Double-folding Potential Research Articles

The Folding Potential of Elastically Scattered d+ 24Mg Employing B3Y-Fetal Interaction within the Double Folding Model Framework

Study’s Excerpt/Novelty In this study, double-folding model with the B3Y-Fetal interaction was applied to derive optical potentials for deuteron scattering from 24Mg. The research validates the efficacy of mass-dependent interactions in optical potential calculations by accurately reproducing experimental differential cross-sections across a broad energy range. This work advances the understanding of nuclear reactions by demonstrating the suitability of the B3Y-Fetal interaction in modeling elastic scattering phenomena. Full Abstract The analysis of the deuteron scattering from was performed in the elastic channel using the double-folding model to evaluate the optical potentials of the present study. Both the real and the imaginary parts of the optical potentials were computed using a mass-dependent interaction (B3Y-Fetal) in the double-folding formalism. The derived double-folding potentials were used to analyse the differential cross-sections of within the energy range of 60-170 MeV. With the derived optical potentials, the reaction and differential cross-sections of were extracted in the optical model. The plots of the computed differential cross-sections were made and the results were compared to those obtained experimentally to ascertain the suitability of the derived potentials and the B3Y-Fetal interaction. In conclusion, the optical potentials obtained using the double-folding model with the B3Y-Fetal interaction were successful in reproducing the experimental data.

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.

The competition between α-decay and spontaneous fission for even–even isotopes of superheavy nuclei in the range 106≤Z≤124

The [Formula: see text]-decay and spontaneous fission (SF) half-lives for even–even isotopes of superheavy nuclei in the range [Formula: see text] are predicted using nuclear double-folding and Coulomb potentials. The [Formula: see text]-decay half-lives are computed based on WKB approximation for tunneling probability through potential barrier. The half-lives of SF have also been calculated using a semi-empirical relation constructed by Santhosh et al. [Nucl. Phys. A 832, 220 (2009)]. Our calculated half-lives of cold SF and [Formula: see text]-decay are compared with the available experimental data. This comparison indicates that our obtained half-lives are in good agreement with the available experimental data. The competition between [Formula: see text]-decay and SF is also analyzed in detail and the decay modes are predicted for the unknown cases. Variation of [Formula: see text]-decay and SF half-lives with mass number of the parent isotopes for each nucleus revealed the major role played with shell effect.

Probing nuclear equation of state with the cdm3y version of B3y-fetal effective interaction

This paper is a study of the nuclear Equation of State (EOS) of cold nuclear matter with the B3Y-Fetal effective interaction in its CDM3Y density-dependent version within the framework of Hartree-Fock approximation. The well-known saturation properties of both symmetric and asymmetric nuclear matter are well-reproduced in this work. Using the CDM3Y-K approach, this study has evolved a new set of user interactions, some of which are CDB3Y1-, CDB3Y2-, CDB3Y3-, CDB3Y4-, CDB3Y5-, CDB3Y6-Fetal interactions with corresponding incompressibilities K0 = 188, 204, 217,228, 241 and 252 MeV respectively, in excellent agreement with those of the M3Y-Paris and M3Y-Reid effective interactions. For asymmetric nuclear matter, the new set of interactions has produced the symmetry energy Esym = 32.00 MeV with an associated slope parameter L = 55 MeV at a saturation density ρ = 0.17fm−3 and asymmetry parameter δ = 1.00 (pure neutron matter) in good agreement with the standard values obtained from coupled channel analysis of charge exchange reactions, statistical multifragmentation model and terrestrial Nuclear Physics experimental analyses. Furthermore, the new set of interactions has been found to have bright prospects in a nuclear reaction as the real folded potential computed with the CDB3Y6-Fetal interaction within the framework of double folding potential has been found to be good and similar to that of CDB3Y6-Paris whose optical potential has a repulsive direct component.

Comprehensive examination of the elastic scattering angular distributions of 10C+4He, 27Al, 58Ni and 208Pb using various potentials.

The recently measured elastic scattering angular distributions for 10C + 4He, 10C + 27Al, 10C + 58Ni and 10C + 208Pb nuclear systems are investigated in the current study using various potentials based on phenomenological, semi microscopic as well as microscopic approaches. The implemented potentials are: optical potential, double folding potentials based on both Sao Paulo and CDM3Y6 interactions with and without taking into account the effect of the rearrangement term, as well as the cluster folding potential. The cluster nature of 10C as a core of 9B with a valence proton orbiting this core is applied to generate the cluster folding potentials for the different considered systems. The concerned experimental data is fairly reproduced with all the aforementioned potentials.

Influence of the Pauli exclusion principle on heavy-cluster radioactivity

The effects of the Pauli exclusion principle are investigated regarding the calculations of the nuclear cluster radioactivity using the double-folding formalism. To this purpose, the variation in the internal kinetic energy is considered at the overlapping regions between the densities of the two interacting nuclei as a modification term by employing the extended Thomas-Fermi approach. The effects of the Pauli exclusion principle on the internal energy of the dinuclear system and the standard deviation of the calculated half-lives from their corresponding experimental data are discussed. The results reveal that considering such corrections in calculating the double-folding potential leads to lower standard deviations, which are more consistent with experimental data than other semiempirical formulas.

Double Folding Potential and the Deuteron-Nucleus Inelastic Scattering in the Optical Model Framework

Double Folding Potential and the Deuteron-Nucleus Inelastic Scattering in the Optical Model Framework

BiFold: A Python code for the calculation of double-folded (bifold) potentials with density-in/dependent nucleon-nucleon interactions

BiFold calculates the density-dependent (DDM3Yn, BDM3Yn, CDM3Yn) or independent double-folded potentials between two colliding spherical nuclei. It is written in a Python package form to give the ability to use the potentials directly in a nuclear reaction/structure code. In addition to using Woods-Saxon/Fermi or Gaussian functions, the code also allows the definition of nuclear matter densities using pre-calculated densities in a data file. The manuscript provides an overview of the double folding model and the use of the code. Program summaryProgram Title: BiFoldCPC Library link to program files:https://doi.org/10.17632/rmdx86p9dg.1Developer's repository link:https://github.com/mkarakoc/BiFoldCode Ocean capsule:https://codeocean.com/capsule/5286231Licensing provisions: GPLv3Programming language: Python 3.xNature of problem: BiFold calculates the real part of the nuclear potential between two colliding spherical nuclei by integrating a density-independent/dependent nucleon-nucleon (NN) interaction [1,2,3] over the nuclear matter densities of the two nuclei. The code is based on M3Y Reid/Paris NN interactions [1,2,3] by default, but it is possible to define custom NN interactions when necessary.Solution method: The code uses the Fourier transform method in spherical coordinates to calculate the potential. The method simplifies the sixfold integration [1] and makes the calculation significantly faster. The integration is done by default using Simpson's integration method, but Filon's integration method is also available.

Favored α -decay half-lives of odd- A and odd-odd nuclei using an improved density-dependent cluster model with anisotropic surface diffuseness

We extend the improved density-dependent cluster model (DDCM+) of our recent work [Wang et al., Phys. Rev. C 105, 024327 (2022)] to study the favored $\ensuremath{\alpha}$ decays of odd-$A$ and odd-odd nuclei with $Z\ensuremath{\geqslant}82$. In this work, the effective $\ensuremath{\alpha}$-core interactions are determined using the double-folding potential with a realistic M3Y-Reid nucleon-nucleon interaction plus proton-proton Coulomb interaction, in which a deformation-dependent diffuseness correction is validated to address the surface anisotropy and polarization effects in nucleon density distribution. It is found that calculations within the anisotropic diffuseness would yield longer calculated $\ensuremath{\alpha}$ decay half-lives and suggest larger estimated $\ensuremath{\alpha}$-preformation factors, which is quite consistent with the conclusions obtained for the even-even $\ensuremath{\alpha}$ emitters. Meanwhile, the theoretical half-lives agree very well with the experimental data for the favored $\ensuremath{\alpha}$ decays of the odd-$A$ and odd-odd nuclei with a mean factor of 1.94 and 1.61, respectively. Remarkably, the experimental $\ensuremath{\alpha}$-decay half-life of the new thorium isotope $^{207}\mathrm{Th}$ [Yang et al., Phys. Rev. C 105, L051302 (2022)] is also well reproduced with a factor of about 2.50. Furthermore, we present the quantitative predictions on the favored $\ensuremath{\alpha}$-decay half-lives of $^{293,294}119$ and $^{294,295}120\phantom{\rule{4pt}{0ex}}\ensuremath{\alpha}$-decay chains in this work, which are expected to serve as useful references for the synthesis of new isotopes in the future.

Study of elastic and inelastic scattering of 7Be + 12C at 35 MeV

The elastic and inelastic scattering of 7Be from 12C have been measured at an incident energy of 35 MeV. The inelastic scattering leading to the 4.439 MeV excited state of 12C has been measured for the first time. The experimental data cover an angular range of θcm = 15∘-120∘. Optical model analyses were carried out with Woods-Saxon and double-folding potential using the density dependent M3Y (DDM3Y) effective interaction. The microscopic analysis of the elastic data indicates breakup channel coupling effect. A coupled-channel analysis of the inelastic scattering, based on collective form factors, shows that mutual excitation of both 7Be and 12C is significantly smaller than the single excitation of 12C. The larger deformation length obtained from the DWBA analysis could be explained by including the excitation of 7Be in a coupled-channel analysis. The breakup cross section of 7Be is estimated to be less than 10% of the reaction cross section. The intrinsic deformation length obtained for the 12C⁎ (4.439 MeV) state is δ2 = 1.37 fm. The total reaction cross section deduced from the analysis agrees very well with Wong's calculations for similar weakly bound light nuclei on 12C target.

Effect of 9 Li internal structure on 9 Li + 70 Zn fusion reaction

The fusion cross-section of 9 Li + 70 Zn system is analyzed for different cluster models and various density distributions of the 9 Li nucleus by using the optical model at energies near and below Coulomb barrier. To make a comprehensive analysis and show the effect of neutron rich 9 Li nucleus, our study consists of two parts. First, we obtain five different density distribution of the 9 Li nucleus. As a second part, we evaluate some cluster models of 9 Li which consist of 4 He + 3 H + n + n, 6 He + 3 H, 7 Li + n + n and 8 Li + n. The microscopic nucleon-nucleon double folding potential for real and imaginary parts is applied. It is seen that the results obtained with this study are in better agreement with the experimental data than previous works, especially at low energies. Finally, we acquire the RB and VB parameters for all the densities and cluster cases of the 9 Li + 70 Zn fusion reaction.

Elastic scattering investigation of radioactive B13 and O13 projectiles on a Pb208 target at intermediate energies

Elastic scattering measurements were performed for the proton drip-line nucleus $^{13}\mathrm{O}$ (with ${S}_{p}=1.512$ MeV) and its partner mirror nucleus $^{13}\mathrm{B}$ (with ${S}_{n}=4.878$ MeV) projectiles on a $^{208}\mathrm{Pb}$ target at intermediate energies, namely ${E}_{\mathrm{lab}}=413$ and 254 MeV, respectively. These secondary radioactive ion beams were produced at the Radioactive Ion Beam Line in Lanzhou (RIBLL), Heavy-Ion Research Facility in Lanzhou (HIRFL). The elastic scattering angular distributions for these projectiles show a typical Fresnel diffraction peak at forward angles. Optical model analyses of the angular distributions, using double-folding and global potentials, were performed and different densities for these projectiles were probed.

Search for a viable nucleus–nucleus potential in heavy-ion nuclear reactions

We have constructed an empirical formulae for the fusion and interaction barriers using experimental values available till date. The fusion barriers so obtained have been compared with different model predictions based on the proximity, Woods-Saxon and double folding potentials along with several empirical formulas, time dependent Hartree-Fock theories, and the experimental results. The comparison allows us to find the best model, which is nothing but the present empirical formula only. Most remarkably, the fusion barrier and radius show excellent consonance with the experimental findings for the reactions meant for synthesis of the superheavy elements also. Furthermore, it is seen that substitution of the predicted fusion barrier and radius in classic Wong formula [C. Wong, Phys. Rev. Lett. {31}, 766 (1973)] for the total fusion cross sections satisfies very well with the experiments. Similarly, current interaction barrier predictions have also been compared well with a few experimental results available and Bass potential model meant for the interaction barrier predictions. Importantly, the present formulae for the fusion as well as interaction barrier will have practical implications in carrying out the physics research near the Coulomb barrier energies. Furthermore, present fusion barrier and radius provide us a good nucleus-nucleus potential useful for numerous theoretical applications.

Comparison between Different Interaction Models of Double Folding Potential for 6He + 12C Elastic Scattering up to 500 MeV

Comparison between Different Interaction Models of Double Folding Potential for 6He + 12C Elastic Scattering up to 500 MeV

Cluster decay half-lives using asymmetry dependent densities

By adopting different neutron and proton density distributions, cluster decay half-lives were investigated using double-folding potentials with constant and nuclear asymmetry dependent sets of nuclear density parameters. Two adopted asymmetry dependent sets of parameters were fitted based on microscopic calculations, and they were calculated based on the neutron skin/halo-type nuclei assumption and by employing experimental rms charge radii. A bulk agreement between theory and experiment was obtained for all sets of parameters using a calculated cluster preformation probability. Few differences were observed between the skin and halo-type assumptions. However, the notable role of the asymmetry parameter was observed in the relatively large differences between the skin and skin-type with zero thickness.

The influence of the nuclear matter incompressibility on heavy-ion fusion reactions at near- and above-barrier energies

Based on simulating the saturation property of cold nuclear matter for complete fusion channel of two approaching nuclei, we systematically investigate the role of nuclear incompressibility in the nucleus-nucleus potential and fusion-evaporation cross section of 69 medium-heavy and heavy mass systems with 208≤Z1Z2≤1520. Our observations based on the uncoupled single-barrier potential model and the M3Y double-folding potential which is corrected with a repulsive core term reveal that the incompressibility of cold nuclear matter can be responsible for the discrepancy between the measured and calculated values of the fusion cross sections at energies around and above the Coulomb barrier. In other words, one can find that the high energy fusion cross sections can not be reproduced using the standard form of the M3Y-DF potential model without considering the repulsive core effects. We show that the strength of the repulsive contact term and also the incompressibility of the compound nuclei exhibit systematic behaviors with respect to the atomic and mass numbers of reacting nuclei. It is shown that the hardness level of nuclear matter reduces when one passes from lighter to heavier systems.

Exploring α decay properties in the superheavy region through the double-folding formalism and Skyrme interactions

In this study, $\ensuremath{\alpha}$ decay properties of yet unknown nuclei are investigated through the systematic behavior of the parameters of $\ensuremath{\alpha}$-nucleus double-folding (DF) potentials. To calculate DF potentials, the density distributions of the protons and neutrons are being employed by use of the self-consistent Hartree-Fock-Bogoliubov (HFB) calculations based on the SLy4 Skyrme interaction widely used for the $\ensuremath{\alpha}$-emitter systems and the superheavy region. In addition, a new set of effective Skyrme force parameters is presented so that more precise estimations, labeled OMGA, are optimized to describe the ground-state properties of superheavy nuclei with $82\ensuremath{\le}Z\ensuremath{\le}120$. Consequently, a good mass fit and half-lives are thus obtained by the optimized Skyrme force with more consistency with experimental data.

Further investigation of 10,11B + 58Ni elastic scattering

The recently measured 10,11B + 58Ni elastic scattering angular distributions are subjected to thorough analysis using different potentials such as optical and double folding, based on the CDM3Y6, with and without taking into account the effect of the rearrangement term, as well as the cluster folding potential. The cluster structure for 10B (11B) as composed of 6Li (7Li) core with an alpha particle orbiting this core is hence studied. The experimental data for the 10,11B + 58Ni nuclear systems are fairly reproduced with all the aforementioned potentials. The renormalization factors for the real double folded potential (N r ) indicate the need to reduce the strength of the produced potentials by ∼ 50% and ∼ 36% to reproduce the considered data for the 10B + 58Ni and the 11B + 58Ni nuclear systems, respectively. As a result of applying a rearrangement term to the double folding potential, a small change can be observed in the N r values. Cluster folding analysis for the 10B + 58Ni elastic scattering cross sections reveals a similar trend; the strength of the renormalization factor for the real part of the potential constructed based on the cluster folding model ( N RCF ) needs to be reduced by ∼ 48%. The observed reduction in the strength of the constructed double and cluster folding potentials reflects the weak binding nature of the 10B and 11B nuclei. It was somewhat surprising that the extracted N RCF = 1.24 ± 0.064 for the 11B + 58Ni system.

São Paulo potential version 2 (SPP2) and Brazilian nuclear potential (BNP)

The REGINA code calculates the São Paulo potential version 2 (SPP2) and the Brazilian nuclear potential (BNP). The code also provides nuclear densities obtained from the Dirac-Hartree-Bogoliubov model, which are used to calculate the nuclear potentials. Elastic scattering cross sections are obtained within the context of the optical model, with different options for the real and imaginary parts of the optical potential. In this manuscript, we provide a summary of the theoretical framework and information about the use of the code. Program summaryProgram Title: REGINA.fCPC Library link to program files:https://doi.org/10.17632/vfkkjb8dv7.1Licensing provisions: GPLv3Programming language: Fortran-77Nature of problem: We provide a code to calculate the nuclear potential between two nuclei according to two different models: the São Paulo potential version 2 (SPP2), that includes a dependence on the relative velocity between the nuclei, and the velocity independent Brazilian nuclear potential (BNP). These potentials assume the effective nuclear interactions proposed in [1,2], and are obtained within the double-folding approach with nuclear densities calculated through the Dirac-Hartree-Bogoliubov model [3].Solution method: The code involves two files containing previously calculated results for theoretical neutron and proton distributions and also experimental charge densities obtained from electron scattering experiments. These results are used to obtain matter densities through convolution using Fourier transforms. The Fourier transform method is also employed to obtain the double-folding potentials. Integration of the Schrödinger equation with a complex optical potential is performed using the Cowell method [4,5]. With this, for a given system and energy, we obtain the S-matrix and the elastic scattering cross sections.Additional comments including restrictions and unusual features: The maximum angular momentum supported in the optical model calculations is 2000.

Sub-barrier fusion of 34,36S+204,206,208Pb: Signature of isotopic dependence of repulsive core potential in heavy-ion fusion reactions

The measurements of the excitation function for the heavy-ion fusion-fission cross sections in negative Q-value systems 34S+204,206,208Pb and 36S+204,206,208Pb have been analyzed by coupled-channels (CC) calculations based on the M3Y double-folding (DF) potential that is supplemented with a short-ranged repulsive potential. The standard Aage Winther potential is also employed to explore the occurrence of the unexpected steep fall-off phenomenon of the measured cross sections in fusion between sulfur and lead nuclei. Our analysis based on the deep phenomenological potentials clearly demonstrates that the fusion data are strongly hindered at incident energies well below the Coulomb barrier for the four heavy-ion systems 34S+206Pb, 34S+208Pb, 36S+206Pb and 36S+208Pb. In addition, a first indication of a maximum in the trend of the experimental data of the S-factor representation has been observed for each of the fusions of 34,36S with 206,208Pb targets. It is shown that the M3Y+Repulsion potential accompanied by the CC calculations provides a satisfactory description of the experimental fusion cross sections and S factors in the whole energy range under study for all the six cases of interest. A discussion is also presented concerning the isotopic dependence of the parameters existing in simulation of the repulsive core potential. Our detailed study reveals that the strength of the repulsive interaction and incompressibility of the nuclear matter (NM) increases and decrease linearly with addition of neutrons in the isotopic systems, respectively. Further, we show that the repulsive part of the density distribution becomes more diffuse with increasing neutrons from 34S+204Pb to 36S+208Pb.