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 Calcium isotope chain. Experimental key observables that facilitate a test of our findings are discussed.
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.
Isotope shifts in the nuclear charge radius of even and odd calcium isotopes are calculated within the nuclear shell model. The model space includes all configurations of nucleons in the $2s, 1d_{3/2}, 1f_{7/2}, {\rm and} ~2p_{3/2}$ orbits. The shell model describes well the energies of the intruder states in Sc and Ca, as well as the energies of the low-lying $2^+$ and $3^-$ states in the even Ca isotopes. The characteristic features of the isotope shifts, the parabolic dependence on $A$ and the prominent odd-even staggering, are well reproduced by the model. These features are related to the…
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…
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…
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 perform large shell model calculations for Calcium isotopes in the full fp shell by using the realistic Kuo-Brown interaction. The Calcium isotopes are especially interesting because the nearest-neighbour spacing distribution P(s) of low-lying energy levels shows significant deviations from the predictions of the Gaussian Orthogonal Ensemble of random--matrix theory. This contrasts with other neighbouring nuclei which show fully chaotic spectral distributions. We study the chaotic behaviour as a function of the excitation energy. In addition, a clear signature of chaos suppression is obtain…
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）
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 resu…
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…
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…
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…
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）
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 …
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 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 …
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…
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…
We investigate emergence of halos and Efimov states in nuclei by use of a newly designed model which combines self-consistent mean-field and three-body descriptions. Recent interest in neutron heavy calcium isotopes makes $^{72}$Ca ($^{70}$Ca+n+n) an ideal realistic candidate on the neutron dripline, and we use it as a representative example that illustrates our broadly applicable conclusions. By smooth variation of the interactions we simulate the crossover from well-bound systems to structures beyond the threshold of binding, and find that halo-configurations emerge from the mean-field struc…
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…
Neutron rich Ca and Ni nuclei have been studied in spherical Relativistic Mean Field formalism in co-ordinate space. A delta interaction has been has been adopted to treat the pairing correlations for the neutrons. Odd nuclei have been treated in the blocking approximation. The effect of the positive energy continuum and the role of pairing in the stability of nuclei have been investigated using the resonant-BCS (rBCS) approach. In Ca isotopes, N=50 is no longer a magic number while in Ni nuclei, a new magic number emerges at N=70. There is a remarkable difference in the relative positions of …
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…
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_{…
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 describe 19B in terms of a 17B-n-n three-body system, where the two-body subsystems 17B-n and n-n are unbound (virtual) states close to the unitary limit. The energy of 19B ground state is well reproduced and two low-lying resonances are predicted. Their eventual link with the Efimov physics is discussed. This model can be extended to describe the recently discovered resonant states in 20,21B.
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）
We study the effects of the phonon-phonon coupling on the low-energy electric dipole response within a microscopic model based on an effective Skyrme interaction. The finite rank separable approach for the quasiparticle random phase approximation is used. Choosing as an example the isotopic chain of Calcium, we show the ability of the method to describe the low-energy $E1$ strength distribution. With one and the same set of parameters we describe available experimental data for $^{48}$Ca and predict the electric dipole strength function for $^{50}$Ca.
We computed ground-state energies of calcium isotopes from 42Ca to 48Ca by means of the Auxiliary Field Diffusion Monte Carlo (AFDMC) method. Calculations were performed by replacing the 40Ca core with a mean-field self consistent potential computed using Skyrme interaction. The energy of the external neutrons is calculated by projecting the ground-state from a wave function built with the single particle orbitals computed in the self consistent external potential. The shells considered were the 1F_7/2 and the 1F_5/2. The Hamiltonian employed is semi-realistic and includes tensor, spin--orbit …
We study the effects of the tensor term of the effective nucleon-nucleon interaction on nuclear excited states. Our investigation has been conducted by using a self-consistent Random Phase Approximation approach. We investigate various nuclei in different regions of the isotopes chart. Results for a set of calcium isotopes are shown.
We present microscopic valence-shell calculations of pairing gaps in the calcium isotopes, focusing on the role of three-nucleon (3N) forces and many-body processes. In most cases, we find a reduction in pairing strength when the leading chiral 3N forces are included, compared to results with low-momentum two-nucleon (NN) interactions only. This is in agreement with a recent energy density functional study. At the NN level, calculations that include particle-particle and hole-hole ladder contributions lead to smaller pairing gaps compared with experiment. When particle-hole contributions as we…
We discuss the need of including tensor terms in the effective Gogny interaction used in mean-field calculations. We show in one illustrative case that, with the usual tensor term that is employed in the Skyrme interaction (and that allows us to separate the like-nucleon and the neutron-proton tensor contributions), we can describe the evolution of the N=28 neutron gap in calcium isotopes. We propose to include a tensor and a tensor-isospin term in finite-range interactions of Gogny type. The parameters of the two tensor terms allow us to treat separately the like-nucleon and the neutron-proto…
The location of the neutron drip line, currently known for only the lightest elements, remains a fundamental question in nuclear physics. Its description is a challenge for microscopic nuclear energy density functionals, as it must take into account in a realistic way not only the nuclear potential, but also pairing correlations, deformation effects and coupling to the continuum. The recently developed deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) aims to provide a unified description of even-even nuclei throughout the nuclear chart. Here, the DRHBc with the successful d…
We show the first results for the elastic scattering of neutrons off oxygen and calcium isotopes obtained from ab initio optical potentials. The potential is derived using self consistent Green's function theory (SCGF) with the saturating chiral interaction NNLO$_{\textrm{sat}}$. Our calculations are compared to available scattering data and show that it is possible to reproduce low energy scattering observables in medium mass nuclei from first principles.
We use the recently proposed In-Medium Similarity Renormalization Group (IM-SRG) to carry out a systematic study of closed-shell nuclei up to $\nuc{Ni}{56}$, based on chiral two- plus three-nucleon interactions. We analyze the capabilities of the IM-SRG by comparing our results for the ground-state energy to Coupled Cluster calculations, as well as to quasi-exact results from the Importance-Truncated No-Core Shell Model. Using chiral two- plus three-nucleon Hamiltonians whose resolution scales are lowered by free-space SRG evolution, we obtain good agreement with experimental binding energies …
Mass measurements continue to provide invaluable information for elucidating nuclear structure and scenarios of astrophysical interest. The transition region between the $Z = 20$ and $28$ proton shell closures is particularly interesting due to the onset and evolution of nuclear deformation as nuclei become more neutron rich. This provides a critical testing ground for emerging ab-initio nuclear structure models. Here, we present high-precision mass measurements of neutron-rich chromium isotopes using the sensitive electrostatic Multiple-Reflection Time-Of-Flight Mass Spectrometer (MR-TOF-MS) …
We present a model description of the bound $^{17}$B isotope in terms of a $^{17}$B-n-n three-body system where the two-body subsystems $^{17}$B-n and n-n are unbound (virtual) states close to the unitary limit. The $^{17}$B ground state is well described in terms of two-body potentials only, and two low-lying resonances are predicted. Their eventual link with the Efimov physics is discussed. This model can be naturally used to describe the recently discovered resonant states in $^{20,21}$B.
We perform Hartree-Fock-Bogoliubov (HFB) calculations for semi-magic Calcium, Nickel, Tin and Lead isotopes and $N$=20, 28, 50 and 82 isotones using density-dependent pairing interactions recently derived from a microscopic nucleon-nucleon interaction. These interactions have an isovector component so that the pairing gaps in symmetric and neutron matter are reproduced. Our calculations well account for the experimental data for the neutron number dependence of binding energy, two neutrons separation energy, and odd-even mass staggering of these isotopes. This result suggests that by introduci…
We show that the contributions of three-quasiparticle interactions to normal Fermi systems at low energies and temperatures are suppressed by n_q/n compared to two-body interactions, where n_q is the density of excited or added quasiparticles and n is the ground-state density. For finite Fermi systems, three-quasiparticle contributions are suppressed by the corresponding ratio of particle numbers N_q/N. This is illustrated for polarons in strongly interacting spin-polarized Fermi gases and for valence neutrons in neutron-rich calcium isotopes.
Configurational information entropy (CIE) theory was employed to determine the neutron skin thickness of neutron-rich calcium isotopes. The nuclear density distributions and fragment cross-sections in 350 MeV/u $^{40-60}$Ca + $^{9}$Be projectile fragmentation reactions were calculated using a modified statistical abrasion-ablation model. CIE quantities were determined from the nuclear density, isotopic, mass, and charge distributions. The linear correlations between the CIE determined using the isotopic, mass, and charge distributions and the neutron skin thickness of the projectile nucleus sh…
The structure of the isovector dipole resonance in neutron-rich calcium isotope, $^{60}Ca$, has been investigated by implementing a careful treatment of the differences of neutron and proton radii in the continuum random phase approximation ($RPA$). The calculations have taken into account the current estimates of the neutron skin. The estimates of the escape widths for direct neutron decay from the pygmy dipole resonance ($PDR$) were shown rather wide, implicating a strong coupling to the continuum. The width of the giant dipole resonance ($GDR$) was evaluated, bringing on a detailed discussi…
