Nuclides sharing the same mass number (isobars) are observed ubiquitously along the stability line. While having nearly identical radii, stable isobars can differ in shape, and present in particular different quadrupole deformations. We show that even small differences in these deformations can be probed by relativistic nuclear collisions experiments, where they manifest as deviations from unity in the ratios of elliptic flow coefficients taken between isobaric systems. Collider experiments with isobars represent, thus, a unique means to obtain quantitative information about the geometric shape of atomic nuclei.
One Delta- isobar components of the wave function in closed shell nuclei are considered within the framework of the harmonic oscillator model. Conventional transition potential is the pi- and rho- exchange potential. On the basis of the Delta- isobar configuration wave function, the momentum distribution of the Delta- isobar is calculated for the light nuclei $^4 He$,$^{16}O$,$^{12}C$
We perform a self-consistent relativistic RPA calculation for the isobaric analogue and Gamow-Teller resonances based on relativistic mean field theory results for the ground states of $^{48}$Ca, $^{90}$Zr and $^{208}$Pb. We use the parameter set NL1 for the $σ$, $ω$ and $ρ$ mesons, and experimental values for the pion and nucleon. An extra parameter, related to the intensity of the contact term in the pion-exchange interaction, is crucial to reproduce the latter resonances.
An algebraic sp(4) shell model is introduced to achieve a deeper understanding and interpretation of the properties of pairing-governed 0+ states in medium mass atomic nuclei. The theory, which embodies the simplicity of a dynamical symmetry approach to nuclear structure, is shown to reproduce the excitation spectra and fine structure effects driven by proton-neutron interactions and isovector pairing correlations across a broad range of nuclei.
The influence of $Δ$ isobar components on the ground state properties of nuclear systems is investigated for nuclear matter as well as finite nuclei. Many-body wave functions, including isobar configurations, and binding energies are evaluated employing the framework of the coupled-cluster theory. It is demonstrated that the effect of isobar configurations depends in a rather sensitive way on the model used for the baryon-baryon interaction. As examples for realistic baryon-baryon interactions with explicit inclusion of isobar channels we use the local ($V28$) and non-local meson exchange pote…
We investigate the properties of electromagnetic fields in isobaric $_{44}^{96}\textrm{Ru}+\,_{44}^{96}\textrm{Ru}$ and $_{40}^{96}\textrm{Zr}+\,_{40}^{96}\textrm{Zr}$ collisions at $\sqrt{s}$ = 200 GeV by using a multiphase transport model, with special emphasis on the correlation between magnetic field direction and participant plane angle $Ψ_{2}$ (or spectator plane angle $Ψ_{2}^{\rm SP}$), i.e. $\langle{\rm cos}\ 2(Ψ_B - Ψ_{2})\rangle$ [or $\langle{\rm cos}\ 2(Ψ_B - Ψ_{2}^{\rm SP})\rangle$]. We confirm that the magnetic fields of $_{44}^{96}\textrm{Ru}+\,_{44}^{96}\textrm{Ru}$ collisions a…
We present calculations for the $c$-coefficients of the isobaric mass multiplet equation for nuclei from $A=42$ to $A=54$ based on input from three realistic nucleon-nucleon interactions. We demonstrate that there is a clear dependence on the short-ranged charge-symmetry breaking (CSB) part of the strong interaction and that there is significant disagreement in the CSB part between the commonly used CD-Bonn, N$^3$LO, and Argonne V18 nucleon-nucleon interactions. In addition, we show that all three interactions give a CSB contribution to the $c$-coefficient that is too large when compared to ex…
Particle production in ultrarelativistic heavy ion collisions depends on the details of the nucleon density distributions in the colliding nuclei. We demonstrate that the charged hadron multiplicity distributions in isobaric collisions at ultrarelativistic energies provide a novel approach to determine the poorly known neutron density distributions and thus the neutron skin thickness in finite nuclei, which can in turn put stringent constraints on the nuclear symmetry energy.
A model of $πN$ pair photoproduction on nuclei at high momentum transfer is presented. The $A(γ,πN)B$ reaction amplitude is obtained by means of an extended impulse approximation, according to which the nuclear wavefunction includes delta-isobar components in addition to nucleon components. A one-particle transition operator is defined in terms of the two-body $γN\toπN$ and $γΔ\toπN$ photoproduction amplitudes. Direct and exchange mechanisms of the nuclear photoproduction reaction are studied, and numerical estimates are made and presented of $^{12}{\rm C}(γ,π^- p){^{11}{\rm C}}$ and $^{12}{\r…
We optimize $Δ$-full nuclear interactions from chiral effective field theory. The low-energy constants of the contact potentials are constrained by two-body scattering phase shifts, and by properties of bound-state of $A=2$ to $4$ nucleon systems and nuclear matter. The pion-nucleon couplings are taken from a Roy-Steiner analysis. The resulting interactions yield accurate binding energies and radii for a range of nuclei from $A=16$ to $A=132$, and provide accurate equations of state for nuclear matter and realistic symmetry energies. Selected excited states are also in agreement with data.
We present an analysis of the spectator mechanism of $Δ$-isobar production in the pion photoproduction on nuclei with the emission of two nucleons. The reaction mechanism is studied within the framework of the $ΔN$-correlation model, which considers the isobar and nucleon of the $ΔN$-system produced in the nucleus at the virtual $NN \to ΔN$ transition, to be in a dynamic relationship. The two-particle transition operator for nuclei is obtained by the \textit{S}-matrix approach. We consider the properties of the spectator mechanism of isobar production using the example of the reaction $^{16}$O…
We study photoproduction off nuclei based on a self consistent and covariant many body approach for the pion and isobar propagation in infinite nuclear matter. For the first time the t-channel exchange of an in-medium pion is evaluated in the presence of vertex correction effects consistently. In particular the interference pattern with the s-channel in-medium nucleon and isobar exchange contribution is considered. Electromagnetic gauge invariance is kept as a consequence of various Ward identities obeyed by the computation. Adjusting the set of Migdal parameters to the data set we predict an …
Eight pairs of rare earth normally deformed nuclei around the isobaric nuclei with A = 164 and have identical values of F-spin have been studied. These pairs of identical bands cover 16 mass units and are classified. We suggested a theoretical collective rotational formula containing three parameters (CRF3) as an extended version of Bohr-Mottelson model to calculate the ground state positive parity excitation energies. Also, the sd-version of the interacting boson model (IBM) has been used to describe the nuclear shapes by using the intrinsic coherent-state. The optimized models parameters for…
The effects of the presence of $Δ$-isobars in nuclear matter are studied in the framework of relativistic mean-field theory. The existence of stable nuclei at saturation density imposes constraints on the $Δ$-isobar self-energy and thereby on the mean-field coupling constants of the scalar and vector mesons with $Δ$-isobars. The range of possible values for the scalar and vector coupling constants of $Δ$-isobars with respect to the nucleon coupling is investigated and compared to recent predictions of QCD sum-rule calculations.
The ratios of bulk observables, such as harmonic flow $v_2$ and $v_3$, between high-energy $^{96}$Ru+$^{96}$Ru and $^{96}$Zr+$^{96}$Zr collisions were recently argued to be a clean probe of the nuclear structure differences between $^{96}$Ru and $^{96}$Zr. Using a transport model simulation of isobar collisions, we quantify this claim from the dependence of the ratios $v_{2,\mathrm{Ru}}/v_{2,\mathrm{Zr}}$ and $v_{3,\mathrm{Ru}}/v_{3,\mathrm{Zr}}$ on various final state effects, such as the shear viscosity, hadronization and hadronic cascade. Although the $v_2$ and $v_3$ change by more than 50%…
We show how exclusive vector meson production off light ions can be used to probe the spatial distribution of small-$x$ gluons in the deuteron and $^3$He wave functions. In particular, we demonstrate how short range repulsive nucleon-nucleon interactions affect the predicted coherent $J/Ψ$ production spectra. Fluctuations of the nucleon substructure are shown to have a significant effect on the incoherent cross section above $|t|\gtrsim 0.2\,\mathrm{GeV}^2$. By explicitly performing the JIMWLK evolution, we predict the $x$-dependence of coherent and incoherent cross sections in the EIC energy …
A theoretical investigation on the shape transitions with neutron number, temperature and spin for A $=$100 isobars of Z$=$42 to 50 is presented. A variety of shape transitions are observed while moving from neutron rich 100 Mo to proton rich 100 Sn with predominant triaxial shapes. Temperature and spin induced shape transitions are explored within the microscopic theoretical framework of and statistical theory of hot rotating nuclei. Prolate non-collective which is a rare shape phase is reported in this mass region on the proton rich side of the nuclear chart.
We study the role of the $Δ$-isobar current on the response functions for high energy inclusive quasielastic electron scattering from nuclei. We consider a general Lagrangian which is compatible with contact invariance and perform a fully relativistic calculation in first-order perturbation theory for one-particle emission. The dependence of the responses upon off-shell parametrizations is analyzed and found to be mild. A discussion of scaling behaviour and a comparison with various non-relativistic approaches are also presented.
The unambiguous observation of a Chiral Magnetic Effect (CME)-driven charge separation is the core aim of the isobar program at RHIC consisting of ${^{96}_{40}}$Zr+${^{96}_{40}}$Zr and ${^{96}_{44}}$Ru+${^{96}_{44}}$Ru collisions at $\sqrt {s_{\rm NN}}\!=\!200$ GeV. We quantify the role of the spatial distributions of the nucleons in the isobars on both eccentricity and magnetic field strength within a relativistic hadronic transport approach (SMASH, Simulating Many Accelerated Strongly-interacting Hadrons). In particular, we introduce isospin-dependent nucleon-nucleon spatial correlations in …
Accurate mass determination of short-lived nuclides by Penning-trap spectrometers and progress in the spectroscopy of proton-rich nuclei have triggered renewed interest in the isobaric multiplet mass equation (IMME). The energy levels of the members of $T=1/2, 1, 3/2,$ and 2 multiplets and the coefficients of the IMME are tabulated for $A\le 71$. The new compilation is based on the most recent mass evaluation (AME2011) and it includes the experimental results on energies of the states evaluated up to end of 2011. Taking into account the error bars, a significant deviation from the quadratic fo…
Ground-state properties of A = 20 nuclei ($^{20}$N, $^{20}$O, $^{20}$F, $^{20}$Ne, $^{20}$Na, $^{20}$Mg) are described in the framework of Relativistic Hartree-Bogoliubov (RHB) theory. The model uses the NL3 effective interaction in the mean-field Lagrangian, and describes pairing correlations by the pairing part of the finite range Gogny interaction D1S. Binding energies, quadrupole deformations, nuclear matter radii, and differences in radii of proton and neutron distributions are compared with recent experimental data.
$^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{_{\rm NN}}}=200$ GeV provide unique opportunities to study the geometry and fluctuations raised from the deformation of the colliding nuclei. Using iEBE-VISHNU hybrid model, we predict ${\rm ac}_{2}\{3\}$ ratios between these two collision systems and demonstrate that the ratios of ${\rm ac}_{2}\{3\}$, as well as the ratios of the involving flow harmonics and event-plane correlations, are sensitive to quadrupole and octupole deformations, which could provide strong constrains on the shape differences betwee…
We investigate effects of nuclear medium on antiquark distribution in nuclei applying the results of a recently developed relativistically-covariant self-consistent model for the pion and the isobar. We take into account Fermi motion including Pauli blocking and binding effects on the nucleons and medium effects on the isobar and pion leading to modest enhancement of the pion light-cone-momentum distribution in large nuclei. As a consequence the Drell-Yan cross-section ratio with respect to the deuteron exceeds one only for small values of the light-cone momentum.
Isobaric single charge-exchange reactions, changing nuclear charges by one unit but leaving the mass partitions unaffected, have been for the first time investigated by peripheral collisions of $^{112}$Sn ions accelerated up to 1\textit{A} GeV at the GSI facilities. The high-resolving power of the FRS spectrometer allows us to obtain $(p, n)$-type isobaric charge-exchange cross sections with an uncertainty of $3.5\%$ and to separate quasi-elastic and inelastic components in the missing-energy spectra of the ejectiles. The inelastic component is associated to the excitation of the $Δ$(1232) iso…
The question of isospin-symmetry breaking in nuclei of the $sd$ shell is addressed. We propose a new global parameterization of the isospin-nonconserving (INC) shell-model Hamiltonian which accurately describes experimentally known isobaric mass splittings. The isospin-symmetry violating part of the Hamiltonian consists of the Coulomb interaction and effective charge-dependent forces of nuclear origin. Particular attention has been paid to the effect of the short-range correlations. The behavior of $b$ and $c$ coefficients of the isobaric-mass-multiplet equation (IMME) is explored in detail. I…
Study of the shape coexistence in the 96Zr, 96Mo, 96Ru isobars
Academy of Romanian Scientists（罗马尼亚科学家学院）；ESMaR, Department of Physics, Faculty of Science, Mohammed V University in Rabat（拉巴特穆罕默德五世大学理学院物理系ESMaR）；High Energy Physics and Astrophysics Laboratory, Department of Physics, Faculty of Science Semlalia, Cadi Ayyad University（卡迪阿尤德大学塞马拉利亚理学院物理系高能物理与天体物理实验室）
We propose a method to extract the properties of the isobaric mass parabola based on the total double $β$ decay energies of isobaric nuclei. Two important parameters of the mass parabola, the location of the most $β$-stable nuclei $Z_{A}$ and the curvature parameter $b_{A}$, are obtained for 251 A values based on the total double $β$ decay energies of nuclei compiled in AME2016 database.The advantage of this approach is that we can remove the pairing energy term $P_{A}$ caused by odd-even variation, and the mass excess $M(A,Z_{A})$ of the most stable nuclide for mass number $A$ in the performa…
A nucleon-nucleus interaction model has been applied to ascertain the underlying character of the negative-parity spectra of four isobars of mass seven, from neutron-- to proton--emitter driplines. With one single nuclear potential defined by a simple coupled-channel model, a multichannel algebraic scattering approach (MCAS) has been used to determine the bound and resonant spectra of the four nuclides, of which ^7He and ^7B are particle unstable. Incorporation of Pauli blocking in the model enables a description of all known spin-parity states of the mass-7 isobars. We have also obtained spec…
Isospin-symmetry breaking is responsible for the energy difference of excited states in mirror nuclei. It also influences the coefficient of the isobaric multiplet mass equation. In the present work, we extensively investigate isospin-symmetry breaking in medium mass nuclei within ab initio frameworks. For this, we employ the ab initio valence-space in-medium similarity renormalization group approach, in which charge-symmetry and charge-independence breakings are included in the adopted nuclear force. The mirror energies of sd- and pf- shell nuclei are computed for that matter. The effects of …
The spectra of mass-11 nuclei are unusual, and so pose a challenge for theoretical models of their structure. The set of isobars range from being well bound to nucleon emission (11B,11C) through weakly bound (11Li, 11Be), with the former taking the form of a two neutron halo, to being proton unstable (11N,11O). A self-consistent approach to understand this set of nuclei is especially important as the mirror pair 11Be-11N exhibit a parity-inverted ground state compared to their neighbouring nuclei. Herein the Multi-Channel Algebraic Scattering (MCAS) method has been used to describe the low exc…
Isobar models for the electromagnetic production of kaons are discussed with emphasis on the K^+ photoproduction at very small kaon angles and K^0 photoproduction on deuteron. Distorted-wave impuls approximation calculations of the cross sections for the electroproduction of hypernuclei are presented on the case of the ^{12}B_Λproduction.
A new non-relativistic expansion in terms of the nucleon's momentum inside nuclear matter of the current for isobar electro-excitation from the nucleon is performed. Being exact with respect to the transferred energy and momentum, this yields new current operators which retain important aspects of relativity not taken into account in the traditional non-relativistic reductions. The transition current thus obtained differs from the leading order of the traditional expansion by simple multiplicative factors. These depend on the momentum and energy transfer and can be easily included together wit…
The improved Kelson-Garvey (ImKG) mass relations are proposed from the mass differences of mirror nuclei. The masses of 31 measured proton-rich nuclei with $7\leq A\leq41$ and $-5\leq (N-Z)\leq-3$ can be remarkably well reproduced by using the proposed relations, with a root-mean-square deviation of 0.398 MeV, which is much smaller than the results of Kelson-Garvey (0.502 MeV) and Isobar-Mirror mass relations (0.647 MeV). This is because many more masses of participating nuclei are involved in the ImKG mass relations for predicting the masses of unknown proton-rich nuclei. The masses for 144 u…
We have calculated the multinucleon transfer reactions of $^{208}$Os, $^{208}$Pt, $^{208}$Hg, $^{208}$Pb,$^{208}$Po, $^{208}$Rn, $^{208}$Ra,$^{132,136}$Xe bombarding on $^{232}$Th and $^{248}$Cm at Coulomb barrier energies within the dinuclear system model, systematically. The results are in good agreement with the available experimental data. Coulomb effect and shell effect on production of actinides in these reactions have been investigated thoroughly. Potential energy surface and total kinetic energy mass distributions in the reactions $^{208}$Hg, $^{208}$Pb and$^{208}$Po colliding on $^{24…
The STAR isobar data of $^{96}$Ru+$^{96}$Ru and $^{96}$Zr+$^{96}$Zr collisions at $\sqrt{s_{\mathrm{NN}}}= 200$ GeV show that ratios of observables ($R_{\mathcal{O}}$) such as the multiplicity distribution, $p(N_{\mathrm{ch}})$, and the harmonic flow, $v_n$, deviate from unity, when presented as a function of centrality, $c$. These deviations have been attributed to the differences in the shape and radial profiles between $^{96}$Ru and $^{96}$Zr nuclei. In addition, the ratios $R_{\mathcal{O}}(x)$ depend on the choice of the event activity variable $x$, which could be either $N_{\mathrm{ch}}$ …
In these proceedings, we present the measurements of centrality, transverse momentum and rapidity dependences of proton ($p$) and light nuclei ($d$ ($\overline{d}$), $t$, $^{3}\mathrm{He}$ ($\overline{^{3}\mathrm{He}}$), and $^{4}\mathrm{He}$) production in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 3 GeV, and isobaric (Ru+Ru and Zr+Zr) collisions at $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV. The compound yield ratios in central collisions at 3 GeV are found to be larger than the transport model calculations. Furthermore, the kinetic freeze-out parameters at 3 GeV show a different trend compared …
The charge-exchange excitations in nuclei are studied within the fully self-consistent proton-neutron quasiparticle random-phase approximation using the finite-range Gogny interaction. No additional parameters beyond those included in the effective nuclear force are included. Axially symmetric deformations are consistently taken into account, both in the description of the ground states and spin-isospin excitations. We focus on the isobaric analog and Gamow-Teller resonances. A comparison of the predicted strength distributions to the existing experimental data is presented and the role of nuc…
A systematics of the atomic nuclei in the frame of the nucleon number $A = Z + N$ and the proton-neutron difference $F = Z - N$ is considered. The classification scheme is provided by means of the non-compact algebra $sp(4,R)$. In this scheme the nuclei are ordered into isobaric multiplets, for which $A={fix}$, as well as in F-multiplets, for which $F={fix}$. The dependence of the mass excess $Δ$, the first exited states $E_{2^+}$ and the ratio $R_2=E_{4^+}/E_{2^+}$ on the nucleon number $A$ is empirically investigated within the $F$-multiplets. Appropriate filters are used to study the proper…
In this paper, we report a systematic study of the heaviest nuclei within the relativistic mean field (RMF) model. By comparing our results with those of the Hartree-Fock-Bogoliubov method (HFB) and the finite range droplet model (FRDM), the stability and the shape of the heaviest nuclei are discussed. The theoretical predictions as well as the existing experimental data indicate that the experimentally synthesized superheavy nuclei are in between the fission stability line, the line connecting the nucleus with maximum binding energy per nucleon in each isotopic chain, and the $β$-stability li…
In a previous letter (Phys. Rev. Lett. 96, 072502 (2006)), the multi-channel algebraic scattering (MCAS) technique was used to calculate spectral properties for proton-unstable $^{15}$F and its mirror, $^{15}$C. MCAS achieved a close match to the then-new data for $p+^{14}$O elastic scattering and predicted several unusually narrow resonances at higher energies. Subsequently, such narrow resonance states were found. New cross section data has been published characterising the shape of the $J^π=\frac{1}{2}^-$ resonance. Herein we update that first MCAS analysis and its predictions. We also stud…
