Abstract
Nuclear charge radii are sensitive probes of different aspects of the nucleon–nucleon interaction and the bulk properties of nuclear matter, providing a stringent test and challenge for ...nuclear theory. Experimental evidence suggested a new magic neutron number at
N
= 32 (refs.
1–3
) in the calcium region, whereas the unexpectedly large increases in the charge radii
4,5
open new questions about the evolution of nuclear size in neutron-rich systems. By combining the collinear resonance ionization spectroscopy method with β-decay detection, we were able to extend charge radii measurements of potassium isotopes beyond
N
= 32. Here we provide a charge radius measurement of
52
K. It does not show a signature of magic behaviour at
N
= 32 in potassium. The results are interpreted with two state-of-the-art nuclear theories. The coupled cluster theory reproduces the odd–even variations in charge radii but not the notable increase beyond
N
= 28. This rise is well captured by Fayans nuclear density functional theory, which, however, overestimates the odd–even staggering effect in charge radii. These findings highlight our limited understanding of the nuclear size of neutron-rich systems, and expose problems that are present in some of the best current models of nuclear theory.
Abstract
Nuclear charge radii globally scale with atomic mass number
A
as
A
1∕3
, and isotopes with an odd number of neutrons are usually slightly smaller in size than their even-neutron neighbours. ...This odd–even staggering, ubiquitous throughout the nuclear landscape
1
, varies with the number of protons and neutrons, and poses a substantial challenge for nuclear theory
2–4
. Here, we report measurements of the charge radii of short-lived copper isotopes up to the very exotic
78
Cu (with proton number
Z
= 29 and neutron number
N
= 49), produced at only 20 ions s
–1
, using the collinear resonance ionization spectroscopy method at the Isotope Mass Separator On-Line Device facility (ISOLDE) at CERN. We observe an unexpected reduction in the odd–even staggering for isotopes approaching the
N
= 50 shell gap. To describe the data, we applied models based on nuclear density functional theory
5,6
and
A
-body valence-space in-medium similarity renormalization group theory
7,8
. Through these comparisons, we demonstrate a relation between the global behaviour of charge radii and the saturation density of nuclear matter, and show that the local charge radii variations, which reflect the many-body polarization effects, naturally emerge from
A
-body calculations fitted to properties of
A
≤ 4 nuclei.
Molecular spectroscopy offers opportunities for the exploration of the fundamental laws of nature and the search for new particle physics beyond the standard model
. Radioactive molecules-in which ...one or more of the atoms possesses a radioactive nucleus-can contain heavy and deformed nuclei, offering high sensitivity for investigating parity- and time-reversal-violation effects
. Radium monofluoride, RaF, is of particular interest because it is predicted to have an electronic structure appropriate for laser cooling
, thus paving the way for its use in high-precision spectroscopic studies. Furthermore, the effects of symmetry-violating nuclear moments are strongly enhanced
in molecules containing octupole-deformed radium isotopes
. However, the study of RaF has been impeded by the lack of stable isotopes of radium. Here we present an experimental approach to studying short-lived radioactive molecules, which allows us to measure molecules with lifetimes of just tens of milliseconds. Energetically low-lying electronic states were measured for different isotopically pure RaF molecules using collinear resonance ionisation at the ISOLDE ion-beam facility at CERN. Our results provide evidence of the existence of a suitable laser-cooling scheme for these molecules and represent a key step towards high-precision studies in these systems. Our findings will enable further studies of short-lived radioactive molecules for fundamental physics research.
In rare cases, the removal of a single proton (Z) or neutron (N) from an atomic nucleus leads to a dramatic shape change. These instances are crucial for understanding the components of the nuclear ...interactions that drive deformation. The mercury isotopes (Z = 80) are a striking example1,2: their close neighbours, the lead isotopes (Z = 82), are spherical and steadily shrink with decreasing N. The even-mass (A = N + Z) mercury isotopes follow this trend. The odd-mass mercury isotopes 181,183,185Hg, however, exhibit noticeably larger charge radii. Due to the experimental difficulties of probing extremely neutron-deficient systems, and the computational complexity of modelling such heavy nuclides, the microscopic origin of this unique shape staggering has remained unclear. Here, by applying resonance ionization spectroscopy, mass spectrometry and nuclear spectroscopy as far as 177Hg, we determine 181Hg as the shape-staggering endpoint. By combining our experimental measurements with Monte Carlo shell model calculations, we conclude that this phenomenon results from the interplay between monopole and quadrupole interactions driving a quantum phase transition, for which we identify the participating orbitals. Although shape staggering in the mercury isotopes is a unique and localized feature in the nuclear chart, it nicely illustrates the concurrence of single-particle and collective degrees of freedom at play in atomic nuclei.
Over three and a half decades of collinear laser spectroscopy and the COLLAPS setup have played a major role in the ISOLDE physics programme. Based on a general experimental principle and diverse ...approaches towards higher sensitivity, it has provided unique access to basic nuclear properties such as spins, magnetic moments and electric quadrupole moments as well as isotopic variations of nuclear mean square charge radii. While previous methods of outstanding sensitivity were restricted to selected chemical elements with special atomic properties or nuclear decay modes, recent developments have yielded a breakthrough in sensitivity for nuclides in wide mass ranges. These developments include the use of bunched beams from the radiofrequency quadrupole cooler-buncher ISCOOL, which allows a suppression of background by several orders of magnitude. Very recently, the combination of collinear laser spectroscopy with the principle of laser resonance ionisation took shape in the new CRIS setup, providing a very selective and efficient detection of optical resonance. We outline the basic experimental developments and discuss important results on nuclei or chains of isotopes in different mass ranges.
With increasing demand for accurate calculation of isotope shifts of atomic systems for fundamental and nuclear structure research, an analytic energy derivative approach is presented in the ...relativistic coupled-cluster (CC) theory framework to determine the atomic field shift and mass shift (MS) factors. This approach allows the determination of expectation values of atomic operators, overcoming fundamental problems that are present in existing atomic physics methods, i.e. it satisfies the Hellmann-Feynman theorem, does not involve any non-terminating series, and is free from choice of any perturbative parameter. As a proof of concept, the developed analytic response relativistic CC theory has been applied to determine MS and field shift factors for different atomic states of indium. High-precision isotope-shift measurements of 104 − 127 In were performed in the 246.8 nm (5p 2P3/2 → 9s 2S1/2) and 246.0 nm (5p 2P1/2 → 8s 2S1/2) transitions to test our theoretical results. An excellent agreement between the theoretical and measured values is found, which is known to be challenging in multi-electron atoms. The calculated atomic factors allowed an accurate determination of the nuclear charge radii of the ground and isomeric states of the 104 − 127 In isotopes, providing an isotone-independent comparison of the absolute charge radii.
Collinear laser spectroscopy measurements were performed on 68−74Ge isotopes (Z=32) at ISOLDE-CERN, by probing the 4s24p2P13→4s24p5sP1o3 atomic transition (269 nm) of germanium. Nuclear charge radii ...are determined via the measured isotope shifts, revealing a larger local variation than the neighboring isotopic chains. Nuclear density functional theory with the Fayans functionals Fy(Δr,HFB) and Fy(IVP), and the SV-min Skyrme describes the experimental data for the differential charge radii δ〈r2〉 and charge radii Rc within the theoretical uncertainties. The observed large variation in the charge radii of germanium isotopes is better accounted for by theoretical models incorporating ground state quadrupole correlations. This suggests that the polarization effects due to pairing and deformation contribute to the observed large odd-even staggering in the charge radii of the Ge isotopic chain.
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 ofthese 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.
Collinear laser spectroscopy was performed on Zn (Z=30) isotopes at ISOLDE, CERN. The study of hyperfine spectra of nuclei across the Zn isotopic chain, N=33–49, allowed the measurement of nuclear ...spins for the ground and isomeric states in odd-A neutron-rich nuclei up to N=50. Exactly one long-lived (>10 ms) isomeric state has been established in each 69–79Zn isotope. The nuclear magnetic dipole moments and spectroscopic quadrupole moments are well reproduced by large-scale shell–model calculations in the f5pg9 and fpg9d5 model spaces, thus establishing the dominant term in their wave function. The magnetic moment of the intruder Iπ=1/2+ isomer in 79Zn is reproduced only if the νs1/2 orbital is added to the valence space, as realized in the recently developed PFSDG-U interaction. The spin and moments of the low-lying isomeric state in 73Zn suggest a strong onset of deformation at N=43, while the progression towards 79Zn points to the stability of the Z=28 and N=50 shell gaps, supporting the magicity of 78Ni.
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