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

Collinear Laser Spectroscopy of 2 ^{3}S_{1}→2 ^{3}P_{J} Transitions in Helium-like ^{12}C^{4+}

Transition frequencies and fine-structure splittings of the 2 ^{3}S_{1}→2 ^{3}P_{J} transitions in helium-like ^{12}C^{4+} were measured by collinear laser spectroscopy on a 1-ppb level. Accuracy is increased by more than 3 orders of magnitude with respect to previous measurements, enabling tests of recent nonrelativistic (NR) QED calculations including terms up to mα^{7}. Deviations between the theoretical and experimental values are within theoretical uncertainties and are ascribed to mα^{8} and higher-order contributions in the series expansion of the NR QED calculations. Finally, prospects for an all-optical charge radius determination of light isotopes are evaluated.

Absolute Frequency Measurements of the D Lines in ^{9}Be^{+} Using a Single Trapped Ion

Optical frequencies of the D line transitions in ^{9}Be^{+} were measured with a relative uncertainty of Δν/ν=5×10^{-11}. The results represent the highest accuracy achieved on a broad electric dipole-allowed (E1) transition in a trapped ion experiment to date, enabled in part by detailed consideration of photon recoil and quantum interference. Measurements were made on a single laser-cooled ion stored in a radio frequency Paul trap, using a spectroscopy laser stabilized to an optical frequency comb and referenced to UTC (NIST). The uncertainties in the D_{1} and D_{2} lines have been reduced by a factor of 10 and 30, respectively, compared to previous work. We have extracted the ^{2}P fine structure splitting, Δν_{fs}=197 064.54(7)  MHz, and the ^{2}P_{1/2} hyperfine constant, A_{P_{1/2}}=-117.92(4)  MHz.

An Introduction to Relativistic Theory as Implemented in GRASP

Computational atomic physics continues to play a crucial role in both increasing the understanding of fundamental physics (e.g., quantum electrodynamics and correlation) and producing atomic data for interpreting observations from large-scale research facilities ranging from fusion reactors to high-power laser systems, space-based telescopes and isotope separators. A number of different computational methods, each with their own strengths and weaknesses, is available to meet these tasks. Here, we review the relativistic multiconfiguration method as it applies to the General Relativistic Atomic Structure Package [grasp2018, C. Froese Fischer, G. Gaigalas, P. Jönsson, J. Bieroń, Comput. Phys. Commun. (2018). DOI: 10.1016/j.cpc.2018.10.032]. To illustrate the capacity of the package, examples of calculations of relevance for nuclear physics and astrophysics are presented.

A new Collinear Apparatus for Laser Spectroscopy and Applied Science (COALA)

We present a new collinear laser spectroscopy setup that has been designed to overcome systematic uncertainty limits arising from high-voltage and frequency measurements, beam superposition, and collisions with residual gas that are present in other installations utilizing this technique. The applied methods and experimental realizations are described, including an active stabilization of the ion-source potential, new types of ion sources that have not been used for collinear laser spectroscopy so far, dedicated installations for pump-and-probe measurements, and a versatile laser system referenced to a frequency comb. The advanced setup enables us to routinely determine transition frequencies, which was so far demonstrated only for a few cases and with lower accuracy at other facilities. It has also been designed to perform accurate high-voltage measurements for metrological applications. Demonstration and performance measurements were carried out with Ca⁺ and In⁺ ions.

Nuclear Charge Radii of ^{10,11}B

The first laser spectroscopic determination of the change in the nuclear charge radius for a five-electron system is reported. This is achieved by combining high-accuracy ab initio mass-shift calculations and a high-accuracy measurement of the isotope shift in the 2s^{2}2p  ^{2}P_{1/2}→2s^{2}3s  ^{2}S_{1/2} ground state transition in boron atoms. Accuracy is increased by orders of magnitude for the stable isotopes ^{10,11}B and the results are used to extract their difference in the mean-square charge radius ⟨r_{c}^{2}⟩^{11}-⟨r_{c}^{2}⟩^{10}=-0.49(12)  fm^{2}. The result is qualitatively explained by a possible cluster structure of the boron nuclei and quantitatively used to benchmark new ab initio nuclear structure calculations using the no-core shell model and Green's function Monte Carlo approaches. These results are the foundation for a laser spectroscopic determination of the charge radius of the proton-halo candidate ^{8}B.

Structure and Reactions of ^{11}Be: Many-Body Basis for Single-Neutron Halo

The exotic nucleus ^{11}Be has been extensively studied and much experimental information is available on the structure of this system. We treat, within the framework of renormalized nuclear field theory in both configuration and 3D space, the mixing of bound and continuum single-particle states through the coupling to collective vibrations of the ^{10}Be core. We also take care of the Pauli principle acting not only between the single valence particle explicitly considered and those participating in the collective states, but also between fermions involved in two-phonon virtual states dressing the single-particle motion. In this way, it is possible to simultaneously and quantitatively account for the energies of the 1/2^{+}, 1/2^{-} low-lying states, the centroid and line shape of the 5/2^{+} resonance and the one-nucleon stripping and pickup absolute differential cross sections involving ^{11}Be as either target or residual nucleus. Also for the dipole transition connecting the 1/2^{+} and 1/2^{-} parity inverted levels as well as the isotopic shift of the charge radius. Theory provides a unified and exhaustive nuclear structure and reaction characterization of the many-body effects which are at the basis of this paradigmatic one-neutron halo system.

Proton Distribution Radii of ^{12-19}C Illuminate Features of Neutron Halos

Proton radii of ^{12-19}C densities derived from first accurate charge changing cross section measurements at 900A  MeV with a carbon target are reported. A thick neutron surface evolves from ∼0.5  fm in ^{15}C to ∼1  fm in ^{19}C. The halo radius in ^{19}C is found to be 6.4±0.7  fm as large as ^{11}Li. Ab initio calculations based on chiral nucleon-nucleon and three-nucleon forces reproduce the radii well.

Simple Nuclear Structure in (111-129)Cd from Atomic Isomer Shifts

Isomer shifts have been determined in ^{111-129}Cd by high-resolution laser spectroscopy at CERN-ISOLDE. The corresponding mean square charge-radii changes, from the 1/2^{+} and the 3/2^{+} ground states to the 11/2^{-} isomers, have been found to follow a distinct parabolic dependence as a function of the atomic mass number. Since the isomers have been previously associated with simplicity due to the linear mass dependence of their quadrupole moments, the regularity of the isomer shifts suggests a higher order of symmetry affecting the ground states in addition. A comprehensive description assuming nuclear deformation is found to accurately reproduce the radii differences in conjunction with the known quadrupole moments. This intuitive interpretation is supported by covariant density functional theory.

Precision Test of Many-Body QED in the Be+ 2p Fine Structure Doublet Using Short-Lived Isotopes

Absolute transition frequencies of the 2s 2S{1/2}→2p2P{1/2,3/2} transitions in Be^{+} were measured for the isotopes ^{7,9-12}Be. The fine structure splitting of the 2p state and its isotope dependence are extracted and compared to results of ab initio calculations using explicitly correlated basis functions, including relativistic and quantum electrodynamics effects at the order of mα(6) and mα(7) ⁢ln α. Accuracy has been improved in both the theory and experiment by 2 orders of magnitude, and good agreement is observed. This represents one of the most accurate tests of quantum electrodynamics for many-electron systems, being insensitive to nuclear uncertainties.

Proton radii of (12-17)B define a thick neutron surface in ¹⁷B

The first determination of radii of point proton distribution (proton radii) of (12-17)B from charge-changing cross sections (σ(CC)) measurements at the FRS, GSI, Darmstadt is reported. The proton radii are deduced from a finite-range Glauber model analysis of the σ(CC). The radii show an increase from ¹³B to ¹⁷B and are consistent with predictions from the antisymmetrized molecular dynamics model for the neutron-rich nuclei. The measurements show the existence of a thick neutron surface with neutron-proton radius difference of 0.51(0.11) fm in ¹⁷B.

Hyperfine structure constant of the neutron halo nucleus (11)Be(+)

The hyperfine splittings of ground state Be+11 have been measured precisely by laser-microwave double resonance spectroscopy for trapped and laser cooled beryllium ions. The ions were produced at relativistic energies and subsequently slowed down and trapped at mK temperatures. The magnetic hyperfine structure constant of Be+11 was determined to be A11=-2677.302 988(72)  MHz from the measurements of the mF-mF'=0-0 field independent transition. This measurement provides essential data for the study of the distribution of the halo neutron in the single neutron halo nucleus Be11 through the Bohr-Weisskopf effect.

First use of high-frequency intensity modulation of narrow-linewidth laser light and its application in determination of 206,205,204Fr ground-state properties

Collinear laser spectroscopy was performed on the nuclear ground states of the neutron-deficient isotopes (206,205,204)Fr. A new technique was developed to suppress hyperfine pumping in collinear laser spectroscopy of atoms. This involved high-frequency intensity modulation of narrow-linewidth laser light using fast-switching electro-optical modulators. The nuclear ground-state spins of (206,205,204)Fr were determined to be 3, 9/2, and 3, respectively. Both the changes in mean-squared charge radii and nuclear magnetic dipole moments indicate a departure from single-particle estimates.

Nuclear charge radius of 12Be

The nuclear charge radius of (12)Be was precisely determined using the technique of collinear laser spectroscopy on the 2s(1/2)→2p(1/2,3/2) transition in the Be(+) ion. The mean square charge radius increases from (10)Be to (12)Be by δ<r(c)(2)>(10,12)=0.69(5) fm(2) compared to δ<r(c)(2)>(10,11)=0.49(5) fm(2) for the one-neutron halo isotope ^{11}Be. Calculations in the fermionic molecular dynamics approach show a strong sensitivity of the charge radius to the structure of ^{12}Be. The experimental charge radius is consistent with a breakdown of the N=8 shell closure.

Nuclear structure experiments along the neutron drip line

Invariant mass measurements and breakup reactions of neutron-rich nuclei have been instrumental in the study of nuclear structure effects at the limit of nuclear existence. The measurements of neutron-unbound states rely on the detection of neutrons in coincidence with fragments at energies between 100 and 1000 MeV/u. Charged particle and γ-ray coincidence measurements yield additional information. The production and detection methods for these experiments and examples of results in light nuclei are presented. Future opportunities with new facilities and the development of new detectors are described.

QED theory of the nuclear magnetic shielding in hydrogenlike ions

The shielding of the nuclear magnetic moment by the bound electron in hydrogenlike ions is calculated ab initio with inclusion of relativistic, nuclear, and quantum electrodynamics (QED) effects. The QED correction is evaluated to all orders in the nuclear binding strength parameter and, independently, to the first order in the expansion in this parameter. The results obtained lay the basis for the high-precision determination of nuclear magnetic dipole moments from measurements of the g factor of hydrogenlike ions.

Scaling of charge-changing interaction cross sections and point-proton radii of neutron-rich carbon isotopes

Charge-changing cross sections σ(cc) of stable and unstable nuclei ((9-11)Be, (14-16)C, and (16-18)O) on a carbon target were investigated at 300  MeV/nucleon. A phenomenological analysis based on the Glauber theory indicates an approximate, but universal, scaling of σ(cc) over a wide range of A/Z. This allows the determination of the density distributions of protons tightly bound in the nuclei. An application to (16)C, which is considered to be an anomalously deformed nucleus, indicates a systematic evolution of proton root-mean-square radii and has revealed for the first time a neutron skin effect in carbon isotopes. Being complementary to isotope-shift and electron-scattering experiments, the present method can open up a new approach to explore the structure of exotic nuclei.

Nuclear structure corrections in muonic deuterium

The muonic hydrogen experiment measuring the 2P-2S transition energy [R. Pohl et al., Nature (London) 466, 213 (2010)] is significantly discrepant with theoretical predictions based on quantum electrodynamics. A possible approach to resolve this conundrum is to compare experimental values with theoretical predictions in another system, muonic deuterium μD. The only correction which might be questioned in μD is that due to the deuteron polarizability. We investigate this effect in detail and observe cancellation with the elastic contribution. The total value obtained for the deuteron structure correction in the 2P-2S transition is 1.680(16) meV.

Microscopic calculation of the 3He(α,γ)7Be and 3H(α,γ)7Li capture cross sections using realistic interactions

The radiative capture cross sections for the 3He(α,γ)7Be and 3H(α,γ)7Li reactions are calculated in the fully microscopic fermionic molecular dynamics approach using a realistic effective interaction that reproduces the nucleon-nucleon scattering data. At large distances bound and scattering states are described by antisymmetrized products of 4He and 3He/3H ground states. At short distances the many-body Hilbert space is extended with additional many-body wave functions needed to represent polarized clusters and shell-model-like configurations. Properties of the bound states are described well, as are the scattering phase shifts. The calculated S factor for the 3He(α,γ)7Be reaction agrees very well with recent experimental data in both absolute normalization and energy dependence. In the case of the 3H(α,γ)7Li reaction the calculated S factor is larger than available experimental data by about 15%.

Precise electromagnetic tests of ab initio calculations of light nuclei: states in 10Be

In order to test ab initio calculations of light nuclei, we have remeasured lifetimes in 10Be using the Doppler shift attenuation method (DSAM) following the 7Li(7Li,alpha)10Be reaction at 8 and 10 MeV. The new experiments significantly reduce systematic uncertainties in the DSAM technique. The J(pi) = 2(1)(+) state at 3.37 MeV has tau = 205 +/- (5)(stat) +/- (7)(sys) fs corresponding to a B(E2 down) of 9.2(3)e(2) fm(4) in broad agreement with many calculations. The J(pi) = 2(2)(+) state at 5.96 MeV was found to have a B(E2 down) of 0.11(2)e(2) fm(4) and provides a more discriminating test of nuclear models. New Green's function Monte Carlo calculations for these states and transitions with a number of Hamiltonians are also reported and compared to experiment.