The magnetic octupole moment of 87Rb is determined from hyperfine intervals in the 5p 2P[3/2] state measured by Ye et al. [Opt. Lett. 21, 1280 (1996)]. Hyperfine constants A = 84.7189(22) MHz, B = 12.4942(43) MHz, and C = -0.12(09) kHz are obtained from the published measurements. The existence of a significant value for C indicates the presence of a nuclear magnetic octupole moment Omega. Combining the hyperfine constants with atomic structure calculations, we obtain Omega = -0.58(39) (b muN). Second-order corrections arising from interaction with the nearby 5p 2P[1/2] state are found to be insignificant.
Hyperfine-induced electric dipole contributions may significantly increase probabilities of otherwise very weak electric octupole and magnetic quadrupole atomic clock transitions (e.g. transitions between $s$ and $f$ electron orbitals). These transitions can be used for exceptionally accurate atomic clocks, quantum information processing and search for dark matter. They are very sensitive to new physics beyond the Standard Model, such as temporal variation of the fine structure constant, the Lorentz invariance and Einstein equivalence principle violation. We formulate conditions under which th…
The hyperfine structure of the long-lived $5D_{3/2}$ and $5D_{5/2}$ levels of Ba$^+$ ion is analyzed. A procedure for extracting relatively unexplored nuclear magnetic moments $Ω$ is presented. The relevant electronic matrix elements are computed in the framework of the ab initio relativistic many-body perturbation theory. Both the first- and the second-order (in the hyperfine interaction) corrections to the energy levels are analyzed. It is shown that a simultaneous measurement of the hyperfine structure of the entire $5D_J$ fine-structure manifold allows one to extract $Ω$ without contaminat…
We present precision measurements of the hyperfine intervals in the 5D3/2 manifold of a single trapped Barium ion, 137 Ba+ . Measurements of the hyperfine intervals are made between mF = 0 sublevels over a range of magnetic fields allowing us to interpolate to the zero field values with an accuracy below a few Hz, an improvement on previous measurements by three orders of magnitude. Our results, in conjunction with theoretical calculations, provide a 30-fold reduction in the uncertainty of the magnetic dipole (A) and electric quadrupole (B) hyperfine constants. In addition, we obtain the magne…
Measuring the hyperfine structure (HFS) of long-lived $^3P_2$ states of divalent atoms may offer the opportunity of extracting relatively unexplored nuclear magnetic octupole and electric hexadecapole moments. Here, using relativistic many-body methods of atomic structure and the nuclear shell model, we evaluate the effect of these higher nuclear moments on the hyperfine structure. We find that the sensitivity of HFS interval measurements in $^{87}$Sr needed to reveal the perturbation caused by the nuclear octupole moment is on the order of kHz. Results of similar analyses for $^{9}$Be, $^{25}…
We measure hyperfine structure in the metastable ${^3P}_2$ state of $^{173}$Yb and extract the nuclear magnetic octupole moment. We populate the state using dipole-allowed transitions through the ${^3P}_1$ and ${^3S}_1$ states. We measure frequencies of hyperfine transitions of the ${^3P}_2 \rightarrow {^3S}_1$ line at 770 nm using a Rb-stabilized ring cavity resonator with a precision of 200 kHz. Second-order corrections due to perturbations from the nearby ${^3P}_1$ and ${^1P}_1$ states are below 30 kHz. We obtain the hyperfine coefficients as: $A=-742.11(2)$ MHz, $B=1339.2(2)$ MHz, which re…
Hyperfine-structure constants of odd Ra$^{+}$ due to the interactions of nuclear magnetic dipole, electric quadrupole, and magnetic octupole moments with the electrons are investigated in the framework of relativistic coupled-cluster method within single- and double-excitation approximation. The calculated energies and magnetic dipole hyperfine-structure constants $A$ exhibit a good agreement with available experimental values. Combining with the experimental electric quadrupole hyperfine-structure constant, we also extracted the electric quadrupole moments $Q$ of $^{209,211,221,223}$Ra. Our $…
Hyperfine structures of $^{211}$Fr due to the interactions of magnetic dipole ($μ$), electric quadrupole ($Q$) and magnetic octupole ($Ω$) moments with the electrons are investigated using the relativistic coupled-cluster (RCC) theory with an approximation of singles, doubles and important valence triples excitations in the perturbative approach. Validity of our calculations are substantiated by comparing the results with their available experimental values. Its $Q$ value has also been elevated by combining the measured hyperfine structure constant of the $7p \ ^2P_{3/2}$ state with our improv…
We perform precision measurements on the 5D$_{5/2}$ manifold hyperfine intervals of a single trapped ion, $^{137}$Ba$^+$. RF spectroscopy is used to measure the hyperfine intervals to an accuracy of a few Hz. Our results provide a three orders of magnitude improvement in accuracy over previous work and also provide a 10-fold improvement in the value of $g_J$ for this level. These results complement our previous work on the 5D$_{3/2}$ manifold of $^{137}$Ba$^+$, providing an independent measurement of the nuclear octupole, and a consistency check on atomic structure calculations.
Hyperfine structure (HFS) of atomic energy levels arises due to interactions of atomic electrons with a hierarchy of nuclear multipole moments, including magnetic dipole, electric quadrupole and higher rank moments. Recently, a determination of the magnetic octupole moment of the $^{173}\mathrm{Yb}$ nucleus was reported from HFS measurements in neutral ${}^{173}\mathrm{Yb}$ [PRA 87, 012512 (2013)], and is four orders of magnitude larger than the nuclear theory prediction. Considering this substantial discrepancy between the spectroscopically extracted value and nuclear theory, here we propose …
The hyperfine constants of the $^3$P$^{\circ}_2$ state in neutral Yb have been measured using three different dipole transitions. This state was recently shown to have a comparatively large hyperfine magnetic octupole splitting, and thus a puzzlingly large magnetic octupole moment. The measurement is performed using collinear laser spectroscopy on a fast atomic beam, which provides a straightforward route to probing long-lived metastable atomic states with high resolution. From the combined analysis of all three lines we find no significant evidence for a non-zero octupole moment in $^{173}$Yb…
We report the measurement of the hyperfine splitting in the $7D_{5/2}$ state of $^{133}$Cs using high resolution Doppler-free two-photon spectroscopy enabled by precise frequency scans using an acousto-optic modulator. All the six hyperfine levels are resolved in our spectra. We determine the hyperfine coupling constants A = -1.70867(62) MHz and B = 0.050(14) MHz which represent over 20-times improvement in the precision of both A and B. Moreover, our measurement is sufficiently precise to put bounds on the value of the magnetic octupole coupling constant C = 0.4(1.4) kHz for the $7D_{5/2}$ st…
$^{229}$Th is a promising candidate for developing a nuclear optical clock and searching the new physics beyond the standard model. Accurate knowledge of the nuclear properties of $^{229}$Th is very important. In this work, we calculate hyperfine-structure constants for the first four states of $^{229}$Th$^{3+}$ using the relativistic coupled-cluster method based on the Gauss basis set. The no-pair Dirac-Coulomb-Breit Hamiltonian with the lowest-order quantum electrodynamics (QED) correction is the starting point, together with all linear and non-linear terms of single and double excitations a…
An angle-resolved x-ray spectroscopic scheme is presented for determining the hyperfine splitting of highly charged ions. For helium-like ions, in particular, we propose to measure either the angular distribution or polarization of the $1s2p~^{3}P_{1}, F \rightarrow 1s^{2}~^{1}S_{0}, F_{f}$ emission following the stimulated decay of the initial $1s2s~^{1}S_{0}, F_{i}$ level. It is found that both the angular and polarization characteristics of the emitted x-ray photons strongly depends on the (relative) \textit{splitting} of the partially overlapping hyperfine $1s2p~^{3}P_{1}, F$ resonances an…
Doppler-free saturated absorption spectroscopy is performed on an enriched radioactive Ar-39 sample. The spectrum of the 3s^2 3p^5 4s [3/2]_2 - 3s^2 3p^5 4p [5/2]_3 cycling transition at 811.8 nm is recorded, and its isotope shift between Ar-39 and Ar-40 is derived. The hyperfine coupling constants A and B for both the 4s [3/2]_2 and 4p [5/2]_3 energy levels in Ar-39 are also determined. The results partially disagree with a recently published measurement of the same transition. Based on earlier measurements as well as the current work, the isotope shift and hyperfine structure of the correspo…
We perform high resolution spectroscopy on $^{176}$Lu$^+$ including the $^1S_0\leftrightarrow{^3}D_1$ and $^1S_0\leftrightarrow{^3}D_2$ clock transitions. Hyperfine structures and optical frequencies relative to the $^1S_0$ ground state of four low lying excited states are given to a few tens of kHz resolution. This covers the most relevant transitions involved in clock operation with this isotope. Additionally, measurements of the $^3D_2$ hyperfine structure may provide access to higher order nuclear moments, specifically the magnetic octupole and electric hexadecapole moments.
In this work we describe the latest results for the measurements of the hyperfine structure of antiprotonic helium-3. Two out of four measurable super-super-hyperfine SSHF transition lines of the (n,L)=(36,34) state of antiprotonic helium-3 were observed. The measured frequencies of the individual transitions are 11.12548(08) GHz and 11.15793(13) GHz, with an increased precision of about 43% and 25% respectively compared to our first measurements with antiprotonic helium-3 [S. Friedreich et al., Phys. Lett. B 700 (2011) 1--6]. They are less than 0.5 MHz higher with respect to the most recent t…
High precision spectroscopy of the $^1S_0$-to-${^1}D_2$ clock transition of $^{176}$Lu is reported. Measurements are performed with Hertz level precision with the accuracy of the hyperfine-averaged frequency limited by the calibration of an active hydrogen maser to the SI definition of the second via a GPS link. The measurements also provide accurate determination of the $^1D_2$ hyperfine structure. Hyperfine structure constants associated with the magnetic octupole and electric hexadecapole moments of the nucleus are considered, which includes a derivation of correction terms from third-order…
Accurate calculations of the fine and hyperfine splitting of the 2P state in Li and Be$^+$ isotopes using the explicitly correlated Hylleraas basis set are presented. Theoretical predictions including the mixing of $P_{1/2}$ and $P_{3/2}$ states, relativistic and quantum electrodynamics effects on hyperfine interactions, are compared with experimental values. It is concluded that precise spectroscopic determination of the nuclear magnetic moments requires elimination of nuclear structure effects by combining measurements for two different states.
Energy levels, wavelengths, lifetimes and hyperfine structure constants for the isotopes of the first and second spectra of radium, Ra I and Ra II have been compiled. Wavelengths and wave numbers are tabulated for 226Ra and for other Ra isotopes. Isotope shifts and hyperfine structure constants of even and odd-A isotopes of neutral radium atom and singly ionized radium are included. Experimental lifetimes of the states for both neutral and ionic Ra are also added, where available. The information is beneficial for present and future experiments aimed at different physics motivations using neut…
Rare-earth ion doped crystals are promising systems for quantum communication and quantum information processing. In particular, paramagnetic rare-earth centres can be utilized to realize quantum coherent interfaces simultaneously for optical and microwave photons. In this article, we study hyperfine and magnetic properties of a Y$_2$SiO$_5$ crystal doped with $^{171}$Yb$^{3+}$ ions. This isotope is particularly interesting since it is the only rare--earth ion having electronic spin $S=\frac{1}{2}$ and nuclear spin $I=\frac{1}{2}$, which results in the simplest possible hyperfine level structu…
We report the measurement of hyperfine splitting in the $7d$ $^{2}D_{3/2}$ state of $^{133}$Cs using high resolution Doppler-free two-photon spectroscopy in a Cs vapor cell. We determine the hyperfine coupling constants $A = 7.3509(9)$ MHz and $B = -0.041(8)$ MHz, which represent an order of magnitude improvement in the precision. We also obtain bounds on the magnitude of the nuclear magnetic octupole coupling constant $C$. Additionally, we measure the ac Stark shift of the $6s$ $^{2}S_{1/2} \rightarrow 7d$ $^{2}D_{3/2}$ transition at 767.8 nm to be $-49 \pm 5$ Hz/(W/cm$^2$), in agreement with…
A combined experimental and theoretical spectroscopic study of high-$n$, ${30 \lesssim n \lesssim 100}$, triplet $\text{S}$ and $\text{D}$ Rydberg states in $^{87}\text{Sr}$ is presented. $^{87}\text{Sr}$ has a large nuclear spin, ${I=9/2}$, and at high-$n$ the hyperfine interaction becomes comparable to, or even larger than, the fine structure and singlet-triplet splittings which poses a considerable challenge both for precision spectroscopy and for theory. For high-$n$ $\text{S}$ states, the hyperfine shifts are evaluated non-perturbatively taking advantage of earlier spectroscopic data for …
Recently the first laser spectroscopy measurement of the radioactive RaF molecule has been reported by Ruiz \textit{et al.} [Nature \textbf{581}, 396 (2020)]. This and similar molecules are considered to search for the New Physics effects. The radium nucleus is of interest as it is octupole-deformed and has close levels of opposite parity. The preparation of such experiments can be simplified if there are reliable theoretical predictions. It is shown that the accurate prediction of the hyperfine structure of the RaF molecule requires to take into account the finite magnetization distribution i…
A systematic study of Ca+ atomic properties is carried out using high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the levels up to n = 7. Recommended values and estimates of their uncertainties are provided for a large number of electric-dipole transitions. Electric-dipole scalar polarizabilities for the 5s, 6s, 7s, 8s, 4p, 5p, 3d, and 4d states and tensor polari…
We have produced laser-cooled Wigner crystals of 229Th3+ in a linear Paul trap. The magnetic dipole (A) and electric quadrupole (B) hyperfine constants for four low-lying electronic levels and the relative isotope shifts with respect to 232Th3+ for three low-lying optical transitions are measured. Using the hyperfine B constants in conjunction with prior atomic structure calculations, a new value of the spectroscopic nuclear electric quadrupole moment Q = 3.11(16) eb is deduced. These results are a step towards optical excitation of the low-lying isomer level in the 229Th nucleus.
We report detailed spectroscopic measurements of the X(0)$[^3Σ^+]$(v=0) to B(1)$[^3Π]$ (v=5) transition in PbO. Using a Stark-modulated laser absorption technique, we have measured the hyperfine constant of $^{207}$PbO in the B(1) state, as well as B(1)(v=5) rotational constant, X-B isotope shifts, etc. The hyperfine structure of the B(1) state is of interest as a benchmark for calculations of PbO electronic structure, related to experiments to search for the electric dipole moment of the electron.
We performed a laser spectroscopic determination of the $2s$ hyperfine splitting (HFS) of Li-like $^{209}\text{Bi}^{80+}$ and repeated the measurement of the $1s$ HFS of H-like $^{209}\text{Bi}^{82+}$. Both ion species were subsequently stored in the Experimental Storage Ring at the GSI Helmholtzzentrum für Schwerionenforschung Darmstadt and cooled with an electron cooler at a velocity of $\approx 0.71\,c$. Pulsed laser excitation of the $M1$ hyperfine-transition was performed in anticollinear and collinear geometry for $\text{Bi}^{82+}$ and $\text{Bi}^{80+}$, respectively, and observed by flu…
Characterising molecules for fundamental physics: an accurate spectroscopic model of methyltrioxorhenium derived from new infrared and millimetre-wave measurements
We report on hyperfine-resolved spectroscopic measurements of the electric-dipole forbidden 5$p_{3/2} \to 8p_{1/2}$ transition in a sample of ultracold $^{87}$Rb atoms. The hyperfine selection rules enable the weak magnetic-dipole (M1) contribution to the transition strength to be distinguished from the much stronger electric-quadrupole (E2) contribution. An upper limit on the M1 transition strength is determined that is about 50 times smaller than an earlier experimental determination. We also calculate the expected value of the M1 matrix element and find that it is less than the upper limit …
Spectroscopic studies of aluminum monofluoride (AlF) have revealed its highly favorable properties for direct laser cooling. All $Q$ lines of the strong A$^1Π$ $\leftarrow$ X$^1Σ^+$ transition around 227~nm are rotationally closed and thereby suitable for the main cooling cycle. The same holds for the narrow, spin-forbidden a$^3Π$ $\leftarrow$ X$^1Σ^+$ transition around 367 nm which has a recoil limit in the micro Kelvin range. We here report on the spectroscopic characterization of the lowest rotational levels in the a$^3Π$ state of AlF for $v=0-8$ using a jet-cooled, pulsed molecular beam. A…
By combining a recent precise measurement of the ionization energy of $^{87}$Rb with previous measurements of electronic and hyperfine structure, an accurate value for the $^{85}\textrm{Rb}-^{87}\textrm{Rb}$ isotope shift of the 5$^2S_{1/2}$ ground state can be determined. In turn, comparison with additional spectroscopic data makes it possible for the first time to evaluate isotope shifts for the low-lying excited states, accurate in most cases to about 1 MHz. In a few cases, the specific mass shift contribution can be determined in addition to the total shift. This information is particularl…
The measurement of Cesium (Cs) 7D5/2 excited state's hyperfine splitting intervals and hyperfine-interaction constants has been experimentally investigated based on ladder-type (852 nm + 698 nm) three-level Cs system (6S1/2 - 6P3/2 - 7D5/2) with room-temperature Cs atomic vapor cell. By scanning the 698-nm coupling laser's frequency, the Doppler-free high-resolution electromagnetically-induced transparency (EIT) assisted double-resonance optical pumping (DROP) spectra have been demonstrated via transmission enhancement of the locked 852-nm probe laser. The EIT-assisted DROP spectra are employe…
Optical precision spectroscopy of isotope shifts can be used to test for new forces beyond the Standard Model, and to determine basic properties of atomic nuclei. We measure isotope shifts on the highly forbidden ${}^2S_{1/2} \rightarrow {}^2F_{7/2}$ octupole transition of trapped $^{168,170,172,174,176}$Yb ions. When combined with previous measurements in Yb$^+$ and very recent measurements in Yb, the data reveal a King plot nonlinearity of up to 240$σ$. The trends exhibited by experimental data are explained by nuclear density functional theory calculations with the Fayans functional. We als…
We spectroscopically investigate the hyperfine, rotational and Zeeman structure of the vibrational levels $\text{v}'=0$, $7$, $13$ within the electronically excited $c^3Σ_g^+$ state of $^{87}\text{Rb}_2$ for magnetic fields of up to $1000\,\text{G}$. As spectroscopic methods we use short-range photoassociation of ultracold Rb atoms as well as photoexcitation of ultracold molecules which have been previously prepared in several well-defined quantum states of the $a^3Σ_u^+$ potential. As a byproduct, we present optical two-photon transfer of weakly bound Feshbach molecules into $a^3Σ_u^+$, $\tex…
The water molecule occurs in two nuclear-spin isomers that differ by the value of the total nuclear spin of the hydrogen atoms, i.e., $I=0$ for para-H$_2$O and $I=1$ for ortho-H$_2$O. Spectroscopic transitions between rovibrational states of ortho and para water are extremely weak due to the tiny hyperfine nuclear-spin-rotation interaction of only $\sim30$ kHz and so far were not observed. We report the first comprehensive theoretical investigation of the hyperfine effects and ortho-para transitions in H$_2$$^{16}$O due to nuclear-spin-rotation and spin-spin interactions. We also present the d…
An excellent candidate molecule for the measurement of the electron's electric dipole moment (eEDM) is thorium monofluoride (ThF$^+$) because the eEDM-sensitive state, $^3Δ_1$, is the electronic ground state, and thus is immune to decoherence from spontaneous decay. We perform spectroscopy on $X\,^3Δ_1$ to extract three spectroscopic constants crucial to the eEDM experiment: the hyperfine coupling constant, the molecular frame electric dipole moment, and the magnetic $g$-factor. To understand the impact of thermal blackbody radiation on the vibrational ground state, we study the lifetime of th…
We report ab initio relativistic correlation calculations of potential curves and spectroscopic constants for four lowest-lying electronic states of the lead monofluoride. We also calculated parameters of the spin-rotational Hamiltonian for the ground and the first excited states including P,T-odd and P-odd terms. In particular, we have obtained hyperfine constants of the $^{207}$Pb nucleus. For the $^2Π_{1/2}$ state $A_\perp=-6859.6$ MHz, $A_\|=9726.9$ MHz and for the A$^2Σ^+_{1/2}$ $A_\perp=1720.8$ MHz, $A_\|=3073.3$ MHz. Our values of the ground state hyperfine constants are in good agreeme…
Contact $P$-wave interactions connected to the Larmor interaction of a magnetic dipole and Thomas spin precession in the filed of an electric quadrupole are described and their implications for spectroscopy of exotic $Ω^{-}$-atoms are studied. In order to evaluate the magnitude of the contact $P$-wave interactions as compared to the conventional long-range interactions and the sensitivity of spectroscopic data to the $Ω^{-}$-hyperon quadrupole moment, we consider $2P$ states of $Ω^{-}$ atoms formed with light stable nuclei with spins $I \geq 1/2$ and atomic numbers $Z \leq 10$. The energy leve…
Hyperfine structure $A$ and $B$ factors of the atomic $5s\,5p\,\; ^3\rm{P}_2 \rightarrow 5s\,6s\,\; ^3\rm{S}_1$ transition are determined from collinear laser spectroscopy data of $^{107-123}$Cd and $^{111m-123m}$Cd. Nuclear magnetic moments and electric quadrupole moments are extracted using reference dipole moments and calculated electric field gradients, respectively. The hyperfine structure anomaly for isotopes with $s_{1/2}$ and $d_{5/2}$ nuclear ground states and isomeric $h_{11/2}$ states is evaluated and a linear relationship is observed for all nuclear states except $s_{1/2}$. This co…
