We estimate the feeddown contributions from decays of unstable $A = 4$ and $A = 5$ nuclei to the final yields of protons, deuterons, tritons, $^3$He, and $^4$He produced in relativistic heavy-ion collisions at $\sqrt{s_{\rm NN}} > 2.4$ GeV, using the statistical model. The feeddown contribution effects do not exceed 5% at LHC and top RHIC energies due to the large penalty factors involved, but are substantial at intermediate collision energies. We observe large feeddown contributions for tritons, $^3$He, and $^4$He at $\sqrt{s_{\rm NN}} \lesssim 10$ GeV, where they may account for as much as 70% of the final yield at the lower end of the collision energies considered. Sizable ($>10$%) effects for deuteron yields are observed at $\sqrt{s_{\rm NN}} \lesssim 4$ GeV. The results suggest that the excited nuclei feeddown cannot be neglected in the ongoing and future analysis of light nuclei production at intermediate collision energies, including HADES and CBM experiments at FAIR, NICA at JINR, RHIC beam energy scan and fixed-target programmes, and NA61/SHINE at CERN. We further show that the freeze-out curve in the $T$-$μ_B$ plane itself is affected significantly by the light nuclei at high baryochemical potential.
The structure of light nuclei out to the drip lines and beyond up to Z = 8 is interpreted in terms of the shell model. Special emphasis is given to the underlying supermultiplet symmetry of the p-shell nuclei which form cores for neutrons and protons added in sd-shell orbits. Detailed results are given on the wave functions, widths, and Coulomb energy shifts for a wide range of non-normal parity states in the p-shell.
Phenomenological approach to inhomogeneous nuclear matter is useful to describe fundamental properties of atomic nuclei and neutron star crusts in terms of the equation of state of uniform nuclear matter. We review a series of researches that we have developed by following this approach. We start with more than 200 equations of state that are consistent with empirical masses and charge radii of stable nuclei and then apply them to describe matter radii and masses of unstable nuclei, proton elastic scattering and total reaction cross sections off unstable nuclei, and nuclei in neutron star crus…
The method of fusion barrier distribution has been widely used to interpret the effect of nuclear structure on heavy-ion fusion reactions around the Coulomb barrier. We discuss a similar, but less well known, barrier distribution extracted from large-angle quasi-elastic scattering. We argue that this method has several advantages over the fusion barrier distribution, and offers an interesting tool for investigating unstable nuclei.
Cluster structure in stable and unstable nuclei has been studied. We report recent developments of theoretical studies on cluster aspect, which is essential for structure study of light unstable nuclei. We discuss negative parity bands in even-even Be and Ne isotopes and show the importance of cluster aspect. Three-body cluster structure and cluster crystallization are also introduced. It was found that the coexistence of cluster and mean-field aspect brings a variety of structures to unstable nuclei.
Dynamical relativistic effects are often neglected in the description of reactions with unstable nuclear beams at intermediate energies (E ~ 100 MeV/nucleon). Evidently, this introduces sizable errors in experimental analysis and theoretical descriptions of these reactions. This is particularly important for the experiments held in GANIL/France, MSU/USA, RIKEN/Japan and GSI/Germany. I review a few examples where relativistic effects have been studied in nucleus-nucleus scattering at intermediate energies.
Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the resonant states become square integrable. The method is implemented with Skyrme effective interactions. Several Skyrme parametrizations are tested on four unstable nuclei: 10He, 12O, 26O and 28O.
Structures of light unstable nuclei, Li, Be, B, and C isotopes are systematically studied with a microscopic method of antisymmetrized molecular dynamics. The theoretical method is found to be very useful to study ground and excited states of various nuclei covering unstable nuclei. The calculations succeed to reproduce many experimental data for nuclear structures; energies, radii, magnetic dipole moments, electric quadrupole moments, transition strength. In the theoretical results it is found that various exotic phenomena in unstable nuclei such as molecular-like structures, neutron skin, an…
An experimental overview of reactions induced by the stable, but weakly-bound nuclei 6Li, 7Li and 9Be, and by the exotic, halo nuclei 6He, 8B, 11Be and 17F on medium-mass targets, such as 58Ni, 59Co or 64Zn, is presented. Existing data on elastic scattering, total reaction cross sections, fusion processes, breakup and transfer channels are discussed in the framework of a CDCC approach taking into account the breakup degree of freedom.
We study the structures of the unstable Be isotopes with the theoretical method of antisymmetrized molecular dynamics. It is found that various structures of the excited states appear in the low-energy region of neutron-rich Be nuclei. Focusing on the 2$α$ clustering, we analyze the intrinsic structures with the help of the experimental data of Gamow-Teller transitions.
The structure of the light proton and neutron rich nuclei is studied in a microscopic multicluster model using the stochastic variational method. This approach enables us to describe the weakly bound nature of these nuclei in a consistent way. Applications for various nuclei $^{6-9}$Li, $^7$Be, $^8$B, $^9$C, $^{9-10}$Be, $^{9-10}$B presented. The paper discusses the relation of this model to other models as well as the possible extension for p and sd shell nuclei.
An analytical solution of the collective Bohr equation with a Coulomb-like and a Kratzer-like $γ-$unstable potential in quadrupole deformation space is presented. Eigenvalues and eigenfunctions are given in closed form and transition rates are calculated for the two cases. The corresponding SO(2,1)$\times$SO(5) algebraic structure is discussed.
According to microscopic calculations with antisymmetrized molecular dynamics, we studied cluster features in stable and unstable nuclei. A variety of structure was found in stable and unstable nuclei in the $p$-shell and $sd$-shell regions. The structure of excited states of $^{12}$Be was investigated, while in $sd$-shell nuclei we focused on molecular states and deformed states. The deformed states in $^{28}$Si and $^{40}$Ca were discussed in connection with the high-lying molecular states. Appealing molecular states in $^{36}$Ar and $^{24}$Mg were suggested. The results signified that both …
We study theoretically how we can determine the neutron density distributions of unstable nuclei from proton elastic scattering. We apply the relativistic impulse model to study the sensitivities of the observables to the density distributionswhich are expressed in Woods-Saxon form. We find that the both radius and diffuseness of densities can be determined from restricted elastic scattering data in principle. We think this result is helpful to design future experiments.
Relativistic mean field calculations suggest that the charge and matter deformations significantly differ in some of the unstable neutron and proton rich nuclei. We discuss the effects of the difference on the fusion reactions induced by them at energies near and below the Coulomb barrier by taking the $^{19,25,37}$Na + $^{208}$Pb reactions as examples. We also discuss whether one can probe the difference by the so called fusion barrier distribution analysis.
Within a microscopic approach which takes into account RPA configurations, the single-particle continuum and more complex $1p1h\otimes phonon$ configurations isoscalar and isovector M1 excitations for the unstable nuclei ${56,78}$Ni and ${100,132}$Sn are calculated. For comparison, the experimentally known M1 excitations in ${40}$Ca and $^{208}$Pb have also been calculated. In the latter nuclei good agreement in the centroid energy, the total transition strength and the resonance width is obtained. With the same parameters we predict the magnetic excitations for the unstable nuclei. The streng…
The themes covered in the present thesis are: a detailed study of double phonon giant resonances in normal nuclei, the enhancement of the excitation of Giant Pairing Vibrations using weakly-bound nuclei, an extension of the Steinwedel-Jensen model for Giant Dipole Resonances to treat surface effects and presence of neutron skin and, finally, a model on breakup reactions in weakly-bound dicluster nuclei.
We reanalyze the results of our extensive Hartree-Fock + BCS calculation from new points of view paying attention to the properties of unstable nuclei. The calculation has been done with the Skyrme SIII force for the ground and shape isomeric states of 1029 even-even nuclei ranging 2 <= Z <= 114. We also discuss the advantages of the employed three-dimensional Cartesian-mesh representation, especially on its remarkably high precision with apparently coarse meshes when applied to atomic nuclei. In Appendices we give the coefficients of finite-point numerical differentiation and integration form…
Exactly solvable solution for the spherical to gamma - unstable transition in transitional nuclei based on dual algebraic structure and nuclear supersymmetry concept is proposed. The duality relations between the unitary and quasispin algebraic structures for the boson and fermion systems are extended to mixed boson-fermion system. It is shown that the relation between the even-even and odd-A neighbors implied by nuclear supersymmetry in addition to dynamical symmetry limits can be also used for transitional regions. The experimental evidences are presented for even- even [E(5)] and odd-mass […
We investigate the Coulomb excitation of low-lying states of unstable nuclei in intermediate energy collisions ($E_{lab}\sim10-500$ MeV/nucleon). It is shown that the cross sections for the $E1$ and $E2$ transitions are larger at lower energies, much less than 10 MeV/nucleon. Retardation effects and Coulomb distortion are found to be both relevant for energies as low as 10 MeV/nucleon and as high as 500 MeV/nucleon. Implications for studies at radioactive beam facilities are discussed.
In this contribution, I will discuss two topics related to the clustering of atomic nuclei. The first is dual character of the ground state. Recently, it was pointed out that the ground states of atomic nuclei have dual character of shell and cluster implying that both of the single-particle excitation and cluster excitation occur as the fundamental excitation modes. The isoscalar monopole and dipole transitions are regarded as the triggers to induce the cluster excitation. By referring the Hartree-Fock and antisymmetrized molecular dynamics calculations, the dual character and those transitio…
This work aims at a global assessment of the effect of the density dependence of the zero-range pairing interaction. Systematic Skyrme-Hartree-Fock-Bogoliubov calculations with the volume, surface and mixed pairing forces are carried out to study the pairing gaps in even-even nuclei over the whole nuclear chart. Calculations are also done in coordinate representation for unstable semi-magic even-even nuclei. The calculated pairing gaps are compared with empirical values from four different odd-even staggering formulae. Calculations with the three pairing interactions are comparable for most nu…
A nuclear structure model based on linear response theory (i.e., Random Phase Approximation) and which includes pairing correlations and anharmonicities (coupling with collective vibrations), has been implemented in such a way that it can be applied on the same footing to magic as well as open-shell nuclei. As applications, we have chosen to study the dipole excitations both in well-known, stable isotopes like $^{208}$Pb and $^{120}$Sn as well as in the neutron-rich, unstable $^{132}$Sn nucleus, by addressing in the latter case the question about the nature of the low-lying strength. Our resul…
We study nuclear reaction cross-sections for stable and unstable projectiles and targets within Glauber model, using densities obtained from various relativistic mean field formalisms. The calculated cross-sections are compared with the experimental data in some specific cases. We also evaluate the differential scattering cross-sections at several incident energies, and observe that the results found from various densities are similar at smaller scattering angles, whereas a systematic deviation is noticed at large angles. In general, these results agree fairly well with the experimental data.
We study the explosion mechanism of collapse-driven supernovae by numerical simulations with a new nuclear EOS based on unstable nuclei. We report new results of simulations of general relativistic hydrodynamics together with the Boltzmann neutrino-transport in spherical symmetry. We adopt the new data set of relativistic EOS and the conventional set of EOS (Lattimer-Swesty EOS) to examine the influence on dynamics of core-collapse, bounce and shock propagation. We follow the behavior of stalled shock more than 500 ms after the bounce and compare the evolutions of supernova core.
The recent availability of radioactive beams has opened up a new era in nuclear physics. The interactions and structure of exotic nuclei close to the drip lines have been studied extensively world wide, and it has been revealed that unstable nuclei, having weakly bound nucleons, exhibit characteristic features such as a halo structure and a soft dipole excitation. We here review the developments of the physics of unstable nuclei in the past few decades. The topics discussed in this Chapter include the halo and skin structures, the Coulomb breakup, the dineutron correlation, the pair transfer r…
We examine relations among the parameters characterizing the phenomenological equation of state (EOS) of nearly symmetric, uniform nuclear matter near the saturation density by comparing macroscopic calculations of radii and masses of stable nuclei with the experimental data. The EOS parameters of interest here are the symmetry energy S_0, the symmetry energy density-derivative coefficient L and the incompressibility K_0 at the normal nuclear density. We find a constraint on the relation between K_0 and L from the empirically allowed values of the slope of the saturation line (the line joining…
Sturmian theory for nucleon-nucleus scattering is discussed in the presence of all the phenomenological ingredients necessary for the description of weakly-bound (or particle-unstable) light nuclear systems. Currently, we use a macroscopic potential model of collective nature. The analysis shows that the couplings to low-energy collective-core excitations are fundamental but they are physically meaningful only if the constraints introduced by the Pauli principle are taken into account. The formalism leads one to discuss a new concept, Pauli hindrance, which appears to be important to understan…
In this review, a new method is proposed based on Cantor's theory of Cardinality to analyze the experimental data on unstable nuclear systems which includes fundamental particles and their flavours, $β$-decay including spin and parity, $α$-decay and the systematics of the energy levels of light nuclei. The method also derives a formula for the Binding Energies of unstable nuclei. All this is based on the theory of discreteness and continuity.
The physics of radioactive ion beams implies the description of weakly-bound nuclear systems. One key aspect concerns the coupling to low-lying collective-type excited states, which for these systems might not be stable levels, but particle emitting resonances. In this work we describe how the scattering cross section and compound spectra change when the colliding fragments have such collective excitations featuring particle emission. We explore this question in the framework of a multi-channel algebraic scattering method of determining nucleon-nucleus cross sections at low energies. For a ran…
We calculate densities of excited states in the quasiparticle random-phase approximation (QRPA)with Skyrme interactions and volume pairing. We focus on low-energy peaks/bumps in the strength functions of a range of Ca, Ni, and Sn isotopes for J pi = 0+, 1-, and 2+. We define an "emitted-neutron number", which we then use to distinguish localized states from scattering-like states. The degree of delocalization either increases as the neutron-drip line is approached or stays high between the stability line and the drip line. In the 2+ channel of Sn, however, the low-lying states, not even counti…
A microscopic study of proton elastic scattering from unstable nuclei at intermediate energies using a relativistic formalism is presented. We have employed both the original relativistic impulse approximation (IA1) and the generalised impulse approximation (IA2) formalisms to calculate the relativistic optical potentials, with target densities derived from relativistic mean field (RMF) theory using the NL3 and FSUGold parameter sets. Comparisons between the optical potentials computed using both IA1 and IA2 formalisms, and the different RMF Lagrangians are presented for both stable and unstab…
Microscopic optical model potential results for reaction cross sections of proton elastic scattering are presented. The applications cover the 10-1000 MeV energy range and consider both stable and unstable nuclei. The study is based on in-medium g-matrix full-folding optical model approach with the appropriate relativistic kinematic corrections needed for the higher energy applications. The effective interactions are based on realistic NN potentials supplemented with a separable non-Hermitian term to allow optimum agreement with current NN phase-shift analyzes, particularly the inelasticities …
We study (p,2p) and (p,pn) reactions at proton energies in the range of 100 MeV -- 1 GeV. Our purpose is to explore the most sensitive observables in unpolarized reactions with inverse kinematics involving radioactive nuclei. We formulate a model based on the eikonal theory to describe total cross sections and momentum distributions of the recoiled residual nucleus. The model is similar to the one adopted for knockout reactions with heavy ions. We show that momentum distributions are sensitive to the angular momentum of the ejected nucleon which can be used as an spectroscopic tool. The total …
Electron scattering on unstable nuclei is planned in future facilities of the GSI and RIKEN upgrades. Motivated by this fact, we study theoretical predictions for elastic electron scattering in the N=82, N=50, and N=14 isotonic chains from very proton-deficient to very proton-rich isotones. We compute the scattering observables by performing Dirac partial-wave calculations. The charge density of the nucleus is obtained with a covariant nuclear mean-field model that accounts for the low-energy electromagnetic structure of the nucleon. For the discussion of the dependence of scattering observabl…
We have used a self-consistent Skyrme-Hartree-Fock plus Continuum-RPA model to study the low-multipole response of stable and neutron/proton-rich Ni and Sn isotopes. We focus on the momentum-transfer dependence of the strength distribution, as it provides information on the structure of excited nuclear states and in particular on the variations of the transition form factor (TFF) with the energy. Our results show, among other things, that the TFF may show significant energy dependence in the region of the isoscalar giant monopole resonance and that the TFF corresponding to the threshold streng…
In the presented review we discuss the problem of extraction the parameters of nuclear matter and charge distribution in stable and unstable isotopes. A substantial amount of information on the nuclear radii and other distribution parameters in light exotic nuclei has been obtained from experiments on intermediate-energy nucleus-nucleus collisions. The analyses of these experiments is usually performed with the help of the Glauber Theory. We review the main assumptions the Glauber Theory and show how this theoretical approach is used to calculate reaction and interaction cross sections. We als…
We report here an empirical formalism for predicting the cross-sections of neutron-rich nuclei produced in fragmentation of relativistic \b{eta}-unstable neutron-rich projectiles in the mid-mass region. The formalism is based on the abrasion-ablation picture of the projectile fragmentation reaction. It has been shown that the formalism can accurately reproduce the experimental cross-section data for nuclei produced in the fragmentation of 132Sn. The formalism, it is shown, can also reproduce the experimental cross-sections of neutron-rich nuclei produced in the fragmentation of 129Xe fairly ac…
The isoscalar E1 and E2 resonances in the proton-rich nuclei ^{48,49}Ni and the {f_{7/2}3^-} multiplet in ^{49}Ni have been calculated taking into account the single-particle continuum exactly. The analogous calculations for the mirror nuclei ^{48}Ca and ^{49}Sc are presented. The models used are the continuum RPA for ^{48}Ni, ^{48}Ca and the Odd RPA for ^{49}Ni, ^{49}Sc, the latter has been developed recently and describes both single-particle and collective excitations of an odd nucleus on a common basis. In all four nuclei we obtained a distinct splitting of the isoscalar E1 resonance into …
The coupling of the high-lying dipole mode to the low-lying quadrupole modes for the case of deformed gamma-unstable nuclei is studied. Results from the geometrical model are compared to those obtained within the dipole boson model. Consistent results are obtained in both models. The dipole boson model is treated within the intrinsic frame, with subsequent projection onto the laboratory frame. As an application, calculations of photonuclear cross-sections in gamma-unstable nuclei are presented.
Energies and transition probabilities for low lying states in $^{134}$Ba and $^{104$Ru were calculated within a hybrid model.The ground and the first $2^+$ states are described alternatively as a harmonic and anharmonic vibrator states while the remaining states as states with E(5) symmetry. One concludes that a gradual setting of the 'critical' potential yields a better agreement with the experimental data. Very good agreement with the data is obtained for $^{104}$Ru. Comparing the present results with those of E(5) symmetry, it is conspicuous that the present formalism add corrections to the…
Nucleon Correlations in Unstable Nuclei via Knockout Reactions
East Texas A&M University（东德克萨斯农工大学）；Technische Universität Darmstadt（达姆施塔特工业大学）；ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH（极端物质研究所EMMI，GSI重离子研究中心有限公司）
The fundamental ingredients of the MCAS (multi-channel algebraic scattering) method are discussed. The main feature, namely the application of the sturmian theory for nucleon-nucleus scattering, allows solution of the scattering problem given the phenomenological ingredients necessary for the description of weakly-bound (or particle-unstable) light nuclear systems. Currently, to describe these systems, we use a macroscopic, collective model. Analyses show that the couplings to low-energy collective-core excitations are fundamental but they are physically meaningful only if the constraints intr…
Fully quantal calculations of the total reaction cross sections \sigR and interaction cross sections \sigI, induced by stable and unstable He, Li, C and O isotopes on $^{12}$C target at $E_{\rm lab}\approx 0.8$ and 1 GeV/nucleon have been performed, for the first time, in the distorted wave impulse approximation (DWIA) using the microscopic \emph{complex} optical potential and inelastic form factors given by the folding model. Realistic nuclear densities for the projectiles and $^{12}$C target as well as the complex $t$-matrix parameterization of free nucleon-nucleon interaction by Franey and …
The E1 strength function for 15 stable and unstable Sn even-even isotopes from A=100 till A=176 are calculated using the self-consistent microscopic theory which, in addition to the standard (Q)RPA approach, takes into account the single-particle continuum and the phonon coupling. Our analysis shows two distinct regions for which the integral characteristics of both the giant and pygmy resonances behave rather differently. For neutron-rich nuclei, starting from $^{132}$Sn, we obtain a giant E1 resonance which significantly deviates from the widely-used systematics extrapolated from experimenta…
We present a review of recent works on clustering phenomena in unstable nuclei studied by antisymmetrized molecular dynamics (AMD). The AMD studies in these decades have uncovered novel types of clustering phenomena brought about by the excess neutrons. Among them, this review focuses on the molecule-like structure of unstable nuclei. One of the earliest discussions on the clustering in unstable nuclei was made for neutron-rich Be and B isotopes. AMD calculations predicted that the ground state clustering is enhanced or reduced depending on the number of excess neutrons. Today, the experiments…
Best Reaction Target To Determine Proton Distribution Radii of Atomic Nuclei
Beihang University（北京航空航天大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Shanghai Institute of Applied Physics, Chinese Academy of Sciences（中国科学院上海应用物理研究所）；Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University（中山大学中法核工程与技术学院）；Medaustron
Eigenfunctions of the collective Bohr Hamiltonian with the Morse potential have been obtained by using the Asymptotic Iteration Method (AIM) for both gamma-unstable and rotational structures. B(E2) transition rates have been calculated and compared to experimental data. Overall good agreement is obtained for transitions within the ground state band, while some interband transitions appear to be systematically underpredicted in gamma-unstable nuclei and overpredicted in rotational nuclei.
We look for collective excitations originating from the strong surface pairing in unstable nuclei near the neutron drip-line. The soft dipole excitation is such a pairing mode as it exhibits a character of core-vs-dineutron motion. Possibility of the hydrodynamic phonon mode (the Anderson-Bogoliubov mode) is also discussed.
We study the postacceleration of charged fragments in reactions with unstable nuclear beams. For elastic breakup processes we show that the postaceleration effect can be well understood in terms of closed analytical forms derived in a quantum mechanical formulation. This gives theoretical support to the effect experimentally observed in the breakup of Li-11 projectiles at intermediate energies.
In the present work, we have obtained closed analytical expressions for eigenvalues and eigenfunctions of the Bohr Hamiltonian with the Manning-Rosen potential for γ-unstable nuclei as well as exactly separable rotational ones with γ=0. Some heavy nuclei with known \b{eta} and γ bandheads have been fitted by using two parameters in the ν-unstable case and three parameters in the axially symmetric prolate deformed one. A good agreement with experimental data has been achieved.
Approximate analytical solutions in closed form are obtained for the 5-dimensional Bohr Hamiltonian with the Woods-Saxon potential, taking advantage of the Pekeris approximation and the exactly soluble one-dimensional extended Woods-Saxon potential with a dip near its surface. Comparison to the data for several gamma-unstable and prolate deformed nuclei indicates that the potential can describe well the ground state and gamma-1 bands of many prolate deformed nuclei corresponding to large enough "well size" and diffuseness, while it fails in describing the beta-1 bands, due to its lack of a har…
The covariant density functional theory with a few number of parameters has been widely used to describe the ground-state and excited-state properties for the nuclei all over the nuclear chart. In order to describe exotic properties of unstable nuclei, the contribution of the continuum and its coupling with bound states should be treated properly. In this Topical Review, the development of the covariant density functional theory in continuum will be introduced, including the relativistic continuum Hartree-Bogoliubov theory, the relativistic Hartree-Fock-Bogoliubov theory in continuum, and the …
Even if the theoretical definition of an unstable state is straightforward, its experimental identification often depends on the method used in the analysis and extraction of data. A good example is the case of eta mesic nuclei where strong hints of their existence led to about three decades of extensive theoretical and experimental searches. Considering the still undecided status of these states and the limitations in the understanding of the eta-nucleon as well as the eta-nucleus interaction, the present article tries to look back at some unresolved problems in the production mechanism and f…
