Colloquium: Laser probing of neutron-rich nuclei in light atoms

The neutron-rich ${}^6\mathrm{He}$ and ${}^8\mathrm{He}$ isotopes exhibit an exotic nuclear structure that consists of a tightly bound ${}^4\mathrm{He}$-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 ${}^4\mathrm{He}\mathrm{\text{−}}{}^6\mathrm{He}\mathrm{\text{−}}{}^8\mathrm{He}$ 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.

Figure 1

Borromean rings depicted here as a marble inlay in the Church of San Pancrazio, Florence. The topology is such that the three rings are linked even though no two-ring pairs are linked. Analogies are found in certain nuclear bindings such as the $\alpha \mathrm{\text{−}}n\mathrm{\text{−}}n$ structure of ${}^6\mathrm{He}$.

Figure 2

Illustration of the nuclear structure of ${}^4\mathrm{He}$, ${}^6\mathrm{He}$, and ${}^8\mathrm{He}$. Red spheres represent protons, and blue spheres represent neutrons. The red shadows indicate the areas of motion of the protons; the blue shadows indicate the areas of motion of the neutrons. The nuclear charge radius is predominantly a measure of the center-of-mass motion of the charge carrying a ${}^4\mathrm{He}$-like core in ${}^6\mathrm{He}$ and ${}^8\mathrm{He}$ and depends on the correlation of the halo neutrons.

Figure 3

The energy level diagram of the neutral helium atom. The $2{}^{3}S_1$ state is metastable. Laser excitation on the $2{}^{3}S_1\mathrm{\text{−}}2{}^{3}P_2$ transition at 1083 nm was used to trap and cool helium atoms. Laser excitation on the $2{}^{3}S_1\mathrm{\text{−}}3{}^{3}P_J$ transition at 389 nm was used to detect the trapped atoms and measure their isotope shifts. Details are provided in Sec. 4a.

Figure 4

The electrostatic potential and energy of bound $s$- and $p$-electronic levels are illustrated in (a) for a hypothetical point nucleus, and in (b) for the real case of a nucleus with a finite volume. The higher potential within the finite-sized nucleus causes the electrons to be less bound. This so-called volume effect is most pronounced for $s$ electrons.

Figure 5

Schematic of the ${}^{6,8}\mathrm{He}$ trap apparatus. A beam of metastable helium atoms is provided by a gas discharge source. Subsequently, the atoms are collimated through transverse cooling, decelerated in a Zeeman slower and captured by a magneto-optical trap (MOT). Light from the spectroscopy laser beams that is scattered by the trapped atoms is imaged onto a photon detector. More details are provided in 107.

Figure 6

Sample spectra for ${}^8\mathrm{He}$ taken on the $2{}^{3}S_1\mathrm{\text{−}}3{}^{3}P_2$ transition at a probing laser intensity of $\sim 3\times I_{\mathrm{sat}}$. Error bars are statistical uncertainties, and the lines represent least squares fits using Gaussian profiles. (a) Spectrum of a single ${}^8\mathrm{He}$ atom, the first observed in the trap. It stayed in the trap for an extra long time of 0.4 s. The fit results in a statistical frequency uncertainty of 320 kHz with ${\chi }^2=0.84$. (b) Spectrum accumulated over 30 trapped atoms. Uncertainty is 110 kHz with ${\chi }^2=0.87$.

Figure 7

Experimental isotope shifts relative to ${}^4\mathrm{He}$ from the individual measurements for (a) ${}^8\mathrm{He}$ and (b) ${}^6\mathrm{He}$. As expected, the total isotope shift depends on the $J$ of the upper $3{}^{3}P_J$ state. The extracted field shift values plotted in (c) show no systematic $J$ dependence for either isotope. The horizontal lines in (c) mark the weighted averages and statistical error bands of the field shift.

Figure 8

Comparison between experimental and theoretical values of point-proton and matter radii for ${}^6\mathrm{He}$ (top panel) and ${}^8\mathrm{He}$ (bottom panel) (see also Tables ).

Figure 9

${}^6\mathrm{He}$ point-proton radius vs two-neutron separation energy obtained from a number of GFMC calculations with different initial conditions and three-body potentials.

Figure 10

Point-proton and point-neutron densities of the even helium isotopes as extracted from GFMC calculations.

Figure 11

Model-space dependence of the ${}^6\mathrm{He}$ point-proton (solid curves) and neutron (dashed curves) radii in NCSM calculations using the JISP16 $NN$ potential. From 55.

Figure 12

Proton-proton pair densities ${\rho }_{pp}$ of the even helium isotopes as extracted from GFMC calculations. From 77.

Figure 13

Density distributions of valence neutrons in ${}^6\mathrm{He}$ for the special case of both neutrons being equally distant from the ${}^4\mathrm{He}$ core. The densities are shown as a function of the distance of the neutrons from the core and the angle between them relative to the ${}^4\mathrm{He}$ core. From 74.

Figure 14

Laser excitation scheme (left) and experimental setup (right) to measure the $2s{}^{2}S_{1/2}\to 3s{}^{2}S_{1/2}$ electronic transition in lithium. CDEM, continuous dynode electron multiplier; QMF, quadrupole mass filter; PZT, piezoelectric transducer. Adapted from 67.

Figure 15

Point-proton radii of lithium and beryllium isotopes obtained from isotope shift measurements (66; 51). Error bars are based on the isotope shift uncertainty only. The additional systematic uncertainty caused by the reference charge radius uncertainty is indicated by the dashed lines. The GFMC values are for the $\mathrm{AV}18+\mathrm{IL}7$ Hamiltonian.