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Atomic Physics Hyperfine structure Atomic Physics Hyperfine structure

Atomic Physics Hyperfine structure - PowerPoint Presentation

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Atomic Physics Hyperfine structure - PPT Presentation

Part 3 Higher order multipole moment effects A general theory Some experiments Elaborating our topic hyperfine structure Higher order multipole moment hyperfine effects Ref ID: 810571

states hyperfine interaction beam hyperfine states beam interaction hfs atoms multipole nuclear magnetic doppler structure probe ref small electron

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Slide1

Atomic Physics

Hyperfine structure

Part 3

Higher order

multipole

moment effects

A general

theory

Some experiments

Slide2

Elaborating our topic – hyperfine structure….

Slide3

Higher order multipole moment hyperfine effects

Ref:

Theory of hyperfine structure

: Schwartz, Phys. Rev.

97

, 380 (1955)

The previous work on the E0, M1 and E2 interactions between the nucleus and the electron(s) suggests that the general nuclear interaction can be written in the form:

H

(hfs) =

k

T

e

(k)

• T

n

(k)

where the T

k

are tensor operators of rank k which operate on the electronic or the nuclear coordinates only.

For k≥1, the Hamiltonian terms are small, and can then yield 1

st

order perturbation energies:

Δ

E(hfs) = <IJF |

H

(hfs) | IJF> =

k

<IJF | T

e

(k)

• T

n

(k)

| IJF>

Slide4

The energy is independent of M(J &F) – hence we can use reduced matrix elements Racah – properties of spherical tensor operators – see below

Slide5

EvaluationDefinitions:

With the usual definition of K, these become…

M1

Q2

O3

Slide6

Evaluation of the matrix elements

Expand the electrostatic interaction due to charge distributions:

next terms in spherical harmonic expansion used for the Q2 interaction – next term is the hexadecapole term E16 (never observed in hfs, but observed in nuclear charge distributions)

Question:

What is the name of the next multipole – 2

5

? (static version not allowed)

And the one after that - 2

6

?

check out

http://physics.unl.edu/~tgay/content/multipoles.html

Slide7

Expand the nuclear current for the magnetic interactions: requires expansion in vector spherical harmonics – see Schwartz paper, plus an E&M text such as Jackson….

Yielding working definitions for the magnetic and electric nuclear multipole moments

Evaluation - 2

The multipole expansions of the potentials are then:

Slide8

Evaluation -3 Since these one-electron matrix elements depend sensitively on the electronic

wavefunctions

near the nucleus, we really need their correct relativistic form

Further topics

– We need to learn how to solve the Dirac equation for the relativistic hydrogen atom.

Second part of the Schwartz paper evaluates these equations, and also generalizes the hyperfine interactions to 2-electron systems, off-diagonal interactions (needed for some second order interaction cases).

For more information on

irreducible tensor operators

, see:

Ref. 1 – see Fischer et al, appendix (word version on

Berry website

) http://atoms.vuse.vanderbilt.edu/Elements/CompMeth/HF/node24.html Ref. 2 – see Breinig - Rotations, spherical tensor operators and the Wigner-Eckart Theorem (word version on Berry website) at http://electron6.phys.utk.edu/qm2/modules/m4/wigner.htm

Now we turn to the only measurement of the hyperfine structure due to an octupole moment.

Slide9

Slide10

Doppler broadening

Challenge #1:

You have a discharge containing rubidium:

Calculate the width of the spectral line of the resonance transition in rubidium at room temperature.

Procedure:

1 - Work in pairs

2 – (a) understand the problem

(b) develop a set of steps to reach the solution

(c) estimate the answer

3 - What parameter values do you need to get an answer?

(Use symbols for these parameters until you get to the end of the problem)

Slide11

Beginning the calculation…

Kinetic theory -> atom velocity gives a spectral distribution

Kinetic energy: mv

2

/2 = (3/2)kT ->

Hence

Calculating the detailed profile:

Slide12

The Sodium and Rubidium “D-lines”

Which of these structures can be resolved in a room-temperature discharge?

Slide13

A “Doppler-free” technique

In case (b) the second beam sees fewer ground state atoms ready to excite:

Consider the resonant frequencies for these atoms: only those atoms whose velocities match in both cases will be affected

– hence

OPPOSING

PUMP and PROBE laser beams will only affect atoms with velocities at 90

0

to the two beams

Slide14

Example of a doppler-free spectrum for Balmer-

α

in deuterium

Note the “cross-over resonance”:

Challenge 2:

Where does this come from?

Slide15

More details of the experimental arrangement:

– 2 probe beams

Slide16

More details of the experimental arrangement:

(b) – chopping the probe beam

Slide17

Results from a “doppler-free” measurement in rubidium (ND advanced lab)

Doppler broadening

with hfs from probe beam

with chopping frequency

Slide18

Slide19

Slide20

Cs vapor is heated in an oven to 170 C. The atoms effuse through a nozzle constructed from an array of stainless steel tubes to produce a dense atomic beam, collimated with a stack of microscope cover slips. The resulting atomic beam has an angular divergence less than 13.6 mrad in the horizontal plane confirmed by the experimentally determined 2.3(1) MHz residual Doppler width of the spectral lines. The Cs atoms are excited with a probe laser perpendicular to the atomic beam. The fluorescence intensity is detected with a large area photodiode placed below the laser-atom interaction region. A second detector monitors the transmission of the probe beam.

The crossed-beam experiment

Slide21

Results

Slide22

See arXiv:0810.5745v2 [

physics.atom-ph

]

5 Dec 2008

Another example – by the same group

Slide23

Previous results (1996)

New results (2008)

Slide24

The

Octupole

moment is

only just non-zero

!

Slide25

Another example – (as simple as possible): Important for (near) level-crossings of states of the SAME parityTheory

: hyperfine interaction is NOT ALWAYS a diagonal

HFS can mix states of the same J, but from different parent levels

N

eutral helium, isotope-3

nuclear spin ½ (i.e. only magnetic dipole)

Almost completely LS-structure, with small JJ mixing (all states)

Expect almost no

hfs

in singlet states!!!

1snd Triplet D and singlet D states: fine structure is small

But 1s hyperfine structure is large!Hence, off-diagonal matrix elements…

See Brooks et al, Nucl. Instr. Meths. 202, 113 (1982)[Expt and theory]

Q? Are there any “heavy ion” examples – eg in close-lying ground states?? Or excited states??

Slide26

The Hamiltonian for the 1snD states

H

0

defines the energy of the

1

D term,

the other two terms are treated

perturbatively

together

Note

the off-diagonal term between the J=2 states:

(Gets large in JJ coupling…)

Slide27

Slide28

(Highest & lowest F are diagonal)

Slide29

Slide30

After matrix diagonalization

Slide31

Slide32

Beam-foil experiment – result for one transition decay

Slide33

Slide34

One of the most interesting phenomena in the theory of highly forbidden transitions is the effect of hyperfine quenching, whereby mixing by the hyperfine interaction can significantly alter the lifetimes of the levels. The

phenomenon was first discussed by

Bowen in 1930

, who

pointed out that the substantial strength that

was observed

in the

6S

2 1

S

0

- 6S6p 3P2 line at 2270 A in the spectrum of Hg I was primarily due to E1 radiation caused by coupling with the nuclear spin and not to

possible higher-order multipole radiation as had been suggested.Hyperfine quenching in atomic spectra ref: Dunford

et al Phys. Rev. A44, 764 (1991)Bowen's conclusion was confirmed in 1937 by Mrozowski [3],

who experimentally observed

the 6s

2

'So—6s6p

3

Po

line at 2656 A in Hg I. This

transition would

be rigorously forbidden to all

multipole

orders

of single-photon

decay in an atom with a

spinless

nucleus

by the

J=0~J=0 selection rule of

angular-momentum conservation

.

Slide35

Slide36

Slide37

Indelicato

et al – Phys. Rev. A3505 (1989)

Slide38

Slide39

For more details, see alsoDunford et al – Phys. Rev A 48, 2729 (1993)

Abstract

Slide40

A Bondarevskaya et al Abstract.

The

hyperfine

quenching (HFQ) mechanism of metastable states in polarized

He-like

heavy ions is considered. The lifetime dependence of these states on the ion polarization

in an

external magnetic

field

is established. This dependence is presented for the 2

3

P0 state of the europium (Z = 63) ion and is proposed as a method for the measurement of the ion

polarization in the experiments for the search of parity violating effects.

The hyperfine quenching of polarized two-electron ions in an external magnetic field

Slide41

Note: refs 6 and 7: (see next 2 slides for brief explanation…)

Slide42

Ref. 6

Slide43

Concerning the possible 1s2 1S0 – 1s2s 1

S

0

2 photon transition

Hyperfine mixing with

3

S

1

state

(see Indelicato et al)Weak interaction mixing with

3P0 state

The weak interaction HamiltonianMixes nearby opposite parity statesPossible experiment requires an electron polarized beam:One possibility is a tilted thin foil target -

Then, observations should see a small 180 degree anisotropy

(note: anisotropy is very small – less than 1 in 10

3

)

Slide44

Ground state hyperfine levels

In H-like

Eu

(I=5/2)

Zero-field separation = 1.513 eV

Apply magnetic field and

laser

excite to different Zeeman levels

Ref 7.