Laser Spectroscopic Determination of the ${}^6\mathrm{H}\mathrm{e}$ Nuclear Charge Radius

We have performed precision laser spectroscopy on individual ${}^6\mathrm{H}\mathrm{e}$ ($t_{1/2}=0.8\mathrm{s}$) atoms confined and cooled in a magneto-optical trap, and measured the isotope shift between ${}^6\mathrm{H}\mathrm{e}$ and ${}^4\mathrm{H}\mathrm{e}$ to be $43194.772\pm 0.056\mathrm{M}\mathrm{H}\mathrm{z}$ for the $2^3{S}_1-3^3{P}_2$ transition. Based on this measurement and atomic theory, the nuclear charge radius of ${}^6\mathrm{H}\mathrm{e}$ is determined for the first time in a method independent of nuclear models to be $2.054\pm 0.014\mathrm{f}\mathrm{m}$. 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.

Figure 1

The fluorescence signal of a single trapped metastable ${}^6\mathrm{H}\mathrm{e}$ atom. The count rate of the 389 nm fluorescence photons emitted from a single trapped atom is 35 counts in 50 ms, or $7\times {10}^2{\mathrm{s}}^{-1}$; the rate of background photons scattered off the walls and windows of the trap chamber is $2\times {10}^2{\mathrm{s}}^{-1}$.

Figure 2

Laser spectroscopy of helium atoms in the MOT. Fluorescence is recorded while the probing laser frequency is scanned over the resonance of the $2^3{S}_1-3^3{P}_2$ transition. (a) Spectrum of ${}^4\mathrm{H}\mathrm{e}$ accumulated with a total approximately 1 000 atoms in 5 min. The best fit with a Gaussian function gives a statistical error of 0.029 MHz in the center frequency, a FWHM of $6.8\pm 0.1\mathrm{M}\mathrm{H}\mathrm{z}$, and a reduced chi square of 0.77. (b) Spectrum of ${}^6\mathrm{H}\mathrm{e}$ accumulated with approximately 100 atoms in 1 h. The best fit with a Gaussian function gives a statistical error of 0.111 MHz in the center frequency, a FWHM of $6.2\pm 0.4\mathrm{M}\mathrm{H}\mathrm{z}$, and a reduced chi square of 1.1.

Figure 3

Experimental (the top three data points) and theoretical (all remaining points) values of the point-proton radius of ${}^6\mathrm{H}\mathrm{e}$. Reference 5 was determined in nuclear reaction measurements, while 6 was extracted from elastic scattering on protons. References 17, 18, 19, 20, 21 are results of calculations with cluster models. Reference 22 was calculated using the no-core shell model, and 23 refers to the quantum Monte Carlo technique described in the text with the three displayed values corresponding to different potentials between nucleons.