Laser Spectroscopy of Neutron-Rich ${}^{207,208}\mathrm{Hg}$ Isotopes: Illuminating the Kink and Odd-Even Staggering in Charge Radii across the $N=126$ Shell Closure

The mean-square charge radii of ${}^{207,208}\mathrm{Hg}$ ($Z=80$, $N=127$, 128) have been studied for the first time and those of ${}^{202,203,206}\mathrm{Hg}$ ($N=122$, 123, 126) remeasured by the application of in-source resonance-ionization laser spectroscopy at ISOLDE (CERN). The characteristic 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 nonrelativistic 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.

Figure 1

Systematics of the difference in mercury ground state (g.s.) and isomer mean-square charge radii. Data from the present Letter are shown by red symbols; earlier data are taken from Refs. [16] (black) and [17] (blue). The inset highlights the kink at $N=126$ and the neighboring OES in both the mercury and lead [18] isotopic chains. The lead isotopes are arbitrarily displaced from those of mercury for clarity. The dashed lines through $N=124$ and 126 in the inset are added to highlight the kinks. Statistical uncertainties are smaller than the data points.

Figure 2

Sample hyperfine spectra for ${}^{206–208}\mathrm{Hg}$, with the photoion rate measured using the MR-ToF MS. The centroids are indicated with black lines; red lines represent fitting with Voigt profiles.

Figure 3

Panels (a) and (b) show $\delta ⟨r^2{⟩}^{A,A^{\prime }}$ of lead and mercury isotopes relative to ${}^{208}\mathrm{Pb}$ and ${}^{206}\mathrm{Hg}$ ($N=126$), respectively. Experimental mercury data: this Letter and Ref. [16]. Experimental lead data: Ref. [18]. The statistical uncertainties are smaller than the data points. RHB(DD-ME2) results: this Letter. NR-HFB(M3Y-P6a) results: this Letter (mercury) and Ref. [14] (lead). NR-HFB(UNEDF1) results: Ref. [35].

Figure 4

Comparison of experimental and theoretical $\mathrm{\Delta }{R}^{(3)}(A)$ and $\mathrm{\Delta }⟨r^2{⟩}^{(3)}(A)$ values for isotopes of lead (a) and (c), respectively and mercury (b) and (d), respectively. Experimental values are taken from this Letter and from Ref. [16] (mercury) and Ref. [18] (lead). The RHB (DD-ME2) and NR-HFB (M3Y-P6a) results are obtained in this Letter, and the NR-HFB results with $\mathrm{Fy}(\mathrm{\Delta }r)$ and UNEDF1 are taken from Refs. [8, 35], respectively. Experimental uncertainty is depicted as translucent gray bars in (a) and (b), and as error bars in (c) and (d).

Figure 5

Comparison of experimental and theoretical $\mathrm{\Delta }⟨r^2{⟩}^{(3)}(A)$ values for lead isotopes. Experimental data are from Ref. [18]; theoretical results are from this Letter. See text for details.