Probing Nuclear Interactions Through Isotope Shift Spectroscopy of Mercury

Abstract

We present precision isotope shift spectroscopy of the $\mathrm{6s^{2}}\, {}^{1}\mathrm{S}_{0}{\rightarrow\,}\mathrm{6s\, 6p}\, {}^{3}\mathrm{P}_{1}$ intercombination line and the $\mathrm{6s\,6p}\, {}^{3}\mathrm{P}_{1}{\rightarrow\,}\mathrm{6s\,6d}\, {}^{3}\mathrm{D}_{J}$ ($J=1,2$) transitions in neutral mercury, performed on the five naturally abundant even isotopes, including the low-abundant isotope ${}^{196}\mathrm{Hg}$. Using laser-cooled atoms in a magneto-optical trap, we achieve uncertainties down to $20\,\mathrm{kHz}$, resolving the isotope shift to a fractional uncertainty of ${\sim}\,2{\,\times\,}10^{-6}$. A King plot analysis comparing our ${}^{1}\mathrm{S}_{0}{\rightarrow}{}^{3}\mathrm{P}_{1}$ data to previous results on the $\mathrm{6s\,6p}\,{}^{3}\mathrm{P}_{2}{\rightarrow\,}\mathrm{6s\,7s}\,{}^{3}\mathrm{S}_{1}$ line reveals a nonlinearity with $4.9\,σ$ significance. Our generalized King plot nonlinear decomposition analysis discusses potential contributions from quadratic ($\propto δ\langle r^{2}\rangle^{2}$) and higher order field shifts ($\propto δ\langle r^{4}\rangle$) also induced by nuclear deformation. These measurements yield new insights into the structure of the $\mathrm{Hg}$ nucleus and provide benchmarks for nuclear-structure models. They further establish mercury as a potential platform to search for hypothetical Yukawa-type boson-mediated forces coupling electrons to neutrons.

Figures (4)

• Figure 1: (a) Level scheme of relevant for ISS within this work (natural linewidths given in brackets). (b) Experimental setup for spectroscopy of the ${}^{1}\mathrm{S}_{0}{{\rightarrow}}{}^{3}\mathrm{P}_{1}$ intercombination line at 253.7nm and the ${}^{3}\mathrm{P}_{1}{{\rightarrow}}{}^{3}\mathrm{D}_{J}$ lines at 313.2nm ($J=1$) and 312.7nm ($J=2$). Atoms are cooled in a at 253.7nm. For resolving the ${}^{1}\mathrm{S}_{0}{{\rightarrow}}{}^{3}\mathrm{P}_{1}$ line, atoms are probed in free fall via absorption imaging at 253.7nm. The light is vertically polarized via a PBS, propagates in the $xy$-plane and is imaged on a UV-sensitive CCD sensor via a single objective lens (L). For resolving the ${}^{3}\mathrm{P}_{1}{{\rightarrow}}{}^{3}\mathrm{D}_{J}$ lines, vertically polarized light at 313nm depletes the atom number via optical pumping and subsequent decay to $\mathrm{{}^3P_{0,2}}$ and $\mathrm{{}^1P_1}$ (gray, dashed lines). Atom numbers within the are then determined by fluorescence imaging at 253.7nm.
• Figure 2: Exemplary spectroscopy data on the (a) ${}^{1}\mathrm{S}_{0}{{\rightarrow}}{}^{3}\mathrm{P}_{1}$ ([200]Hg) and (b) ${}^{3}\mathrm{P}_{1}{{\rightarrow}}{}^{3}\mathrm{D}_{1}$ ([202]Hg) transitions in . Atom numbers $N$ and fluorescence counts $n_\text{fluo}$ extracted from images (see inset); the error bars include all systematic shifts and uncertainties. The ${}^{1}\mathrm{S}_{0}{{\rightarrow}}{}^{3}\mathrm{P}_{1}$ fit model takes into account the asymmetry induced by the recoil shift of scattered probe beam photons. Minor residual deviations arise from a simplified steady-state optical Bloch solution neglecting Doppler broadening, which does not affect the line center. Dashed vertical lines mark the extracted atomic resonances.
• Figure 3: Two-dimensional KP analysis of the mass-normalized IS $\overline{\delta\nu}_i{}^{A-A'} = \delta\nu_i^{A-A'} / \mu^{A-A'}\space$ with isotope pairs $A'=A+2$, revealing a $4.9\sigma$ nonlinearity in the ${}^{1}\mathrm{S}_{0}{{\rightarrow}}{}^{3}\mathrm{P}_{1} \rightleftharpoons {}^{3}\mathrm{P}_{2}{{\rightarrow}}{}^{3}\mathrm{S}_{1}$ comparison. Residuals are orthogonal distances to the linear fit.
• Figure 4: GKP nonlinear decomposition analysis of the mass-normalized IS vectors $\boldsymbol{\overline{\delta\nu}_i}$ projected via $\left(F_{ij},\, K_{ij},\, \lambda_+,\, \lambda_- \right) = \left(\boldsymbol{\overline{\delta\nu}}_j \;\; \boldsymbol{\mathbb{1}} \;\; \boldsymbol{\Lambda}_+ \;\; \boldsymbol{\Lambda}_- \right)^{-1} \cdot\, \boldsymbol{\overline{\delta\nu}}_j$ via of reference line $j = {}^{1}\mathrm{S}_{0}{{\rightarrow}}{}^{3}\mathrm{P}_{1}$ and vectors $\boldsymbol{\Lambda}_\pm$ given by Eq. \ref{['eq:projection_vectors']}. Higher order nuclear and physics contribution vectors, $\boldsymbol{\delta\eta}_{(\kappa)}$, show characteristic nonlinearity patterns that form lines through the origin with slopes $\lambda_- / \lambda_+ =$ -3.418(28) for $\propto \delta\langle r^2 \rangle^2$Angeli2013, -3.0(69) for $\propto {\delta\langle r^4 \rangle}$Shang2024, 1.061(15) for $\propto {\delta (\Delta E_\mathrm{tran, ND})}$ from highly-charged ion calculations Sun2024, -2.2542(5) for 2nd-order $\propto {\delta(1/m^2)}$Shang2024 and -2.3227(7) for -coupling to a new boson $\propto (A - Z)$. The $1\sigma$ uncertainty bands (shaded) are partially within the linewidth and omitted for $\propto {\delta\langle r^4 \rangle}$ to improve visibility.