The spin polarisability of the electron.

Journal of Molecular Liquids, 48 ( 1 9 9 1 ) 7 7 - 8 4

77

E l s e v i e r Science P u b l i s h e r s B.V., A m s t e r d a m

THE

SPIN

POLARISABILITY

OF

THE

ELECTRON.

by M.

W.

Evans,

ThBory Center, Cornell

University,

Ithaca, NY

1~850.

( R e c e i v e d 2 S e p t e m b e r 1990) Abstract The

concept

polarisability, has

no

a

classical

experimentally analogue

of

resonance.

a

modified

It angular which

no

responsible ESR)

and

for

anomalous In

~

using

this

property

the

well

which

the

polarisability"

la~er

be

tested

induced

electron

experimental

for

that a

th~

of

a

spin

Nd:YAG

el~ct,'urm|,d~

fundamental

analogue.

The

splittings

(or

such

as

by

static

introduce

an

analogous

electron, $

which The

theoretically using

its

experimental

the

anomalous Zeeman effect

is

symmetry,

investigation and

those

but

culled

and

using

spin)

magnetic

existence

of a

a

d

property

electronic

paramagnetic

{1}

d~

can

the

for

0167-7322/91/$03-50

predicted

Qlectron which

and

is

Zeeman effect

of

existence

conjugate product

electron

we

the

suggested

knoan

spectral

of

pump

laser

spectrometer.

classical

letter

whose

spin

Zeeman effect

are

NMR/ESR

for

and

electron

property

theoretically

anomalous

is

of

fundamental

counterpart

momBntum,

has

introduced

Conditions

investigation, in

n~w

5y

the

is

qudntis~d of

spin

induced flux

spin

~ 1991 - - E l s e v i e r S c i e n c e P u b l i s h e r s B.V.

or

the

density

(8).

fundamental

property

suggestion

electron

in

(EPR

"spin

this

laser

and

is

resonance

novel

its

matter

5pin

I~

induced

is

made

argued for

analogue

resonance.

of

78

The ~-~

relevant

which

is

parameter

and

Nd:YAG,

a

quarter

product

is

-

laser

property

proportional

~hich

is

(2,21)

to

isolated using

~ave

p l a t e

and

is

a

Nicol

the

conjugate

product,

the

third

Stokes

pump

laser

~uch

p r i s m

{4}.

The

as

a

conjugate

(1)

-

--I

where the

E

is

th~

subscripts

circularly minus

L

and

frame.

(T)

from

and

left It

hamiltonian

The of

been ~

a

unit

with

parity

circular

s h o w n

left

vector

,

and

and

p l a n e in

(P)

plus

wave

th~

Z

negative

inversion

~ h ~ r e

right and

from

axis

to

and

of

the

m o t i o n change~

polarisation.

(-I ~ ° t )

atomic

is

m

-- d e n o t e

electromagnetic

is

to

v o l t ~

and

+

con3ugate product

right

i~

respectively

the k

positive

has

strength

superscripts

Here

The

to

of

field

denote

{4-6}

equations.

laboratory reversal

R

polarised.

conjugates

Maxwell's

~ign

electric

or

that

the

interaction

molecular

ensembles

is

II

q#

!

where

.~o{

orbital axial is

is

a

vector

(i.e.

proportional

"-3"-

where known

new

fundamental

polarisabillty.

V

~

=

is

a

to

spln

rank

th~

a

property

latter

two

total

L

resonance.

S

between It

a

T

called

has

or

the

negative,

antisymmetric

L'oo3-

ratio

is

atomic

proportionality

gyromagnetic

electron

The

polar

o

angular

÷

analogous

J

used

been

B

s h o w n

{

in ~

}

w h i c h momentum

--

constant and

positive

tensor)

molecular

=

electronic P

to

the that

the

~ll

theory

of

'79 where of

~o

the

is

the

laser,

c

scalar the

amplitude

v~loclty

of

of

the

light,

electric

and

~(

field the

~trength

gyromagnetic

ratio. In orbital

general

and

spin

the

angular

componentS.

'5" where

L

is

the

spin

angular

from

the

follows both

an

=

eqns

orbital

(

using

the

and

)

of

product laser

the

~--

g~nerates

quarter

wave

Here

~ ; ~

l(

)

subjects its axis the left

denotes

through

its

Y

oriented exccs~

in

a

the

at

which

radiation.

accepts

Note

that

by

ha~

this

2S

the

written

( electronic

essentially

OL l,

quantity

is

being

a

named

classical

It

has

new

here

the

counterpart.

experimentally

by

anomalous Zeeman effect

In

both

ca~es

the

attributed

following

conjugate

to

B.

configuration

(the

pump

of

quarter

retardation an

~

analyzer to

radiation

the by

the

laser wave ~L-

with X

a

over

circularly is

be

quantum mechanics.

latter

no

or

transmitted

right

can

of

pump

The

{4}

of

prism

a

angle

circularly polarised

device

the

intensity

followed an

the

(~L).

r e t a r d ~

intensity

of

that

investigated

the

to

it

derived

Dirac

customarily

Nicol

component

X • omponent,

be

role

composite

and

81~ctron which

using

and

being

)

resonance

the

~'~'-

2

by

~hich

can

spin

plate

transmitted

electron,

component, the

a

---

~

hamiltonian

plays

L

(

and

e×istenc~

by

is

÷

factor

and

spin

property

electron

generated

the

treatment

~

"'spin p o l a r i s a b i l i t y " , Its

t_.

the

relativistic

fundamental

For

J

quanti~ed electronic orbital

momentum,

from

momentum

radiation plat~}

with its

axis.

Thus

of

I(

~

r~- )

is

accepts

transmitted

pola~Ised

definition

t~

transmission

device which that

which

respect

by

a

electromagnetic the

intensity

corresponding is

{

(0

}

proportional

to

the

The

conjugate

inexpensive~ generates the

sam~

I)

laser

electron

1)

Pump

the

the

product

obtained

in

this

and

new

positive

property anomalous

uf

P

way

from pump

symmetries

electron

spin

Zeeman effect;

• ~hich

3

through

available Nd:YAG

Induced

Anomalous

smallj

laser

to

Two

a

Bw

which

polarisability

and

2)

haB

~xample6

laser

are

induced

Zeeman effect

is

Zeeman Effect

customarily

splitting

of

spectral

absorption

Z~eman effect

is

due

to

combination

orbital

and

spin

electron

~]~

S

resonance.

Laser The

conjugate

effects customarily attributed T

induced

spin

third Stokes parameter

commercially

spectral

to

the

product

negative

relevant z

and

to

a

angular

generated

llneg of

{

the

momentum

l~

}.

by The

effect5

through

~,

of

and

is

anomalouB B

on

the

hamiltonlan

An

analogous effect

due

to

The

quantity

and

the

the

pump ~

o

~

hamiltonian

(

can

lager L~

~ )

the

the

can

generated

induced

is is

be

be

through

optical

"electronic

'"electronic re--wrltten

conjugat~ orbltal

spin in

the

hamiltonian

product polarisability",

polarlsabillty".

terms

of

the

The

L a n d ~ factor :

81

(11 ~ J

where

C

~

•.

is

the

total It

depends spllt

electronic

is

clear

both

on

L

different

angular

from

and

terms

(

10)

momentum, that

S,

and

in

different

the

~hen

laser

of S

magnitude ~

conjugate

degrees.

For

M~.

Land~ factor

the

Os

I la.~

(J(2+1))

product

will

example,

a

oni~

a.

line

atomic

doublets

transition

by

selection

the

PLI~

conjugate

to

the

Z

component

existence

in

this

three

the

new

of

these

fundamental

under

the

s

--

J

lines would confirm

properties,

the

th~

effect

investigation.

The

approximate

For

is

an

given

order

of

~T

spln on

and

the

frequency

by

of

electronic polarisability

the

electronic

mediating

doublets

I

of

six

magnitude estimate

a:clal

vector

of

for

10

the

~)--I

is

terms

laser can

of

radians

total

in

of

vapour

spacing

by

into

O

quantum number

polarlsabilities

atomic

split

rul~

Observation

orbital

be

, governed

product

__

on

will

D

in

of

the

volts

deliver

great

{

po~er,

resonating

square m

.

~ }

up

so

probe

that of

A

of

the

small to the

electric

Q--switched

10

volt

splitting

customary

ESR

m

field and in

is

In

strength

focussed

GH~

spectrometers

pump

laser

pulses

range for

the

Nd:YAG

ultra short the

of

E o

of

of

the of

about

$2

10

volt

m

increased

The

greatly

magnitude by

transition

frequency

much

pump

2}

lower

Pump

La~er

is GHz

to

range~

designed

as

for

resonance

of

atomic vapour~

due

for us~

to

ronditlon

B

through constant

must

be

will

also

llne

through

where nuclear

where

Bplit

J--

a

the

is

.

in

of

a

a

on Z

a

allowing

be

natural the

use

o~

~ k

is

in

The

principle

GHz

to

splitfing

customary

existence component

ESR

the

anomalous

just

dlscu~sed

radiation

in

the

spectrometer

magnet.

of is

taking values

In

general,

th~

on

the

In

~qno

the

1/2

and

quantity (

electron

--~Y~%~#~/~S

t4r ).

The

with

--1/2.

~11~

~pln a

The

defined

proportionality

experimentally.

clear

that

conventional

the

con3ugate product

nuclear magnetic

resonance

(NMR}

hamiltonian

the

nuclear

gyromagnetlc ratio.

a

Resonance.

homogeneous

the

axis

determined it

Spin

~l"

proportionality

Finally

to

can

~leld strength.

similar

~requency ~epend~

the

frequenry

~

is

whose

quantum number

resonance

pump

probe elertromagnetic

example with

polarisability,

Is

with

which depends directly

spin

the

~lectrlc

technique

resonate

polarlsability

the

Induced Electron

splittings

made

the

tuning

laser

This Zeeman

of

spin This

quantum number can

be

and

re-written

~ in

the

the

form

88

$

is

the

total

customary

angular

NMR

line,

momentum quantum number. defined

= is

split

into

a

ne~

through

±

i

pattern

of

the

For

I

selection

~

O,

th~

rule

_ llne~ dependent

on

the

selection

rule

I

and

on

th~

potential

individual application

modifications instruments, imaging

for

electric

values

to

in

the

include

~-

including

of

and

J

This

analytical can

t~o-D

and

different nucl~i,

field

I

be

vast

laboratory,

made

Fourier

pump

has

in

standard

transform

laser

because NMR

NMR,

frequencies,

and

NMR

and

strengths.

Acknowledgements This which and

research

receives major

Members

of

the

was

supported

funding

Corporate

from

by

the

thB

Research

Cornell

NSF,

IBM,

Theory Center,

New

York

State,

Institute.

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