The ground-state properties of neutron-rich exotic Na and Mg isotopes with even numbers of neutrons, N, are studied up to driplines. The shell-model calculations with an ab initio effective nucleon-nucleon interaction reported in [Tsunoda, Otsuka, Takayanagi et al., Nature 587, 66 (2020)] are extended to observables such as magnetic dipole and electric quadrupole moments, and charge and matter radii. Good agreements with experimental data are found, and predictions are shown up to driplines. A prescription to extract the deformation parameters for the eigenstates of Monte Carlo Shell Model is presented, and the obtained values are used to calculate charge and matter radii. The increase of these radii from the Droplet model is described as the consequences of the varying deformation of the surface and the growing neutron excitations or occupations in the pf shell, consistently with the dripline mechanism presented in the above reference. The neutron skin thickness is shown to be about 0.1 fm for N=20, which can be compared to the value for 208Pb in an A1/3 scaling. The relation of the neutron skin thickness to the electromagnetic moments is discussed for an exotic nucleus, 31Na.
In this work, Na isotopes with mass varying from $A=$ 20 to 31 have been studied using DJ16A, JISP16 and N3LO microscopic effective interactions in the $sd$-shell. These effective interactions are derived for $sd$-shell using no-core shell model wavefunctions and a unitary transformation method. We have also performed calculation with IMSRG effective interactions targeted for a particular nucleus. The studies include a detailed analysis of ground state binding energy, low-lying spectra, and electromagnetic properties such as reduced electric quadrupole transition strengths, quadrupole and magn…
Systematic trends in nuclear charge radii are of great interest due to universal shell effects and odd-even staggering (OES). The modified root mean square (rms) charge radius formula, which phenomenologically accounts for the formation of neutron-proton ($np$) correlations, is here applied for the first time to the study of odd-$Z$ copper and indium isotopes. Theoretical results obtained by the relativistic mean field (RMF) model with NL3, PK1 and NL3$^{*}$ parameter sets are compared with experimental data. Our results show that both OES and the abrupt changes across $N=50$ and $82$ shell cl…
Collinear laser spectroscopy is performed on the nickel isotopes $^{58-68,70}$Ni, using a time-resolved photon counting system. From the measured isotope shifts, nuclear charge radii $R_c$ are extracted and compared to theoretical results. Three ab initio approaches all employ, among others, the chiral interaction NNLO$_{\rm sat}$, which allows an assessment of their accuracy. We find agreement with experiment in differential radii $δ\left\langle r_\mathrm{c}^2 \right\rangle$ for all employed ab initio methods and interactions, while the absolute radii are consistent with data only for NNLO$_{…
The accuracy of atomic theory calculations limits the extraction of nuclear charge radii from isotope shift measurements of odd-proton nuclei. For Na isotopes, though precise spectroscopic measurements have existed since more than half a century, calculations by different methods offer a wide range of values. Here, we present accurate atomic calculations to reliably extract the Na charge radii. By combining experimental matter radii with nuclear coupled-cluster calculations based on nucleon-nucleon and three-nucleon forces, we constrain the parameters obtained from the atomic calculations. The…
Quadrupole moments and charge radii in cadmium isotopes are studied from a microscopic perspective. The results obtained from self-consistent deformed Hartree-Fock+BCS calculations with Skyrme forces are compared with isomer and isotope shifts measured from high resolution laser spectroscopy experiments. The microscopic calculations reproduce fairly well the main features observed in those isotopes that include the linear increase with the neutron number of the quadrupole moments of the 11/2- isomers, as well as the parabolic behavior of the mean-square charge radii difference between isomers …
Nuclear charge radii of $^{55,56}$Ni were measured by collinear laser spectroscopy. The obtained information completes the behavior of the charge radii at the shell closure of the doubly magic nucleus $^{56}$Ni. The trend of charge radii across the shell closures in calcium and nickel is surprisingly similar despite the fact that the $^{56}$Ni core is supposed to be much softer than the $^{48}$Ca core. The very low magnetic moment $μ(^{55}\mathrm{Ni})=-1.108(20)\,μ_N$ indicates the impact of M1 excitations between spin-orbit partners across the $N,Z=28$ shell gaps. Our charge-radii results are…
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…
The mesoscopic nature of the atomic nucleus gives rise to a wide array of macroscopic and microscopic phenomena. The size of the nucleus is a window into this duality: while the charge radii globally scale as $A^{1/3}$, their evolution across isotopic chains reveals unanticipated structural phenomena [1-3]. The most ubiquitous of these is perhaps the Odd-Even Staggering (OES) [4]: isotopes with an odd number of neutrons are usually smaller in size than the trend of their even-neutron neighbours suggests. This OES effect varies with the number of protons and neutrons and poses a significant cha…
A feed-forward neural network model is trained to calculate the nuclear charge radii. The model trained with input data set of proton and neutron number $Z,N$, the electric quadrupole transition strength $B(E2)$ from the first excited 2$^+$ state to the ground state, together with the symmetry energy. The model reproduces well not only the isotope dependence of charge radii, but also the kinks of charge radii at the neutron magic numbers $N=82$ for Sn and Sm isotopes, and also $N=126$ for Pb isotopes. The important role of $B(E2)$ value is pointed out to reproduce the kink of the isotope depen…
We compute the charge radii of even-mass neon and magnesium isotopes from neutron number N = 8 to the dripline. Our calculations are based on nucleon-nucleon and three-nucleon potentials from chiral effective field theory that include delta isobars. These potentials yield an accurate saturation point and symmetry energy of nuclear matter. We use the coupled-cluster method and start from an axially symmetric reference state. Binding energies and two-neutron separation energies largely agree with data and the dripline in neon is accurate. The computed charge radii have an estimated uncertainty o…
We present the first ab initio calculations for open-shell nuclei past the tin isotopic line, focusing on Xe isotopes as well as doubly-magic Sn isotopes. We show that, even for moderately hard interactions, it is possible to obtain meaningful predictions and that the NNLOsat chiral interaction predicts radii and charge density distributions close to the experiment. We then make a new prediction for ${}^{100}$Sn. This paves the way for ab initio studies of exotic charge density distributions at the limit of the present ab initio mass domain, where experimental data is becoming available. The p…
Benchmarking ANN extrapolations of the ground-state energies and radii of Li isotopes
Technische Universität Darmstadt（达姆施塔特工业大学）；Iowa State University（爱荷华州立大学）；Helmholtz Forschungsakademie Hessen für FAIR, GSI Helmholtzzentrum（黑森亥姆霍兹FAIR研究中心，GSI亥姆霍兹重离子研究中心）
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 study the effects of short- and long-range correlations on the charge radii of Ca isotopes. We start our investigation with an independent particle model consisting in Hartree-Fock plus Bardeen-Cooper-Schrieffer calculations with finite-range effective nucleon-nucleon interactions of Gogny type. The short-range correlations effects are evaluated by considering all the terms of a cluster expansion containing a single correlation line. The long-range correlations are taken into account by including the coupling with the quasi-particle random phase approximation phonons. While the effects of t…
We apply the recently proposed RMF(BCS)* ansatz to study the charge radii of the potassium isotopic chain up to $^{52}$K. It is shown that the experimental data can be reproduced rather well, qualitatively similar to the Fayans nuclear density functional theory, but with a slightly better description of the odd-even staggerings (OES). Nonetheless, both methods fail for $^{50}$K and to a lesser extent for $^{48,52}$K. It is shown that if these nuclei are deformed with a $β_{20}\approx-0.2$, then one can obtain results consistent with experiments for both charge radii and spin-parities. We argue…
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）
Electronic factors for the field and mass isotope shifts in the $6p\ ^{2}P_{3/2} \to 7s\ ^{2}S_{1/2}$ (535 nm), $6p\ ^{2}P_{1/2} \to 6d\ ^{2}D_{3/2}$ (277 nm) and $6p\ ^{2}P_{1/2} \to 7s\ ^{2}S_{1/2}$ (378~nm) transitions in the neutral thallium were calculated within the high-order relativistic coupled cluster approach. These factors were used to reinterpret previous experimental isotope shift measurements in terms of charge radii of a wide range of Tl isotopes. Good agreement between theoretical and experimental King-plot parameters was found for the $6p\ ^{2}P_{3/2} \to 7s\ ^{2}S_{1/2}$ and…
Combining laser spectroscopy in a Versatile Arc Discharge and Laser Ion Source, with Penning-trap mass spectrometry at the CERN-ISOLDE facility, this work reports on mean-square charge radii of neutron-rich mercury isotopes across the $N = 126$ shell closure, the electromagnetic moments of $^{207}$Hg and more precise mass values of $^{206-208}$Hg. The odd-even staggering (OES) of the mean square charge radii and the kink at $N = 126$ are analyzed within the framework of covariant density functional theory (CDFT), with comparisons between different functionals to investigate the dependence of t…
Nuclear charge radii of aluminium isotopes at the proton drip line
Massachusetts Institute of Technology（麻省理工学院）；Texas A&M University（德克萨斯农工大学）；Michigan State University（密歇根州立大学）；Université Paris-Saclay（巴黎萨克雷大学）；Gaziantep Islam Science and Technology University（加济安泰普伊斯兰科学与技术大学）
