1. New Measurements of the Hyperfine Interactions and Dipole Moment of KI
Ben McDonald,
Advisor: Professor James Cederberg

2. Various Nuclear Moments. L to R: Quadrupole, Octuple, Hexadecapole
Charge Distribution
The ultimate goal of our work was to find the field gradient acting on the nuclei in the molecule and the shapes of the charge distributions within the nuclei.
Various Nuclear Moments. L to R: Quadrupole, Octuple, Hexadecapole
Our work finds the constants that describe the shape of the charge and current distributions in the nucleus.

3. Energy States
Hyperfine
Our research focused on the Hyperfine energy transitions within the KI molecule.
Rotational
Rotational
Hyperfine
Vibrational
Vibrational

4. Inducing Transitions
To find the different energy states, we measured the energy required to induce a transition.
We do this by stimulating the KI with an electric field.
Frequency corresponds to energy.
Final State
Initial State
Transition
Electric Field

5. Measuring Transitions
We measure the number of molecules that don’t make a transition.
At the frequency where a transition occurs, we measure a drop in the detector signal.
We invert the image to see peaks.

6. Fitting Transitions
We use software to fit lines to transition data using the Rabi function.

7. Taking the Data
First, we used theoretical predictions to give a rough estimate of transition frequencies.
Then, we performed an initial run that allowed a refinement of the molecular constants, which in turn improved our predictions for subsequent runs.
Using this “bootstrapping” technique, we achieved an increase in precision of four orders of magnitude over previous measurements.

8. Stark Effect
With RF and DC fields, we induced transitions within the hyperfine energy levels using the Stark Effect.
We needed to fit these Stark splits to achieve the desired precision in pinpointing the hyperfine levels.
The Stark Effect involves a change in the molecule’s energy levels due to a KI’s orientation relative to the RF and DC electric fields.
Positive energy shift
Negative energy shift

9. RF-induced Transitions
After finding the desired range in frequency for a transition, we used the RF field to get a Stark splitting of the hyperfine energy levels.
Fitting for this RF-induced Stark split gave a measurement of the RF factor.
The RF factor is an indicator of the RF field’s behavior within the transition region of the beam.

10. RF-induced Transitions
We fit RF Stark split data to obtain the RF factor.

11. DC-induced Transitions
Once we found the correct RF factor, which was not under our control, we used it to help fit data from transitions due to the DC field, which was under our control.

12. The Dipole Moment
The Stark splitting is proportional to the square of the dipole and the sum of the squares of the RF and DC fields.
Since we knew about the Stark splits, the RF fields, and the DC fields, we then calculated a value for the
dipole moment =
11.064(14) (23)(v +½) debye

13. 39KI and 41KI
We found a mysterious shift in the nuclear electric quadrupole moment of Iodine when comparing 39KI and 41KI. 1 2 3 1 2 3

14. 39KI and 41KI
This is a fit of the same spectrum with frequencies adjusted for the transitions at MHz,
MHz, and MHz. 1 2 3 1 2 3

16. Old Potassium eQq = -4120  120 kHz
Our Results
Old Potassium eQq =  120 kHz
New Potassium eQq =
 kHz
Old Iodine eQq =  120 kHz
New Iodine eQq =  kHz

17. eQq
The expanded eQq, or nuclear electric quadrupole interaction, for Iodine is
(12) (19) · (v + ½) (63) · (v + ½)2
(65) · (v + ½) (67) · J(J + 1)
(59) · J(J + 1) · (v + ½) kHz
and for Potassium, it is
(22) (49) · (v + ½) (22) · (v + ½)2
(17) · J(J + 1) kHz

18. Further Results K spin rotation interaction =
(65) (52) · (v + ½) (19) · (v + ½)2 kHz
I spin rotation interaction =
(45) (61) · (v + ½) (24) · (v + ½)2 kHz
Tensor spin-spin interaction =
(69) (52) · (v + ½) kHz
Scalar spin-spin interaction =
(36) (38) · (v + ½) kHz

19. Thanks!