Measurement of Hyperfine Structure and the Zemach Radius in

We investigate the 2^{3}S_{1}-2^{3}P_{J} (J=0, 1, 2) transitions in ^{6}Li^{+} 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 ^{6}Li 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 ^{6}Li Zemach radius.

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 23S1 state of helium between transitions to the 23P and 33P manifolds and compare it with new theoretical QED calculations. The experimentally determined value of 725,736,700(260) megahertz differs from theory [725,736,252(9) megahertz] by 1.7 times the measurement uncertainty and resolves both the QED contributions and retardation corrections.

Precision Calculation of Hyperfine Structure and the Zemach Radii of

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 [Phys. Rev. Lett. 111, 243001 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.243001] 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 [Phys. Rev. A 78, 012513 (2008)PLRAAN1050-294710.1103/PhysRevA.78.012513] by more than 6σ, 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^{+}.

Critical nuclear charge for two-electron atoms.

The critical nuclear charge Z(c) required to bind a nucleus plus two electrons in a heliumlike atom has recently been an area of active study, resulting in a disagreement with earlier calculations and with the value obtained from the radius of convergence 1/Z* of a 1/Z expansion of the energy. In order to resolve the disagreement, have performed high-precision variational calculations in Hylleraas coordinates. With the double basis set method, we have been able to obtain good convergence for Z very close to Z(c), which together with the Hellmann-Feynman theorem yields the value Z(c) = 0.911,028,224,077,255,73(4), corresponding to 1/Z(c) = 1.097,660,833,738,559,80(5). This value is in agreement with the value obtained by Baker et al. [Phys. Rev. A 41, 1247 (1990)]. A significant feature of the results is that the outer electron remains localized near the nucleus, even at Z = Z(c), and the bound state evidently changes smoothly into a shape resonance for Z

Fine structure and ionization energy of the 1s2s2p 4P state of the helium negative ion He-.

The fine structure and ionization energy of the 1s2s2p (4)P state of the helium negative ion He(-) are calculated in Hylleraas coordinates, including relativistic and QED corrections up to O(α(4)mc(2)), O((µ/M)α(4)mc(2)), O(α(5)mc(2)), and O((µ/M)α(5)mc(2)). Higher order corrections are estimated for the ionization energy. A comparison is made with other calculations and experiments. We find that the present results for the fine structure splittings agree with experiment very well. However, the calculated ionization energy deviates from the experimental result by about 1 standard deviation. The estimated theoretical uncertainty in the ionization energy is much less than the experimental accuracy.

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 4σ. With these new mass values and the previously measured atomic isotope shifts we obtain charge radii of 2.060(8) 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.

Nuclear charge radii of 7,9,10Be and the one-neutron halo nucleus 11Be.

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}-->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. Combining this with accurate calculations of the mass-dependent isotope shifts yields nuclear charge radii. The charge radius decreases from 7Be to 10Be and then increases for the halo nucleus 11Be. When comparing our results with predictions of ab initio nuclear-structure calculations we find good agreement. Additionally, the nuclear magnetic moment of 7Be was determined to be -1.3995(5)micro_{N} and that of 11Be was confirmed with an accuracy similar to previous beta-NMR measurements.

First Penning-trap mass measurement of the exotic halo nucleus 11Li.

In this Letter, we report a new mass for 11Li using the trapping experiment TITAN at TRIUMF's ISAC facility. This is by far the shortest-lived nuclide, t_{1/2}=8.8 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 7 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 11Li. This result is a remarkable confluence of nuclear and atomic physics.

Hyperfine suppression of 2 3 S 1--3 3 P J transitions in 3He.

Two anomalously weak transitions within the 2(3)S_(1)--3(3)P_(J) manifolds in 3He have been identified. Their transition strengths are measured to be 1000 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 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 IS coupling model are fully accounted for by an exact diagonalization of the strongly interacting states.

High precision atomic theory for Li and Be+: QED shifts and isotope shifts.

High-precision results are presented for calculations of the nonrelativistic energies, relativistic corrections, and quantum electrodynamic corrections for the 2 2S, 2 2P, and 3 2S states of Li and Be+, using nonrelativistic wave functions expressed in Hylleraas coordinates. Bethe logarithms are obtained for the states of Be+. Finite mass corrections are calculated with sufficient accuracy to extract the nuclear charge radius from measurements of the isotope shift for the 2 2S-2 2P and 2 2S-3 2S transitions. The calculated ionization potential for Be+ is 146 882.923+/-0.005 cm{-1}.

Nuclear charge radius of 8He.

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.

Nuclear charge radii of 9,11Li: the influence of halo neutrons.

The nuclear charge radius of 11Li has been determined for the first time by high-precision laser spectroscopy. On-line measurements at TRIUMF-ISAC yielded a 7Li-11Li isotope shift (IS) of 25 101.23(13) MHz for the Doppler-free [FORMULA: SEE TEXT]transition. IS accuracy for all other bound Li isotopes was also improved. Differences from calculated mass-based IS yield values for change in charge radius along the isotope chain. The charge radius decreases monotonically from 6Li to 9Li, and then increases from 2.217(35) to 2.467(37) fm for 11Li. This is compared to various models, and it is found that a combination of halo neutron correlation and intrinsic core excitation best reproduces the experimental results.

Fine structure of the 1s3p 3PJ level in atomic 4He: theory and experiment.

The fine structure intervals in helium have been the focus of many theoretical and experimental studies in recent years with most of them concentrating on the 1s2p (3)P(J) levels. Here, we report on a theoretical calculation and an experimental determination of the 1s2p (3)P(J) fine structure intervals. The values from the theoretical calculation are 8113.730(6) and 658.801(6) MHz for the nu(01) and nu(12) intervals, respectively. The laser spectroscopic measurement reported here yields 8113.714(28) and 658.810(18) MHz for these intervals and is in excellent agreement with the theoretical calculation. Both, however, disagree significantly with the previous most precise experimental results.

Laser spectroscopic determination of the 6He nuclear charge radius.

We have performed precision laser spectroscopy on individual 6He (t(1/2)=0.8 s) atoms confined and cooled in a magneto-optical trap, and measured the isotope shift between 6He and 4He to be 43 194.772+/-0.056 MHz for the 2(3)S1-3(3)P2 transition. Based on this measurement and atomic theory, the nuclear charge radius of 6He is determined for the first time in a method independent of nuclear models to be 2.054+/-0.014 fm. The result is compared with the values predicted by a number of nuclear structure calculations and tests their ability to characterize this loosely bound halo nucleus.

Nuclear charge radii of 8,9Li determined by laser spectroscopy.

The 2s-->3s transition of (6,7,8,9)Li was studied by high-resolution laser spectroscopy using two-photon Doppler-free excitation and resonance-ionization detection. Hyperfine structure splittings and isotope shifts were determined with precision at the 100 kHz level. Combined with recent theoretical work, the changes in the nuclear-charge radii of (8,9)Li were determined. These are now the lightest short-lived isotopes for which the charge radii have been measured. It is found that the charge radii monotonically decrease with increasing neutron number from 6Li to 9Li.

Bethe logarithm and QED shift for lithium.

A novel finite basis set method is used to calculate the Bethe logarithm for the ground 2 (2)S(1/2) and excited 3 (2)S(1/2) states of lithium. The basis sets are constructed to span a huge range of distance scales within a single calculation, leading to well-converged values for the Bethe logarithm. The results are used to calculate an accurate value for the complete quantum electrodynamic energy shift up to order alpha(3) Ry. The calculated 3 (2)S(1/2)-2 (2)S(1/2) transition frequency for 7Li is 27 206.092 6(9) cm(-1), and the ionization potential for the 2 (2)S(1/2) state is 43 487.158 3(6) cm(-1). The 7Li-6Li isotope shift is also considered, and all the results compared with experiment.

Hyperfine splitting, isotope shift, and level energy of the 3S states of (6,7)Li.

We study the 2S-3S transition of (6,7)Li by high-precision laser spectroscopy using two-photon Doppler-free excitation and photoionization detection. Interferometric cross referencing to metrologic Rb 3S-5D two-photon transitions allowed measurement of the transition isotope shift and hyperfine splitting in the 3S state with precision at the 30 kHz level. The results are IS=11 453.734(30) MHz, A(3S)(6Li)=35.263(15) MHz, and A(3S)(7Li)=93.106(11) MHz. Combined with recent theoretical work, the isotope shift yields a new value for the change in squared nuclear charge radii DeltaR(2)=0.47(5) fm(2). This is compared with other work and some existing discrepancies are resolved.

Green's function analysis of electromagnetic waves in two-layered periodic structures with fluctuations in thickness.

A general method for the construction of the Green's function for finite one-dimensional inhomogeneous layers is developed. Using the results of this method the exact analytical Green's function for periodic dielectric structures is found. As an example of its application, the influence of fluctuations of the widths of the basic layers on the reflection and transmission of electromagnetic waves propagating through the structure is investigated. The results are applied to the design of optical switching systems with periodic dielectric structures as the operating medium. The same Green's function can be used to solve a wide variety of other problems.

Switching of electromagnetic waves by two-layered periodic dielectric structures.

The propagation of electromagnetic waves in two-layered periodic dielectric structures is investigated. The systematic dependence of the reflection coefficient on the parameters characterizing the structure is studied in detail. Using results of this exact analysis we investigate the influence of variation of the structure parameters on the reflection and transmission coefficients. As an example, we consider the changes in the structure parameters under an elastic stress. We show that under practically realizable conditions the reflection and transmission of the electromagnetic wave can be changed by as much as 80-90 % by creating a constant elastic stress inside the structure.