Obtaining the Optical Field Isotope Shifts of a Light Element

Abstract

The problem of obtaining field isotope shifts for light elements is discussed, and it is shown to be possible, in principle, to extract this information solely from an optical-isotope-shift experiment. We attempted such an experiment with the even-even calcium isotopes: Ca 40, 42, 44, and 48. We found that an accuracy of ∼${10}^{-5\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ in the measurements would be required to effect the separation. Lacking that accuracy, we considered the conditions under which optical-isotope-shift measurements may be combined with those of other isotope-shift experiments. The even-even calcium isotopes fulfill these conditions, allowing the desired separation of optical mass- and field-effect isotope shifts to be accomplished by drawing on the results of muonic x-ray and electron-scattering experiments. The optical field-effect shifts thereby found are shown to corroborate the picture of the calcium nuclei derived from those experiments. A correlation between the relative isotope shift and the binding energy per nucleon, proposed by Gerstenkorn, is shown to apply to the calcium isotope shifts.