Principle of Charge Radius Determination

Charge radii cannot be obtained in a model-independent way from nuclear reaction studies. They are usually determined by means of electron scattering, muonic or electronic X-ray spectroscopy, or optical isotope shift measurements. While the first methods are mainly restricted to stable and long-lived isotopes, laser spectroscopic isotope shift measurements have been used to measure charge radii in long chains of unstable isotopes far away from the valley of stability.

For light nuclei the volume part of the isotope shift, which carries the nuclear charge radius information, is by far smaller than the mass shift (for Li it is only a 1 MHz contribution to a total isotope shift of 36 GHz). In order to separate the mass- and the field-induced contributions to the isotope shift, a very accurate theoretical prediction of the mass shift must be performed. Particularly, the specific mass shift is difficult to calculate because it depends on the electron correlations. Recently, powerful numerical methods have been developed to calculate the mass shift in Li-like systems very accurately. Yan and Drake presented a formula to calculate the difference in charge radii between ⁶Li and any other lithium isotope if the isotope shift in either the 2S-3S or a 2S-2P transition is measured. The accuracy of the mass shift calculation for ¹¹Li is better than 200 kHz). Such a resolution can only be obtained by cw laser spectroscopy on a thermal atomic beam or on atoms stored in a trap. Our approach is Two-Photon Resonance Ionization Mass Spectroscopy in the 2S - 3S transition of lithium performed on an atomic beam.

A similar approach has been used recently to measure the charge radius of the halo nucleus ⁶He at Argonne National Lab.

Excitation Scheme

Our approach for the isotope shift measurement is a resonant excitation of the 2S_1/2 - 3S_1/2 two-photon transition, followed by resonance ionization (RIS) and single-ion detection. Ions are easily extracted by electric fields and can be detected with an efficiency of almost 100%. All processes have to be optimized with respect to both, accuracy and efficiency.

High-accuracy calculations for the mass shift of lithium isotopes exist for the 2S_1/2 - 3S_1/2 and the 2S_1/2 - 2P_1/2,3/2 transitions. Of these, the 2S - 3S transition has the following advantages:

• It is a two-photon excitation that excites all atoms of the ensemble independent of their velocity. Provided that the laser intensity required to saturate this non-linear process can be obtained, this is an efficient method to excite "hot" atoms from a thermal source. 
• The expected linewidth is dominated by the lifetime of the 3S state (5.3 MHz) and thus facilitates the determination of the line center with the required accuracy of about 200 kHz
• All lithium isotopes have a non-zero nuclear spin and thus all electronic states exhibit a hyperfine structure splitting. The selection rule DF=0 for a S - S two-photon transition limits the number of hyperfine transitions to two. These lines are well separated, while the hyperfine transitions in the S - P transitions are not or only barely resolved.

Figure 1 shows the excitation scheme, which we use for our measurements. A Doppler-free two photon transition from the 2s ground state into the 3s excited state provides high resolution for the isotope shift measurement. The two-photon transition is followed by spontaneous emission into the 2P_1/2,3/2 levels. Light of a dye laser at 610 nm is then used to excite atoms in the 2P_3/2 state into the 3D levels from which they can be ionized with a single photon from either the 610nm or the 735 nm laser light. The intensity of the dye laser is sufficient to introduce a strong power broadening in the 2P - 3D transition and this leads to an overlapp of the 3D_3/2,5/2 states. The line profile has been investigated and it was found that the excitation and ionization efficiency is independent of the exact dye laser frequency over an range of about 1 GHz.

22 April 2005