We search for potential isovector signatures in the neutron-rich oxygen and calcium isotopes within the framework of a relativistic mean-field theory with an exact treatment of pairing correlations. To probe the isovector sector we calibrate a few relativistic density functionals using the same isoscalar constraints but with one differing isovector assumption. It is found that under certain conditions, the isotopic chain in oxygen can be made to terminate at the experimentally observed ${}^{24}$O isotope and in the case of the calcium isotopes at ${}^{60}$Ca. To produce such behavior, the resulting symmetry energy must be soft, with predicted values for the symmetry energy and its slope at saturation density being $J\!=\!(30.92\pm0.47)$ MeV and $L\!=\!(51.0\pm1.5)$ MeV, respectively. As a consequence, the neutron-skin thickness of ${}^{208}$Pb is rather small: $R_{\rm skin}^{208}\!=\!(0.161\pm0.011)$ fm. This same model - labelled "FSUGarnet" - predicts $R_{1.4}\!=\!(13.1\pm0.1)$ km for the radius of a "canonical" 1.4$M_{\odot}$ neutron star, yet is also able to support a two-solar-mass neutron star.
We study excited-state properties of neutron-rich calcium isotopes based on chiral two- and three-nucleon interactions. We first discuss the details of our many-body framework, investigate convergence properties, and for two-nucleon interactions benchmark against coupled-cluster calculations. We then focus on the spectroscopy of 47-56Ca, finding that with both 3N forces and an extended pfg9/2 valence space, we obtain a good level of agreement with experiment. We also study electromagnetic transitions and find that experimental data are well described by our calculations. In addition, we provid…
The eastern region of the calcium isotope chain of the nuclei chart is, nowadays, of great activity. The experimental assessment of the limit of stability is of interest to confirm or improve microscopic theoretical models. The goal of this work is to provide the drip line of the calcium isotopes from the exact solution of the pairing Hamiltonian which incorporates explicitly the correlations with the continuum spectrum of energy. The modified Richardson equations, which include correlations with the continuum spectrum of energy modeled by the continuum single particle level density, is used t…
We present precision Penning-trap mass measurements of neutron-rich calcium and potassium isotopes in the vicinity of neutron number N=32. Using the TITAN system the mass of $^{51}$K was measured for the first time, and the precision of the $^{51,52}$Ca mass values were improved significantly. The new mass values show a dramatic increase of the binding energy compared to those reported in the atomic mass evaluation. In particular, $^{52}$Ca is more bound by 1.74 MeV, and the behavior with neutron number deviates substantially from the tabulated values. An increased binding was predicted recent…
Despite being a complex many-body system, the atomic nucleus exhibits simple structures for certain "magic" numbers of protons and neutrons. The calcium chain in particular is both unique and puzzling: evidence of doubly-magic features are known in 40,48Ca, and recently suggested in two radioactive isotopes, 52,54Ca. Although many properties of experimentally known Ca isotopes have been successfully described by nuclear theory, it is still a challenge to predict their charge radii evolution. Here we present the first measurements of the charge radii of 49,51,52Ca, obtained from laser spectrosc…
We use the newly developed Multi-Reference In-Medium Similarity Renormalization Group to study all even isotopes of the calcium and nickel isotopic chains, based on two- plus three-nucleon interactions derived from chiral effective field theory. We present results for ground-state and two-neutron separation energies and quantify their theoretical uncertainties. At shell closures, we find excellent agreement with Coupled Cluster results obtained with the same Hamiltonians. Our results highlight the importance of the chiral 3N interaction to obtain a correct reproduction of experimental energy t…
The nuclear reaction induced by photon is one of the important tools in the investigation of atomic nuclei. In the reaction, a target material is bombarded by photons with high-energies in the range of gamma-ray energy range. In the bombarding process, the photons can statistically be absorbed by a nucleus in the target material. Then the excited nucleus can decay by emitting proton, neutron, alpha and light particles or photons. By performing photonuclear reaction on the target, it can be easily investigated low-lying excited states of the nuclei. In the present work, (γ, n) photonuclear reac…
High-resolution bunched-beam collinear laser spectroscopy was used to measure the optical hyperfine spectra of the $^{43-51}$Ca isotopes. The ground state magnetic moments of $^{49,51}$Ca and quadrupole moments of $^{47,49,51}$Ca were measured for the first time, and the $^{51}$Ca ground state spin $I=3/2$ was determined in a model-independent way. Our results provide a critical test of modern nuclear theories based on shell-model calculations using phenomenological as well as microscopic interactions. The results for the neutron-rich isotopes are in excellent agreement with predictions using …
The isoscalar monopole response of neutron-rich nuclei is sensitive to both the incompressibility coefficient of symmetric nuclear matter and the density dependence of the symmetry energy. The main goal of this paper is to explore the emergence, evolution, and origin of low energy monopole strength along the even-even calcium isotopes: from 40Ca to 60Ca. The distribution of isoscalar monopole strength is computed in a relativistic random phase approximation (RPA) using three effective interactions that have been calibrated to the properties of finite nuclei and neutron stars. A non-spectral ap…
In this paper we study the issue of the puzzle of the radii of calcium isotopes. Despite an excess of eight neutrons, strangely $^{48}{\rm Ca}$ exhibits essentially the same charge radius as $^{40}{\rm Ca}$ does. A fundamental microscopic description of this is still lacking. Also strange is a peak in charge radius of calcium at N = 24. The $^{52}{\rm Ca}$ (N = 32) nucleus, well known to be doubly magical, amazingly has recently been found to have a very large charge radius. Also amazing is the property of $^{42}_{14}{\rm Si}_{28}$ which simultaneously appears to be both magical/spherical and …
We have studied neutron-rich calcium isotopes in terms of the shell model employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. The short-range repulsion of the potential is renormalized by way of the V-low-k approach. The calculated results are in very good agreement with the available experimental data, thus supporting our predictions for the hitherto unknown spectra of 53-56Ca nuclei. In this context, the possible existence of an N=34 shell closure is discussed.
We calculate the neutron-Calcium-60 S-wave scattering phase shifts using state of the art coupled-cluster theory combined with modern ab initio interactions derived from chiral effective theory. Effects of three-nucleon forces are included schematically as density dependent nucleon-nucleon interactions. This information is combined with halo effective field theory in order to investigate the Calcium-60-neutron-neutron system. We predict correlations between different three-body observables and the two-neutron separation energy of Calcium-62. This provides evidence of Efimov physics along the C…
Based on the realistic nuclear force of the high-precision CD-Bonn potential, we have performed comprehensive calculations for neutron-rich calcium isotopes using the Gamow shell model (GSM) which includes resonance and continuum. The realistic GSM calculations produce well binding energies, one- and two-neutron separation energies, predicting that $^{57}$Ca is the heaviest bound odd isotope and $^{70}$Ca is the dripline nucleus. Resonant states are predicted, which provides useful information for future experiments on particle emissions in neutron-rich calcium isotopes. Shell evolutions in th…
The calcium isotopes have emerged as an important testing ground for new microscopically derived shell-model interactions, and a great deal of focus has been directed toward this region. We investigate the relative spectroscopic strengths associated with $1f_{7/2}$ neutron hole states in $^{47, 49}$Ca following one-neutron knockout reactions from $^{48,50}$Ca. The observed reduction of strength populating the lowest 7/2$^{-}_{1}$ state in $^{49}$Ca, as compared to $^{47}$Ca, is consistent with the description given by shell-model calculations based on two- and three-nucleon forces in the neutr…
Based on the isospin-dependent quantum molecular dynamics model along with the GEMINI model, heavy-ion collisions at intermediate energies are studied. We calculate the production cross sections of different fragments for reactions of 112Sn+112Sn and 124Sn+124Sn at different beam energies. The species and production cross sections of neutron-rich isotopes are generally dependent on the isospin of the system and the incident energies. The nucleon 48Ca and 54Ca are more productive for the neutron-rich system at 30 to 150 MeV/nucleon.
We study the performance of self-consistent mean-field and beyond-mean-field approximations in shell-model valence spaces. In particular, Hartree-Fock-Bogolyubov, particle-number variation after projection and projected generator coordinate methods are applied to obtain ground-state and excitation energies for even-even and odd-even Calcium isotopes in the pf-shell. The standard (and non-trivial) KB3G nuclear effective interaction has been used. The comparison with the exact solutions -- provided by the full diagonalization of the Hamiltonian -- shows an outstanding agreement when particle-num…
We employ interactions from chiral effective field theory and compute the binding energies and low-lying excitations of calcium isotopes with the coupled-cluster method. Effects of three-nucleon forces are included phenomenologically as in-medium two-nucleon interactions, and the coupling to the particle continuum is taken into account using a Berggren basis. The computed ground-state energies and the low-lying 2+ states for the isotopes 42,48,50,52Ca are in good agreement with data, and we predict the excitation energy of the first 2+ state in 54Ca at 1.9 MeV, displaying only a weak sub-shell…
We study the neutron-rich calcium isotopes performing shell-model calculations with a realistic effective interaction. This is derived from the CD-Bonn nucleon-nucleon potential renormalized by way of the V-low-k approach, considering 48Ca as an inert core and including the neutron 0g9/2 orbital. We compare our results with experiment and with the results of a previous study where 40Ca was assumed as a closed core and the standard 1p0f model space was employed. The calculated spectroscopic properties are in both cases in very good agreement with the available experimental data and enable a dis…
Charge radii of calcium isotopes within relativistic configuration-interaction density functional theory
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University（北京大学物理学院核物理与技术国家重点实验室）；School of Physics, Beihang University（北京航空航天大学物理学院）
Nuclear magnetic-dipole (M1) and Gamow-Teller (GT) transitions provide insight into the spin-isospin properties of atomic nuclei. By considering them as unified spin-isospin transitions, the M1/GT transition strengths and excitation energies are subject to isospin symmetry. The excitation properties associated to the M1/GT symmetry need to be clarified within consistent theoretical approach. In this work, the relationship between the M1 and GT transitions in Ca isotopes is investigated in a unified framework based on the relativistic energy-density functional (REDF) with point-coupling interac…
We report in this paper a study in terms of the nuclear shell model about the location of the calcium isotopes drip line. The starting point is considering the realistic two-body potential derived by Entem and Machleidt within chiral perturbation theory at next-to-next-to-next-to-leading order (N3LO), as well as a chiral three-body force at next-to-next-to-leading order (N2LO) whose structure and low-energy constants are consistent with the two-body potential. Then we construct the effective single-particle energies and residual interaction needed to diagonalize the shell-model Hamiltonian. Th…
Three-nucleon forces (3NFs), and in particular terms of the Fujita-Miyazawa type, strongly influence the structure of neutron-rich exotic isotopes. Ab-initio calculations have shown that chiral two- and three-nucleon interactions correctly reproduce binding energy systematics and neutron driplines of oxygen and nearby isotopes. Exploiting the novel self-consistent Gorkov-Green's function approach, we present the first investigation of Ar, K, Ca, Sc and Ti isotopic chains. Leading chiral 3N interactions are mandatory to reproduce the trend of binding energies throughout these chains and to obta…
Understanding and predicting the formation of shell structure from nuclear forces is a central challenge for nuclear physics. While the magic numbers N=2,8,20 are generally well understood, N=28 is the first standard magic number that is not reproduced in microscopic theories with two-nucleon forces. In this Letter, we show that three-nucleon forces give rise to repulsive interactions between two valence neutrons that are key to explain 48Ca as a magic nucleus, with a high 2+ excitation energy and a concentrated magnetic dipole transition strength. The repulsive three-nucleon mechanism improve…
New results for electric dipole strength in the chain of even-even Calcium isotopes with the mass numbers A = 40 - 54 are presented. Starting from the covariant Lagrangian of Quantum Hadrodynamics, spectra of collective vibrations (phonons) and phonon-nucleon coupling vertices for $J \leq 6$ and normal parity were computed in a self-consistent relativistic quasiparticle random phase approximation (RQRPA). These vibrations coupled to Bogoliubov two-quasiparticle configurations (2q$\otimes$phonon) form the model space for the calculations of the dipole response function in the relativistic quasi…
A numerical method to integrate the time-dependent Hartree-Fock Bogoliubov (TDHFB) equations with Gogny interaction is proposed. The feasibility of the TDHFB code is illustrated by the conservation of the energy, particle numbers, and center-of-mass in the small amplitude vibrations of oxygen 20. The TDHFB code is applied to the isoscalar quadrupole and/or isovector dipole vibrations in the linear (small amplitude) region in oxygen isotopes (masses A = 18,20,22 and 24), titanium isotopes (A = 44,50,52 and 54), neon isotope (A = 26), and magnesium isotopes (A = 24 and 34). The isoscalar quadrup…
Neutron drip line in calcium isotopes from a chiral interaction
Peking University（北京大学）；Texas A&M University（德克萨斯农工大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Chalmers University of Technology（查尔姆斯理工大学）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）；Johannes Gutenberg-Universität（约翰内斯·古腾堡大学）；University of Tsukuba（筑波大学）
We formulate microscopic neutron-nucleus optical potentials from many-body perturbation theory based on chiral two- and three-body forces. The neutron self energy is first calculated in homogeneous matter to second order in perturbation theory, which gives the central real and imaginary terms of the optical potential. The real spin-orbit term is calculated separately from the density matrix expansion using the same chiral interaction as in the self energy. Finally, the full neutron-nucleus optical potential is derived within the improved local density approximation utilizing mean field models …
The determination of nuclear symmetry energy, and in particular, its density dependence, is a long-standing problem for nuclear physics community. Previous studies have found that the product of electric dipole polarizability $α_D$ and symmetry energy at saturation density $J$ has a strong linear correlation with $L$, the slope parameter of symmetry energy. However, current uncertainty of $J$ hinders the precise constraint on $L$. We investigate the correlations between electric dipole polarizability $α_D$ (or times symmetry energy at saturation density $J$) in Sn isotopes and the slope parame…
We formulate microscopic optical potentials for nucleon-nucleus scattering from chiral two- and three-nucleon forces. The real and imaginary central terms of the optical potentials are obtained from the nucleon self energy in infinite nuclear matter at a given density and isospin asymmetry, calculated self-consistently to second order in many-body perturbation theory. The real spin-orbit term is extracted from the same chiral potential using an improved density matrix expansion. The density-dependent optical potential is then folded with the nuclear density distributions of 40Ca, 42Ca, 44Ca, a…
Through inelastic scattering cross section measurements for $^{42-51}$Ca on a carbon target at 280 MeV/nucleon recently, Tanaka {\it et al.} [ arXiv:1911.05262 [nucl-ex]], in a very significant experiment, have demonstrated large swelling of doubly magic $^{48}$Ca core in calcium isotopes beyond N=28. The matter radii observed in these experiments, are surprisingly much larger than the corresponding, already amazingly large charge radii of the same calcium isotopes, by Garcia {\it et al.} [Nat. Phys. 12 (2016) 594]. Here we propose a novel solution, wherein the breathing mode states $0^{+}$ of…
Impact of tensor-rank components of chiral three-nucleon forces on the single-particle structure of calcium isotopes
Kyushu University（九州大学）；RIKEN Nishina Center（理化学研究所西村中心）；Università degli Studi della Campania “Luigi Vanvitelli”（坎帕尼亚路易吉·范维泰利大学）；Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）；Peking University（北京大学）
The $N = 28$ shell gap in sulfur, argon, calcium and titanium isotopes is investigated in the framework of relativistic continuum Hartree-Bogoliubov (RCHB) theory. The evolutions of neutron shell gap, separation energy, single particle energy and pairing energy are analyzed, and it is found that $N = 28$ shell gap is quenched in sulfur isotopes but persists in argon, calcium and titanium isotopes. The evolution of $N = 28$ shell gap in $N = 28$ isotonic chain is discussed, and the erosion of $N = 28$ shell gap is understood with the evolution of potential with proton number.
We construct nucleonic microscopic optical potentials by combining the Green's function approach with the coupled-cluster method for $\rm{^{40}Ca}$ and $\rm{^{48}Ca}$. For the computation of the ground-state of $\rm{^{40}Ca}$ and $\rm{^{48}Ca}$, we use the coupled-cluster method in the singles-and-doubles approximation, while for the A = $\pm 1$ nuclei we use particle-attached/removed equation-of-motion method truncated at two-particle-one-hole and one-particle-two-hole excitations, respectively. Our calculations are based on the chiral nucleon-nucleon and three-nucleon interaction $\rm{NNLO_{…
The lightest Xenon isotopes are studied in the framework of the Interacting Shell Model (ISM). The valence space comprises all the orbits lying between the magic closures N=Z=50 and N=Z=82. The calculations produce collective deformed structures of triaxial nature that encompass nicely the known experimental data. Predictions are made for the (still unknown) N=Z nucleus 108-Xe. The results are interpreted in terms of the competition between the quadrupole correlations enhanced by the pseudo-SU(3) structure of the positive parity orbits and the pairing correlations brought in by the 0h11/2 orbi…
We study the couplings between collective vibrations such as the isovector giant dipole and isoscalar giant quadrupole resonances in tin isotopes in the framework of the time-dependent Hartree-Fock theory with a Skyrme energy density functional. These couplings are a source of anharmonicity in the multiphonon spectrum. In particular, the residual interaction is known to couple the isovector giant dipole resonance with the isoscalar giant quadrupole resonance built on top of it, inducing a nonlinear evolution of the quadrupole moment after a dipole boost. This coupling also affects the dipole m…
We utilize a nuclear shell model Hamiltonian with only two adjustable parameters to generate, for the first time, exact solutions for pairing correlations for light to medium-mass nuclei, including the challenging proton-neutron pairs, while also identifying the primary physics involved. In addition to single-particle energy and Coulomb potential terms, the shell model Hamiltonian consists of an isovector $T=1$ pairing interaction and an average proton-neutron isoscalar $T=0$ interaction, where the $T=0$ term describes the average interaction between non-paired protons and neutrons. This Hamil…
We investigate the microscopic structure of the low-lying isovector-dipole excitation mode in neutron-rich $^{36,38,40}$Mg close to the drip line by means of the deformed quasiparticle-random-phase-approximation employing the Skyrme and the local pairing energy-density functionals. It is found that the low-lying bump structure above the neutron emission-threshold energy develops when the drip line is approached, and that the isovector dipole strength at $E_{x} < 10$ MeV exhausts about $6.0 %$ of the classical Thomas-Reiche-Kuhn dipole sum rule in $^{40}$Mg. We obtained the collective dipole mo…
Charge radii are one of the most fundamental properties of atomic nuclei characterizing their charge distributions. Though the general trend as a function of the mass number is well described by the $A^{1/3}$ rule, some fine structures, such as the evolution along the calcium isotopic chain and the corresponding odd-even staggerings, are notoriously difficult to describe both in density functional theories and ab initio methods. In this letter, we propose a novel ansatz to describe the charge radii of calcium isotopes, by adding a correction term, proportional to the number of Cooper pairs, an…
We perform Time Dependent Hartree-Fock (TDHF) calculations to investigate the small amplitude dipole response of selected neutron-rich nuclei and Sn isotopes. A detailed comparison with the dipole strength predicted by Random-Phase Approximation (RPA) calculations is presented for the first time. TDHF results are also confronted to Vlasov calculations, to explore up to which extent a semi-classical picture can explain the properties of the nuclear response. The focus is on the low-energy response, below the Giant Dipole Resonance region, where different modes of non negligible strength are ide…
Following a previous paper [Y. Shi, Phys. Rev. C 98, 014329(2018)], we present an extension of the density-functional theory to allow for dynamic calculations based on the obtained static Hartree-Fock results. We perform extensive benchmark calculations, by comparing the calculated results with that of an existing code Sky3D. To perform linear-response calculations using the TDDFT method, comparisons have been made with the finite-amplitude quasiparticle random-phase approximation (FAM-QRPA) method. We plan to apply the TDDFT method to a systematic description of the IVD resonances in the Zr, …
