Neutron-rich Calcium Isotopes Research Articles

Nuclear charge radii in Bayesian neural networks revisited

In this work, a refined Bayesian neural network (BNN) based approach with six inputs including the proton number, mass number, and engineered features associated with the pairing effect, shell effect, isospin effect, and “abnormal” shape staggering effect of 181,183,185Hg, is proposed to accurately describe nuclear charge radii. The new approach is able to well describe the charge radii of atomic nuclei with A≥40 and Z≥20. The standard root-mean-square deviation is 0.014 fm for both the training and validation data. In particular, the predicted charge radii of proton-rich and neutron-rich calcium isotopes are found in good agreement with data. We further demonstrate the reliability of the BNN approach by investigating the variations of the root-mean-square deviations with extrapolation distances, mass numbers, and isospin asymmetries.

Determination of neutron-skin thickness using configurational information entropy

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 show that CIE provides new methods to extract the neutron skin thickness of neutron-rich nuclei.

Data-driven configuration-interaction Hamiltonian extrapolation to Ca60

Following the many successful implementations of effective universal configuration-interaction Hamiltonians, we endeavored to produce a universal $fp$ shell interaction tailored for the calcium isotopes, which we call UFP-CA. Starting from a state-of-the-art in-medium similarity renormalization group (IMSRG) interaction, linear combinations of Hamiltonian parameters that define the natural basis of the parameter space are constrained by the latest experimental data for the neutron-rich calcium isotopes. We show that this data-driven method for improving the Hamiltonian provides an excellent description of the known binding energies and spectra for the calcium isotopes within the $fp$ model space. This together with comparisons to results from energy-density functional models leads us to conclude that $^{60}\mathrm{Ca}$ is doubly magic at a similar level to $^{68}\mathrm{Ni}$. Several predictions are presented for unobserved low-lying excited states in $^{55\ensuremath{-}59}\mathrm{Ca}$ that will be accessible to future experiments.

Neutron-rich calcium isotopes within realistic Gamow shell model calculations with continuum coupling

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 the calcium chain around neutron numbers \textit{N} = 32, 34 and 40 are understood by calculating effective single-particle energies, the excitation energies of the first $2^+$ states and two-neutron separation energies. The calculations support shell closures at $^{52}$Ca (\textit{N} = 32) and $^{54}$Ca (\textit{N} = 34) but show a weakening of shell closure at $^{60}$Ca (\textit{N} = 40). The possible shell closure at $^{70}$Ca (\textit{N} = 50) is predicted.

The structure of neutron-rich calcium isotopes studied by the shell model with realistic effective interactions * * Supported by National Natural Science Foundation of China (U1732138, 11605054,11505056, 11305108, 11790325, 11847315)

We study the structure of neutron-rich calcium isotopes in the shell model with realistic interactions. The CD-Bonn and Kuo-Brown (KB) interactions are used. As these interactions do not include the three-body force, their direct use leads to poor results. We tested whether the adjustment of the single particle energies (SPEs) would be sufficient to include the three-body correlations empirically. It turns out that the CD-Bonn interaction, after the adjustment of SPEs, gives good agreement with the experimental data for the energies and spectroscopy. For the KB interaction, both the SPEs and monopole terms require adjustments. Thus, the monopole problem is less serious for modern realistic interactions which include perturbations up to the third order. We also tested the effect of the non-central force on the shell structure. It is found that the effect of the tensor force in the CD-Bonn interaction is weaker than in the KB interaction.

Quasifree Neutron Knockout from ^{54}Ca Corroborates Arising N=34 Neutron Magic Number.

Exclusive cross sections and momentum distributions have been measured for quasifree one-neutron knockout reactions from a ^{54}Ca beam striking on a liquid hydrogen target at ∼200 MeV/u. A significantly larger cross section to the p_{3/2} state compared to the f_{5/2} state observed in the excitation of ^{53}Ca provides direct evidence for the nature of the N=34 shell closure. This finding corroborates the arising of a new shell closure in neutron-rich calcium isotopes. The distorted-wave impulse approximation reaction formalism with shell model calculations using the effective GXPF1Bs interaction and abinitio calculations concur our experimental findings. Obtained transverse and parallel momentum distributions demonstrate the sensitivity of quasifree one-neutron knockout in inverse kinematics on a thick liquid hydrogen target with the reaction vertex reconstructed to final state spin-parity assignments.

New γ-ray detector CATANA for in-beam γ-ray spectroscopy with fast RI beams

The γ-ray detector CATANA (CAesium iodide array for γ-ray Transitions in Atomic Nuclei at high isospin Asymmetry) has been constructed to detect γ-rays from nuclear reaction with radioactive ion beams at RIKEN RIBF. CATANA consists of 100 square frustum-shaped CsI(Na) crystals coupled with photomultiplier tubes. The crystal shapes and positions are arranged to minimize the distance between the crystals so as to have better calorimetric properties and Doppler-shift correction capability. The CATANA array was employed to measure the dipole response of the neutron-rich calcium isotopes 50,52Ca, and the γ-rays from several known transitions were observed.

Magic Nature of Neutrons in ^{54}Ca: First Mass Measurements of ^{55-57}Ca.

We perform the first direct mass measurements of neutron-rich calcium isotopes beyond neutron number 34 at the RIKEN Radioactive Isotope Beam Factory by using the time-of-flight magnetic-rigidity technique. The atomic mass excesses of ^{55-57}Ca are determined for the first time to be -18650(160), -13510(250), and -7370(990) keV, respectively. We examine the emergence of neutron magicity at N=34 based on the new atomic masses. The new masses provide experimental evidence for the appearance of a sizable energy gap between the neutron 2p_{1/2} and 1f_{5/2} orbitals in ^{54}Ca, comparable to the gap between the neutron 2p_{3/2} and 2p_{1/2} orbitals in ^{52}Ca. For the ^{56}Ca nucleus, an open-shell property in neutrons is suggested.

Emergence of low-energy monopole strength in the neutron-rich calcium isotopes

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 approach is adopted that allows for an exact treatment of the continuum without any reliance on discretization. For the stable calcium isotopes, no evidence of low-energy monopole strength is observed, even as the 1f7/2 neutron orbital is being filled and the neutron-skin thickness progressively grows. Further, in contrast to experimental findings, a mild softening of the monopole response with increasing mass number is predicted. Beyond 48Ca, a significant amount of low-energy monopole strength emerges as soon as the weak-binding neutron orbitals (2p and 1f5/2) become populated. The emergence and evolution of low-energy strength is identified with transitions from these weakly-bound states into the continuum. Moreover, given that models with a soft symmetry energy tend to reach the neutron-drip line earlier than their stiffer counterparts, we identify an inverse correlation between the neutron-skin thickness and the inverse energy weighted sum.

Development of a sensitive setup for laser spectroscopy studies of very exotic calcium isotopes

An experimental setup for sensitive high-resolution measurements of hyperfine structure spectra of exotic calcium isotopes has been developed and commissioned at the COLLAPS beam line at ISOLDE, CERN. The technique is based on the radioactive detection of decaying isotopes after optical pumping and state selective neutralization (ROC) (Vermeeren et al 1992 Phys. Rev. Lett. 68 1679). The improvements and developments necessary to extend the applicability of the experimental technique to calcium isotopes produced at rates as low as few ions s–1 are discussed. Numerical calculations of laser-ion interaction and ion-beam simulations were explored to obtain the optimum performance of the experimental setup. Among the implemented features are a multi-step optical pumping region for sensitive measurements of isotopes with hyperfine splitting, a high-voltage platform for adequate control of low-energy ion beams and simultaneous β-detection of neutralized and remaining ions. The commissioning of the experimental setup, and the first online results on neutron-rich calcium isotopes are presented.

Status of the TRIGA-LASER experiment

We report on the newly developed control system called TRITON and the new data acquisition called TILDA as well as on improved isotope shift measurements of the isotopes 40,42,44,48Ca in the 4s 2S1/2 → 4p 2P3/2 (D2) transition at the TRIGA-LASER experiment in Mainz using collinear laser spectroscopy. Well known isotope shift measurements in the 4s 2S1/2 → 4p 2P1/2 (D1) transition act as calibration points to reduce the uncertainties in the D2-line to provide reference values for the determination of nuclear charge radii and quadrupole moments of neutron rich calcium isotopes at COLLAPS.

Electric dipole response of neutron-rich calcium isotopes in relativistic quasiparticle time blocking approximation

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 quasiparticle time blocking approximation (RQTBA). The results for giant dipole resonance in the latter approach are compared to those obtained in RQRPA and to available data. Evolution of the dipole strength with neutron number is investigated for both high-frequency giant dipole resonance (GDR) and low-lying strength. Development of a pygmy resonant structure on the low-energy shoulder of GDR is traced and analyzed in terms of transition densities. A dependence of the pygmy dipole strength on the isospin asymmetry parameter is extracted.

Dynamical effects in fusion with exotic nuclei

[Background] Reactions with stable beams have demonstrated a strong interplay between nuclear structure and fusion. Exotic beam facilities open new perspectives to understand the impact of neutron skin, large isospin, and weak binding energies on fusion. Microscopic theories of fusion are required to guide future experiments. [Purpose] To investigate new effects of exotic structures and dynamics in near-barrier fusion with exotic nuclei. [Method] Microscopic approaches based on the Hartree-Fock (HF) mean-field theory are used for studying fusion barriers in $^{40-54}$Ca+$^{116}$Sn reactions for even isotopes. Bare potential barriers are obtained assuming frozen HF ground-state densities. Dynamical effects on the barrier are accounted for in time-dependent Hartree-Fock (TDHF) calculations of the collisions. Vibrational couplings are studied in the coupled-channel framework and near-barrier nucleon transfer is investigated with TDHF calculations. [Results] The development of a neutron skin in exotic calcium isotopes strongly lowers the bare potential barrier. However, this static effect is not apparent when dynamical effects are included. On the contrary, a fusion hindrance is observed in TDHF calculations with the most neutron rich calcium isotopes which cannot be explained by vibrational couplings. Transfer reactions are also important in these systems due to charge equilibration processes. [Conclusions] Despite its impact on the bare potential, the neutron skin is not seen as playing an important role in the fusion dynamics. However, the charge transfer with exotic projectiles could lead to an increase of the Coulomb repulsion between the fragments, suppressing fusion. The effect of transfer and dissipative mechanisms on fusion with exotic nuclei deserve further studies.

Octupole strength in the neutron-rich calcium isotopes

Low-lying excited states of the neutron-rich calcium isotopes $^{48-52}$Ca have been studied via $\gamma$-ray spectroscopy following inverse-kinematics proton scattering on a liquid hydrogen target using the GRETINA $\gamma$-ray tracking array. The energies and strengths of the octupole states in these isotopes are remarkably constant, indicating that these states are dominated by proton excitations.

Unexpectedly large charge radii of neutron-rich calcium isotopes

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 spectroscopy experiments at ISOLDE, CERN. The experimental results are complemented by state-of-the-art theoretical calculations. The large and unexpected increase of the size of the neutron-rich calcium isotopes beyond N = 28 challenges the doubly-magic nature of 52Ca and opens new intriguing questions on the evolution of nuclear sizes away from stability, which are of importance for our understanding of neutron-rich atomic nuclei.

Revisiting the monopole components of effective interactions for the shell model

In this paper, we revisit the monopole components of effective interactions for the shell model. Without going through specific nuclei or shell gaps, universal roles of central, tensor, and spin–orbit forces can be proved, reflecting the intrinsic features of shell model effective interactions. For monopole matrix elements, even and odd channels of central force often have a canceling effect. However, for the contributions to the shell evolution, its even and odd channels could have both positive or negative contributions, enhancing the role of central force on the shell structure. Tensor force is generally weaker than central force. However, for the effect on shell evolutions, tensor force can dominate or play a competitive role. A different systematics has been discovered between T = 1 and 0 channels. For example, tensor force, well established in the T = 0 channel, becomes uncertain in the T = 1 channel. We calculate the properties of neutron-rich oxygen and calcium isotopes in order to study T = 1 channel interactions further. It is learned that the main improvements of empirical interactions are traced to the central force. For non-central forces, antisymmetric spin–orbit (ALS) force, originated from many-body perturbations or three-body force, could also play an explicit role. T = 1 tensor forces are less constrained so their effect can differ in different empirical interactions. The influence of tensor force may sometimes be canceled by many-body effects. For T = 0 channels of effective interactions, which is the main source of neutron–proton correlations, central and tensor forces are the leading components. For T = 1 channels, which can act between like-particles, the request for many-body correlations could be more demanding, so that the monopole anomaly of the T = 1 channel might be more serious.

Nuclear Forces and Their Impact on Neutron-Rich Nuclei and Neutron-Rich Matter

We review the impact of nuclear forces on matter at neutron-rich extremes. Recent results have shown that neutron-rich nuclei become increasingly sensitive to three-nucleon forces, which are at the forefront of theoretical developments based on effective field theories of quantum chromodynamics. These developments include the formation of shell structure, the spectroscopy of exotic nuclei, and the location of the neutron drip line. Nuclear forces also constrain the properties of neutron-rich matter, including the neutron skin, the symmetry energy, and the structure of neutron stars. First, we review our understanding of three-nucleon forces and show how chiral effective field theory makes unique predictions for many-body forces. Then, we survey results with three-nucleon forces in neutron-rich oxygen and calcium isotopes and neutron-rich matter, which have been explored with a range of many-body methods. Three-nucleon forces therefore provide an exciting link between theoretical, experimental, and observational nuclear physics frontiers.

Searching for isovector signatures in the neutron-rich oxygen and calcium isotopes

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 24O isotope and in the case of the calcium isotopes at 60Ca. 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±0.47) MeV and L=(51.0±1.5) MeV, respectively. As a consequence, the neutron-skin thickness of 208Pb is rather small: Rskin208=(0.161±0.011) fm. This same model—labeled “FSUGarnet”—predicts R1.4=(13.0±0.1) km for the radius of a “canonical” 1.4M⊙ neutron star, yet is also able to support a two-solar-mass neutron star.

Production cross section of neutron-rich calcium isotopes in heavy ion collisions**Supported by National Natural Science Foundation of China (11025524, 11161130520), National Basic Research Program of China (2010CB832903), and the European Commission's 7th Framework Programme (FP7-PEOPLE-2010-IRSES) (269131)

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 isotopes 48Ca and 54Ca are more productive for the neutron-rich system at 30 to 150 MeV/nucleon.

Shell-model study of spin modes in nuclei and nuclear forces

Spin-dependent modes in nuclei are studied by shell-model method with the use of new shell-model Hamiltonians which properly take into account important roles of tensor interactions. New Hamiltonians can describe spin degrees of freedom in nuclei remarkably well. Nuclear weak processes at stellar environments are investigated based on these successes. New neutrino-nucleus reaction cross sections on 12C are applied to light-element synthesis in supernova explosions. The production rate for 11B/7Li is pointed out to be useful to determine v-oscillation parameters, in particular, v-mass hierarchy. New e-capture rates in Ni isotopes are obtained and implications for element synthesis are discussed. The monopole-based universal interaction is applied to study structure of p-sd shell nuclei and 40Ar as well as v-induced reactions on 40Ar. Repulsive corrections in the isospin T=1 monopoles are shown to be important for proper shell evolutions in neutron-rich carbon isotopes. The repulsive correction is pointed out to be due to three-body forces, in particular, the Fujita-Miyazawa force. Roles of the three-body forces on the shell evolution of neutron-rich calcium isotopes, the closed- shell nature of 48 Ca and M1 transition in 48 Ca are studied on top of the two-body G-matrix obtained by including core-polarization effects in larger spaces (≤24ℏω). Effects of the inclusion of g9/2-shell are also discussed.