Phenomenological Optical Potential Research Articles

Measurement of proton induced absolute production cross-section of 6.13, 6.92 and 7.12 MeV γ-rays from 16O(p,p ′γ )16O reaction

In this article, we report the absolute production cross-section of 6.13, 6.92 and 7.12 MeV γ-rays from the 16O(p,p ′γ )16O reaction for incident proton energy range of 8-16 MeV. Angular distributions of the three γ-rays have been measured for seven angles at 9 MeV proton energy. A detailed phenomenological optical model potential (OMP) was set up to analyse the cross-section data. The OMP parameters were optimised using elastic, polarization and total reaction data available in the literature for protons and neutrons. Low-lying states of 16O were coupled, the optical potential was deformed using deformation parameters, and several resonances were included in the calculations to account for the nuclear structure effects. The potentials so generated have been used to calculate the differential and total cross sections for both 16O(p,p ′ )16O and 16O(p,p ′γ )16O reactions. Our calculated cross-sections are in fairly good agreement with our measured data for 6.13, 6.92 and 7.12 MeV γ-rays. However, there still exist discrepancies in reproduction of the finer details of the cross sections. The comparisons of the calculations with the data bring forth the rather complex roles of channel couplings, resonances in the p+16O system and target deformation in the variation of the cross sections with projectile energy. The increased contribution of nuclear structure effects in light mass nuclei, leads to an apparent loss of predictive power of the theoretical calculation, as we approach the low-energy region of less than 10 MeV projectile energy.

New model comparison for semi-inclusive charged-current electron and muon neutrino scattering by Ar40 in the energy range of the MicroBooNE experiment

In this work we present a comparison of semi-inclusive muon and electron neutrino cross sections with Ar40 target measured by the MicroBooNE collaboration with the predictions of an unfactorized model based on the relativistic distorted wave impulse approximation (RDWIA) and the SuSAv2-MEC model implemented in the neutrino event generator GENIE. The predictions based on the RDWIA approach, with a realistic description of the initial state and a phenomenological relativistic complex optical potential for the description of final state interactions, better describe the measured cross sections than GENIE-SuSAv2 and RDWIA with a purely real potential. Published by the American Physical Society 2024

The Abnormal Threshold Anomaly in the 6Li + 208Pb System

Numerous studies have demonstrated that the phenomenological optical potential of tightly bound nuclear systems presents a threshold anomaly phenomenon in the near-Coulomb barrier energy region, where the relationship between the real and imaginary potentials can be well described by the dispersion relation. However, for some weakly bound nuclear systems, the phenomenological optical potential seems to manifest differently, and the dispersion relation struggles to describe the behavior between real and imaginary potentials. Recently, we measured the angular distributions of the transfer reaction 207Pb(7Li,6Li)208Pb in both near and deep barrier energy regions, as well as the elastic scattering angular distributions of the entrance channel 7Li+207Pb. Optical potentials of the 6Li+208Pb system were extracted.The current results indicate that the optical potentials exhibit an abnormal threshold anomaly, and the dispersion relation is not applicable. Possible explanations are discussed, yet further investigations into the underlying physics are required.

Nuclear reaction cross sections and the optical potentials and for the n-12C and N-12C scattering

In this talk we first discuss total cross sections for the system n-12C in the incident energy range 20-500 MeV, calculated with a phenomenological optical potential and the optical model. We compare with calculations done with the eikonal model using the same potential and a single folding potential in the optical limit. Several single folding potentials are obtained using 12C densities from different models. These potentials are sensitive to the density used and none of them reproduces the characteristics of the phenomenological potential nor the cross section results. We then discuss nucleus-nucleus potentials and reaction cross sections for some projectiles on 12C within the eikonal formalism. We find that single folded projectile-target imaginary potentials and double folded potentials can produce similar energy dependence of the reaction cross sections but the single folding results agree better with experimental data provided the radius parameter of the phenomenological n-target potential is allowed to be energy dependent. We conclude that a single folding nucleusnucleus potential build on a phenomenological nucleon-nucleus potential can constitute an interesting and useful alternative to double folding potentials.

Construction of density-dependent α-nucleon interaction to describe α-nucleus scattering

We provide a global density-dependent α-nucleon (DD-αN) interaction to construct the α-nucleus optical potential in a wide range of incident energies. The α-nucleus potential based on the folding model with the present DD-αN interaction reproduces the experimental data up to backward angles using the point-nucleon density obtained by the mean-field model. The present DD-αN interaction is based on the phenomenological optical potential to reproduce the p + 4He elastic scattering at the incident energies at 12.04–1000 MeV. Namely, the α-nucleon system is considered an elementary process. The density dependence (medium effect) of the DD-αN interaction is phenomenologically added to reproduce the α elastic scatterings by the 16O, 40Ca, 58Ni, 90Zr and 208Pb targets at E/A = 10–342.5 MeV. The total reaction cross sections are also compared with the experimental data.

Description of elastic scattering for 7Li-induced reactions on 1p-shell nuclei* *Supported by the National Natural Science Foundation of China (11405099, 11575291, 12065003), the Natural Science Foundation of Shanxi Province, China (202103021224309, 201901D111317). This work is also a part of IAEA Coordinated Research Projects (CRPs) on Recommended Input Parameter Library (RIPL) for Fission Cross Section Calculations (20464)

The experimental data of elastic scattering angular distributions for 9Be, 10B, 11B, 12C, 13C, 15N, and 16O targets from 4.5 to 131.8 MeV and 7Li target from 8.0 to 42.0 MeV are fitted to realize the global phenomenological optical potentials (GPOPs) for the 7Li-induced reactions on 1p-shell nuclei. Thus, the 7Li elastic scattering from the 1p-shell nuclei can be systematically described using the established GPOPs. The elastic scattering angular distributions are also reanalyzed using a microscopic method within the framework of the new version of double folding São Paulo potential (SPP2). To better describe the elastic scattering at backward angles, the contribution of elastic transfer is further estimated by the distorted wave Born approximation (DWBA) method. Based on the obtained GPOPs, the inelastic scattering angular distributions are also obtained through the coupled channels (CC) method for the different excited states.

Elastic scattering and total reaction cross sections of 6Li examined via a microscopic continuum discretized coupled-channels model* *Supported by the National Natural Science Foundation of China (U2067205)

We present a systematic study of 6Li elastic scattering and total reaction cross sections at incident energies around the Coulomb barrier within the continuum discretized coupled-channels (CDCC) framework, where 6Li is treated in an α+d two-body model. Collisions with 27Al, 64Zn, 138Ba, and 208Pa are analyzed. The microscopic optical potentials (MOP) based on Skyrme nucleon-nucleon interaction for α and d are adopted in CDCC calculations and satisfactory agreement with the experimental data is obtained without any adjustment on MOPs. For comparison, α and d global phenomenological optical potentials (GOP) are also used in CDCC analysis and a reduction of no less than 50% on the surface imaginary part of deuteron GOP is required for describing the data. In all cases, the 6Li breakup effect is significant and provides repulsive correction to the folding model potential. The reduction on the surface imaginary part of GOP of deuteron reveals a strong suppression of the reaction probability of deuteron as a component of 6Li when compared with that of a free deuteron. Further investigation is performed by considering the d breakup process equivalently within the dynamic polarization potential approach, and the results show that d behaves in a manner similar to a tightly bound nucleus in 6Li induced reactions.

Measurements of the Zr96(α,n)Mo99 cross section for astrophysics and applications

The reaction $^{96}\mathrm{Zr}(\ensuremath{\alpha},\mathrm{n})^{99}\mathrm{Mo}$ plays an important role in $\ensuremath{\nu}$-driven wind nucleosynthesis in core-collapse supernovae and is a possible avenue for medical isotope production. Cross-section measurements were performed using the activation technique at the Edwards Accelerator Laboratory. Results were analyzed along with world data on the $^{96}\mathrm{Zr}(\ensuremath{\alpha},n)$ cross section and $^{96}\mathrm{Zr}(\ensuremath{\alpha},\ensuremath{\alpha})$ differential cross section using large-scale Hauser-Feshbach calculations. We compare our data, previous measurements, and a statistical description of the reaction. We find a larger cross section at low energies compared to prior experimental results, allowing for a larger astrophysical reaction rate. This may impact results of core-collapse supernova $\ensuremath{\nu}$-driven wind nucleosynthesis calculations but does not significantly alter prior conclusions about $^{99}\mathrm{Mo}$ production for medical physics applications. The results from our large-scale Hauser-Feshbach calculations demonstrate that phenomenological optical potentials may yet be adequate to describe $(\ensuremath{\alpha},n)$ reactions of interest for $\ensuremath{\nu}$-driven wind nucleosynthesis, albeit with regionally adjusted model parameters.

Prediction for ( p,n ) charge-exchange reactions with uncertainty quantification

Background: Charge-exchange reactions are a powerful tool for exploring nuclear structure and nuclear astrophysics; however, a robust charge-exchange reaction theory with quantified uncertainties is essential for extracting reliable physics.Purpose: The goal of this work is to determine the uncertainties due to optical potentials used in the theory for charge-exchange reactions to isobaric analog states.Method: We implement a two-body reaction model to study $(p,n)$ charge-exchange transitions and perform a Bayesian analysis. The $(p,n)$ reaction to the isobaric analog states of $^{14}\mathrm{C}$, $^{48}\mathrm{Ca}$, and $^{90}\mathrm{Zr}$ targets are studied over a range of beam energies. We compare predictions using standard phenomenological optical potentials with those obtained microscopically.Results: Charge-exchange cross sections are reasonably reproduced by modern optical potentials. However, when uncertainties in the optical potentials are accounted for, the resulting predictions of charge-exchange cross sections have very large uncertainties.Conclusions: The charge-exchange reaction cross section is strongly sensitive to the input interactions, making it a good candidate to further constrain nuclear forces and aspects of bulk nuclear matter. However, further constraints on the optical potentials are necessary for a robust connection between this tool and the underlying isovector properties of nuclei.

First application of the dispersive optical model to (p,2p) reaction analysis within the distorted-wave impulse approximation framework

Both ($e$,$e'p$) and ($p$,$2p$) reactions have been performed to study the proton single-particle character of nuclear states with its related spectroscopic factor. Recently, the dispersive optical model (DOM) was applied to the ($e$,$e'p$) analysis revealing that the traditional treatment of the single-particle overlap function, distorted waves, and nonlocality must be further improved to achieve quantitative nuclear spectroscopy. We apply the DOM wave functions to the traditional ($p$,$2p$) analysis and investigate the consistency of the DOM spectroscopic factor that describes the ($e$,$e'p$) cross section with the result of the ($p$,$2p$) analysis. Additionally, we make a comparison with a phenomenological single-particle wave function and optical potential. Uncertainty arising from a choice of $p$-$p$ interaction is also investigated. We implement the DOM wave functions to the distorted wave impulse approximation (DWIA) framework for ($p$,$2p$) reactions. DOM + DWIA analysis on $^{40}$Ca($p$,$2p$)$^{39}$K data generates a proton $0d_{3/2}$ spectroscopic factor of 0.560, which is meaningfully smaller than the DOM value of 0.71 shown to be consistent with the ($e$,$e'p$) analysis. Uncertainties arising from choices of single-particle wave function, optical potential, and $p$-$p$ interaction do not explain this inconsistency. The inconsistency in the spectroscopic factor suggests there is urgent need for improving the description of $p$-$p$ scattering in a nucleus and the resulting in-medium interaction with corresponding implications for the analysis of this reaction in inverse kinematics.

Global phenomenological optical model potential for 14N-nucleus elastic scattering

In this paper, a set of global optical model potential parameters of [Formula: see text]N is obtained by fitting the experimental data of the elastic scattering angular distributions for the targets from [Formula: see text]Mg to [Formula: see text]Pb below 200 MeV. The global optical model potential parameters of [Formula: see text]N-nucleus reactions obtained are analyzed and used to describe the experimental data. It is found that the present form of the global optical model potential could reproduce the experimental data. Moreover, the elastic scattering angular distributions for the reactions of [Formula: see text]N inducing on some lighter targets and the elastic scattering observable quantity for the reactions involving [Formula: see text]N projectile are predicted using the obtained global optical model potential, and a reasonable description of the experimental data is obtained by comparing with the existing corresponding experimental data.

The São Paulo Potential and the 3He Breakup Reaction at 130 MeV on 93Nb and 197Au

Nuclear reactions induced by weakly bound nuclei often result in the emission of light particles as products of the projectile breakup. The incident particle is expected to fragment before reaching the interior of the target nuclei, a characteristic that tends to favor forward angular emission. Although the first models developed for such reactions were proposed many decades ago by Udagawa and Tamura, Ichimura, Austern, Vincent, and Kasano, and Hussein and McVoy, to this date most of the attention has been dedicated to the breakup of the deuteron and other very weakly bound systems, while more strongly bound projectiles have not been fully explored. Here, we describe the production of protons and deuterons from the breakup of 3He. The breakup of 3He on two heavy targets, 93Nb and 197Au, is analyzed in this study. However, the incoming energy involved is much larger than that of the standard phenomenological optical potentials available in the literature for the 3He entrance channel. We have overcome this difficulty by using the São Paulo potential and adjusting the nuclear diffusivity. The deuteron inclusive spectra were calculated at several angles and compared well with the experimental data. Theoretical proton emission predictions are also given for future reference, since no inclusive measurements were performed for the targets under study. One of our goals is to verify the description of deuteron emission from fast projectiles, for which many partial waves contribute to the scattering process.

Eikonal method for charge-exchange reactions at intermediate energies

A novel description of charge-exchange reactions at intermediate energies is developed, based on both phenomenological or microscopic eikonal phase-shift functions. The results obtained within this eikonal approach are in good agreement with the distorted-wave Born approximation calculations within the energy region where both approximations should be valid. They also compare well with the experimental data, even at relatively low energy domain. At higher energies, relativistic kinematics have also been added and shown to be relevant. Owing to the microscopic feature of the formulation, our theory also has the advantage that it can be applied to high energies where the phenomenological optical potentials are rarely available.

Localization of peripheral reactions and sensitivity to the imaginary potential

The aim of the present study is to make for the first time in the literature a systematic and quantitative assessment of the evaluation of the imaginary part of the optical potential calculated within the folding model and its consequences on the localization of surface reactions. Comparing theoretical and experimental reaction cross sections, for some light projectiles on a 9Be target, it has recently been shown that a single-folded s.f. (light-) nucleus-9Be imaginary optical potential is more accurate than a double-folded d.f. optical potential. Within the eikonal formalism for the cross sections and phase shifts, the single-folded potential was obtained using a n-9Be phenomenological optical potential and microscopic projectile densities. This paper is a follow-up in which we systematically study a series of different light and medium-mass projectile induced reactions on 9Be. Our results confirm that the s.f. cross sections are larger than the d.f. cross sections and the effect increases with the projectile mass. Furthermore the strong absorption radius parameter extracted from the S matrices calculated with the s.f. has a stable value rs=1.3−1.4 fm for all projectile masses in the range of incident energies 40-100 A.MeV. This indicates that a clear geometrical separation can be made between the region of surface reactions, the region of strong absorption into other channels and the region of weak nuclear interaction. The d.f. results are instead much scattered and the separation between surface reactions and other channels does not seem to be consistent. Excellent agreement with recent experimental results confirms the validity of our approach.

X(2239) and as hidden-strange molecular states from interaction * *Supported by the National Natural Science Foundation of China (11675228, 11775050, 61871124), the Fundamental Research Funds for the Central Universities, the national defense Pre-Research foundation of China, by State Key Laboratory of Acoustics, Chinese Academy of Sciences (SKLA201604), Science and Technology on Sonar Laboratory, the Stable Supporting Fund of Acoustic Science

In this work, we propose the possible assignment of the newly observed , as well as , as a molecular state from the interaction of a baryon and an antibaryon . With the help of effective Lagrangians, the interaction is described within the one-boson-exchange model with , , , , and exchanges considered. After inserting the potential kernel into the quasipotential Bethe-Salpeter equation, the bound states from the interaction can be studied by searching for the pole of the scattering amplitude. Two loosely bound states with spin parities and appear near the threshold with almost the same parameter. The state can be assigned to observed at BESIII, which is very close to the threshold. The scalar meson can be interpreted as a state from the interaction. The annihilation effect is also discussed through a coupled-channel calculation plus a phenomenological optical potential. It provides large widths to two bound states produced from the interaction. The mass of the state is slightly larger than the mass of the state after including the annihilation effect, which is consistent with our assignment of these two states as and , respectively. The results suggest that further investigation is required to understand the structures near the threshold, such as , , and .

Angular zone of influence for fusion and direct reactions on elastic scattering of 6Li with 58Ni, 59Co, 64Ni, and 64Zn

Recently, a systematic study of fusion and elastic scattering data was performed for the 6Li + (58Ni, 59Co, 64Ni, 64Zn) systems. Appropriate polarization potentials satisfying the dispersion relation were extracted, which can be associated to fusion and direct reaction couplings, respectively. By examining the relative strengths of the corresponding absorptive parts, a semiclassical analysis can be carried out which gives an indication about the angular range where direct (fusion) reactions are more important in determining the elastic scattering angular distributions. The results of such an analysis are presented for all four systems. The developed method is useful to explore the sensitivity of the elastic scattering angular distributions to the radial details of the phenomenological optical model potential. An example is presented where large sensitivity to distances smaller than the Coulomb barrier radius is evident.

Microscopic study of 7Li-nucleus potential * * Supported by National Natural Science Foundation of China (11705009, 11575291) and Science Challenge Project (TZ2018005)

A microscopic approach is employed to study the optical potential for the 7Li-nucleus interaction system without any free parameters. It is obtained by folding the microscopic optical potentials of the constituent nucleons of 7Li over their density distributions. We employ an isospin-dependent nucleon microscopic optical potential, which is based on the Skyrme nucleon-nucleon effective interaction and derived using the Green's function method, as the nucleon optical potential. The harmonic oscillator shell model is used to describe the internal wave function of 7Li and obtain the nucleon density distribution. The 7Li microscopic optical potential is used to predict the reaction cross-sections and elastic scattering angular distributions for the target range from 27Al to 208Pb and energy range below 450 MeV. Generally, the results can reproduce the measured data reasonably well. In addition, the microscopic optical potential is comparable to a global phenomenological optical potential by fitting the presently existing measured data.

Microscopic optical potential for 7Li

A microscopic optical potential (MOP) for 7Li without free parameter is obtained by folding the MOPs of its internal nucleons with their density distributions. An isospin-dependent nucleon MOP based on the Skyrme nucleon–nucleon effective interaction is used as the nucleon optical potential. Cluster model is employed to construct the internal wave function of 7Li and derive the density distributions of the internal nucleons. The 7Li MOP is used to calculate the elastic-scattering angular distributions and reaction cross sections for target nuclei from 27Al to 208Pb at incident energies up to 450 MeV. The results are compared with experimental data and the calculated results by a global phenomenological optical model potential. Generally the MOP can reproduce the experimental data reasonably well, and in many cases it is comparable to the global phenomenological optical potential.

Applicability of 9Be global optical potential to description of 8,10,11B elastic scattering * * Supported by the National Natural Science Foundation of China (11405099 and 11575291). This work is also a part of IAEA Coordinated Research Projects (CRPs) on Recommended Input Parameter Library (RIPL) for Fission Cross Section Calculations (20464)

We achieved a set of 9Be global phenomenological optical model potentials by fitting a large experimental dataset of the elastic scattering observable for target mass numbers from 24 to 209. The obtained 9Be global optical model potential was applied to predict elastic-scattering angular distributions and total reaction cross-sections of 8,10,11B projectiles. The predictions are made by performing a detailed analysis comparing with the available experimental data. Furthermore, these elastic scattering observables are also predicted for some lighter targets outside of the given mass number range, and reasonable results are obtained. Possible physical explanations for the observed differences are also discussed.

Microscopic optical potentials for Li isotopes

The microscopic optical potentials for Li isotopes (A=6,7) without free parameter are obtained by folding the microscopic optical potentials of their internal nucleons with density distributions generated from corresponding internal wave functions of Li isotopes. An isospin-dependent nucleon microscopic optical potential based on the Skyrme nucleon-nucleon effective interaction is used as the nucleon optical potential. Shell model is employed to construct the internal wave functions of Li isotopes and derive their density distributions of internal nucleons. The Li microscopic optical potentials are used to calculate the elastic-scattering angular distributions and reaction cross sections. The results reproduce experimental data well and are comparable to those calculated by phenomenological optical model potentials in many cases.