arXiv subjects

G. W. F. Drake

Publications and source records attributed to G. W. F. Drake.

At least 19 recordsLinked to original sources

arXiv2026

Theory for the Rydberg states of helium: quantum defect extensions and comparison with experiment up to $n = 102$ for the singlet and triplet $P$-states

High precision variational calculations for helium in Hylleraas coordinates are used to obtain a combination of quantum defect expansions for the nonrelativistic energy and $1/n$ expansions for the relativistic and quantum electrodynamic (QED) corrections. The extrapolations based on direct calculations for the singlet and triplet $P$-states up to principal quantum number $n = 35$ provide ionization energies of the $1snp\;^1P_1$ and $^3P_c$ (centroid) states up to $n=102$ with accuracies better than $\pm$1 kHz. The calculated ionization energies are combined with 28 measured transition frequencies to obtain values for the ionization energy of the $1s2s\;^3S_1$ state. The final result of 1152 842 742.705(16) MHz differs from theory by $0.474\pm 0.052$ MHz, and provides a strong confirmation of the 9$σ$ disagreement between theory and experiment obtained previously by quantum defect extrapolation of experimental data to the series limit. An analysis of the quantum defect method is presented, and second-order mass polarization (recoil) terms are identified that vary as $1/n^2$ in lowest order. The nonrelativistic part provides a theoretical justification for the effective reduced-mass Rydberg $R_M^{(+)}$ based on the phenomenological model of a Rydberg electron scattering from a He$^+$ core. The Ritz expansion for the nonrelativistic energy is verified to an unprecedented 20-figure accuracy.

physics.atom-ph↗

arXiv2025

Theory for the Rydberg states of helium: Results for $2 \le n \le 35$ and comparison with experiment for the singlet and triplet $P$-states

High precision variational calculations in Hylleraas coordinates are presented for all singlet and triplet $P$-states of helium up to principal quantum number $n = 35$ with a uniform accuracy of 1 part in $10^{22}$ for the nonrelativistic energy. Mass polarization, relativistic and quantum electrodynamic effects are included to achieve a final accuracy of $\pm$1 kHz or better for the ionization energy of the Rydberg states of $^4$He in the range $24\le n \le 35$. The results are combined with 11 transition frequency measurements of Clausen et al. Phys. Rev. A 111, 012817 (2025) to obtain complementary measurements of the ionization energy of the $1s2s\;^3S_1$ state that do not depend on quantum defect extrapolations to the series limit. The result from the triplet spectrum yields an ionization energy of 1152 842 742.728(6) MHz, which agrees with but is larger than the experimental value by 14 $\pm$17 kHz. However, it confirms a much larger 9$σ$ discrepancy of $0.468\pm0.055$ MHz with the theoretical ionization energy of Patkóš et al. Phys. Rev. A 103, 042809 (2021). The results provide a test of the quantum defect extrapolation method at the level of $\pm$17 kHz. This revised version contains an additional table of spin-dependent matrix elements of the Breit interaction in the appendix for $24\le n\le 35$. (12 pages, 1 figure).

physics.atom-ph↗

arXiv2025

Direct Extraction of Nuclear Structure Information Using Precision Lithium-Ion Spectroscopy

Accurately describing nuclear interactions within atomic nuclei remains a challenge, which hinders our exploration of new physics beyond the Standard Model. However, these nuclear interactions can be characterized by nuclear parameters such as the Zemach radius and the electric quadrupole moment, which are reflected in atomic spectra. Our work has achieved high-precision measurements of lithium ion hyperfine splittings at the level of $10$~kHz, and directly extracted these important nuclear structure parameters. We observed significant discrepancies between our results and both nuclear theory and molecular spectra regarding the electric quadrupole moment. The result for $^7$Li deviated by $2.3σ$ from the currently recommended value, whereas the result for $^6$Li deviated by up to $6.2σ$ from the recommended value determined by molecular spectroscopy. These discrepancies motivated us to conduct independent calculations based on nuclear structure theory, which provided support for the results obtained from ion spectroscopy. Our results provide valuable information for characterizing nuclear forces, serve as sensitive benchmarks for testing nuclear structure theories, and enable critical comparisons with both electron-nuclear scattering and molecular spectroscopy.

physics.atom-ph↗

arXiv2025

Theory for the Rydberg states of helium: Comparison with experiment for the $1s24p\;^1P_1$ state ($n=24$)

Recent measurements of the ionization energies of the Rydberg $^1P$ states of helium for principal quantum number $n = 24$ and higher present a new challenge to theoretical atomic physics. A long-standing obstacle to high precision atomic theory for three-body systems is a rapid loss of accuracy for variational calculations with increasing principal quantum number $n$. We show that this problem can be overcome with the use of a ``triple" basis set in Hylleraas coordinates. Nonrelativistic energies accurate to 23 significant figures are obtained with basis sets of relatively modest size (6744 terms). Relativistic and quantum electrodynamic effects are calculated, including an estimate of terms of order $mα^6$ from a $1/n^3$ extrapolation, resulting in an estimated accuracy of $\pm$1 kHz. The calculated ionization energy of 5704 980.348(1) MHz is in excellent agreement with the experimental value 5704 980.312(95) MHz. These results establish the ionization energy of the $1s24p\;^1P_1$ state as an absolute point of reference for transitions to lower-lying states, and they confirm an $11σ$ disagreement between theory and experiment in the triplet spectrum of helium. Results are also given for the $1s24p\;^3P_J$ states in agreement with a recent experiment on the triplet Rydberg series, thereby confirming a discrepancy of of $0.468 \pm 0.055$ MHz for the ionization energy of the $1s2s\;^3S_1$ state.

physics.atom-ph↗

arXiv2023

Measurement of hyperfine structure and the Zemach radius in $\rm^6Li^+$ using optical Ramsey technique

We investigate the $2\,^3\!S_1$--$2\,^3\!P_J$ ($J = 0, 1, 2$) transitions in $\rm^6Li^+$ using the optical Ramsey technique and achieve the most precise values of the hyperfine splittings of the $2\,^3\!S_1$ and $2\,^3\!P_J$ states, with smallest uncertainty of about 10~kHz. The present results reduce the uncertainties of previous experiments by a factor of 5 for the $2\,^3\!S_1$ state and a factor of 50 for the $2\,^3\!P_J$ states, and are in better agreement with theoretical values. Combining our measured hyperfine intervals of the $2\,^3\!S_1$ state with the latest quantum electrodynamic (QED) calculations, the improved Zemach radius of the $\rm^6Li$ nucleus is determined to be 2.44(2)~fm, with the uncertainty entirely due to the uncalculated QED effects of order $mα^7$. The result is in sharp disagreement with the value 3.71(16) fm determined from simple models of the nuclear charge and magnetization distribution. We call for a more definitive nuclear physics value of the $\rm^6Li$ Zemach radius.

physics.atom-ph↗

arXiv2022

Precision calculation of hyperfine structure of $^{7,9}$Be$^{2+}$ ions

The hyperfine structures of the $2\,^3\!S_1$ and $2\,^3\!P_J$ states of the $^7$Be$^{2+}$ and $^9$Be$^{2+}$ ions are investigated within the framework of the nonrelativistic quantum electrodynamics (NRQED). The uncertainties of present hyperfine splitting results of $^9$Be$^{2+}$ are in the order of several tens of ppm, where two orders of magnitude improvement over the previous theory and experiment values has been achieved. The contribution of nuclear electric quadrupole moment to hyperfine splitting of $^7$Be$^{2+}$ has been studied. A scheme for determining the properties of Be nuclei in terms of Zemach radius or the electric quadrupole moment based on precise spectra is proposed, and it opens a new window for the study of Be nuclei.

physics.atom-ph↗

arXiv2022

Measurement of a helium tune-out frequency: an independent test of quantum electrodynamics

Despite quantum electrodynamics (QED) being one of the most stringently tested theories underpinning modern physics, recent precision atomic spectroscopy measurements have uncovered several small discrepancies between experiment and theory. One particularly powerful experimental observable that tests QED independently of traditional energy level measurements is the `tune-out' frequency, where the dynamic polarizability vanishes and the atom does not interact with applied laser light. In this work, we measure the `tune-out' frequency for the $2^{3\!}S_1$ state of helium between transitions to the $2^{3\!}P$ and $3^{3\!}P$ manifolds and compare it to new theoretical QED calculations. The experimentally determined value of $725\,736\,700\,$$(40_{\mathrm{stat}},260_{\mathrm{syst}})$ MHz is within ${\sim} 1.7σ$ of theory ($725\,736\,252(9)$ MHz), and importantly resolves both the QED contributions (${\sim} 30 σ$) and novel retardation (${\sim} 2 σ$) corrections.

physics.atom-ph↗

arXiv2020

Precision calculation of hyperfine structure and the Zemach radii of $^{6,7}$Li$^+$ ions

The hyperfine structures of the $2\,^3\!S_1$ states of the $^6$Li$^+$ and $^7$Li$^+$ ions are investigated theoretically to extract the Zemach radii of the $^6$Li and $^7$Li nuclei by comparing with precision measurements. The obtained Zemach radii are larger than the previous values of Puchalski and Pachucki [\href{https://link.aps.org/doi/10.1103/PhysRevLett.111.243001}{Phys. Rev. Lett. {\bf 111}, 243001 (2013)}] and disagree with them by about 1.5 and 2.2 standard deviations for $^6$Li and $^7$Li, respectively. Furthermore, our Zemach radius of $^6$Li differs significantly from the nuclear physics value, derived from the nuclear charge and magnetic radii [\href{https://link.aps.org/doi/10.1103/PhysRevA.78.012513}{Phys. Rev. A {\bf 78}, 012513 (2008)}], by more than 6 sigma, indicating an anomalous nuclear structure for $^6$Li. The conclusion that the Zemach radius of $^7$Li is about 40\% larger than that of $^6$Li is confirmed. The obtained Zemach radii are used to calculate the hyperfine splittings of the $2\,^3\!P_J$ states of $^{6,7}$Li$^+$, where an order of magnitude improvement over the previous theory has been achieved for $^7$Li$^+$.

physics.atom-ph↗

arXiv2016

Uncertainty Estimates for Theoretical Atomic and Molecular Data

Sources of uncertainty are reviewed for calculated atomic and molecular data that are important for plasma modeling: atomic and molecular structure and cross sections for electron-atom, electron-molecule, and heavy particle collisions. We concentrate on model uncertainties due to approximations to the fundamental many-body quantum mechanical equations and we aim to provide guidelines to estimate uncertainties as a routine part of computations of data for structure and scattering.

physics.atom-ph↗

arXiv2013

Laser Probing of Neutron-Rich Nuclei in Light Atoms

The neutron-rich 6He and 8He isotopes exhibit an exotic nuclear structure that consists of a tightly bound 4He-like core with additional neutrons orbiting at a relatively large distance, forming a halo. Recent experimental efforts have succeeded in laser trapping and cooling these short-lived, rare helium atoms, and have measured the atomic isotope shifts along the 4He-6He-8He chain by performing laser spectroscopy on individual trapped atoms. Meanwhile, the few-electron atomic structure theory, including relativistic and QED corrections, has reached a comparable degree of accuracy in the calculation of the isotope shifts. In parallel efforts, also by measuring atomic isotope shifts, the nuclear charge radii of lithium and beryllium isotopes have been studied. The techniques employed were resonance ionization spectroscopy on neutral, thermal lithium atoms and collinear laser spectroscopy on beryllium ions. Combining advances in both atomic theory and laser spectroscopy, the charge radii of these light halo nuclei have now been determined for the first time independent of nuclear structure models. The results are compared with the values predicted by a number of nuclear structure calculations, and are used to guide our understanding of the nuclear forces in the extremely neutron-rich environment.

nucl-ex↗

arXiv2011

First direct mass-measurement of the two-neutron halo nucleus 6He and improved mass for the four-neutron halo 8He

The first direct mass-measurement of $^{6}$He has been performed with the TITAN Penning trap mass spectrometer at the ISAC facility. In addition, the mass of $^{8}$He was determined with improved precision over our previous measurement. The obtained masses are $m$($^{6}$He) = 6.018 885 883(57) u and $m$($^{8}$He) = 8.033 934 44(11) u. The $^{6}$He value shows a deviation from the literature of 4$σ$. With these new mass values and the previously measured atomic isotope shifts we obtain charge radii of 2.060(8) fm and 1.959(16) fm for $^{6}$He and $^{8}$He respectively. We present a detailed comparison to nuclear theory for $^6$He, including new hyperspherical harmonics results. A correlation plot of the point-proton radius with the two-neutron separation energy demonstrates clearly the importance of three-nucleon forces.

nucl-ex↗

arXiv2011

Time-dependent pointer states of the generalized spin-boson model and consequences regarding the decoherence of the central system

We consider a spin-boson Hamiltonian which is generalized such that the Hamiltonians for the system ($\hat{H}_{\cal S}$) and the interaction with the environment ($\hat{H}_{\rm int}$) do not commute with each other. Considering a single-mode quantized field in exact resonance with the tunneling matrix element of the system, we obtain the time-evolution operator for our model. Using our time-evolution operator we calculate the time-dependent pointer states of the system and the environment (which are characterized by their ability not to entangle with each other) for the case that the environment initially is prepared in the coherent state. We show that our solution for the pointer states of the system and the environment is valid over a length of time which is proportional to $\bar{n}$, the average number of bosons in the environment. We also obtain a closed form for the offdiagonal element of the reduced density matrix of the system and study the decoherence of the central system in our model. We show that for the case that the system initially is prepared in one of its pointer states, the offdiagonal element of the reduced density matrix of the system will be a \emph{sinusoidal function} with a slow decaying envelope which is characterized by a decay time proportional to $\bar{n}$; while it will experience a much faster decoherence, when the system initially is \emph{not} prepared in one of its initial pointer states.

quant-ph↗

arXiv2011

Time-dependent pointer states and determination of the preferred basis of measurement

We present a general analytic method for evaluating the generally time-dependent pointer states of a subsystem, which are defined by their capability not to entangle with the states of another subsystem. In this way, we show how in practice the global state of the system and the environment may evolve into a diagonal state as a result of the natural evolution of the total composite system. We explore the conditions under which the pointer states of the system become independent of time; so that a preferred basis of measurement can be realized. As we show, these conditions include the so-called quantum limit of decoherence and the so-called quantum measurement limit; as well as some other specific conditions which are discussed in the paper. We relate the mathematical conditions for having time-independent pointer states to some classes of possible symmetries in the Hamiltonian of the total composite system. Indeed, our theory would serve as a generalization of the existing theory for determination of the preferred basis of measurement. By exploiting this new theory we can obtain those regimes of the parameter space for a given total Hamiltonian defining our system-environment model for which a preferred basis of measurement can be realized. Moreover, we can predict the corresponding preferred basis of measurement for each regime. We can also obtain the time-dependent pointer states of the system and the environment in most of the other regimes where the pointer states of the system are time-dependent and a preferred basis of measurement cannot be realized at all. This ability to obtain time-dependent pointer states is specifically important in decoherence studies; as pointer states correspond to those initial conditions for the state of the system and the environment for which we can have longer decoherence times.

quant-ph↗

arXiv2010

Isotope Shift Measurements of Stable and Short-Lived Lithium Isotopes for Nuclear Charge Radii Determination

Changes in the mean-square nuclear charge radii along the lithium isotopic chain were determined using a combination of precise isotope shift measurements and theoretical atomic structure calculations. Nuclear charge radii of light elements are of high interest due to the appearance of the nuclear halo phenomenon in this region of the nuclear chart. During the past years we have developed a new laser spectroscopic approach to determine the charge radii of lithium isotopes which combines high sensitivity, speed, and accuracy to measure the extremely small field shift of an 8 ms lifetime isotope with production rates on the order of only 10,000 atoms/s. The method was applied to all bound isotopes of lithium including the two-neutron halo isotope Li-11 at the on-line isotope separators at GSI, Darmstadt, Germany and at TRIUMF, Vancouver, Canada. We describe the laser spectroscopic method in detail, present updated and improved values from theory and experiment, and discuss the results.

physics.atom-ph↗

arXiv2009

Nuclear Charge Radii of Be-7,9,10 and the one-neutron halo nucleus Be-11

Nuclear charge radii of $^{7,9,10,11}$Be have been determined by high-precision laser spectroscopy. On-line measurements were performed with collinear laser spectroscopy in the $2s_{1/2} \to 2p_{1/2}$ transition on a beam of Be$^{+}$ ions. Collinear and anticollinear laser beams were used simultaneously and the absolute frequency determination using a frequency comb yielded an accuracy in the isotope-shift measurements of about 1 MHz. Combination with accurate calculations of the mass-dependent isotope shifts yield nuclear charge radii. The charge radius decreases from $^7$Be to $^{10}$Be and then increases for the halo nucleus $^{11}$Be. When comparing our results with predictions of {\it ab initio} nuclear structure calculations we find good agreement. Additionally, the nuclear magnetic moment of $^7$Be was determined to be $-1.3995(5)μ_{\rm N}$ and that of $^{11}$Be from a previous $β$-NMR measurement was confirmed.

nucl-ex↗

arXiv2008

Hyperfine Suppression of $2^3{\rm S}_1 - 3^3{\rm P}_J$ Transitions in $^3$He

Two anomalously weak transitions within the $2 ^3{\rm S}_1~-~3 ^3{\rm P}_J$ manifolds in $^3$He have been identified. Their transition strengths are measured to be 1,000 times weaker than that of the strongest transition in the same group. This dramatic suppression of transition strengths is due to the dominance of the hyperfine interaction over the fine structure interaction. An alternative selection rule based on \textit{IS}-coupling (where the nuclear spin is first coupled to the total electron spin) is proposed. This provides qualitative understanding of the transition strengths. It is shown that the small deviations from the \textit{IS}-coupling model are fully accounted for by an exact diagonalization of the strongly interacting states.

physics.atom-ph↗

arXiv2008

First Penning-trap mass measurement in the millisecond half-life range: the exotic halo nucleus 11Li

In this letter, we report a new mass for $^{11}$Li using the trapping experiment TITAN at TRIUMF's ISAC facility. This is by far the shortest-lived nuclide, $t_{1/2} = 8.8 \rm{ms}$, for which a mass measurement has ever been performed with a Penning trap. Combined with our mass measurements of $^{8,9}$Li we derive a new two-neutron separation energy of 369.15(65) keV: a factor of seven more precise than the best previous value. This new value is a critical ingredient for the determination of the halo charge radius from isotope-shift measurements. We also report results from state-of-the-art atomic-physics calculations using the new mass and extract a new charge radius for $^{11}$Li. This result is a remarkable confluence of nuclear and atomic physics.

nucl-ex↗

arXiv2008

Nuclear charge radius of $^8$He

The root-mean-square (rms) nuclear charge radius of ^8He, the most neutron-rich of all particle-stable nuclei, has been determined for the first time to be 1.93(3) fm. In addition, the rms charge radius of ^6He was measured to be 2.068(11) fm, in excellent agreement with a previous result. The significant reduction in charge radius from ^6He to ^8He is an indication of the change in the correlations of the excess neutrons and is consistent with the ^8He neutron halo structure. The experiment was based on laser spectroscopy of individual helium atoms cooled and confined in a magneto-optical trap. Charge radii were extracted from the measured isotope shifts with the help of precision atomic theory calculations.

nucl-ex↗