Nuclear Charge Radii of Th229 from Isotope and Isomer Shifts

Abstract

The isotope 229 Th is unique in that it possesses an isomeric state of only a few eV above the ground state, suitable for nuclear laser excitation. An optical clock based on this transition is expected to be a very sensitive probe for variations of fundamental constants, but the nuclear properties of both states have to be determined precisely to derive the actual sensitivity. We carry out isotope shift calculations in Th + and Th 2+ including the specific mass shift, using a combination of configuration interaction and all-order linearized coupled-cluster methods and estimate the uncertainty of this approach. We perform experimental measurements of the hyperfine structure of Th 2+ and isotopic shift between 229 Th 2+ and 232 Th 2+ to extract the difference in root-mean-square radii as δ r 2 232,229 = 0.299(15) fm 2 . Using the recently measured values of the isomer shift of lines of 229m Th, we derive the value for the mean-square radius change between 229 Th and its low lying isomer to be 229m Th δ r 2 229m,229 = 0.0105(13) fm 2 .

The $$^{229}$$Th isomer: prospects for a nuclear optical clock

“…This value is of high importance for the determination of the sensitivity of a nuclear clock for time variations of fundamental constants [19]. For this reason the experimental data were analyzed in more detail in [304], resulting in a value of 0.0105(13) fm 2 . Direct laser cooling and trapping of 229 Th 3+ ions, as required for the development of a single-ion nuclear clock, has already been accomplished in 2011 [57].…”

“…In 2018 an experimental determination of the nuclear charge radius and electric quadrupole moments of 229m Th was achieved [344]. Although the precision of this measurement did not allow for an immediate determination of the sensitivity to variations in α [304], recently a value for the sensitivity factor of k = −(0.9 ± 0.3) • 10 4 was obtained under the additional assumption of an identical charge density of the ground and the isomeric state [87].…”

“…4.1 for details), as the uncertainties of the hyperfine constants were still too large. The mean-square charge-radii of the ground-and isomeric states was investigated in finer detail in [304], leading to a value of 0.0105(13) fm 2 . Using the additional assumption of identical nuclear charge density for the ground and isomeric state, a sensitivity factor of −(0.9 ± 0.3) • 10 4 was obtained in [87].…”

Laser Spectroscopy of the y$^7$P$_J^{\circ}$ states of Cr I

“…Second, these measurements provide a high-precision benchmark for the first application of the configuration interaction (CI) and the linearized coupled cluster method (CI+all-order method) for a system with 6 valence electrons. The CI+all-order method was demonstrated to produce accurate results for a wide range of atomic properties for atoms and ions with 2 to 4 valence electrons [19][20][21][22]. This method has provided precision data for many applications, including development of ultra-precise clocks [19,21,23], studies of fundamental symmetries [24,25], searches for the variation of fundamental constants [26], quantum simulation and computation [27,28], plasma physics [29], nuclear physics [22,30], and many others.…”

“…The CI+all-order method was demonstrated to produce accurate results for a wide range of atomic properties for atoms and ions with 2 to 4 valence electrons [19][20][21][22]. This method has provided precision data for many applications, including development of ultra-precise clocks [19,21,23], studies of fundamental symmetries [24,25], searches for the variation of fundamental constants [26], quantum simulation and computation [27,28], plasma physics [29], nuclear physics [22,30], and many others. It was previously thought to be unfeasible to apply this method to systems such as Cr due to extremely large number of configurations that have to be considered as well as limitation of the initial closed-shell approximation.…”