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Register a new userMeasurement and microscopic description of odd-even staggering of charge radii of exotic copper isotopes
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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 challenge for nuclear theory [5-7]. Here, we examine this problem with new measurements of the charge radii of short-lived copper isotopes up to the very exotic $^{78}$Cu $(Z=29, N=49)$, produced at only 20 ions/s, using the highly-sensitive Collinear Resonance Ionisation Spectroscopy (CRIS) method at ISOLDE-CERN. Due to the presence of a single proton outside of the closed Z=28 shell, these measurements provide crucial insights into the single-particle proton structure and how this affects the charge radii. We observe an unexpected reduction in the OES for isotopes approaching the $N=50$ shell gap. To describe the data, we applied models based on nuclear Density Functional Theory [2,8] (DFT) and ab-initio Valence-Space In-Medium Similarity Renormalization Group (VS-IMSRG) theory [9,10]. Through these comparisons, we demonstrate a relation between the global behavior 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 due to the odd neutron, naturally emerge from the VS-IMSRG calculations.
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A unified theoretical model reproducing charge radii of known atomic nuclei plays an essential role to make extrapolations in the regions of unknown nuclear size. Recently developed new ansatz which phenomenally takes into account the neutron-proton short-range correlations (np-SRCs) can describe the discontinuity properties and odd-even staggering (OES) effect of charge radii along isotopic chains remarkably well. In this work, we further review the modified rms charge radii formula in the framework of relativistic mean field (RMF) theory. The charge radii are calculated along various isotopic chains that include the nuclei featuring the $N=50$ and $82$ magic shells. Our results suggest that RMF with and without considering correction term give almost similar trend of nuclear size for some isotopic chains with open proton shell, especially the shrink phenomena of charge radii at strong neutron closed shells and the OES behaviors. This suggests that the np-SRCs has almost no influence for some nuclei due to the strong coupling between different levels around Fermi surface. The weakening OES behavior of nuclear charge radii is observed generally at completely filled neutron shells and this may be proposed as a signature of magic indicator.
The mean-square charge radii of $^{207,208}$Hg ($Z=80, N=127,128$) have been studied for the first time and those of $^{202,203,206}$Hg ($N=122,123,126$) remeasured by the application of in-source resonance-ionization laser spectroscopy at ISOLDE (CERN). The characteristic textit{kink} in the charge radii at the $N=126$ neutron shell closure has been revealed, providing the first information on its behavior below the $Z=82$ proton shell closure. A theoretical analysis has been performed within relativistic Hartree-Bogoliubov and non-relativistic Hartree-Fock-Bogoliubov approaches, considering both the new mercury results and existing lead data. Contrary to previous interpretations, it is demonstrated that both the kink at $N=126$ and the odd-even staggering (OES) in its vicinity can be described predominately at the mean-field level, and that pairing does not need to play a crucial role in their origin. A new OES mechanism is suggested, related to the staggering in the occupation of the different neutron orbitals in odd- and even-$A$ nuclei, facilitated by particle-vibration coupling for odd-$A$ nuclei.
Nuclear charge radii are sensitive probes of different aspects of the nucleon-nucleon interaction and the bulk properties of nuclear matter; thus, they provide a stringent test and challenge for nuclear theory. The calcium region has been of particular interest, as experimental evidence has suggested a new magic number at $N = 32$ [1-3], while 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 $beta$-decay detection, we were able to extend the charge radii measurement of potassium ($Z =19$) isotopes up to the exotic $^{52}$K ($t_{1/2}$ = 110 ms), produced in minute quantities. Our work provides the first charge radii measurement beyond $N = 32$ in the region, revealing no signature of the magic character at this neutron number. The results are interpreted with two state-of-the-art nuclear theories. For the first time, a long sequence of isotopes could be calculated with coupled-cluster calculations based on newly developed nuclear interactions. The strong increase in the charge radii beyond $N = 28$ is not well captured by these calculations, but is well reproduced by Fayans nuclear density functional theory, which, however, overestimates the odd-even staggering effect. These findings highlight our limited understanding on the nuclear size of neutron-rich systems, and expose pressing problems that are present in some of the best current models of nuclear theory.
The systematic trend in charge radii along isotopic chain is of great interest due to its distinctive aspect at the nucleon-shell closure and the odd-even staggering (OES) behavior. In this work, the modified root mean square (rms) charge radius formula to phenomenally account for the formation of neutron-proton short-range correlations (np-SRCs) is firstly extended to study the heavier odd-$Z$ copper and indium isotopic chains. The parabolic-like shape of rms charge radii can be remarkably reproduced between two strong closure shells. In addition, the OES and abrupt changes in the slope of the rms charge radii across $N=50$ and $82$ shell closure are also identified evidently, but the odd-even oscillation is slightly overestimated for cooper isotopes. This means the np-SRCs play an indispensable role to determine the fine structures of nuclear charge radii along isotopic chain quantitatively.
We present the mass excesses of 52-57Sc, obtained from recent time-of-flight nuclear mass measurements at the National Superconducting Cyclotron Laboratory at Michigan State University. The masses of 56Sc and 57Sc were determined for the first time with atomic mass excesses of -24.85(59)(+0 -54) MeV and -21.0(1.3) MeV, respectively, where the asymmetric uncertainty for 56Sc was included due to possible contamination from a long-lived isomer. The 56Sc mass indicates a small odd-even mass staggering in the A = 56 mass-chain towards the neutron drip line, significantly deviating from trends predicted by the global FRDM mass model and favoring trends predicted by the UNEDF0 and UNEDF1 density functional calculations. Together with new shell-model calculations of the electron-capture strength function of 56Sc, our results strongly reduce uncertainties in model calculations of the heating and cooling at the 56Ti electron-capture layer in the outer crust of accreting neutron stars. We found that, in contrast to previous studies, neither strong neutrino cooling nor strong heating occurs in this layer. We conclude that Urca cooling in the outer crusts of accreting neutron stars that exhibit superbursts or high temperature steady-state burning, which are predicted to be rich in A=56 nuclei, is considerably weaker than predicted. Urca cooling must instead be dominated by electron capture on the small amounts of adjacent odd-A nuclei contained in the superburst and high temperature steady-state burning ashes. This may explain the absence of strong crust Urca cooling inferred from the observed cooling light curve of the transiently accreting x-ray source MAXI J0556-332.
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