We present here a first application of the Fermionic Molecular Dynamics (FMD) approach to low-energy nuclear reactions, namely the $^3$He($α$,$γ$)$^7$Be radiative capture reaction. We divide the Hilbert space into an external region where the system is described as $^3$He and $^4$He clusters interacting only via the Coulomb interaction and an internal region where the nuclear interaction will polarize the clusters. Polarized configurations are obtained by a variation after parity and angular momentum projection procedure with respect to the parameters of all single particle states. A constraint on the radius of the intrinsic many-body state is employed to obtain polarized clusters at desired distances. The boundary conditions for bound and scattering states are implemented using the Bloch operator.
The FMD calculations reproduce the correct energy for the centroid of the $3/2^-$ and $1/2^-$ bound states in $^7$Be. The charge radius of the ground state is in good agreement with recent experimental results. The FMD calculations also describe well the experimental phase shift data in the $1/2^+$, $3/2^+$ and $5/2^+$ channels that are important for the capture reaction at low energies. Using the bound and scattering many-body wave functions we calculate the radiative capture cross section. The calculated $S$ factor agrees very well, both in absolute normalization and energy dependence, with the recent experimental data from the Weizmann, LUNA, Seattle and ERNA experiments.
Low energy capture cross sections are calculated within a microscopic many-body approach using an effective Hamiltonian derived from the Argonne V18 potential. The dynamics is treated within Fermionic Molecular Dynamics (FMD) which uses a Gaussian wave-packet basis to represent the many-body states. A phase-shift equivalent effective interaction derived within the Unitary Correlation Operator Method (UCOM) that treats explicitly short-range central and tensor correlations is employed. As a first application the 3He(alpha,gamma)7Be reaction is presented. Within the FMD approach the microscopic …
The microscopic effective reaction theory is applied to deuteron-induced reactions. A reaction model-space characterized by a $p+n+{\rm A}$ three-body model is adopted, where A is the target nucleus, and the nucleon-target potential is described by a microscopic folding model based on an effective nucleon-nucleon interaction in nuclear medium and a one-body nuclear density of A. The three-body scattering wave function in the model space is obtained with the continuum-discretized coupled-channels method (CDCC), and the eikonal reaction theory (ERT), an extension of CDCC, is applied to the calcu…
Radiative capture reactions for low energy protons have been theoretically studied for Ni and Cu isotopes using the microscopic optical model. The optical potential has been obtained in the folding model using different microscopic interactions with the nuclear densities from Relativistic Mean Field calculations. The calculated total cross sections as well as the cross sections for individually low lying levels have been compared with measurements involving stable nuclear targets. Rates for the rapid proton capture process have been evaluated for astrophysically important reactions.
The fermionic molecular dynamics approach uses Gaussian wave packets as single-particle basis states. Many-body basis states are Slater determinants projected on parity, angular momentum and total linear momentum. The wave-packet basis is very flexible - FMD contains harmonic oscillator shell model and Brink-type cluster states as special cases. The parameters of the wave packets are obtained by variation. A realistic effective interaction derived from the Argonne V18 interaction by means of the unitary correlation operator method is employed. We discuss the fully microscopic calculation of th…
Microscopic optical potentials obtained by folding the DDM3Y interaction with the densities from Relativistic Mean Field approach have been utilized to evaluate S-factors of low-energy $(p,γ)$ reactions in mass 60-80 region and to compare with experiments. The Lagrangian density FSU Gold has been employed. Astrophysical rates for important proton capture reactions have been calculated to study the behaviour of rapid proton nucleosynthesis for waiting point nuclei with mass less than A=80.
Low energy proton capture reactions have been studied in statistical model using the semi-microscopic optical potential in the mass range A=110-125. Nuclear density obtained from relativistic mean field calculation has been folded with nucleon-nucleon interaction to obtain the optical potential. Theoretical results have been compared with experimental measurements to normalize the potential. Results have also been compared with a standard calculation available in the literature.
The understanding of the fusion probability is of particular importance to reveal the mechanism of producing superheavy elements. We present a microscopic study of the compound nucleus formation by combining time-dependent density functional theory, coupled-channels approach, and dynamical diffusion models. The fusion probability and compound nucleus formation cross sections for cold-fusion reactions $^{48}$Ca+$^{208}$Pb, $^{50}$Ti+$^{208}$Pb, and $^{54}$Cr+$^{208}$Pb are investigated and it is found that the deduced capture barriers, capture cross sections for these reactions are consistent w…
An isospin and spin dependent form of the equation of state for nuclear matter is presented. This form is used for the description of nucleon interaction in a new dynamic model. Preliminary calculations show that the new approach makes possible predicting the alpha structures appearing in the case of the ground state even-even nuclei.
We present a microscopic dynamical study of the reactions involving three $^{4}$He clusters. We show that the much discussed triple-$α$ linear chain configuration of $^{12}$C is formed with a certain lifetime and subsequently decays into a triangular configuration of $^{12}$C and then to a configuration near the ground state. Time-dependent Hartree-Fock (TDHF) theory coupled with a density constraint is used to study the properties of these configurations. We find a sequence of dynamical transitions analogous to the suggested astrophysical mechanism for the formation of $^{12}$C nuclei.
On the base of potential theory of light nuclei cluster photodisintegration the characteristics of Lithium nuclei cluster photodisintegration reactions are considered in the range of low and intermediate energies. For the inverse reaction the interference has an opposite character: in forward semisphere it is deconstructive, and in backward semisphere it is constructive. In the energy range above several MeV the E2-multipole becomes dominating. The effect of appearance of the node structure of the wave function of relative motion has been considered in the characteristics of Li cluster photodi…
Collective inertial mass coefficients with respect to translational, relative, and rotational motions are microscopically calculated, along the collective reaction path self-consistently determined, based on the adiabatic self-consistent collective coordinate (ASCC) method. The impact of the time-odd component of the mean-field potential on the inertial masses are investigated. The results are compared with those calculated with the cranking formulae. The inertial masses based on the ASCC method reproduce the exact total nuclear mass for the translational motion as well as the exact reduced ma…
The breakup cross sections in the reaction $^6$He+$^{12}$C are calculated at about 40 MeV/nucleon using the high-energy approximation (HEA) and with the help of microscopic optical potentials (OP) of interaction with the target nucleus $^{12}$C of the projectile nucleus fragments $^4$He and 2n. Considering the di-neutron $h$=2n as a single particle the relative motion $hα$ wave function is estimated so that to explain both the separation energy of $h$ in $^6$He and the rms radius of the latter. The stripping and absorbtion total cross sections are calculated and their sum is compared with the …
In this work we want to study quasielastic (p, n) exchange reactions using a semi-microscopic optical model derived in a previous work [1] based on a nuclear matter approach where the real and imaginary parts are given by the first and second order terms, respectively, of the mass operator obtained by a Brueckner-Hartree-Fock calculation using a G-matrix built up with an effective Gogny interaction. The study of these quasielastic reactions is performed within a Distorted Wave Born Approximation (DWBA) to evaluate the wave functions in the entrance and exit channels, which in turn are used to …
We study reactions between neutron-rich $^{132}$Sn nucleus and $^{96}$Zr within a dynamic microscopic theory at energies in the vicinity of the ion-ion potential barrier peak, and we compare the properties to those of the stable system $^{124}$Sn+$^{96}$Zr. The calculations are carried out on a three-dimensional lattice using the density-constrained Time-Dependent Hartree-Fock method. In particular, we calculate the dynamic excitation energy $E^*(t)$ and the quadrupole moment of the dinuclear system, $Q_{20}(t)$, during the initial stages of the heavy-ion collision. Capture cross sections for …
We investigate $^6$Li($n$, $n'$)$^6$Li$^*$ $\to$ $d$ + $α$ reactions by using the continuum-discretized coupled-channels method with the complex Jeukenne-Lejeune-Mahaux effective nucleon-nucleon interaction. In this study, the $^6$Li nucleus is described as a $d$ + $α$ cluster model. The calculated elastic cross sections for incident energies between 7.47 and 24.0 MeV are good agreement with experimental data. Furthermore, we show the neutron spectra to $^6$Li breakup states measured at selected angular points and incident energies can be also reproduced systematically.
The low-lying states of the $^{9}$Li nucleus are investigated with a unified framework of microscopic structure and reaction models. In the structure model, the wave function is fully antisymmetrized and the $^{9}$Li nucleus is described as an $α$ + $t$ + $n$ + $n$ four-body system, and low-lying 1/2$^{-}$, 3/2$^{-}$, 5/2$^{-}$, and 7/2$^{-}$ states are obtained by the stochastic multi-configuration mixing method. Using these wave functions, the quasi-elastic cross section at $E/A$ = 60 MeV and the elastic and inelastic cross sections at $E/A$ = 50 MeV on the $^{12}$C target are calculated in …
The neutron capture cross sections and average radiative widths of neutron resonances for two double-magic nuclei 132Sn and 208Pb have been calculated using the microscopic photon strength functions, which were obtained within the microscopic self-consistent version of the extended theory of finite Fermi systems in the time blocking approximation. For the first time, the microscopic PSFs have been obtained within the fully self-consistent approach with exact accounting for the single particle continuum (for 208Pb). The approach includes phonon coupling effects in addition to the standard RPA a…
In the search for superheavy elements quasifission reactions represent one of the reaction pathways that curtail the formation of an evaporation residue. In addition to its importance in these searches quasifission is also an interesting dynamic process that could assist our understanding of many-body dynamical shell effects and energy dissipation thus forming a gateway between deep-inelastic reactions and fission. This manuscript gives a summary of recent progress in microscopic calculations of quasifission employing time-dependent Hartree-Fock (TDHF) theory and its extensions.
The radiative thermal neutron capture cross sections over the range of thermal energies from 1 keV to 1 MeV are studied in statistical Hauser-Feshbach formalism. The optical model potential is constructed by folding the density dependent M3Y nucleon-nucleon interaction with radial matter densities of target nuclei obtained from relativistic-mean-field (RMF) theory. The standard nuclear reaction code TALYS1.8 is used for calculation of cross sections. The nuclei studied in the present work reside near the $Z=28$ proton shell closure and are of astrophysical interests taking part in p-, s-, and …
We present a microscopic formalism that extends the traditional formulation of Williams, Ericson and Bloch and permits to obtain the transition strengths (TS) of pre-equilibrium nuclear reactions directly from their quantum microscopic description. We calculate the TS without resorting to the Laplace transform approach and the use of the saddle point approximation. We also analyze some problems that may appear in connection with these mathematical tools and the Darwin-Fowler approach in this case. We show that, analogously to the nuclear densities, the strengths for transitions that change the…
Clustering plays an important role in the structure of nuclei, especially for light nuclei in the $p$-shell. In nuclear cluster models these degrees of freedom are introduced explicitly. In the Resonating Group Method or in the Generator Coordinate Method the clusters are built from individual nucleons interacting via an effective nucleon-nucleon interaction; the total wave function is antisymmetrized. Fermionic Molecular Dynamics (FMD) goes beyond pure cluster models. It is a microscopic many-body approach using a Gaussian wave packet basis that includes the harmonic oscillator shell model an…
The heavy-ion fusion reactions induced by neutron-rich nuclei are investigated with the improved quantum molecular dynamics (ImQMD) model. With a subtle consideration of the neutron skin thickness of nuclei and the symmetry potential, the stability of nuclei and the fusion excitation functions of heavy-ion fusion reactions $^{16}$O+$^{76}$Ge, $^{16}$O+$^{154}$Sm, $^{40}$Ca+$^{96}$Zr and $^{132}$Sn+$^{40}$Ca are systematically studied. The fusion cross sections of these reactions at energies around the Coulomb barrier can be well reproduced by using the ImQMD model. The corresponding slope para…
A new framework for $A(d,p)B$ reactions is introduced by merging the microscopic approach to computing the properties of the nucleon-target systems and the three-body $n+p+A$ reaction formalism, thus providing a consistent link between the reaction cross sections and the underlying microscopic structure. In this first step toward a full microscopic description, we focus on the inclusion of the neutron-target microscopic properties. The properties of the neutron-target subsystem are encapsulated in the Green's function which is computed with the Coupled Cluster theory using a chiral nucleon-nuc…
We study pre-equilibrium giant dipole resonance excitation and fusion in the neutron-rich system $^{132}$Sn+$^{48}$Ca at energies near the Coulomb barrier, and we compare photon yields and total fusion cross sections to those of the stable system $^{124}$Sn+$^{40}$Ca. The dynamic microscopic calculations are carried out on a three-dimensional lattice using both the Time-Dependent Hartree-Fock method and the Density Constrained TDHF method. We demonstrate that the peak of the GDR excitation spectrum occurs at a substantially lower energy than expected for an equilibrated system, thus reflecting…
We present our current studies and our future plans on microscopic potential based on effective nucleon-nucleon interaction and many-body theory. This framework treats in an unified way nuclear structure and reaction. It offers the opportunity to link the underlying effective interaction to nucleon scattering observables. The more consistently connected to a variety of reaction and structure experimental data the framework will be, the more constrained effective interaction will be. As a proof of concept, we present some recent results for both neutron and proton scattered from spherical targe…
A microscopic calculation of reaction cross sections for nucleon-nucleus scattering has been performed by explicitly coupling the elastic channel to all particle-hole excitations in the target and one-nucleon pickup channels. The particle-hole states may be regarded as doorway states through which the flux flows to more complicated configurations, and subsequently to long-lived compound nucleus resonances. Target excitations for $^{40,48}$Ca, $^{58}$Ni, $^{90}$Zr and $^{144}$Sm were described in a random-phase framework using a Skyrme functional. Reaction cross sections obtained agree very wel…
We provide a microscopic description of the fusion reactions between $^{40,48}$Ca and $^{78}$Ni. The internuclear potentials are obtained using the density-constrained (DC) time-dependent Hartree-Fock (TDHF) approach and fusion cross sections are calculated via the incoming wave boundary condition method. By performing DC-TDHF calculations at several selected incident energies, the internuclear potentials for both systems are obtained and the energy-dependence of fusion barrier are revealed. The influence of tensor force on internuclear potentials of $^{48}\mathrm{Ca}+{}^{78}\mathrm{Ni}$ is mo…
We present updated predictions of effective elastic nucleon-nucleon cross sections intended for use in nucleus-nucleus reactions. A novel characteristic of the present approach combines all microscopic medium effects included in the Dirac-Brueckner-Hartree-Fock G-matrix with a Pauli blocking mechanism which is more appropriate for applications in ion-ion reaction models as compared to a previous approach. The effective in-medium cross section is found to be quite sensitive to the description of Pauli blocking in the final configurations.
Low-energy 17O(n,g)18O reaction within the microscopic potential model and its role for the weak r-process
Ho Chi Minh City University of Education（胡志明市教育大学）；California State University East Bay（加州州立大学东湾分校）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；San Diego State University（圣地亚哥州立大学）
The nuclear structure dependence of direct reactions that remove a pair of like or unlike nucleons from a fast $^{12}$C projectile beam are considered. Specifically, we study the differences in the two-nucleon correlations present and the predicted removal cross sections when using $p$-shell shell-model and multi-$\hbarω$ no-core shell-model (NCSM) descriptions of the two-nucleon overlaps for the transitions to the mass $A$=10 projectile residues. The NCSM calculations use modern chiral two-nucleon and three-nucleon (NN+3N) interactions. The $np$-removal cross sections to low-lying $T$=0, $^{1…
We study the exotic deformed nucleus $^{31}$Ne using an approach that combines self-consistent structure and reaction theory. We utilize the fully-relativistic, microscopic deformed Hartree-Bogoliubov theory in continuum (DRHBc) to demonstrate that deformation and pairing correlations give rise to a halo structure with large-amplitude $p$-wave configuration in $^{31}$Ne. We then use the valence nucleon wave functions and angle-averaged density distributions of $^{30}$Ne from this model as input for a Glauber reaction model to study the observables of neutron-rich Neon isotopes and search for h…
Modelling fission with microscopic input: excitation-energy-dependent fission paths for neutron-induced reactions
Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles（布鲁塞尔天文与天体物理研究所，布鲁塞尔自由大学）；Brussels Laboratory of the Universe - BLU-ULB（宇宙布鲁塞尔实验室）
Nucleon transfer in symmetric heavy-ion reactions at energies below the Coulomb barrier is investigated in the framework of a microscopic stochastic mean-field theory. While mean-field alone is known to significantly underpredict the dispersion of the fragment mass distribution, a considerable enhancement of the dispersion is obtained in the stochastic mean-field theory. The variance of the fragment mass distribution deduced from the stochastic theory scales with the number of exchanged nucleon. Therefore, the new approach provides the first fully microscopic theory consistent with the phenome…
We analyze the $α$-$^{12}$C inelastic scattering to the $0^+_2$ state of $^{12}$C, the Hoyle state, in a fully microscopic framework. With no free adjustable parameter, the inelastic cross sections at forward angles are well reproduced by the microscopic reaction calculation using the transition density of $^{12}$C obtained by the resonating group method and the nucleon-nucleon $g$ matrix interaction developed by the Melbourne group. It is thus shown that the monopole transition strength obtained by the structural calculation is consistent with that extracted from the reaction observable, sugg…
\item[Background] Multinucleon transfer reaction at low-energy collisions is considered to be a promising method for the production of new exotic nuclei, which are difficult to be produced by other methods. The theoretical studies are required to provide reliable predictions for the experiments and promote the understanding of the microscopic mechanism in multinucleon transfer reactions. \item[Purpose] We provide a predictive approach for production cross sections, and testify how and to what extent the microscopic approach works well in multinucleon transfer reaction. \item[Methods] We employ…
We studied the complete dynamics of the proton-induced spallation process with the microscopic framework of the Constrained Molecular Dynamics (CoMD) Model. We performed calculations of proton-induced spallation reactions on 181Ta, 208Pb, and 238U targets with the CoMD model and compared the results with a standard two-step approach based on an intranuclear cascade model (INC) followed by a statistical deexcitation model. The calculations were also compared with recent experimental data from the literature. Our calculations showed an overall satisfactory agreement with the experimental data an…
Two-neutron transfer reactions are studied within the interacting boson model based on the nuclear energy density functional theory. Constrained self-consistent mean-field calculations with the Skyrme energy density functional are performed to provide microscopic input to completely determine the Hamiltonian of the IBM. Spectroscopic properties are calculated only from the nucleonic degrees of freedom. This method is applied to study the $(t,p)$ and $(p,t)$ transfer reactions in the assorted set of rare-earth nuclei $^{146-158}$Sm, $^{148-160}$Gd, and $^{150-162}$Dy, where spherical-to-axially…
Elastic scattering observables (differential cross section and analyzing power) are calculated for the reaction $^6$He(p,p)$^6$He at projectile energies starting at 71 MeV/nucleon. The optical potential needed to describe the reaction is based on a microscopic Watson first-order folding potential, which explicitly takes into account that the two neutrons outside the $^4$He-core occupy an open p-shell. The folding of the single-particle harmonic oscillator density matrix with the nucleon-nucleon t-matrix leads for this case to new terms not present in traditional folding optical potentials for …
We have studied the ground state properties (binding energy and charge radius) using relativistic mean filed formalism (RMF) for Mg-isotopes in the valley of stability to drip line region. The RMF densities have been analyzed in context of reaction dynamics. The calculated results of $^{24-40}$Mg+$^{12}$C reactions at projectile energy 240 AMeV using Glauber model with the conjunction of densities from relativistic mean field formalism are compared with experimental data. We found remarkable agreement of estimated values of reaction cross sections with experimental data except for $^{37}$Mg is…
A microscopic analysis of the optical potentials (OPs) and cross sections of quasielastic scattering of $^{12,14}$Be on $^{12}$C at 56 MeV/nucleon and on protons at energy near 700 MeV is carried out. For lower energy scattering the real part of the OP is calculated by using of double-folding procedure accounting for the anti-symmetrization effects, while the imaginary part is obtained on the base of the high-energy approximation (HEA). The HEA is also applied to the calculations of both real and imaginary OPs when solving the relativistic equation for the high-energy proton-nucleus elastic sc…
Elastic and inelastic cross sections of the $p+{}^6\textrm{He}$, $p+{}^8\textrm{He}$, and $α+{}^8\textrm{He}$ reactions were investigated using the Melbourne $g$-matrix folding approach with the theoretical densities of ${}^6\textrm{He}$ and ${}^8\textrm{He}$ obtained by a microscopic structure model of antisymmetrized molecular dynamics (AMD). Microscopic coupled-channel (MCC) calculations of the $p+{}^6\textrm{He}$ and $p+{}^8\textrm{He}$ reactions were performed to investigate transition properties of the ${}^6\textrm{He}(2^+_1)$ and ${}^8\textrm{He}(2^+_1)$ states. The MCC+AMD calculations…
Background: Heavy-ion fusion reactions at energies near the Coulomb barrier are influenced by couplings between the relative motion and nuclear intrinsic degrees of freedom of the colliding nuclei. The time-dependent Hartree-Fock (TDHF) theory, incorporating the couplings at the mean-field level, as well as the coupled-channels (CC) method are standard approaches to describe low energy nuclear reactions. Purpose: To investigate the effect of couplings to inelastic and transfer channels on the fusion cross sections for the reactions $^{40}$Ca+$^{58}$Ni and $^{40}$Ca+$^{64}$Ni. Methods: Fusion c…
