Investigation of the Use of He-Diatomic Van der Waals Complexes as a Probe of Time Reversal Violation

Jacob Stinnett, Dr. Neil Shafer-Ray, and Dr. Eric AbrahamHomer L. Dodge Department of Physics

University of Oklahoma

This work was funded by the National Science Foundation (NSF-0855431.)

66th OSU International Symposium on Molecular SpectroscopyJune 24, 2011

Outline

• Motivation

• A remarkable observation of pure Stark spectroscopy in NO

• Simple vector model of a extremely weak

He-NO van der Waals complex

• Suspicions

• Implications for an e-EDM measurement

Fabry-Pérot Type Resonator: Spherical Reflectors

PbF

Fourier Transform Microwave Spectrometer: Pure rotational absorption spectrom of the X1 state of PbF. (Collaborators Jens-Uwe Grabow, Richard Mawhorter Hanover Germany)

0 2 4 6 8 1 0

1 2

1 0

8

6

4

2

0

Ek V c m

mH

z10^27

ecm

eEDM of the J12 F1 ,M 1 s tate o f P bF

Many e-EDM candidates require a large (~10kV/cm) field to becomesensitive.

Similar curves forBaF, HgF, YbF

This study was motivated a series of remarkable experimentsinvolving pure Stark spectroscopy of the NO molecule.

Chem Phys Let 341 2001 495.

A DC electric field of order 14 v/cm is crossed with an RF electric field of similar amplitude.At resonant frequencies, the population of NO, as viewed at non-state selective detector, isobserved.

Non state-selective 266nm ionization

The Truly Incredible Amazing

Result

Caceres et al measured a completely linear Stark effect in NO with simple transitions given by

for JU=1/2, 3/2, and 5/2

D = 0.15782(2) Debye Ap J 161 (1970) 779

BUT . . .

D= 0.1578(4) Debye CPL 426 (2006)214

Chem Phys Let 426 2006 214

Two 2P1/2 electronic states form the ground state

Z

YX

W- [Rxz -, Ryz +]W+ [Rxz +, Ryz -]

Y

Z

X

21

21 |1| W = | L + S |=1/2 gives projection of

angular momentum on the nuclear axis: orbital a.m.

(=1 for P states)spin a.m.

(±1/2 because this is a 2P state.)

Motion of the Nuclei

Although the electrons are light, their net angular momentum isnot much smaller than that of the nuclei.

Nuclei move as a symmetric top.

Com

bine

to fo

rm W

+

wav

e fu

nctio

n

Com

bine

to fo

rm W

-

wav

e fu

nctio

n

PARI

TY

PARI

TYIn the absence of an applied field, the wave functions are eigenvectors of parity

and hence have no net dipole moment.

Combined electronic and nuclear motion, DE<<DUW

up

down

For a strong electric field, the wave functions are either pointed up or down and one expects a linear Stark effect.

Combined electronic and nuclear motion DE>>DUW

MotivationThe Stark effect in NO is described by

D is the dipole moment of NOE is the electric field

Parity splitting~= 10 GHz for 2Π1/2 NO~= 10 MHz for 2Π3/2 NO

2222

2

1

21

Jp

JJ

mEDU Stark

Motivation

What suppressed the parity splitting?!!#!@!.

+MAGIC

2222

2

1

21

Jp

JJ

mEDU Stark

“At present we have no explanation why the best fit is obtained with the resonant transition calculated with eq 2.”

In this work we investigate the possibility that a novel He-NO van der Waals complex is responsible for this behavior.

N

Possible He-NO Rydberg-Like van der Waals Complex

O

He

extE�������������� (1) He must be far enough away

so thatDHe <<DNO.

(2) He must be close enoughso that the He-NO van der Waalsinteraction is stronger than the

parity splitting.

Possible for He-NO(2P3/2) at ~ 20 Angstroms.

extNO

extHeNO

EDU

EDDU

)(

)(

Because the van der Waals energy must be much less thanthe rotational energy, the interaction may be treated as a perturbation

to the NO spin rotational Hamiltonian

SR vdw StarkH H H H

222

3

221 1

2 0 12 23

ˆ ˆ3 12

4 4

2ˆ ˆ ˆ ˆ ˆ ˆ( ) ( ) ( )

4

vdwo

dcm cm cmR

o

n sDH

R

DP n r P n r P n r

R

For the case of dipole-flipping transitions with

|MHe|=JHe= |M| = ½, W=3/2, this reduces to

This theory leads to a linear Stark effect that follows a simple vector model at low fields.

(Ignoring E Dinduced)

A Simple Vector Model

This simple model allows us to recover their formula.

3

Our model explains lines that Caceras et al have assigned to a J=3/2, J=5/2 transition.

It also does a reasonable job predicted the substructure surrounding these lines.

For the JU = 1/2 line, this vector model can not explain the observation.

2/5'

2/1||

2/3

HeHeHe mmJ

m

J

2/1'

2/1||

2/3

HeHeHe mmJ

m

J

ExperimentalTheoretical

• The He-NO bond distance required to suppress the parity splitting leads to a polarized He atom that changes the magnitude of the Stark interaction by much more than 0.2%.

Suspicions

Chem Phys Let 426 2006 214

1) A simple model indicates that the polarizability of a He-NO complex may be much greater than that of NO and gives reasonable agreement to the J=3/2 and J=5/2 lines observed by Caceres et al.

2) We cannot explain the magnitude of the linear Stark effect observed by Caceres et al and suspect their data analysis may be flawed. It is likely that their data is probing a known rather than exotic He-NO species.

3) He-[eEDM molecule] clusters formed in laser ablation sources may have increased polarizability and hence be worth investigating.

Conclusions

Acknowledgements

Dr. Neil Shafer Ray

Dr. Eric Abraham

NSF

Questions?

NO(2P3/2)-He(slow moving) + hnRF NO(2P3/2)-He(fast moving)

NO(2P3/2)-He(fast moving) + NO NO(2P1/2) + He + NO + kinetic energy

Resonant thermalization of the Omega-Doublet energy (120 cm-1/molecule) and transverse kinetic energy of the beam (~1E-3 cm-1/ molecule).

Zeeman-effect in PbF(X1) pure rotational spectra

B = 0

DM = 0 DM = +/-1

~3 kHz

FREQUENCY / MHz22574.4 22575.4