1. Microwave Spectroscopy of the Autoionizing 5d 3/2 n l States of Barium Edward Shuman Tom Gallagher

2. Outline Motivation Background Experimental Setup Experimental Results Theory Conclusion

3. Motivation Microwave spectroscopy on rapidly decaying Rydberg states has never been done before. Very little is known experimentally about the interaction of a Rydberg electron with an anisotropic core despite the many years spent studying Rydberg atoms. By studying high l states we can probe the properties of the ion core. Specifically we can measure the polarizability and the permanent moments of the core.

4. Rydberg Atoms A Rydberg atom is an atom with a high principle quantum number n. These atoms have exaggerated properties. For instance for n=30, = 900 a 0 μ =900 ea 0 W =-120 cm -1 W=-1/2n 2 = n 2

5. Detection by Field Ionization Field requried for ionization given by E=1/16n 4 For n=30, E= 400V/cm V=-1/r-Ez

6. Autoionization When the two electrons are near each other the probability that autoionization will occur is higher. For this reason autoionization scales as (radius) -1 of the state. Quantum mechanically the autoionization rate is given by A ~ 2 2

7. l Dependence of Autoionization Low l states have more elliptical orbits. High l states have more circular orbits. Because the two electrons must be close to each other to autoionize, low l states have higher A.I. rates than do high l  states.

8. Experimental Apparatus

9. Excitation and Timing k=5/2

10. Observations At high microwave power we observe two transitions corresponding to ng  n±1h. At low microwave power we see one dominant microwave transition. We attribute this feature to the ng  n±1h transition.

11. Quantum defect theory According to quantum defect theory Here  l is known as the quantum defect and gives the energy shift of the Rydberg states from hydrogen.  l is also recognized as the phase shift of the non- hydrogenic wave function from the hydrogenic one.

12. Results By combining the ng  n  1h resonance frequencies, we can measure the ng(h)  n  2g (h) intervals. From these intervals we can calculate the quantum defects for the g and h states over the range of n’s we studied. For 45  n  50, we measured an average quantum defect for the g states of +0.019. For the h states, we measured an average quantum defect of 0.003.

13. Initially all four k states are degenerate. The first order effect is the permanent quadrupole moment of the core. This produces large splitting in the fine structure components. The second order effects are the polarizabilities. The scalar dipole polarizability moves all the levels to lower energy, but the tensor component splits the states slightly. The scalar quadrupole polarizability pushes the energy levels up or down. Fine structure in Barium

14. Failure of the core polarization model The adiabatic approximation in the quadrupole case breaks down spectacularly. The spacing between ionic states is very small compared to the Rydberg energy.

15. Conclusion We have performed microwave spectroscopy on autoionizing states for the first time. We believe that the technique used here can be used in other atoms or molecules that have lifetime on the order of a few ns or greater. These results are of special interest because of the few advances in the spectroscopy of atoms or molecules with anisotropic cores.