Nucleus-nucleus Interaction Potential Research Articles

Перерізи пружного розсіяння реакцій 16,18O + 120Sn, одержані на основі потенціалу модифікованого методу Томаса - Фермі з урахуванням кора

Nucleon density distributions and nucleus-nucleus interaction potentials for the reactions 16,18O + 120Sn were obtained within the framework of the modified Thomas - Fermi method. In the calculations, all terms up to the second order in ћ in the quasi-classical distribution of kinetic energy were taken into account. Density-dependent Skyrme forces were used as nucleon-nucleon interaction. Using the found potentials, cross-sections of elastic scattering were calculated, which well describe the corresponding experimental data.

Потенціал модифікованого методу Томаса - Фермі та його аналітичне представлення на прикладі взаємодії 16О з ізотопами олова 112,114,116,118,120,122,124Sn

Nucleon distribution densities and nucleus-nucleus interaction potentials for the 16O nucleus and 112,114,116,118,120,122,124Sn isotopes were calculated within the framework of the modified Thomas - Fermi method, taking into account all terms to the second-order of ħ in the quasiclassical expansion of kinetic energy. Skyrme forces dependent on the nucleon density were used as nucleon-nucleon interaction. A successful parameterization was found for the obtained potential, which allows to present it in an analytical form.

Systematic analysis of the decay of Fl*287,288,290,292 formed in the complete fusion reactions Pu239,240,242,244+Ca48 including Skyrme forces

The fusion evaporation residue cross sections for the decay of the compound nuclear system $^{287,288,290,292}\mathrm{Fl}^{*}$ via $2n$- to $5n$-decay channels, synthesized in $^{239,240,242,244}\mathrm{Pu}+^{48}\mathrm{Ca}$, are studied using the dynamical cluster-decay model (DCM), including quadrupole deformations ${\ensuremath{\beta}}_{2i}$ for compact hot orientations ${\ensuremath{\theta}}_{i}$ at various excitation energies ${E}^{*}=32.5$ to 52.6 MeV. For the nucleus-nucleus interaction potentials, we have employed the Skyrme energy density functional based on the semiclassical extended Thomas-Fermi approach under frozen density approximation. Here, within the DCM, the Skyrme forces used are SLy4, ${\mathrm{SkM}}^{*}$, and, KDE0(v1). The DCM makes use of a single parameter, the neck-length parameter $\mathrm{\ensuremath{\Delta}}R$ that takes different values for different processes at a given temperature and provides an excellent fit to the measured data, independently of the choice of Skyrme force used. We make predictions of probable fusion-fission and quasifission mass regions of fragments and then calculate the evaporation residue cross sections ${\ensuremath{\sigma}}_{\mathrm{ER}}$ for experimentally unobserved neutron channels. Further, the product ${P}_{\mathrm{CN}}{P}_{\mathrm{surv}}$ of compound nucleus (CN) fusion probability ${P}_{\mathrm{CN}}$ and survival probability ${P}_{\mathrm{surv}}$ is calculated to determine the reduced evaporation residue cross section ${\ensuremath{\sigma}}_{\mathrm{ER}}/{\ensuremath{\sigma}}_{\mathrm{fusion}}$, denoted as ${\ensuremath{\sigma}}_{\mathrm{ER}}^{\mathrm{reduced}}$, and we have seen that ${P}_{\mathrm{surv}}$ is the main dominant factor in the product ${P}_{\mathrm{CN}}{P}_{\mathrm{surv}}$. To this end, we have analyzed the effects of mass asymmetry and isospin effect of target nucleus on the ${\ensuremath{\sigma}}_{\mathrm{ER}}$ and have found that the ${\ensuremath{\sigma}}_{\mathrm{ER}}$ for the production of superheavy element ${\mathrm{Fl}}^{*}$ increases slowly with increasing neutron number of the target nucleus. We have also searched for all possible target-projectile combinations forming the hot compound nucleus ${\mathrm{Fl}}^{*}$ at the excitation energy ${E}^{*}$ for compact-hot configurations and have also calculated the fusion evaporation residue cross sections for the proposed new reactions synthesizing Fl.

Перерізи пружного розсіяння, одержані на основі потенціалу модифікованого методу Томаса–Фермі з урахуванням кора

Густини розподiлу нуклонiв та потенцiали взаємодiї мiж ядрами для реакцiй 16O + 40Ca, 16O + 56Fe та 16O + 90Zr було розраховано в рамках модифiкованого методу Томаса–Фермi, з урахуванням усiх доданкiв до членiв другого порядку по ~ у квазикласичному розкладi кiнетичної енергiї. В якостi нуклон-нуклонної взаємодiї використовувалися сили Скiрма, залежнi вiд густини нуклонiв. Знайдено параметризацiю потенцiалу взаємодiї мiж ядрами, яка добре описує величину потенцiалу, розрахованого у рамках модифiкованого пiдходу Томаса–Фермi з залежними вiд густини силами Скiрма. На основi одержаних потенцiалiв було обраховано перерiзи пружного розсiяння, що добре узгоджуються з експериментальними даними.

Systematic application of the M3Y NN forces for describing the capture process in heavy-ion collisions involving deformed target nuclei

We present results of a systematic study of the capture process through the barrier penetration model. The nucleus-nucleus interaction potential is calculated using the double-folding model (DFM) with the M3Y Paris $\mathit{NN}$ forces. The nucleon densities entering the model are generated from the experimental three-parameter Fermi charge densities. The DFM has been extended to the case of deformed target nuclei. It is shown that the density-dependent M3Y $\mathit{NN}$ forces with the finite range exchange part can be mimicked successfully by the zero-range density-independent forces. The latter option significantly reduces the required computer time. For the nucleon densities and target nuclei deformations, we employ the values from the commonly used data bases. Thus, we do not vary any parameters to reach a better agreement with the data. The resulting cross sections are compared with data for 20 reactions with the product of the charge numbers ${Z}_{P}{Z}_{T}$ ranging from 216 up to 2576. We discuss the opinion met in the literature that the M3Y $\mathit{NN}$ forces provide a poorer description of the capture cross sections in heavy-ion collisions in comparison to the $\mathit{NN}$ forces coming from the relativistic mean-field approach. Our calculations show that the M3Y $\mathit{NN}$ forces give an agreement with the data which is not perfect yet is not worse than the one resulting from the relativistic mean-field approach $\mathit{NN}$ forces.

Subbarrier fusion and elastic scattering cross-sections based on modified Thomas-Fermi method potentials

The nucleon density distributions and nucleus-nucleus interaction potentials for the reactions 16O+92Zr and 16O+116Sn were calculated using the modified Thomas-Fermi method, taking into account all terms up to members of the second order by ħ in the quasiclassical decomposition of the kinetic energy. As a nucleon-nucleon interaction, density depended Skyrme forces were used. Based on the obtained potentials, the cross-sections of subbarrier fusion and elastic scattering were calculated. It is shown that the obtained cross-sections of the reactions agree well with the latest experimental data.

Fusion cross section of the superheavy Z=120 nuclei within the relativistic mean-field formalism

Background: Isotopes of $Z=107\text{--}118$ have been synthesized using cold fusion at GSI, Darmstadt, and hot fusion reactions at JINR, Dubna. Recently theoretical models have predicted $Z=120$ with $N=184$ as an island of stability in the superheavy valley. Hence it is crucial and exciting to predict theoretically the possible combination of projectiles and targets for the synthesis of $Z=120$, which can be informative for upcoming experiments.Purpose: Present theoretical investigations aim to explore the fusion characteristics of various isotopes of $Z=120$ within the relativistic mean-field formalism. We predict the most suitable projectile-target combination for the synthesis of element $Z=120$. The increase in fusion cross section of nuclei in the superheavy island directly signals the nuclear shell effects. Besides these, the analysis will be crucial and relevant for future experiments to synthesize superheavy nuclei.Methods: The microscopic nucleon-nucleon R3Y interaction and the density distributions for targets and projectiles are calculated using a relativistic mean-field formalism with the ${\mathrm{NL3}}^{*}$ parameter set. These densities and R3Y nucleon-nucleon (NN) interaction are then used to calculate the nuclear interaction potential using the double folding approach. Seventeen different projectile-target combinations that allow a high $N$/$Z$ ratio are considered in the present analysis to calculate the capture and/or fusion cross sections of various isotopes of $Z=120$ within the $\ensuremath{\ell}$-summed Wong formula.Results: The nuclear density distributions for the interacting projectile and target nuclei are obtained from relativistic mean-field Lagrangian for the ${\mathrm{NL3}}^{*}$ parameter set. The nucleus-nucleus interaction potential is estimated for seventeen possible projectile-target combinations using the mean-field density and the R3Y NN potential via a double folding approach. The fusion barriers are obtained by adding the Coulomb potential to the nucleus-nucleus interaction potential. Finally, the fusion and/or capture cross section is calculated for all the systems within the $\ensuremath{\ell}$-summed Wong formula. Further, the equivalent surface diffusion parameter is estimated to correlate the surface properties of interacting nuclei with the fusion cross section.Conclusions: The four Ti-based reactions with the heaviest available target $^{\mathrm{x}}\mathrm{Cf}$, namely, $^{46}\mathrm{Ti}+^{248}\mathrm{Cf}$, $^{46}\mathrm{Ti}+^{249}\mathrm{Cf}$, $^{50}\mathrm{Ti}+^{249}\mathrm{Cf}$, and $^{50}\mathrm{Ti}+^{252}\mathrm{Cf}$, and also $^{54}\mathrm{Cr}+^{250}\mathrm{Cm}$ are found to have the most suitable target-projectile combinations for the synthesis of various isotopes $Z=120$. We also notice that $^{48}\mathrm{Ca}$ beams merely provide the required number of protons to synthesize the element with $Z=120$. We established a correlation among the surface properties of interacting nuclei with the fusion characteristics in terms of the equivalent surface diffusion parameter.

The nucleus-nucleus potential within the extended Thomas-Fermi method and the cross-sections of subbarrier fusion and elastic scattering for the systems 16O + 58,60,62,64Ni

The nucleus-nucleus interaction potentials for the O16+58,60,62,64Ni systems are calculated within the extended Thomas-Fermi method by taking into account all terms up to terms of the second order in ħ of the quasiclassical decomposition of kinetic energy. The density-dependent Skyrme force is used as the nucleon-nucleon interactions. Using the obtained potentials, the cross sections of subbarrier fusion and elastic scattering are found, which are in good agreement with the experimental data.

Nucleon density distribution in description of nuclear decays

A correlation is demonstrated between the diffuseness of the self-consistent nucleon distribution and the nucleon-nucleon attraction on nuclear surface. The last two values determine the nucleus-nucleus interaction potential. Because the half-lives of alpha-decay, cluster radioactivity, and spontaneous fission are sensitive to the nucleus-nucleus interaction potential, we try to verify the self-consistent nucleon-nucleon attraction on nuclear surface. Based on the dinuclear system model, the unified approach is proposed for calculating half-lives of different nuclear decay modes using the phenomenological and self-consistent nucleon distributions.

Insight into the radial sensitivity of phenomenological nucleus-nucleus interaction potentials

The optical model potential, which reflects an overall feature of the nuclear property and reaction dynamics, has been widely adopted to describe the nucleus-nucleus interaction phenomenologically. Experimentally, knowledge of the optical potential can only be learned in the vicinity of a sensitive radius. In this study, the notch technique was applied to extract the radial sensitive regions of the tightly bound system $^{16}\mathrm{O}+^{208}\mathrm{Pb}$ and weakly bound systems $^{9}\mathrm{Be}+^{208}\mathrm{Pb}$ and $^{6}\mathrm{He}+^{209}\mathrm{Bi}$ at energies around the Coulomb barrier. It is the first time that we observed two distinct sensitive regions, corresponding to the inner volume absorption and the outer surface absorption processes. Strong energy dependence of the sensitive regions was found as well. Based on this result, we further investigated the interaction property of $^{9}\mathrm{Be}+^{208}\mathrm{Pb}$ and found that the threshold anomaly was observed in the volume interaction, whereas the abnormal near-threshold behavior was presented in the surface part.

Effect of density and nucleon-nucleon potential on the fusion cross section within the relativistic mean field formalism

We have studied the effect of density and the nucleus-nucleus interaction potential on the fusion reaction cross section for the synthesis of heavy and superheavy nuclei within the relativistic mean field formalism. The double-folding procedure is used to obtain the nuclear interaction potential for the well-known M3Y and recently developed R3Y nucleon-nucleon potential for relativistic mean field densities. The $\mathrm{NL}{3}^{*}$ parameter set is used to calculate the density distributions for targets and projectiles and is further used to obtain the nuclear potential. The $\ensuremath{\ell}$-summed Wong formula is used to provide a transparent and analytic way to formulate the fusion cross sections for even-even $^{48}\mathrm{Ca}+^{154}\mathrm{Sm}$, $^{48}\mathrm{Ca}+^{238}\mathrm{U}$, $^{48}\mathrm{Ca}+^{248}\mathrm{Cm}$, $^{64}\mathrm{Ni}+^{238}\mathrm{U}$, $^{26}\mathrm{Mg}+^{248}\mathrm{Cm}$; even-odd $^{46}\mathrm{K}+^{181}\mathrm{Ta}$; and odd-odd $^{31}\mathrm{Al}+^{197}\mathrm{Au}$ and $^{39}\mathrm{K}+^{181}\mathrm{Ta}$ systems. The structural effects are also correlated with the fusion cross section through the equivalent diffuseness parameter using the densities of interacting nuclei for all nuclei (projects and targets) involved in the reactions just listed.

Efektyvnyj yaderno-yadernyj potencial z uraxuvannyam vnesku kinetychnoyi enerhiyi nukloniv ta pererizy pruzhnoho rozsiyannya i pidbar’yernoho zlyttya

The microscopic double-folding approach to the calculation of the nucleus-nucleus interaction has been discussed in detail. The nucleus-nucleus interaction potentials for the 16O+208Pb system with and without the contribution of the kinetic energy of nucleons in the nuclei are constructed, and the cross-sections of elastic scattering and subbarrier fusion are calculated. The experimental values of those cross-sections are shown to be described well, if the contribution of nucleons’ kinetic energy is taken into account.

Studying of the Nucleus-Nucleus Interaction Using Wave Function of the Nucleus and Hyperspherical Formalism

Abstract The current study presents the results of the use of the wave function of a nucleus in place of the nucleus density distribution to calculate the nucleus-nucleus interaction potential. The wave function is obtained by solving the D-dimensional wave equation using the hyperspherical formalism. The interaction potential between two nuclei is calculated using the double folding model. The numerical results for the interaction potential and the scattering cross section are presented to evaluate the formalism used to calculate the nucleus wave function.

Investigation of the nuclear system using the D-dimensional wave equation

We calculate the nucleus-nucleus interaction potential with the DFM using the wavefunctions of two colliding nuclei. The wavefunctions are obtained by solving the D-dimensional wave equation using hyperspherical formalism. The calculations were assumed to be of finite-range and the density dependence of the NN interaction is accounted for. The results have been compared with calculations of zero-range approximation. To evaluate the formalism used to calculate the nucleus wavefunction, the numerical results for the interaction potential and the scattering cross-section are presented.

Microscopic study of noncentral effects in heavy-ion fusion reactions with spherical nuclei

Fusion reactions of $^{16}\mathrm{O}+^{16}\mathrm{O},^{40}\mathrm{Ca}+^{40}\mathrm{Ca}$, and $^{40}\mathrm{Ca}+^{90}\mathrm{Zr}$ have been investigated by using the three-dimensional (3D) time-dependent Hartree-Fock approach with and without density constraint. The interaction potentials and effective mass parameters are studied. It is found that both the nucleus-nucleus interaction potentials and the effective mass parameters of these systems depend on the impact parameter. Such noncentral effects on fusion cross sections are also investigated. It is shown that the noncentral effect can reduce the fusion cross sections significantly when the incident energy is just above the barrier, while it becomes weaker with the increasing incident energy and can be totally neglected when the energy is up to twice as much as the barrier height in these spherical colliding systems.

Quantitative analysis of precise heavy-ion fusion data at above-barrier energies using Skyrme-Hartree-Fock nuclear densities

We calculate the capture (fusion) cross sections for nine reactions involving spherical nuclei: $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$, $^{28}\mathrm{Si}$, $^{92}\mathrm{Zr}$, $^{144}\mathrm{Sm}$, $^{208}\mathrm{Pb}$; $^{28}\mathrm{Si}$ + $^{28}\mathrm{Si}$, $^{92}\mathrm{Zr}$, $^{208}\mathrm{Pb}$; $^{32}\mathrm{S}$ + $^{208}\mathrm{Pb}$. For six of them precision data are available in the literature. Analysis of these precision data within the framework of the single-barrier penetration model based on the Woods-Saxon profile for the strong nucleus-nucleus interaction potential (SnnP) gave rise to the problem of the apparently large diffuseness of the SnnP [Newton et al., Phys. Rev. C 70, 024605 (2004)]. Our fluctuation-dissipation trajectory model is based on the double-folding approach with the density-dependent M3Y NN forces including the finite-range exchange part. For the nuclear matter density the Skyrme-Hartree-Fock approach including the tensor interaction is applied. The resulting nucleus-nucleus potential possesses rather small (normal) diffuseness. The strength of the radial friction ${K}_{R}$ is used as the free parameter of the model. It turns out that for four of the five reactions induced by $^{16}\mathrm{O}$ (except $^{16}\mathrm{O}$ + $^{208}\mathrm{Pb}$) the calculated cross sections cannot be brought into agreement with the data within the experimental errors. This suggests that the calculated nuclear density is incorrect for $^{16}\mathrm{O}$. For the reactions not involving $^{16}\mathrm{O}$ and, surprisingly, for the $^{16}\mathrm{O}$ + $^{208}\mathrm{Pb}$ reaction the agreement with the data within 2-5% is achieved at ${K}_{R}=1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ to $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}\phantom{\rule{0.28em}{0ex}}{\mathrm{MeV}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{zs}$ which is in accord with the previous works.

Retarding friction versus white noise in the description of heavy ion fusion

We performed modeling of the collision of two spherical nuclei resulting in capture. For this aim the stochastic differential equations are used with the white or colored noise and with the instant or retarding friction, respectively. The dissipative forces are proportional to the squared derivative of the strong nucleus-nucleus interaction potential (SnnP). The SnnP is calculated in the framework of the double folding approach with the density-dependent M3Y NN-forces. Calculations performed for 28 Si+ 144 Sm reaction show that accounting for the fluctuations typically reduces the capture cross sections by not more than 10%. In contradistinction, the influence of the memory effects is found resulting in about 20% enhancement of the cross section.

Heavy ion fusion: Possible dynamical solution of the problem of the abnormally large diffuseness of the nucleus-nucleus potential

We attempt to make some progress in the problem of the apparently large diffuseness of the Woods-Saxon strong nucleus-nucleus interaction potential (SnnP) needed to fit a large number of precision fusion excitation functions. This problem has been formulated in Newton et al. [Phys. Lett. B 586, 219 (2004);Phys. Rev. C 70, 024605 (2004)]. We applied the classical dissipative trajectory model to describe the data on fusion (capture) of ${}^{16}\mathrm{O}$ with ${}^{92}\mathrm{Zr},$ ${}^{144}\mathrm{Sm},$ and ${}^{208}\mathrm{Pb}.$ No fluctuations or dynamical deformations of the interacting nuclei are accounted for. The friction force is supposed to be proportional to the squared derivative of the SnnP (the surface friction model). The SnnP is calculated within the framework of the double-folding model with the density-dependent M3Y $NN$ forces. This potential is known to possess rather small diffuseness in contradistinction to what is required by the data analysis in Newton et al. [Phys. Lett. B 586, 219 (2004);Phys. Rev. C 70, 024605 (2004)]. Varying slightly the strength of radial friction (universally for all three reactions) and the diffuseness of the charge density of ${}^{208}\mathrm{Pb}$ we have obtained satisfactory agreement of the calculated excitation functions with the data.

The M3Y Double Folding Dissipative Model in Agreement with Precise Fusion Cross Sections

Large numbers of precision fusion excitation functions were fitted in the literature using the nucleus-nucleus interaction potential having the Woods-Saxon shape. The diffuseness of this potential fusion ranges from 0.75 to 1.5 fm. This is much larger than the value of 0.65 fm required by the elastic scattering data. Trying to resolve this contradiction we develop the dissipative trajectory model based on the density-dependent M3Y NN-forces folded with the nuclear matter distribution. Resulting potential possesses the normal diffuseness about 0.65 fm. With this potential we reach the agreement with the data for 16O+208Pb, 28Si+208Pb, 32S+208Pb reactions within 5%.

New dissipative non-Markovian model treatment of capture: the need for precise above-barrier cross sections

We performed quantitative theoretical analysis of the high precision data on the fusion excitation function in the reaction 16 O + 144 Sm involving spherical nuclei. For this purpose the model is developed in which the collision process is described by the stochastic dynamical equations with the retarding friction and colored noise. The friction force is supposed to be proportional to the squared derivative of nucleus-nucleus interaction potential. The latter is calculated within the framework of the double folding approach with the density-dependent M3Y NN -forces. Varying the radial dissipation strength K R and the matter diffuseness of 144 Sm we reach χ 2 per point equal to 5.4. However the values of KR and the friction retardation time τ C appear to be strongly correlated. More high precision data are needed to make more definite conclusions about the values of K R and τ C .