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Francium Hyperfine Anomaly

The largest contribution to atomic hyperfine splitting arises from the interaction of the magnetic field of atomic electrons with the magnetization of the atomic nucleus. For light elements it is usually sufficient tFrancium Staggeringo treat the nucleus as a point with a pure dipole field when calculating this splitting. As the radius of the nucleus increases, however, the hyperfine coupling constant, A, deviates from the value expected by point-nucleus calculations. This is known as the Bohr-Weisskopf effect, or hyperfine anomaly (HFA). It is affected both by the magnetization radius (rm) of the nucleus and by its internal magnetic distribution.

Francium provides a particularly good laboratory in which to study the hyperfine anomaly. Its single valence electron gives it a particularly simple atomic structure, and its ground state (S1/2) and first excited state (P1/2) wavefunctions both significantly overlap the nucleus, leading to a large predicted HFA effect. The fact that these orbitals have different radial dependences produces a sensitivity to the nuclear magnetization radius which manifests as a change in the ratio of their hyperfine coefficients. Francium's proximity to two “magic” nucleon numbers, particularly in its lighter isotopes, also makes it relatively easy to model as a single-particle system. From such models it is theorized that for odd-neutron isotopes the unpaired neutron will occupy an otherwise vacant f5/2 orbital, leading to a significant increase in the magnetization radius but little change in the charge radius. This results in the theoretical prediction of a measurable odd-even staggering in the S-to-P hyperfine coefficient ratio, which has already been experimentally confirmed by hyperfine structure measurements for the isotopes 208Fr-212Fr.

This experiment proposes to extend these measurements further into the proton-rich region below  208Fr, and also into the neutron-rich region above  220Fr. Successful predFrancium Relative Isotope Shiftiction of the HFA in these regions requires accuracy in both the atomic and nuclear domains, so this experiment provides a unique way to test two fields of physics simultaneously. In addition, the experiment aims to measure the hyperfine structure of Francium's P3/2 orbital, which should allow determination of the electric quadrupole moment of the nucleus. Finally, measurement of Francium's isotope shifts—currently known only for 207Fr-212Fr—would also be extended to these more extreme mass regions. In doing so, it could be seen whether Francium continues to follow the linear correlation—seen all the data collected so far—between its isotope shifts and those of its Pb and Bi isotones. Any deviation from this correlation would likely indicate a deformation in the almost-spherical lead core believed to be at the centre of the Fr nucleus, which would also show up as a shift in the atomic hyperfine levels.

In addition to collinear laser spectroscopy, this experiment will also utilize the resources of TRINAT—TRIUMF's magneto-optical atom trap. This will be used to hold the atoms in place while the hyperfine coefficients of their P1/2 and P3/2 orbitals are precisely measured using an FM-modulated laser probing technique. Such techniques have been the basis for the existing hyperfine measurements of Francium isotopes, performed by Stony Brook's Nuclear Structure Lab.

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