the cross section of the systems under study. We found that the JLM-R and DDM3Y1-FR could reproduce the measured cross sections over the full angular range very well compared to microscopic JLM-RI potential. Our calculated potentials have a clear energy dependence and in addition a weak target mass dependence. The total reaction cross section and volume integral are investigated in comparison to previous studies. The derived potentials are very promising for the construction of a new global α-nucleus potential and provide new parameters of α–induced reactions and scattering at the energy range 17–27 MeV.

Investigation of the 6Li + 40Ca elastic scattering using different folding models

In the present study we investigate the 6Li + 40Ca elastic scattering through the energy range 26-240MeV in the framework of the optical model and $ \alpha$ -cluster structure of the colliding nuclei. The double folding (DF) calculations for the real central part of the nuclear optical potential are performed by folding the $ \alpha$ -$ \alpha$ and $ \alpha$ -n effective interactions over the density distributions of $ \alpha$ -clusters in the target ( 40Ca nucleus and considering the $ \alpha$ -d structure of the projectile ( 6Li nucleus. The imaginary part of the optical potential is expressed in the phenomenological Woods-Saxon form. The measured angular distributions of the elastic scattering differential cross section have been successfully reproduced using the derived semi-microscopic potentials for nine sets of data all over the measured angular range. However, it is found that introducing a real renormalization factor smaller than unity is essential in order to obtain a successful description of the data at bombarding energies larger than 10MeV/nucleon. The obtained results confirm the validity of the $ \alpha$ -cluster structure to generate a realistic representation of nucleus-nucleus optical potentials. For the sake of comparison, the same considered sets of data are reanalyzed using microscopic DF optical potentials based upon the Sao Paulo potential. The energy dependence of the corresponding reaction cross sections and real and imaginary volume integrals of the considered reaction are also investigated.

Weak sensitivity of three-body ( d,p ) reactions to np force models

Adiabatic distorted-wave approximation (ADWA) study of three-body $(d,p)$ transfer reactions [G.W. Bailey, N.K. Timofeyuk, and J.A. Tostevin, Phys. Rev. Lett. 117, 162502 (2016)] reported strong sensitivity of cross sections to the neutron-proton $(np)$ interaction model when the nucleon-nucleus optical potential is nonlocal. The verification of this unusual finding using more reliable methods is aimed for in the present work. A rigorous Faddeev-type three-body scattering theory is applied to the study of $(d,p)$ transfer reactions. The equations for transition operators are solved in the momentum-space partial-wave framework. Differential cross sections for $^{26}$Al$(d,p)^{27}$Al reactions are calculated using nonlocal nuclear optical potentials and a number of realistic $np$ potentials. Only a weak dependence on the $np$ force model is observed, typically one order of magnitude lower than in the previous ADWA study. The shape of the angular distribution of the experimental data is well reproduced. Cross sections of $(d,p)$ transfer reactions calculated using a rigorous three-body method show little sensitivity to the $np$ interaction model. This indicates a failure of the ADWA in the context of nonlocal potentials. Some evident shortcomings of the ADWA are pointed out.

Analysis of 8B Proton Halo Nucleus Scattered from 12C and 58Ni at Different Energies

Angular distributions in the elastic scattering of 8B from 12C and 58Ni targets at different energies have been analyzed in the framework of the double-folding (DF) optical model. The real central part of the nuclear optical potential is obtained by folding the M3Y effective interaction with the cluster density distribution of the 8B nucleus. The experimental angular distributions have been successfully reproduced. This confirms the validity of the cluster structure of the 8B nucleus.

Important role of projectile excitation in O16+Ni60 and O16+Al27 scattering at intermediate energies

The elastic scattering angular distribution of the $^{16}$O$+^{60}$Ni system at $260$ MeV was measured in the range of the Rutherford cross section down to $7$ orders of magnitude below. The cross sections of the lowest $2^{+}$ and $3^{-}$ inelastic states of the target were also measured over a several orders of magnitude range. Coupled channel (CC) calculations were performed and are shown to be compatible with the whole set of data only when including the excitation of the projectile and when the deformations of the imaginary part of the nuclear optical potential are taken into account. Similar results were obtained when the procedure is applied to the existing data on $^{16}$O$+^{27}$Al elastic and inelastic scattering at $100$ and $280$ MeV. An analysis in terms of Dynamical Polarization Potentials (DPP) indicate the major role of coupled channel effects in the overlapping surface region of the colliding nuclei.

Estimation of M1 scissors mode strength for deformed nuclei in the medium- to heavy-mass region by statistical Hauser-Feshbach model calculations

Radiative neutron capture is an important nuclear reaction whose accurate description is needed for many applications ranging from nuclear technology to nuclear astrophysics. The description of such a process relies on the Hauser-Feshbach theory which requires the nuclear optical potential, level density and $\gamma$-strength function as model inputs. It has recently been suggested that the M1 scissors mode may explain discrepancies between theoretical calculations and evaluated data. We explore statistical model calculations with the strength of the M1 scissors mode estimated to be dependent on the nuclear deformation of the compound system. We show that the form of the M1 scissors mode improves the theoretical description of evaluated data and the match to experiment in both the fission product and actinide regions. Since the scissors mode occurs in the range of a few keV $\sim$ a few MeV, it may also impact the neutron capture cross sections of neutron-rich nuclei that participate in the rapid neutron capture process of nucleosynthesis. We comment on the possible impact to nucleosynthesis by evaluating neutron capture rates for neutron-rich nuclei with the M1 scissors mode active.

Recommended Cross Sections and Optical Potential of Dy Isotopes for Neutron Induced Reactions at 14.0 MeV

The evaluation is based mainly on the calculations of the nuclear optical model potential and the relevant parameters which are collected and selected from References Input Parameter Library (RIPL-3) which is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The analyzing of a complete energy range has been done starting from threshold energy for each reaction. The cross sections are reproduced in fine steps of incident neutron energy with 0.01MeV intervals with their corresponding errors. The recommended cross sections for available experimental data taken from EXFOR library have been calculated for all the considered neutron induced reactions for Dy (Z=66; A=162-164) isotopes. The calculated results are analyzed and compared with the experimental data. The optimized optical potential model parameters give a very good agreement with the experimental data over the energy range 13.4-14.87MeV for neutron induced cross section reactions (n,p) for spherical Dy-162 target element, (n,2H), (n,d), (n,n+p),and (n,p) for spherical Dy-163 target element, and (n,2H) and (n,p) for spherical Dy-164 target element.

Recommended Cross Sections and Optical Potential of Dy Isotopes for Neutron Induced Reactions at 14.0 MeV

The evaluation is based mainly on the calculations of the nuclear optical model potential and the relevant parameters which are collected and selected from References Input Parameter Library (RIPL-3) which is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The analyzing of a complete energy range has been done starting from threshold energy for each reaction. The cross sections are reproduced in fine steps of incident neutron energy with 0.01MeV intervals with their corresponding errors. The recommended cross sections for available experimental data taken from EXFOR library have been calculated for all the considered neutron induced reactions for Dy (Z=66; A=162-164) isotopes. The calculated results are analyzed and compared with the experimental data. The optimized optical potential model parameters give a very good agreement with the experimental data over the energy range 13.4-14.87MeV for neutron induced cross section reactions (n,p) for spherical Dy-162 target element, (n,2H), (n,d), (n,n+p),and (n,p) for spherical Dy-163 target element, and (n,2H) and (n,p) for spherical Dy-164 target element.

Optical Model Potential Using CINDA Library for Neutron Induced Cross Section Reactions for Spherical Uranium-235,238 Isotopes

The calculation are based mainly on the nuclear optical model potential and relevant parameters are collected and selected from References Input Parameter Library (RIPL) which is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The analyzing of a complete energy range has done starting from threshold energy for each reaction. The cross sections are reproduced in fine steps of incident neutron energy with 0.01MeV intervals with their corresponding errors. The recommended cross sections for available experimental data taken from CINDA library have been calculated for all the considered neutron induced reactions for spherical U-235 and U-238 isotopes. The calculated results are analyzed and compared with the experimental data. The optimized optical potential model parameters give a very good agreement with the experimental data over the energy range 0.001-20MeV for neutron induced cross section reactions (n,f), (n,tot), (n,el), (n,inl), (n,2n), (n,3n), and (n,γ) for spherical U-235 and U-238 target elements.

Evaluation of Optical Model Potential Using Neutron Induced Cross Section Reaction for Spherical Uranium-238 Isotope up to 20MeV

The evaluation are based on mainly on the calculations of the nuclear optical model potential and relevant parameters are collected and selected from References Input Parameter Library (RIPL) which is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The analyzing of a complete energy range has done starting from threshold energy for each reaction. The cross sections are reproduced in fine steps of incident neutron energy with 0.01MeV intervals with their corresponding errors. The recommended cross sections for available experimental data taken from EXFOR library have been calculated for all the considered neutron induced reactions for U-238 isotopes. The calculated results are analyzed and compared with the experimental data. The optimized optical potential model parameters give a very good agreement with the experimental data over the energy range 0.001-20MeV for neutron induced cross section reactions (n,f), (n,tot), (n,el), (n,inl), (n,2n), (n,3n), and (n,γ) for spherical U-238 target elements.

Optical Model Potential Using CINDA Library for Neutron Induced Cross Section Reactions for Spherical Uranium-235,238 Isotopes

The calculation are based mainly on the nuclear optical model potential and relevant parameters are collected and selected from References Input Parameter Library (RIPL) which is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The analyzing of a complete energy range has done starting from threshold energy for each reaction. The cross sections are reproduced in fine steps of incident neutron energy with 0.01MeV intervals with their corresponding errors. The recommended cross sections for available experimental data taken from CINDA library have been calculated for all the considered neutron induced reactions for spherical U-235 and U-238 isotopes. The calculated results are analyzed and compared with the experimental data. The optimized optical potential model parameters give a very good agreement with the experimental data over the energy range 0.001-20MeV for neutron induced cross section reactions (n,f), (n,tot), (n,el), (n,inl), (n,2n), (n,3n), and (n,γ) for spherical U-235 and U-238 target elements.

Evaluation of Optical Model Potential Using Neutron Induced Cross Section Reaction for Spherical Uranium-238 Isotope up to 20MeV

The evaluation are based on mainly on the calculations of the nuclear optical model potential and relevant parameters are collected and selected from References Input Parameter Library (RIPL) which is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The analyzing of a complete energy range has done starting from threshold energy for each reaction. The cross sections are reproduced in fine steps of incident neutron energy with 0.01MeV intervals with their corresponding errors. The recommended cross sections for available experimental data taken from EXFOR library have been calculated for all the considered neutron induced reactions for U-238 isotopes. The calculated results are analyzed and compared with the experimental data. The optimized optical potential model parameters give a very good agreement with the experimental data over the energy range 0.001-20MeV for neutron induced cross section reactions (n,f), (n,tot), (n,el), (n,inl), (n,2n), (n,3n), and (n,γ) for spherical U-238 target elements.

Comparative study of alpha + nucleus elastic scattering using different models

The alpha (α) elastic scattering from different targets potential over the energy range 10–240 MeV has been analyzed in the framework of the single-folding (SF) optical model. Four targets are considered, namely, 24 Mg , 28 Si , 32 S and 40 Ca . The SF calculations for the real central part of the nuclear optical potential are performed by folding an effective α–α interaction with the α-cluster distribution density in the target nucleus. The imaginary part of the optical potential is expressed in the phenomenological Woods–Saxon (WS) form. The calculated angular distributions of the elastic scattering differential cross-section using the derived semimicroscopic potentials successfully reproduce 36 sets of data all over the measured angular ranges. The obtained results confirm the validity of the α-cluster structure of the considered nuclei. For the sake of comparison, the same sets of data are reanalyzed using microscopic double-folded optical potentials based upon the density-dependent Jeukenne–Lejeune–Mahaux (JLM) effective nucleon–nucleon interaction.