Double-folding Method Research Articles

Be10 -nucleus optical potentials developed from chiral effective field theory NN interactions

We present a determination of optical potentials for $^{10}\mathrm{Be}$-nucleus collisions using the double-folding method to compute the real part and Kramers-Kronig dispersion relations to derive the imaginary part. As microscopic inputs we use chiral effective field theory nucleon-nucleon interactions at next-to-next-to-leading order combined with state-of-the-art nucleonic densities. With these potentials, we compute elastic-scattering cross sections for the exotic nucleus $^{10}\mathrm{Be}$ off various targets, and compare them to experiment. Without any fitting parameter, we obtain good agreement with data. For collisions on light targets, we observe significant uncertainty related to the short-range physics, whereas for heavy targets that uncertainty remains small.

Потенціали взаємодії ізотопів 10,11,12,13В з ядром 12С

A comparative analysis of calculations for the 12С(10В,10В)12С elastic scattering at Еlab(10B) = 41.3 MeV, the 12С(11В,11В)12С elastic scattering at Еlab(11B) = 40.0 MeV, transfer reactions 13С(11В,12С)12В and 14С(11В,12С)13В at Еlab(11B) = 45.0 МеВ was performed within the coupled-reaction-channels method (CRC) using previously deduced Woods-Saxon potentials for the interaction of 10,11,12,13В + 12С nuclei in the exit reaction channels, as well as potentials for these systems of nuclei generated by means of the double-folding method using theoretically modeled shapes for the distributions of protons and neutrons in 10,11,12,13В and 12С. The relationship of isotopic effects (differences of the calculated CRC cross sections when replacing the potential for a given pair of nuclei by interaction potential for one nucleus with the isotope of another nucleus) with the internal structure, e.g. the shapes of nucleon density distributions in the interacting nuclei, is investigated. The shapes (radial dependence) of recently deduced Woods-Saxon potentials and potentials calculated by means of the double-folding methods for the systems of 10,11,12,13В + 12С nuclei are compared. Based on the results of the analysis of experimental data, an assumption is made about the possible differences in the shapes of surface nucleon density distributions from the ones modeled theoretically in 10,11B isotopes.

α -nucleus optical potentials from chiral effective field theory NN interactions

We present a determination of optical potentials for $^4$He-target collisions using the double-folding method. We use chiral effective field theory nucleon-nucleon interactions at next-to-next-to-leading order combined with state-of-the-art nucleonic densities. The imaginary part of the optical potential is obtained from the real double-folding interaction either through a proportionality constant or applying Kramers-Kronig dispersion relations. With these potentials, we compute the elastic scattering of $^4$He off various targets, from $^4$He to $^{120}$Sn. We study the sensitivity of our predicted cross sections to the choice of nucleon-nucleon interactions and nuclear densities. Very good agreement is obtained with existing elastic-scattering data for $^4$He energies between 100 and 400 MeV.

Excitation of isobaric analog states from (p,n) and (He3,t) charge-exchange reactions within the G -matrix folding method

Differential cross sections of ($p,n$) and ($^3$He,$t$) charge-exchange reactions leading to the excitation of the isobaric analog state (IAS) of the target nucleus are calculated with the distorted wave Born approximation. The $G$-matrix double-folding method is employed to determine the nucleus-nucleus optical potential within the framework of the Lane model. $G$-matrices are obtained from a Brueckner-Hartree-Fock calculation using the Argonne Av18 nucleon-nucleon potential. Target densities have been taken from Skyrme-Hartree-Fock calculations which predict values for the neutron skin thickness of heavy nuclei compatible with current existing data. Calculations are compared with experimental data of the reactions ($p,n$)IAS on $^{14}$C at $E_{lab}=135$ MeV and $^{48}$Ca at $E_{lab}=134$ MeV and $E_{lab}=160$ MeV, and ($^3$He,$t$)IAS on $^{58}$Ni, $^{90}$Zr and $^{208}$Pb at $E_{lab}=420$ MeV. Experimental results are well described without the necessity of any rescaling of the strength of the optical potential. A clear improvement in the description of the differential cross sections for the ($^3$He,$t$)IAS reactions on $^{58}$Ni and $^{90}$Zr targets is found when the neutron excess density is used to determine the transition densities. Our results show that the density and isospin dependences of the $G$-matrices play a non-negligible role in the description of the experimental data.

Dispersion relations applied to double-folding potentials from chiral effective field theory

We present a determination of optical potentials using the double-folding method based on chiral effective field theory nucleon-nucleon interactions at next-to-next-to-leading order combined with dispersion relations to constrain the imaginary part. This approach is benchmarked on $^{16}$O--$^{16}$O collisions, and extended to the $^{12}$C--$^{12}$C and $^{12}$C--$^{16}$O cases. Predictions derived from these potentials are compared to data for elastic scattering at energies up to 1000 MeV, as well as for fusion at low energy. Without adjusting parameters, excellent agreement with experiment is found. In addition, we study the sensitivity of the corresponding cross sections to the nucleon-nucleon interactions and nuclear densities used.

Calculation of Q-value and half-life of alpha decay in super heavy elements using S-matrix theory

The half-life and the [Formula: see text]-value of alpha decay in several super heavy elements are calculated. The nuclear potential is computed using the double-folding method. Using the S-matrix theory, the alpha decay is treated as a scattering problem between alpha particle and the daughter nucleus. Nuclear potential was approximated by the parameterized Woods–Saxon potential. This idea has also been extended to predict the half-life and the [Formula: see text]-value of the heaviest elements of few other alpha chains.

Comparative analysis of the Coulomb barrier in heavy-ion collisions by the double-folding method

The double-folding formalism has been applied to calculate the nucleus-nucleus potential by the use of the effective nucleon-nucleon (Migdal) potential and the nuclear densities of the interacting nuclei presented as the Gaussian-type functions and polynomials. The Coulomb barrier heights obtained by this way and by different types of the proximity potentials have been compared. The deviations of the theoretical values of the Coulomb barrier from the values extracted from the experimental data are discussed. The capture cross section calculated for the reactions with the light projectiles is in good agreement with experimental values. The theoretical results obtained for the 16O+144Sm and 17O+144Sm reactions could reproduce a significant difference in the experimental results for these reaction, which is related with the extra neutron in 17O. The overestimation of the experimental data obtained from different sources by the curve of the theoretical results of the 40Ca+96Zr reactions is explained by the appearance of the slight hindrance to complete fusion, i.e the capture and fusion cross sections are not equal in this reaction.

Changes in quadrupole moments during nucleus–nucleus interaction

In this paper, we examine the distribution of nuclei’s charge (the quadrupole moment of nuclei) for stable nuclei with [Formula: see text] when interacting with the [Formula: see text]O nuclei. The interaction potential between the nuclei was achieved using the double-folding method. The wave functions of the interacting nuclei were replaced by the density functions in the double-folding model. The wave functions of the interacting nuclei were obtained through the D-dimensional Schrödinger equation with the pseudo-Coulomb potential plus ring-shaped potential by the Nikiforov–Uvarov solution method.

Importance of α-induced reactions and the inverse (γ,α) process on p-nuclei

We have calculated astrophysical reaction cross-sections for [Formula: see text] reactions of some nuclei important for the calculation of p-process reaction-decay network. Reaction rates for [Formula: see text]-induced reactions are calculated with the semi-microscopic optical potential constructed using double folding method, where nuclear density distributions for finite nuclei along with the effective nucleon–nucleon interaction are the important components of the folded potential. For this purpose, density distributions of target nuclei are obtained from relativistic mean field approach. Astrophysical reaction cross-section for elastic scattering of [Formula: see text]-particle from [Formula: see text] target is compared with the existing experimental results to constrain the newly formed potential. Further, to check the credibility of the present theoretical framework, the astrophysical S-factor for [Formula: see text] reactions are compared with the experimental observation, wherever available. Finally, an estimate of dominant photodisintegration channels at various astrophysical temperature is discussed for p-nuclei [Formula: see text] and [Formula: see text].

Calculation of Q-value and half-life of alpha-decay chains of superheavy elements using double folding method

[Formula: see text]-value and half-life of elements in alpha decay chain of [Formula: see text]117, [Formula: see text]117, [Formula: see text]116 and [Formula: see text]116 were calculated using the Nuclear potential generated by double folding procedure and using the WKB method treating the alpha decay as a tunneling problem. The nuclear potential was parameterized using Woods–Saxon potential. Using this approach, the [Formula: see text]-value and half-life of next heaviest element in the alpha decay chain of element [Formula: see text]116 is predicted. It is proposed to use this to predict the [Formula: see text]-value and half-life of other higher elements in different alpha decay chains.

Repulsive three-body force and channel-coupling effects via C12+C12 scattering at 100A MeV

The angular distributions of differential cross sections of $^{12}\mathrm{C}+^{12}\mathrm{C}$ elastic and inelastic scattering populating the ground and excited states in $^{12}\mathrm{C}$ up to 15 MeV excitation energy are precisely measured for the first time at an incident energy of $100A$ MeV to study the effect of repulsive three-body forces. Using the high-resolution spectrometer Grand Raiden at the Research Center for Nuclear Physics (RCNP), Osaka University, we have obtained the differential cross sections for the ground state (${0}_{1}^{+}$) and 4.44 MeV (${2}_{1}^{+}$) excited state, as well as the summed differential cross sections for the states between 4.44 and 15 MeV in the angular range of $1.{0}^{\ensuremath{\circ}}--7.{5}^{\ensuremath{\circ}}$. The results are compared with microscopic coupled-channel calculations. The potential between the colliding nuclei is determined by the double folding method with three different complex $G$-matrix interactions, the ESC, CEG07b, and MPa interactions. The CEG07b and MPa interactions, which include repulsive three-body forces, describe the data well, whereas the ESC interaction, which does not include repulsive three-body forces, fails to reproduce the data. The results provide evidence of repulsive three-body forces in $^{12}\mathrm{C}$ and demonstrate the possible sensitivity of elastic scattering to three-body forces.

Extreme quadrupole deformation and clusterization

We discuss a simple symmetry-adapted method for the determination of the shape isomers, and for the study of their possible fragmentation. In other words the connection between the quadrupole (collective) and dipole (cluster) degrees of freedom is considered in terms of an easily applicable, yet microscopic method. The energetics is taken into account by the double-folding method. Special attention is focused on those cases in which the theoretical predictions have a direct comparison with experimental observation.

Deep sub-barrier fusion reactions of the light nuclei 12C and 16O

Fusion reactions relevant for the carbon and oxygen burning cycles in highly evolved stars are investigated in a standard approach to fusion. We employ the double folding method to evaluate the ion-ion interactions with Gogny-D1 and M3Y-Paris n – n effective forces. The cross-section evaluation do not indicate a possible hindrance even at the lowest energies under the barrier. Reaction rates at temperatures relevant for the stellar processes are estimated and compared to the traditional and modern extrapolation formulas.

Nuclear Potential and Fusion Cross Sections for SynthesizingSuper-Heavy Elements in Di-nuclear Systems

A double folding method with simplified Skyrme-type nucleon–nucleoninteraction is used to calculate the nuclear interaction potentialbetween two nuclei. The calculation is performed in tip-to-tiporientation of the two nuclei if they are deformed. Based on thismethod, the potential energy surfaces, the fusion probabilities and theevaporation residue cross sections for some cold fusion reactionsleading to super-heavy elements within di-nuclear system model areevaluated. It is indicated that after the improvement, the exponentialdecreasing systematics of the fusion probability with increasing chargenumber of projectile on the Pb based target become better and theevaporation residue cross sections are in better agreement with theexperimental data.

Potential Energy of the Di-nuclear System

We perform the calculation of the nucleus–nucleus interaction potentialof the dinuclear system with deformed nuclei. Based on the calculatedresults by properly treating the double-folding method, some resultsfrom the analytical expressions for calculating both the nuclear and theCoulomb interactions are investigated. It is concluded that theanalytical formula to calculate the Coulomb interaction by Wong [Phys.Rev. Lett. 31 (1973) 766] can reproduce good double folding results.However the results by the parametrized Morse formula, which are usedto calculate the nuclear interaction, greatly deviate from the doublefolding results, unless the distance of nuclei is adjusted to be shiftedto a smaller relative distance determined by the same distance betweenthe nuclear surfaces as one of them pertains to the deformed nuclei.Using the double folding method to calculate the nuclear interaction andemploying Wong's analytical formula to calculate the Coulomb interactioncan keep good precision and can cost much less computation time.

Deformation and orientation effects in the driving potential of the dinuclear model

A double-folding method is used to calculate the nuclear and Coulomb interaction between two deformed nuclei with arbitrary orientations. A simplified Skryme-type interaction is adopted. The contributions of nuclear interaction and Coulomb interaction due to the deformation and orientation of the nuclei are evaluated for the driving potential used in the description of heavy-ion fusion reaction. So far there is no satisfactory theory to describe the evolution of the dynamical nuclear deformation and orientations during the heavy-ion fusion process. Our results estimated the magnitude of above effects.

Isotopic dependence of the ion-ion potential in the systems 16O+58,60,62,64Ni

Abstract Precise measurements of the elastic and inelastic scattering cross sections for the systems 16 O+ 58,60,62,64 Ni at the sub-barrier energies were made. Coupled-channel analysis were performed. The isotopic dependence of the resulting ion-ion potentials is compared with theoretical calculations using the double-folding method with the M3Y as the nucleon-nucleon interaction and shell-model densities.

Heavy-ion optical potentials at finite temperature calculated using a complex effective interaction derived from a realistic force

Hot density distributions of heavy ions generated by a modified Thomas-Fermi calculation at finite temperature are used to calculate the optical potential using the double-folding method and a complex effective energy and density-dependent interaction deduced from a realistic NN (Reid soft-core) force in nuclear matter. The real and the imaginary part of the optical potential become more attractive when the temperature increases.

Test of the proximity theorem for deformed nuclei

We compare a proximity-type potential for two interacting nuclei with the double-folding method. Both spherical and deformed systems are considered. Special orientation windows are found for two deformed nuclei giving rise to nuclear cohesion. If the same nucleon-nucleon interaction is utilized, the proximity and the double-folding potentials agree fairly well for a spherical + deformed system. However, deviations are found in the case of two deformed nuclei.

Neutrons from 11B + 11B Compared with Other Sources of Neutrons from 11B + p Burn

Fewer neutrons are produced from 11B(11B, n) than from 11B(p, n)11C for temperatures from 100 to 800 keV. For temperatures below 300 keV, 11B(d, n)12C produces more neutrons than either of these reactions if the normal isotopic mixture of hydrogen is used. Potentials generated by the double-folding method and tested against 7Li + 7Li data were used to generate 11B + 11B cross sections for energies where there were no measurements.