Carlos A. Bertulani, Angela Bonaccorso
In this brief review we discuss the basic theoretical concepts used in the experimental studies of the most common cases of direct reactions such as (a) elastic scattering, (b) inelastic scattering, (c) Coulomb excitation, (d) transfer reactions and (e) breakup reactions.
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Transfer reactions are an important tool in nuclear astrophysics. These reactions allow us to identify states in nuclei and to find the corresponding energies, to determine if these states can contribute to astrophysical nuclear reactions and ultimately to determine the strength of that contribution. In this paper, the basic details of how transfer reactions may be used in nuclear astrophysics are set out along with some common pitfalls to avoid.
We present an introduction to ab initio nuclear theory with a focus on nuclear reactions. After a high-level overview of ab initio approaches in nuclear physics, we give a more detailed description of the no-core shell model technique equivalent to a large extent to configuration-interaction methods applied in quantum chemistry. We then introduce the no-core shell model with continuum approach that provides a quantum many-body description of nuclear reactions. After a brief review of nuclear reactions important for astrophysics, we present examples of results of ab initio calculations of radia…
Time-dependent Hartree--Fock (TDHF) method has been applied to various low-energy nuclear reactions, such as fusion, fission, and multinucleon transfer reactions. In this Mini Review, we summarize recent attempts to bridge a microscopic nuclear reaction theory, TDHF, and a macroscopic aspect of nuclear reactions through nucleus--nucleus potentials and energy dissipation from macroscopic degrees of freedom to microscopic ones obtained from TDHF in various colliding systems from light to heavy mass regions.
The clear separation of scales observed in halo nuclei between the extended halo and the compact core makes these exotic nuclei a perfect subject for Effective Field Theory (EFT). Such description leads to a systematic expansion of the core-halo Hamiltonian, which naturally orders the nuclear-structure observables. In this short review, I show the advantage there is to include Halo-EFT descriptions within precise models of reactions. It helps identifying the nuclear-structure observables that matter in the description of the reactions, and enables us to easily bridge predictions of nuclear-str…
Nuclear multifragmentation is an important phenomenon, the study of which can throw light on reaction mechanism in heavy ion collisions at intermediate and high energies. Based on statistical and dynamical model studies, this thesis is concentrated mainly on, the following three aspects of nuclear multifragmentation reactions namely (i) production of exotic nuclei which are normally not available in the laboratory (ii) nuclear symmetry energy from heavy ion collisions at intermediate energies and (iii) Nuclear liquid-gas phase transition. In addition to these equivalence of statistical ensembl…
Nuclear reaction rate ($λ$) is a significant factor in the process of nucleosynthesis. A multi-layer directed-weighted nuclear reaction network in which the reaction rate as the weight, and neutron, proton, $^4$He and the remainder nuclei as the criterion for different reaction-layers is for the first time built based on all thermonuclear reactions in the JINA REACLIB database. Our results show that with the increase of the stellar temperature ($T_{9}$), the distribution of nuclear reaction rates on the $R$-layer network demonstrates a transition from unimodal to bimodal distributions. Nuclei …
Based on an isospin dependent transport model IBUU, effects of high density behavior of nuclear symmetry energy in the proton-rich reaction $^{22}$Si+$^{22}$Si at a beam energy of 400 MeV/nucleon are studied. It is found that the symmetry energy affects $π^{+}$ production more than $π^{-}$. More interestingly, comparing with neutron-rich reactions, for $π^{-}/π^{+}$ and dense matter's N/Z ratios, effects of symmetry energy in the proton-rich reaction both show contrary behaviors. The practical experiment by using the proton-rich reaction $^{22}$Si+$^{40}$Ca to study nuclear symmetry energy are…
The theoretical approach to a sequential heavy ion double charge exchange reaction is presented. A brief introduction into the formal theory of second-order nuclear reactions and their application to Double Single Charge Exchange (DSCE) reactions by distorted wave theory is given, thereby completing the theoretical background to our recent work [1]. Formally, the DSCE reaction amplitudes are shown to be separable into superpositions of distortion factors, accounting for initial and final state ion--ion interactions, and nuclear matrix elements. A broad space is given to the construction of nuc…
Improving nuclear data evaluations with predictive reaction theory and indirect measurements
针对核反应数据不完整且不稳定靶核的中子反应难以测量的问题，本文提出利用替代反应法结合核理论，通过微观预测、不确定度量化的光学模型和神经网络参数推断来改进核数据评估。
Within the Time Dependent Hartree Fock (TDHF) approach, we investigate the impact of several ingredients of the nuclear effective interaction, such as incompressibility, symmetry energy, effective mass, derivative of the Lane potential and surface terms on the exit channel (fusion vs quasifission) observed in the reaction $^{238}$U+$^{40}$Ca, close to the Coulomb barrier. Our results show that all the ingredients listed above contribute to the competition between fusion and quasifission processes, however the leading role in determining the outcome of the reaction is played by incompressibilit…
The knowledge of the nuclear matrix elements for the neutrinoless double beta decay is fundamental for neutrino physics. In this paper, an innovative technique to extract information on the nuclear matrix elements by measuring the cross section of a double charge exchange nuclear reaction is proposed. The basic point is that the initial and final state wave functions in the two processes are the same and the transition operators are similar. The double charge exchange cross sections can be factorized in a nuclear structure term containing the matrix elements and a nuclear reaction factor. Firs…
Three-body nuclear reactions in two-nucleon plus core systems are described in the framework of exact scattering equations including the core excitation. A nucleon-core optical potential is constructed that can be easily adjusted to the reference potential and thereby to the experimental two-body data, if available. This constitutes an important improvement over the simple deformation of the potential used previously that violated the original fit to the data. Predictions for elastic, inelastic, and transfer reactions involving $^{10}{Be}$ and $^{24}{Mg}$ nuclear cores are obtained. The new op…
These notes summarise the lectures I gave during the summer school "International Scientific Meeting on Nuclear Physics" at La Rábida in Spain in June 2018. They offer an introduction to nuclear-reaction theory, starting with the basics in quantum scattering theory followed by the main models used to describe breakup reactions: the Continuum Discretised Coupled Channel method (CDCC),the Time-Dependent approach (TD) and the eikonal approximation. These models are illustrated on the study of the exotic structure of halo nuclei.
Opportunities for investigations of nuclear reactions at the future nuclear physics facilities such as radioactive ion beam facilities and high-power laser facilities are considered. Post-accelerated radioactive ion beams offer possibilities for study of the role of isospin asymmetry in the reaction mechanisms at various beam energies. Fission barrier heights of neutron-deficient nuclei can be directly determined at low energies. Post-accelerated radioactive ion beams, specifically at the future facilities such as HIE-ISOLDE, SPIRAL-2 or RAON-RISP can be also considered as a candidate for prod…
Atomic nuclei are composite systems, and they may be dynamically excited during nuclear reactions. Such excitations are not only relevant to inelastic scattering but they also affect other reaction processes such as elastic scattering and fusion. The coupled-channels approach is a framework which can describe these reaction processes in a unified manner. It expands the total wave function of the system in terms of the ground and excited states of the colliding nuclei, and solves the coupled Shrödinger equations to obtain the $S$-matrix, from which several cross sections can be constructed. Thi…
We investigate the impact of ambiguities coming from the choice of optical potentials and nucleon-nucleon scattering cross sections on the spectroscopic factors extracted from the $^{12}$C($p,2p$)$^{11}$B reaction. These ambiguities are evaluated by analyzing the cross sections of the $^{12}$C($p,2p$)$^{11}$B reaction at 100 and 200 MeV within the framework of the distorted-wave impulse approximation with realistic choices of nuclear inputs. The results show that the studied ambiguities are considerably large in this energy region and careful choices of nuclear inputs used in the reaction calc…
The core excitation, being an important reaction mechanism, so far is not properly included in most calculations of three-body nuclear reactions. We aim to include the excitation of the core nucleus using an exact Faddeev-type framework for nuclear reactions in the three-body (core + neutron + proton) system. We employ Alt, Grassberger, and Sandhas (AGS) integral equations for the three-particle transition operators and solve them in the momentum-space framework. The Coulomb interaction is included via the method of screening and renormalization. We calculate elastic, inelastic, and transfer r…
In this contribution, I present a short overview of the theory of direct nuclear reactions, with special emphasis on the case of reactions induced by weakly-bound nuclei. After introducing some general results of quantum scattering theory, I present specific applications to elastic, inelastic, transfer and breakup reactions. For each of them, I first introduce the most standard framework, followed by some alternative models or extensions suitable for the case of weakly bound nuclei. A short discussion on semiclassical theory of Coulomb excitation and its application to breakup of halo nuclei i…
Using adiabatic distorted-wave approximation (ADWA) with nonlocal optical potentials (NLOP) for $(d,p)$ transfer reactions [G.W. Bailey, N.K. Timofeyuk, and J.A. Tostevin, Phys. Rev. Lett. 117, 162502 (2016)] reported strong sensitivity to the $n$-$p$ force model. This sensitivity disappears in rigorous three-body Faddeev-type results. Some shortcomings of ADWA with NLOP are pointed out.
We present a reaction model to describe the fast removal of the $α$-particle core in $^8$He nucleus with eventual emission of four neutrons. The obtained four neutron energy distributions allows to explain the sharp low energy peak observed by studying the missing mass spectra of four neutrons in [Nature Vol. 606, p. 678], as a consequence of dineutron-dineutron correlations.
Nuclear shape dynamics in low-energy heavy-ion reactions
该研究探讨低能重离子反应的理论进展，通过光学势模型单道问题、多道散射问题分析，证明库仑势垒附近聚变反应对核形状敏感，还指出其与相对论重离子碰撞在核形状动力学上的相似性。
Knockout reactions with heavy ion targets in inverse kinematics, as well as "quasi-free" (p,2p) and (p,pn) reactions are useful tools for nuclear spectroscopy. We report calculations on \textit{ab-initio} many-body wavefunctions based on the no-core shell model to study the nucleon removal reactions in light nuclei, including beryllium, carbon, and oxygen isotopic chains, and explore the importance of using an \textit{ab-initio} method. Our study helps clarifying how the extraction of spectroscopic factors from the experiments depend on the details of the many-body wavefunctions being probed. …
Theoretical models of low-energy (d,p) single-neutron transfer reactions are a crucial link between experimentation, nuclear structure and nuclear astrophysical studies. Whereas reaction models that use local optical potentials are insensitive to short-range physics in the deuteron, we show that including the inherent nonlocality of the nucleon-target interactions and realistic deuteron wave functions generates significant sensitivity to high n-p relative momenta and to the underlying nucleon-nucleon interaction. We quantify this effect upon the deuteron channel distorting potentials within th…
We demonstrate, within symmetry unrestricted time-dependent density functional theory, the existence of new effects in low-energy nuclear reactions which originate from superfluidity. The dynamics of the pairing field induces solitonic excitations in the colliding nuclear systems, leading to qualitative changes in the reaction dynamics. The solitonic excitation prevents collective energy dissipation and effectively suppresses fusion cross section. We demonstrate how the variations of the total kinetic energy of the fragments can be traced back to the energy stored in the superfluid junction of…
Based on an isospin- and momentum-dependent hadronic transport model IBUU04, effects of the nuclear symmetry energy on the single and double pi^{-}/pi^{+}ratios in central reactions of ^{132}Sn+^{124}Sn and ^{112}Sn+^{112}Sn at a beam energy of 400 MeV/nucleon are studied. It is found that around the Coulomb peak of the single pi^{-}/pi^{+} ratio the double pi^{-}/pi^{+} ratio taken from the two isotopic reactions retains about the same sensitivity to the density dependence of nuclear symmetry energy. Because the double pi^{-}/pi^{+}ratio can reduce significantly the systematic errors, it is t…
Photo nuclear reactions are shown to be used for studying neutrino/weak nuclear responses involved in astro-neutrino nuclear interactions and double beta decays. Charged current weak responses for ground and excited states are studied by using photo nuclear reactions through isobaric analog states of those states, while neutral current weak responses for excited states are studied by using photo nuclear reactions through the excited states. The weak interaction strengths are studied by measuring the cross sections of the photo nuclear reactions, and the spin and parity of the state are studied…
The relevant energy ranges for stellar nuclear reactions are introduced. Low-energy compound and direct reactions are discussed. Stellar modifications of the cross sections are presented. Implications for experiments are outlined.
We review the Trojan horse method and its applications to resonant reactions in nuclear astrophysics.
Heavy-ion reactions induced by neutron-rich nuclei provide a unique means to investigate the equation of state of isospin-asymmetric nuclear matter, especially the density dependence of the nuclear symmetry energy. In particular, recent analyses of the isospin diffusion data in heavy-ion reactions have already put a stringent constraint on the nuclear symmetry energy around the nuclear matter saturation density. We review this exciting result and discuss its implications on nuclear effective interactions and the neutron skin thickness of heavy nuclei. In addition, we also review the theoretica…
An event generator for the description of nuclear reactions in the Fermi energy range is briefly introduced and first comparisons with experimental data are shown.
Extraction of bulk nuclear properties by comparing reaction observables to results from semiclassical transport-model simulations is discussed. Specific properties include the nuclear viscosity, incompressibility and constraints on the nuclear pressure at supranormal densities.
A short overview of the direct reaction mechanism and the models used for the analysis of such processes is given. Nuclear reactions proceeding through the direct mechanism and involved in solar hydrogen burning are discussed. The significance of these nuclear reactions with respect to the solar neutrino problem is investigated.
We incorporate the coupled-channels optical model into the statistical Hauser-Feshbach nuclear reaction theory, where the scattering matrix is diagonalized by performing the Engelbrecht-Weidenmüller transformation. This technique has been implemented in the coupled-channels optical model code ECIS by J. Raynal, and we extend this method so that all the open channels in a nucleon-induced reaction on a deformed nucleus can be calculated consistently.
The theoretical predictions of the primordial abundances of elements in the big-bang nucleosynthesis (BBN) are dominated by uncertainties in the input nuclear reaction rates. We investigate the effect of modifying these reaction rates on light element abundance yields in BBN by replacing the thirty-five reaction rates out of the existing eighty-eight. We have studied these yields as functions of evolution time or temperature. We find that using these new reaction rates results in only a little increase in helium mass fraction over that obtained previously in BBN calculations. This allows insig…
The main features of nuclear reactions with participation of baryon resonances ($Δ$(1232), S(1535) and $Λ$(1405)), which are interpreted as a manifestation of the bound states of nucleus and corresponding meson are discussed.
The R-function theory of Thomas is used to model neutron inelastic scattering and the fine, intermediate, and gross structure observed in the Dow Jones Industrial Average on a typical trading day.
Many more nuclear transitions have to be known in the determination of stellar reactivities for trans-iron nucleosynthesis than for reactions of light nuclei. This requires different theoretical and experimental approaches. Some of the issues specific for trans-iron nucleosynthesis are discussed.
The nuclear transparency of the charged hadron produced in the inclusive $(e,e^\prime)$ reaction on the nucleus has been calculated using Glauber model for the nuclear reaction. The color transparency (CT) of the produced hadron and the short-range correlation (SRC) of the nucleons in the nucleus have been incorporated in the Glauber model to investigate their effects on the nuclear transparency of the hadron. The calculated nuclear transparencies for the proton and pion are compared with the data.
The calculations of three-body direct nuclear reactions with nonlocal optical potentials are performed for the first time using the framework of Faddeev-type scattering equations. Important nonlocality effect is found for transfer reactions like d+16O -> p + 17O often improving the description of the experimental data.
Compound-nuclear processes play an important role for nuclear physics applications and are crucial for our understanding of the nuclear many-body problem. Despite intensive interest in this area, some of the available theoretical developments have not yet been fully tested and implemented. We revisit the general theory of compound-nuclear reactions, discuss descriptions of pre-equilibrium reactions, and consider extensions that are needed in order to get cross section information from indirect measurements.
Accurate nuclear reaction rates are needed for primordial nucleosynthesis and hydrostatic burning in stars. The relevant reactions are extremely difficult to measure directly in the laboratory at the small astrophysical energies. In recent years direct reactions have been developed and applied to extract low-energy astrophysical S-factors. These methods require a combination of new experimental techniques and theoretical efforts, which are the subject of this presentation.
In the domain of Nuclear reactions at intermediate energies, the QCD coupling constant $α_s$ is large enough ($\sim$ 0.3 - 0.5) to render the perturbative calculational techniques inapplicable. In this regime the quarks are confined into colorless hadrons and it is expected that effective field theories of hadron interactions via exchange of hadrons, provide useful tools to describe such reactions. In this contribution we discuss applications of one such theory, the effective Lagrangian model, in describing the hadronic reactions at intermediate energies whose measurements are the focus of a v…
We study theoretically medium effects on $Ξ^-$ production in the ($K^-$, $K^+$) reaction, using the optimal Fermi-averaging procedure which describes the Fermi motion of a nucleon on the on-energy-shell $K^-p\to K^+Ξ^-$ reaction condition in nuclei. The result shows the strong energy and angular dependence of the in-medium $K^-p\to K^+Ξ^-$ cross section,which affects significantly the shape and magnitude of the production spectrum for $Ξ^-$ hypernuclear states in the ($K^-$, $K^+$) reaction on a nuclear target.The application to the $Ξ^-$ quasi-free production via the ($K^-$, $K^+$) reaction o…
We present a brief overview of recent developments in ab initio calculations of nuclear scattering and reactions with a focus on applications of the no-core shell model with continuum method.
Describing fusion reactions between ^{16}O and ^{154}Dy and, between ^{16}O and ^{144}Sm by the $sd-$ and $sdf-$ interacting boson model, we show that heavy-ion fusion reactions are strongly affected by anharmonic properties of nuclear surface vibrations and nuclear shape, and thus provide a powerful method to study details of nuclear structure and dynamics.
Problems in applying random-matrix theory (RMT) to nuclear reactions arise in two domains. To justify the approach, statistical properties of isolated resonances observed experimentally must agree with RMT predictions. That agreement is less striking than would be desirable. In the implementation of the approach, the range of theoretically predicted observables is too narrow.
Direct nuclear reactions $\vec{d}+A$ and $\vec{p}+(An)$ are described in the framework of three-body Faddeev-type equations. Differential cross section and analyzing powers are calculated using several optical potential models and compared with the experimental data. Quite satisfactory agreement is found except for few systematic discrepancies.
We analyze reactions of several types that are naively below threshold but can proceed because of the release of binding energy from nuclear fission and occasionally the formation of Coulombic bound states. These reactions include (i) photofission with pion production and (ii) charged current neutrino-nucleus reactions that lead to fission and/or formation of a Coulomb bound state of a $μ^-$ with the nucleus of a fission fragment. We comment on the possible experimental observation of these reactions.
The nuclear reaction network is usually studied via precise calculation of differential equation sets, and much research interest has been focused on the characteristics of nuclides, such as half-life and size limit. In this paper, however, we adopt the methods from both multilayer and reaction networks, and obtain a distinctive view by mapping all the nuclear reactions in JINA REACLIB database into a directed network with 4 layers: neutron, proton, $^4$He and the remainder. The layer names correspond to reaction types decided by the currency particles consumed. This combined approach reveals …
Nucleosynthesis is a complex process in astro-nuclear evolution. In this work, we construct a directed multi-layer nuclear reaction network using the substrate-product method from a thermonuclear reaction database, JINA REACLIB. The network contains four layers, namely $n$-, $p$-, $h$- and $r$, corresponding to the reaction types involved in neutrons, protons, $^4$He and the remainder, respectively. The degree values (i.e. numbers of reactions) for three layers of n-, p- and h- have a significant correlation with one another, and their topological structures exhibit a similar regularity. Howev…
We present recent results in theoretical studies on nuclear structure and reaction beyond mean field, using the adiabatic self-consistent collective coordinate method and its extension. We also present new results with the finite-temperature Hartree-Fock-Bogoliubov calculation with the three-dimensional-coordinate-space representation.
Dynamical reaction theory is presented for synthesis of superheavy elements. Characteristic features of formation and surviving are discussed, which combinedly determine final residue cross sections of superheavy elements. Preliminary results on Z=114 are also given.
Calculations of the direct radiative capture reactions are made for the $^{48}$Ca$(n,γ)^{49}$Ca, $^7$Li$(n,γ)^8$Li and $^{12}$C$(p,γ)^{13}$N reactions with the Perey-Buck type nonlocal potentials using a potential model. Our results reproduce the experimental data reasonably well. From comparisons with results obtained by using local potentials, it is found that the cross sections of direct capture reactions may change by around 25\% due to the nonlcality of nuclear potentials.
Recent analyses of several isospin effects in heavy-ion reactions have allowed us to constrain the density dependence of nuclear symmetry energy at sub-saturation densities within a narrow range. Combined with constraints on the Equation of State (EOS) of symmetric nuclear matter obtained previously from analyzing the elliptic flow in relativistic heavy-ion collisions, the EOS of neutron-rich nuclear matter is thus partially constrained. Here we report effects of the partially constrained EOS of neutron-rich nuclear matter on the mass-radius correlation, moment of inertia, elliptical deformati…
Fusion reactions with a weakly bound projectile are studied using the double-folding model along with a repulsive interaction modifying term. Using this modified potential, including nuclear matter incompressibility effects, the fusion reaction cross sections and suppression parameters are calculated for 9Be +209Bi,208Pb,29Si and 27Al reactions. The results show that applying these effects at energies near the Coulomb barrier improves the agreement between the calculated and experimental cross sections, and modifies the mean values of the suppression parameter.
Momentum space three-body Faddeev-like equations are used to calculate elastic, transfer and charge exchange reactions resulting from the scattering of deuterons on 12C and 16O or protons on 13C and 17O; 12C and 16O are treated as inert cores. All possible reactions are calculated in the framework of the same model space. Comparison with previous calculations based on approximate methods used in nuclear reaction theory is discussed.
Multi-electron screening effects encountered in laboratory astrophysical reactions are investigated by considering the reactants Thomas-Fermi atoms. By means of that model, previous studies are extended to derive the corresponding screening enhancement factor (SEF), so that it takes into account ionization, thermal, exchange and relativistic effects. The present study, by imposing a very satisfactory constraint on the possible values of the screening energies and the respective SEFs, corrects the current (and the future) experimental values of the astrophysical factors associated with nuclear …
Sensitivities of nuclear reaction rates to a variation of nuclear properties are studied. Target nuclei range from proton- to neutron-dripline for 10<=Z<=83. Reactions considered are nucleon- and alpha-induced reactions mediated by the strong interaction. The contribution of reactions proceeding on the target ground state to the total stellar rate is also given. General dependences on various input quantities are discussed. Additionally, sensitivities of laboratory cross sections of nucleon-, alpha-, and gamma-induced reactions are shown, allowing to estimate the impact of cross section measur…
The direct radiative capture process is well described by the spherical potential model. In order for the model to explain direct captures more accurately, the effect of the nuclear deformation has been added and analyzed in this work, since most nucleuses are not spherical. The results imply that the nuclear deformation largely affects the direct capture and should be taken into account during discussing direct capture reactions.
The fundamental processes by which nuclear energy is generated in the Sun have been known for many years. However, continuous progress in areas such as neutrino experiments, stellar spectroscopy and helioseismic data and techniques requires ever more accurate and precise determination of nuclear reaction cross sections, a fundamental physical input for solar models. In this work, we review the current status of (standard) solar models and present a detailed discussion on the relevance of nuclear reactions for detailed predictions of solar properties. In addition, we also provide an analytical …
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