Shape coexistence in ${}^{187}\mathrm{Au}$ studied by laser spectroscopy

Hyperfine-structure parameters and isotope shift of the $9/2^{-}$ isomeric state in ${}^{187}\mathrm{Au}$ relative to ${}^{197}\mathrm{Au}$ for the 267.6-nm atomic transition have been measured for the first time using the in-source resonance-ionization spectroscopy technique. The magnetic dipole moment and change in the mean-square charge radius for this $9/2^{-}$ isomer have been deduced. The observed large isomer shift relative to the $1/2^{+}$ ground state in ${}^{187}\mathrm{Au}$ confirms the occurrence of the shape coexistence in ${}^{187}\mathrm{Au}$ proposed earlier from the analysis of the nuclear spectroscopic data and particle plus triaxial rotor calculations. The analysis of the magnetic moment supports the previously proposed $9/2^{-}$, $1/2^{-}\left[541\right]$ assignment at moderate prolate deformation for ${}^{187}\mathrm{Au}^m$.

Figure 1

(a) An example of a typical summed time-of-flight (ToF) spectrum for ${}^{187}\mathrm{Au}^m$ and ${}^{187}\mathrm{Tl}$ recorded during hfs measurements and used to establish the proper ToF gate window (red box). (b) The temporal drifts as observed in the ToF spectrum during the hfs scan. (c) Summed counts as a function of the wave number, considering the whole ToF window (“nongated”) or only the ToF gate (“gated”) indicated with a red box in panel (b).

Figure 2

An hfs spectrum of ${}^{187}\mathrm{Au}^m$ recorded using the MR-ToF MS (black squares). The solid line depicts the Voigt-profile fit to the data. The zero point on the frequency scale corresponds to a wave number of 37 358.90 ${\mathrm{cm}}^{-1}$. The hfs-level scheme for ${}^{187}\mathrm{Au}^m$ is shown in the middle of the figure.

Figure 3

Changes in the mean-square charge radii for gold isotopes relative to ${}^{197}\mathrm{Au}$. Open circle, present paper; squares, Refs. [6, 7, 8, 9]. The dashed lines show the droplet model predictions with constant deformation.

Figure 4

Magnetic moments of the $9/2^{-}$ ($\pi h_{9/2}$) states in bismuth [37, 38], thallium [33, 34, 39, 40, 41], and gold (present paper) isotopes.

Figure 5

A comparison of the experimental $g$ factors (hollow squares) with those calculated using Eqs. (8)–(10) (filled triangles), at $g_R=Z/A$, $g_s=0.8g_{s,\mathrm{free}}$, $g_K(1/2^{-}\left[541\right])=0.84$, and the experimental values of the decoupling parameter $a_{\mathrm{dec}}^{\mathrm{eff}}$. The dotted line shows the Schmidt value for the $\pi h_{9/2}$ state. The dashed line represents the $g$ factor for semimagic ${}^{209}\mathrm{Bi}$ ($I^{\pi }=9/2^{-}$).