Nuclear moments of indium isotopes reveal abrupt change at magic number 82.

In spite of the high-density and strongly correlated nature of the atomic nucleus, experimental and theoretical evidence suggests that around particular 'magic' numbers of nucleons, nuclear properties are governed by a single unpaired nucleon1,2. A microscopic understanding of the extent of this behaviour and its evolution in neutron-rich nuclei remains an open question in nuclear physics3-5. The indium isotopes are considered a textbook example of this phenomenon6, in which the constancy of their electromagnetic properties indicated that a single unpaired proton hole can provide the identity of a complex many-nucleon system6,7. Here we present precision laser spectroscopy measurements performed to investigate the validity of this simple single-particle picture. Observation of an abrupt change in the dipole moment at N = 82 indicates that, whereas the single-particle picture indeed dominates at neutron magic number N = 82 (refs. 2,8), it does not for previously studied isotopes. To investigate the microscopic origin of these observations, our work provides a combined effort with developments in two complementary nuclear many-body methods: ab initio valence-space in-medium similarity renormalization group and density functional theory (DFT). We find that the inclusion of time-symmetry-breaking mean fields is essential for a correct description of nuclear magnetic properties, which were previously poorly constrained. These experimental and theoretical findings are key to understanding how seemingly simple single-particle phenomena naturally emerge from complex interactions among protons and neutrons.

Nuclear Charge Radii of the Nickel Isotopes

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_{sat}, which allows an assessment of their accuracy. We find agreement with experiment in differential radii δ⟨r_{c}^{2}⟩ for all employed ab initio methods and interactions, while the absolute radii are consistent with data only for NNLO_{sat}. Within nuclear density functional theory, the Skyrme functional SV-min matches experiment more closely than the Fayans functional Fy(Δr,HFB).

Charge Radius of the Short-Lived

We present the first laser spectroscopic measurement of the neutron-rich nucleus ^{68}Ni at the N=40 subshell closure and extract its nuclear charge radius. Since this is the only short-lived isotope for which the dipole polarizability α_{D} has been measured, the combination of these observables provides a benchmark for nuclear structure theory. We compare them to novel coupled-cluster calculations based on different chiral two- and three-nucleon interactions, for which a strong correlation between the charge radius and dipole polarizability is observed, similar to the stable nucleus ^{48}Ca. Three-particle-three-hole correlations in coupled-cluster theory substantially improve the description of the experimental data, which allows to constrain the neutron radius and neutron skin of ^{68}Ni.

Laser Spectroscopy of Neutron-Rich Tin Isotopes: A Discontinuity in Charge Radii across the N=82 Shell Closure.

The change in mean-square nuclear charge radii δ⟨r^{2}⟩ along the even-A tin isotopic chain ^{108-134}Sn has been investigated by means of collinear laser spectroscopy at ISOLDE/CERN using the atomic transitions 5p^{2} ^{1}S_{0}→5p6 s^{1}P_{1} and 5p^{2} ^{3}P_{0}→5p6s ^{3}P_{1}. With the determination of the charge radius of ^{134}Sn and corrected values for some of the neutron-rich isotopes, the evolution of the charge radii across the N=82 shell closure is established. A clear kink at the doubly magic ^{132}Sn is revealed, similar to what has been observed at N=82 in other isotopic chains with larger proton numbers, and at the N=126 shell closure in doubly magic ^{208}Pb. While most standard nuclear density functional calculations struggle with a consistent explanation of these discontinuities, we demonstrate that a recently developed Fayans energy density functional provides a coherent description of the kinks at both doubly magic nuclei, ^{132}Sn and ^{208}Pb, without sacrificing the overall performance. A multiple correlation analysis leads to the conclusion that both kinks are related to pairing and surface effects.

From Calcium to Cadmium: Testing the Pairing Functional through Charge Radii Measurements of

Differences in mean-square nuclear charge radii of ^{100-130}Cd are extracted from high-resolution collinear laser spectroscopy of the 5s ^{2}S_{1/2}→5p ^{2}P_{3/2} transition of the ion and from the 5s5p ^{3}P_{2}→5s6s ^{3}S_{1} transition in atomic Cd. The radii show a smooth parabolic behavior on top of a linear trend and a regular odd-even staggering across the almost complete sdgh shell. They serve as a first test for a recently established new Fayans functional and show a remarkably good agreement in the trend as well as in the total nuclear charge radius.

Simple Nuclear Structure in (111-129)Cd from Atomic Isomer Shifts.

Isomer shifts have been determined in ^{111-129}Cd by high-resolution laser spectroscopy at CERN-ISOLDE. The corresponding mean square charge-radii changes, from the 1/2^{+} and the 3/2^{+} ground states to the 11/2^{-} isomers, have been found to follow a distinct parabolic dependence as a function of the atomic mass number. Since the isomers have been previously associated with simplicity due to the linear mass dependence of their quadrupole moments, the regularity of the isomer shifts suggests a higher order of symmetry affecting the ground states in addition. A comprehensive description assuming nuclear deformation is found to accurately reproduce the radii differences in conjunction with the known quadrupole moments. This intuitive interpretation is supported by covariant density functional theory.

Isomer Shift and Magnetic Moment of the Long-Lived 1/2

Collinear laser spectroscopy is performed on the _{30}^{79}Zn_{49} isotope at ISOLDE-CERN. The existence of a long-lived isomer with a few hundred milliseconds half-life is confirmed, and the nuclear spins and moments of the ground and isomeric states in ^{79}Zn as well as the isomer shift are measured. From the observed hyperfine structures, spins I=9/2 and I=1/2 are firmly assigned to the ground and isomeric states. The magnetic moment µ (^{79}Zn)=-1.1866(10)µ_{N}, confirms the spin-parity 9/2^{+} with a νg_{9/2}^{-1} shell-model configuration, in excellent agreement with the prediction from large scale shell-model theories. The magnetic moment µ (^{79m}Zn)=-1.0180(12)µ_{N} supports a positive parity for the isomer, with a wave function dominated by a 2h-1p neutron excitation across the N=50 shell gap. The large isomer shift reveals an increase of the intruder isomer mean square charge radius with respect to that of the ground state, δ⟨r_{c}^{2}⟩^{79,79m}=+0.204(6) fm^{2}, providing first evidence of shape coexistence.

Publisher's Note: Isomer Shift and Magnetic Moment of the Long-Lived 1/2

This corrects the article DOI: 10.1103/PhysRevLett.116.182502.

First Evidence of Shape Coexistence in the

The N=48 ^{80}Ge nucleus is studied by means of ß-delayed electron-conversion spectroscopy at ALTO. The radioactive ^{80}Ga beam is produced through the isotope separation on line photofission technique and collected on a movable tape for the measurement of γ and e^{-} emission following ß decay. An electric monopole E0 transition, which points to a 639(1) keV intruder 0_{2}^{+} state, is observed for the first time. This new state is lower than the 2_{1}^{+} level in ^{80}Ge, and provides evidence of shape coexistence close to one of the most neutron-rich doubly magic nuclei discovered so far, ^{78}Ni. This result is compared with theoretical estimates, helping to explain the role of monopole and quadrupole forces in the weakening of the N=50 gap at Z=32. The evolution of intruder 0_{2}^{+} states towards ^{78}Ni is discussed.

Magnetism of an excited self-conjugate nucleus: precise measurement of the g factor of the 2(1)(+) state in (24)Mg.

A precise measurement of the g factor of the first-excited state in the self-conjugate (N=Z) nucleus (24)Mg is performed by a new time-differential recoil-in-vacuum method based on the hyperfine field of hydrogenlike ions. Theory predicts that the g factors of such states, in which protons and neutrons occupy the same orbits, should depart from 0.5 by a few percent due to configuration mixing and meson-exchange effects. The experimental result, g=0.538±0.013, is in excellent agreement with recent shell-model calculations and shows a departure from 0.5 by almost 3 standard deviations, thus achieving, for the first time, the precision and accuracy needed to test theory. Proof of the new method opens the way for wide applications including measurements of the magnetism of excited states of exotic nuclei produced as radioactive beams.

Proton-neutron pairing correlations in the self-conjugate nucleus (38)K probed via a direct measurement of the isomer shift.

A marked difference in the nuclear charge radius was observed between the I^{π}=3^{+} ground state and the I^{π}=0^{+} isomer of ^{38}K and is qualitatively explained using an intuitive picture of proton-neutron pairing. In a high-precision measurement of the isomer shift using bunched-beam collinear laser spectroscopy at CERN-ISOLDE, a change in the mean-square charge radius of ⟨r_{c}^{2}⟩(^{38}K^{m})-⟨r_{c}^{2}⟩(^{38}K^{g})=0.100(6) fm^{2} was obtained. This is an order of magnitude more accurate than the result of a previous indirect measurement from which it was concluded that both long-lived states in ^{38}K have similar charge radii. Our observation leads to a substantially different understanding since the difference in charge radius is, moreover, opposite in sign to previously reported theoretical predictions. It is demonstrated that the observed isomer shift can be reproduced by large-scale shell-model calculations including proton and neutron excitations across the N,Z=20 shell gaps, confirming the significance of cross-shell correlations in the region of ^{40}Ca.

Spins, electromagnetic moments, and isomers of (107-129)Cd.

The neutron-rich isotopes of cadmium up to the N=82 shell closure have been investigated by high-resolution laser spectroscopy. Deep-uv excitation at 214.5 nm and radioactive-beam bunching provided the required experimental sensitivity. Long-lived isomers are observed in (127)Cd and (129)Cd for the first time. One essential feature of the spherical shell model is unambiguously confirmed by a linear increase of the 11/2(-) quadrupole moments. Remarkably, this mechanism is found to act well beyond the h(11/2) shell.

Spins and magnetic moments of 49K and 51K: establishing the 1/2+ and 3/2+ level ordering beyond N = 28.

The ground-state spins and magnetic moments of (49,51)K have been measured using bunched-beam high-resolution collinear laser spectroscopy at ISOLDE CERN. For 49K a ground-state spin I = 1/2 was firmly established. The observed hyperfine structure of 51K requires a spin I > 1/2 and strongly suggests I = 3/2. From its magnetic moment µ(51K) = +0.5129(22)µ(N) a spin-parity I(π) = 3/2+ with a dominant π1d(3/2)(-1) hole configuration was deduced. This establishes for the first time the reinversion of the single-particle levels and illustrates the prominent role of the residual monopole interaction for single-particle levels and shell evolution.

Nuclear charge radii of (21-32)Mg.

Charge radii of all magnesium isotopes in the sd shell have been measured, revealing evolution of the nuclear shape throughout two prominent regions of assumed deformation centered on (24)Mg and (32)Mg. A striking correspondence is found between the nuclear charge radius and the neutron shell structure. The importance of cluster configurations towards N=8 and collectivity near N=20 is discussed in the framework of the fermionic molecular dynamics model. These essential results have been made possible by the first application of laser-induced nuclear orientation for isotope shift measurements.

Nuclear charge radius of 12Be.

The nuclear charge radius of (12)Be was precisely determined using the technique of collinear laser spectroscopy on the 2s(1/2)→2p(1/2,3/2) transition in the Be(+) ion. The mean square charge radius increases from (10)Be to (12)Be by δ(10,12)=0.69(5) fm(2) compared to δ(10,11)=0.49(5) fm(2) for the one-neutron halo isotope ^{11}Be. Calculations in the fermionic molecular dynamics approach show a strong sensitivity of the charge radius to the structure of ^{12}Be. The experimental charge radius is consistent with a breakdown of the N=8 shell closure.

Nuclear spins and moments of Ga isotopes reveal sudden structural changes between N=40 and N=50.

Collinear laser spectroscopy was performed on Ga (Z=31) isotopes at ISOLDE, CERN. A gas-filled linear Paul trap (ISCOOL) was used to extend measurements towards very neutron-rich isotopes (N=36-50). A ground state (g.s.) spin I=1/2 is measured for 73Ga, being near degenerate with a 3/2{-} isomer (75 eV≲E{ex}≲1 keV). The 79Ga g.s., with I=3/2, is dominated by protons in the πf{5/2} orbital and in 81Ga the 5/2{-} level becomes the g.s. The data are compared to shell-model calculations in the f{5/2}pg{9/2} model space, calling for further theoretical developments and new experiments.

Nuclear spins and magnetic moments of 71,73,75Cu: inversion of pi2p3/2 and pi1f5/2 levels in 75Cu.

We report the first confirmation of the predicted inversion between the pi2p3/2 and pi1f5/2 nuclear states in the nu(g)9/2 midshell. This was achieved at the ISOLDE facility, by using a combination of in-source laser spectroscopy and collinear laser spectroscopy on the ground states of 71,73,75Cu, which measured the nuclear spin and magnetic moments. The obtained values are mu(71Cu)=+2.2747(8)mu(N), mu(73Cu)=+1.7426(8)mu(N), and mu(75Cu)=+1.0062(13)mu(N) corresponding to spins I=3/2 for 71,73Cu and I=5/2 for 75Cu. The results are in fair agreement with large-scale shell-model calculations.

Nuclear charge radii of 7,9,10Be and the one-neutron halo nucleus 11Be.

Nuclear charge radii of ;{7,9,10,11}Be have been determined by high-precision laser spectroscopy. On-line measurements were performed with collinear laser spectroscopy in the 2s_{1/2}-->2p_{1/2} transition on a beam of Be+ ions. Collinear and anticollinear laser beams were used simultaneously, and the absolute frequency determination using a frequency comb yielded an accuracy in the isotope-shift measurements of about 1 MHz. Combining this with accurate calculations of the mass-dependent isotope shifts yields nuclear charge radii. The charge radius decreases from 7Be to 10Be and then increases for the halo nucleus 11Be. When comparing our results with predictions of ab initio nuclear-structure calculations we find good agreement. Additionally, the nuclear magnetic moment of 7Be was determined to be -1.3995(5)micro_{N} and that of 11Be was confirmed with an accuracy similar to previous beta-NMR measurements.

Precision measurement of 11Li moments: influence of halo neutrons on the 9Li core.

The electric quadrupole moment and the magnetic moment of the 11Li halo nucleus have been measured with more than an order of magnitude higher precision than before, |Q| = 33.3(5) mb and mu = +3.6712(3)muN, revealing a 8.8(1.5)% increase of the quadrupole moment relative to that of 9Li. This result is compared to various models that aim at describing the halo properties. In the shell model an increased quadrupole moment points to a significant occupation of the 1d orbits, whereas in a simple halo picture this can be explained by relating the quadrupole moments of the proton distribution to the charge radii. Advanced models so far fail to reproduce simultaneously the trends observed in the radii and quadrupole moments of the lithium isotopes.