The differences between the experimental and the theoretically calculated binding energies in Relativistic Mean Field (RMF) approach have been calculated for a large number of odd-$Z$ nuclei from $A=47$ to 229. Neutron-proton (n-p) interaction is expected to be the major contributor to this difference. This difference, excluding certain mass regions and taking other effects as well as the odd-even mass difference into account, may be linearly parametrized by the Casten factor, a recognized measure of the n-p interaction in the nucleus. The results follow the same pattern as in the case of even-$Z$ nuclei observed earlier.
Evidence for Quartet Binding of Valence Neutrons in $^8$He
Institute for Rare Isotope Sciences, Institute for Basic Science（稀有同位素科学研究所，基础科学研究院）；Facility for Rare Isotope Beams and Department of Physics and Astronomy, Michigan State University（稀有同位素束设施与物理天文学系，密歇根州立大学）
The influence of relativity on the triton binding energy is investigated. The relativistic three-dimensional version of the Bethe-Salpeter equation proposed by Blankenbecler and Sugar (BbS) is used. Relativistic (non-separable) one-boson-exchange potentials (constructed in the BbS framework) are employed for the two-nucleon interaction. In a 34-channel Faddeev calculation, it is found that relativistic effects increase the triton binding energy by about 0.2 MeV. Including charge-dependence (besides relativity), the final triton binding energy predictions are 8.33 and 8.16 MeV for the Bonn A an…
First results for the triton binding energy obtained from the relativistic spectator or Gross equation are reported. The Dirac structure of the nucleons is taken into account. Numerical results are presented for a family of realistic OBE models with off-shell scalar couplings. It is shown that these off-shell couplings improve both the fits to the two-body data and the predictions for the binding energy.
14C is a stable isotope and emitted from medium and heavy mass nuclei. The 14C result is in excellent agreement with a favored ground-state-to-ground-state transition according to the cluster model of Blendowske et al. We study Ra isotopes in relativistic core-cluster model, solve the Dirac equation with the new phenomenological potential by parametric Nikiforov-Uvarov method, and obtain wave function and binding energy.
The differences between the experimental and Relativistic Mean Field binding energies have been calculated for a large number of even-even nuclei from A=50 to 220. Excluding certain mass regions, the differences, after suitable corrections for particular isotope chains, are found to be proportional to the Casten factor $P$, chosen as a measure of n-p interaction strength in a nucleus. Results for even-$Z$ odd-$N$ nuclei are also seen to follow the same relation, if the odd-even mass difference is taken into account following the semiempirical formula. This indicates that the n-p interaction is…
We calculate the binding energy of two $Λ$ hyperons bound to a nuclear core within the relativistic mean field theory. The starting point is a two-body relativistic equation of the Breit type suggested by the RMFT, and corrected for the two-particle interaction. We evaluate the 2 $Λ$ correlation energy and estimate the contribution of the $σ^*$ and $Φ$ mesons, acting solely between hyperons, to the bond energy $Δ{B_{ΛΛ}}$ of $^6_{ΛΛ}He$, $^{10}_{ΛΛ}Be$ and $^{13}_{ΛΛ}B$. Predictions of the $Δ{B_{ΛΛ}}$ A dependence are made for heavier $Λ$-hypernuclei.
Binding energy differences of mirror nuclei for A=15, 17, 27, 29, 31, 33, 39 and 41 are calculated in the framework of relativistic deformed mean-field theory. The spatial components of the vector meson fields and the photon are fully taken into account in a self-consistent manner. The calculated binding energy differences are systematically smaller than the experimental values and lend support to the existency of the Okamoto--Nolen-Schiffer anomaly found decades ago in nonrelativistic calculations. For the majority of the nuclei studied, however, the results are such that the anomaly is signi…
We extend the formulation of relativistic Coulomb sum rules to account for the average effects of nuclear binding on the initial and final states of ejected nucleons. Relativistic interactions are included by using a Dirac representation adapted from a vector-scalar field theory. The scalar field reduces the effective nucleon mass $M^*$ and increases the relativistic effects of recoil and Fermi motion. We consider two models for the off-shell behavior of the nuclear electromagnetic current, and demonstrate that the sum rule is accurate for applications to data over the interesting range of $M^…
Continuum coupling correction to binding energies in the neutron rich oxygen and fluorine isotopes is studied using the Shell Model Embedded in the Continuum. We discuss the importance of different effects, such as the position of one-neutron emission threshold, the effective interaction or the number of valence particles on the magnitude of this correction.
For relativistic three-body calculations, essentially two different approaches are in use: field theory and relativistic direct interactions. Results for relativistic corrections of the triton binding energy obtained from the two approaches differ even in their sign, which is rather puzzling. In this paper, we discuss the origin of such discrepancy. We show that the use of an invariant two-body amplitude, as done in the field-theoretic approach, increases the triton binding energy by about 0.30 MeV. This may explain a large part of the discrepancy.
Quark counting rules derived from recombination models agree well with data on hadron production at intermediate transverse momenta in relativistic heavy-ion collisions. They convey a simple picture of hadrons consisting only of valence quarks. We discuss the inclusion of higher Fock states that add sea quarks and gluons to the hadron structure. We show that, when recombination occurs from a thermal medium, hadron spectra remain unaffected by the inclusion of higher Fock states. However, the quark number scaling for elliptic flow is somewhat affected. We discuss the implications for our unders…
Theoretical investigation of two-proton halo-nucleus 17Ne has revealed that the valence protons are more likely to be positioned in the d-state than the s-state. In this study, this finding is clarified by calculation of the binding energy, it is found that the theoretical values for the d-state are closer to the experimental values, in contrast with those obtained for the s-state. The three-body model and MATLAB software are utilised to obtain theoretical values for the three-body-model 17Ne binding energy and matter radius. 17Ne has halo properties of a weakly bound valence proton, a binding…
Background: The relativistic three-body problem has a long tradition in few-nucleon physics. Calculations of the triton binding energy based on the solution of the relativistic Faddeev equation in general lead to a weaker binding than the corresponding non-relativistic calculation. Purpose: In this work we solve for the three-body binding energy as well as the wave function and its momentum distribution. The effect of the different relativistic ingredients are studied in detail. Method: Relativistic invariance is incorporated within the framework of Poincar{é} invariant quantum mechanics. The …
The role of relativistic off-mass-shell kinematics in the deep inelastic scattering on deuteron is analyzed. It is shown that the relativistic impulse approximation reproduces effects from the binding, Fermi motion, and two-nucleon contribution. The nonrelativistic limit of the deuteron structure function is in agreement with the nonrelativistic calculations.
We study a particular class of relativistic nuclear energy density functionals in which only nucleon degrees of freedom are explicitly used in the construction of effective interaction terms. Short-distance (high-momentum) correlations, as well as intermediate and long-range dynamics, are encoded in the medium (nucleon density) dependence of the strength functionals of an effective interaction Lagrangian. Guided by the density dependence of microscopic nucleon self-energies in nuclear matter, a phenomenological ansatz for the density-dependent coupling functionals is accurately determined in s…
The odd-even staggerings (OES) on nuclear binding energies are studied systematically within the covariant density functional (CDF) theories, specifically the relativistic Hartree-Fock-Bogoliubov (RHFB) and the relativistic Hartree-Bogoliubov (RHB) theories. Taking the finite-range Gogny force D1S as an effective pairing interaction, both CDF models can provide appropriate descriptions on the OESs of nuclear binding energies for C, O, Ca, Ni, Zr, Sn, Ce, Gd and Pb isotopes as well as for N=50 and 82 isotones. However, due to the inconsistence between the non-relativistic pairing interaction an…
A phenomenological formula based on liquid drop model has been proposed for ground state binding energies of nuclei. The effect due to bunching of single particle levels has been incorporated through a term resembling the one-body Hamiltonian. The effect of n-p interaction has been included through a function of valence nucleons. A total of 50 parameters has been used in the present calculation. The r.m.s. deviation for the binding energy values for 2140 nuclei comes out to be 0.376 MeV, and that for 1091 alpha decay energies is 0.284 MeV. The correspondence with the conventional liquid drop m…
The influence of the partial-wave states with nonzero orbital moment of the nucleon pair on the binding energy of the triton in the relativistic case is considered. The relativistic generalization of the Faddeev equation in the Bethe-Salpeter formalism is applied. Two-nucleon t matrix is obtained from the Bethe-Salpeter equation with separable kernel of nucleon-nucleon interaction of the rank one. The kernel form factors are the relativistic type of the Yamaguchi functions. The following two-nucleon partial-wave states are considered: $^1S_0$, $^3S_1$, $^3D_1$, $^3P_0$, $^1P_1$, $^3P_1$. The s…
With the binding energies and configurations determined experimentally, the root-mean-square radii are calculated for a number of single-particle states by numerically solving the Sch{ö}rdinger equations. By studying the relations between the radii and separation energies, the new scaling laws and necessary conditions for neutron halos and proton halos are established, respectively. Especially the existence region of true proton halos is pointed out. It is found that the effects of short-distance behaviours of valence nucleons at the edges of interaction potentials can not be disregarded. More…
The phase equivalent relativistic NN potential, which is related by a nonlinear equation to the original nonrelativistic potential, is used to construct the mass operator (rest Hamiltonian) of the 3-nucleon system. Employing the CD Bonn NN potential, the solution of the relativistic 3N Faddeev equation for $^3$H shows slightly less binding energy than the corresponding nonrelativistic result. The effect of the Wigner spin rotation on the binding is very small.
We study the binding energy, root-mean-square radius and quadrupole deformation parameter for the synthesized superheavy element Z = 115, within the formalism of relativistic mean field theory. The calculation is dones for various isotopes of Z = 115 element, starting from A = 272 to A = 292. A systematic comparison between the binding energies and experimental data is made.The calculated binding energies are in good agreement with experimental result. The results show the prolate deformation for the ground state of these nuclei. The most stable isotope is found to be 282115 nucleus (N = 167) …
Two-body and three-body systems of scalar bosons are considered in the framework of covariant constraint dynamics. The reduced equation obtained after eliminating redundant degrees of freedom can be viewed as an eigenvalue equation for an observable which is intimately related with the relative motion. We display the connection of this observable with binding energy.
We revise the conventional nuclear effects of Fermi motion, binding and pionic effects in deep inelastic lepton scattering using a relativistic formalism for an interacting Fermi sea and the local density approximation to translate results from nuclear matter to finite nuclei. In addition we also consider effects from rho-meson renormalization in the nucleus. The use of nucleon Green's functions in terms of their spectral functions offers a precise way to account for Fermi motion and binding. On the other hand the use of many body Feynman diagrams in a relativistic framework allows one to avoi…
Starting from a covariant relativistic formalism which uses nucleon and pion propagators in a nuclear medium, we revise the traditional effects of Fermi motion, binding and mesonic corrections to the EMC effect. The calculations are done in a very accurate way, using precise nucleon spectral functions and meson self-energies and a good reproduction of the EMC data is obtained outside the shadowing region which is not explored.
We study the properties of double-$Λ$ hypernuclei in the relativistic mean-field theory, which has been successfully used for the description of stable and unstable nuclei. With the meson-hyperon couplings determined by the experimental binding energies of single-$Λ$ hypernuclei, we present a self-consistent calculation of double-$Λ$ hypernuclei in the relativistic mean-field theory, and discuss the influence of hyperons on the nuclear core. The contribution of two mesons with dominant strange quark components (scalar $σ^*$ and vector $ϕ$) to the $ΛΛ$ binding energy of double-$Λ$ hypernuclei i…
We have studied strength in the BCS pairing force, used as a residual interaction to the relativistic mean-field to reproduce the height of the inner fission barriers for actinide nuclei. It was found that increasing the pairing strength by about 13% makes reproduce the inner fission barriers better over a wide range of actinide nuclei. This result was verified by using the moment-of-inertia of pairing rotational energy, which was introduced to avoid mean-field and odd-mass effects in the pairing interaction to deduce purely the pairing strength. The pairing interaction thus determined could s…
Effective Lagrangians suitable for a relativistic Hartree-Fock description of nuclear systems are presented. They include the 4 effective mesons $σ, ω, ρ$ and $π$ with density-dependent meson-nucleon couplings. The criteria for determining the model parameters are the reproduction of the binding energies in a number of selected nuclei, and the bulk properties of nuclear matter (saturation point, compression modulus, symmetry energy). An excellent description of nuclear binding energies and radii is achieved for a range of nuclei encompassing light and heavy systems. The predictions of the pres…
The density dependent relativistic hadron field theory(DDRH) is extended to inclusions of pentaquark $Θ^+$. We investigate In-medium properties of $Θ^+$ and nucleons. As well as the neutron and proton,the effective $Θ^+$ mass decreases as the baryon density increases,and remains larger than nucleons'. The effective mass of $Θ^+$ is calculated,$M^*_{Θ^+}\simeq0.71M_{Θ^+}$ at normal nuclear density with the fraction of $Θ^+$ 0.2. The effective masses of all baryon increase with the increasing fraction of $Θ^+$. The binding energy is also studied. We find the binding energy is much larger than it…
We develop a chiral symmetric relativistic mean field model with logarithmic sigma potential derived in the strong coupling limit of the lattice QCD. We find that both of the nuclear matter and finite nuclei are well described in the present model. The normal vacuum is found to have global stability at zero and finite baryon densities, and an equation of state with moderate stiffness (K ~ 280 MeV) is obtained. The binding energies and charge radii of Z closed even-even nuclei are well reproduced in a wide mass range from C to Pb isotopes, except for the underestimates of binding energies in se…
We calculate the contribution of relativistic dynamics on the neutron-deuteron scattering length and triton binding energy employing five sets trinucleon potential models and four types of three-dimensional relativistic three-body equations suggested in the preceding paper. The relativistic correction to binding energy may vary a lot and even change sign depending on the relativistic formulation employed. The deviations of these observables from those obtained in nonrelativistic models follow the general universal trend of deviations introduced by off- and on-shell variations of two- and three…
Relativistic Hamiltonians are defined as the sum of relativistic one-body kinetic energy, two- and three-body potentials and their boost corrections. In this work we use the variational Monte Carlo method to study two kinds of relativistic effects in the binding energy of 3H and 4He. The first is due to the nonlocalities in the relativistic kinetic energy and relativistic one-pion exchange potential (OPEP), and the second is from boost interaction. The OPEP contribution is reduced by about 15% by the relativistic nonlocality, which may also have significant effects on pion exchange currents. H…
In non-relativistic Brueckner calculations of nuclear matter, the self-consistent single particle potential is strongly momentum dependent. To simplify the calculations, a parabolic approximation is often used in the literature. The variation in the binding energy value introduced by the parabolic approximation is quantitatively analyzed in detail. It is found that the approximation can introduce an uncertainty of 1-2 MeV near the saturation density.
We calculate the quark distribution function for 3He/3H in a relativistic quark model of nuclear structure which adequately reproduces the nucleon approximation, nuclear binding energies, and nuclear sizes for small nuclei. The results show a clear distortion from the quark distribution function for individual nucleons (EMC effect) arising dominantly from a combination of recoil and quark tunneling effects. Antisymmetrization (Pauli) effects are found to be small due to limited spatial overlaps. We compare our predictions with a published parameterization of the nuclear valence quark distribut…
The molecule-like structure of the C isotopes (A=12, 14, 16) is investigated using a microscopic $α+α+α+n+n+\cdot \cdot \cdot$ model. The valence neutrons are classified based on the molecular-orbit (MO) model, and both $π$-orbit and $σ$-orbit are introduced around three $α$-clusters. The valence neutrons which occupy the $π$-orbit increase the binding energy and stabilize the linear-chain of 3$α$ against the breathing-like break-up. However, $^{14}$C with the $π$-orbit does not show clear energy minimum against the bending-like path. The combination of the valence neutrons in the $π$- and the…
A schematic model for baryon excitations is presented in terms of a symmetric Dirac gyroscope, a relativistic model solvable in closed form, that reduces to a rotor in the non-relativistic limit. The model is then mapped on a nearest neighbour tight binding model. In its simplest one-dimensional form this model yields a finite equidistant spectrum. This is experimentally implemented as a chain of dielectric resonators under conditions where their coupling is evanescent and good agreement with the prediction is achieved.
We discuss the effect of relativistic kinematics on the binding energy of multiquark states. For a given potential, the use of relativistic kinematics lowers the energy by a larger amount for the threshold made of two mesons than for a tetraquark, so that its binding is weakened. Some other issues associated with exotic hadrons are also briefly discussed.
Deuteron correlation energy (DCE) of the valence proton-neutron subsystem is evaluated by utilizing a simple three-body model. We focus on the $^6$Li and $^{18}$F nuclei assuming the doubly-closed core and the valence proton and neutron. Two interaction models, schematic density-dependent contact (SDDC) and Minnesota potentials, are utilized to describe the proton-neutron interaction. Evaluating DCE, we conclude that the proton-neutron binding in $^6$Li can be stronger than its counterpart of a deuteron in vacuum. On the other hand, in $^{18}$F, the energetic correlation is remarkably weak, an…
We discuss the Kondo effect for isospin-exchange interaction between a $\bar{D}$, $B$ meson and a valence nucleon in charm/bottom atomic nuclei including the discrete energy-levels for valence nucleons. To investigate the binding energy by the Kondo effect, we introduce the mean-field approach for the bound state of the $\bar{D}$, $B$ meson in charm/bottom nuclei. Assuming a simple model, we examine the validity of the mean-field approximation by comparing the results with the exact solutions. We also estimate the effect of the quantum fluctuation beyond the mean-field approximation. We discus…
We present a model description of the nucleon valence structure function applicable over the entire region of the Bjorken variable x, and above moderate values of Q**2 (> 1 GeV**2). We stress the importance of describing the complete spectrum of intermediate states which are spectator to the deep-inelastic collision. At a scale of 1 GeV**2 the relevant degrees of freedom are constituent quarks and pions. The large-x region is then described in terms of scattering from constituent quarks in the nucleon, while the dressing of constituent quarks by pions plays an important role at intermediate x …
We determine the lowest bound-state pole of the density-density correlator in the scalar Wick-Cutkosky model where two equal-mass constituents interact via the exchange of mesons. This is done by employing the worldline representation of field theory together with a variational approximation as in Feynman's treatment of the polaron. Unlike traditional methods based on the Bethe-Salpeter equation, self-energy and vertex corrections are (approximately) included as are crossed diagrams. Only vacuum-polarization effects of the heavy particles are neglected. The well-known instability of the model …
The numerical solutions of the non-relativistic Yukawa model on a 3-dimensional size lattice with periodic boundary conditions are obtained. The possibility to extract the corresponding -- infinite space -- low energy parameters and bound state binding energies from eigensates computed at finite lattice size is discussed.
In this paper, we study the relativistic effects in a three-body bound state. For this purpose, the relativistic form of the Faddeev equations is solved in momentum space as a function of the Jacobi momentum vectors without using a partial wave decomposition. The inputs for the three-dimensional Faddeev integral equation are the off-shell boost two-body $t-$matrices, which are calculated directly from the boost two-body interactions by solving the Lippmann-Schwinger equation. The matrix elements of the boost interactions are obtained from the nonrelativistic interactions by solving a nonlinear…
We study the octet to decuplet baryon electromagnetic transitions using the covariant spectator quark model, and predict the transition magnetic dipole form factors for those involving the strange baryons. Utilizing SU(3) symmetry, the valence quark contributions are supplemented by the pion cloud dressing based on the one estimated in the $γ^\ast N \to Δ$ reaction. Although the valence quark contributions are dominant in general, the pion cloud effects turn out to be very important to describe the experimental data. We also show that, other mesons besides the pion in particular the kaon, may …
We derive general results for the mass shift of bound states with angular momentum l >= 1 in a periodic cubic box in two and three spatial dimensions. Our results have applications to lattice simulations of hadronic molecules, halo nuclei, and Feshbach molecules. The sign of the mass shift can be related to the symmetry properties of the state under consideration. We verify our analytical results with explicit numerical calculations. Moreover, we comment on the relations connecting the effective range parameter, the binding momentum of a given state and the asymptotic normalization coefficient…
The Bethe-Salpeter equation for two massive scalar particles interacting by scalar massless exchange has solutions of two types, which differ from each other by their behavior in the non-relativistic limit: the normal solutions which turn into the Coulomb ones and the "abnormal" solutions. The latter ones have no non-relativistic counterparts and disappear in the non-relativistic limit. We studied the composition of all these states. It turns out that the normal states, even for large binding energy, are dominated by two massive particles. Whereas, the contribution of the two-body sector into …
