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2 % /( 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 +

2 ' 8 2 2 2 2 2 2 2 2 2 2 2 2 2 2 +

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2 2 2 2 2 2 2 2 2 *

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2 % 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

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T = 273

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129

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n(I Z = − ¹ 2 )

n(I Z = ¹ ₂ ) = exp

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123

! + #

T = 293

^{, 8"}

10

^{$ ,}

~ = 1, 054 · 10 ⁻³⁴

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k B = 1, 38 · 10 ^{− 23}

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γ H = 2, 675 · 10 ⁸

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²

6

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129

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6

3 2 " 7

129

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129

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10 9 8 7 6

129 Xe im therm. Gleichgew. (0,0007%) bei 1,5 MPa

Intensität I = I

0

Chemische Verschiebung d / ppm

2 1 0 -1 -2

Chemische Verschiebung d / ppm hyperpol. ¹²⁹ Xe (27%) bei 0,008 MPa Intensität I = 250 I

0

% 2

129

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219

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¹²³

2

129

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­ 50 %

¯ 50 % ¯

­

B-Feld- Gradient

B-Feld ÑB Diffusion

¯

­ Xenon (Spin in z-Richtung)

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¯

¯

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# #

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|| z ˆ

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∂ z n(z)

^{+ $}

n(z)

⁾

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z

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•

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6

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8

)

m Xe

"

g 0

•

^#

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4π µ m γ Xe (∂ z B(z)) n(z) ,

¹²³

h

^-

∂ _z B (z)

z

^"+

, 8 2

( 7 %

6 "

µ g = µ m = µ

^"

. ,

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^{12 3}

.6&

x

8 4

y

8+* " # + 3

! ! + 1 2 3 , . "

&

n(z)

^{*3 6}

n(z) = n 0 exp − m Xe g + _4π ^h γ Xe ∂ z B(z)

k B T · z

!

12*3

$ -

m _Xe g = 129 · 1, 66 · 10 ^{− 27}

· 9, 81

^>

² = 2, 1 · 10 ^{− 24}

^!

h

4π γ _Xe (∂ _z B(z)) = − 7, 399 · 10 ⁷

^1$3

^{− 1} · ¹ ₂ · 1, 054 · 10 ^{− 34}

^!

· 1

^$>

= − 3, 9 · 10 ^{− 27}

^!

k _B T = 1, 38 · 10 ^{− 23}

^!>,

· 300

^,

= 4, 1 · 10 ^{− 21}

^!2

%

5

^{, 7 , $}

)

0, 999998 ≈ 1

²

, $ , 2

) " %"

, 8

1

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1

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129

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6

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3

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129

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5

$(+( %&/, +.;

'23,$3 &4.$( 42'

<.

2(1&3'1&3,

Gasgemisch aus

98% Helium (1 MPa, “Druckverbreiterung”) 1% Stickstoff (“Quenching”)

1% Xenon (unpolarisiert) Laserlicht Rubidium

Gasgemisch aus 98% Helium 1% Stickstoff

1% Xenon (hyperpolarisiert)

SPINAUSTAUSCHPROZESSE

Magnetfeld (3 mT)

% 2

/

#

./

#

#

$

! !(

+ (

6

"

" % 2 "

/( % 22 /( "

!

- 2% 2+2 (,

* " #

! ,

129

^{) 2}

Laser Rubidium ¹²⁹ Xenon

Bin. Stöße vdW-Mol.

Absorption

Wand Rb-Rb

Rb-Xe

Wand Geometrie,

Absorptionsspektrum (Stöße)

% 2+

7 # *

2 * - , #"

"* 1

794, 8

³

1

# +

5S ¹

2

!

( − ¹ ₂ )

⁽

5P ¹

2

!

(+ ¹ ₂ )

^{2 ("}

* 2

30

^{, . "}

+", - +"

2 % !3 . "

!. (, ,

!"

( ± ¹ 2 )

^{"+, 2 *}

+ "

( − ¹ ₂ )

+ # "

(+ ¹ ₂ )

% 2 2 " #"

100%

²

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, #

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,

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! #

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)

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$

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*

$

1

2

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3 !

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6

7

6

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,

6

2 " !

% % 2 *2 8 "

+ / ) !. 2

/ "

0, 55

^{8 #}

2

0, 6 − 0, 7

^{8 &}

400

^{,2 %}

8 1 /81 %22 *3 +

0 18 3 8 7 1&

2

3 2

0 # 7 "

3 ! 2%

+ & 2 &

$

± 1

^{, 2}

& ( 8 * "

#

6

+0 !

4 32

25

^{-" 1}

794, 8

^{- ,}

1, 5

^{/ 3 8 #"}

!

129

^{) ", 2}

8 % ! 1

3

^{$3 / "}

2 % ) )"#

+ / 0 !.

# + 2"

40

^$"

! ) 2

T 1

"( ) ,

6

!

2

! ) 3

8 8 %

2 , , 2 0 !.

40

^{$" 2 ) 8 '8#"!}

1

6

%

7, 05

^$

¹²⁹

^{) "#}

82, 98

^{8/ 3 2 " "}

6

% 2 22

-, ! "

* " ( 7,

, ( - "

0 / ( "

)

22 ! "

He Xe

N ₂

Mg

Ofen Misch

Laser

Pump- zelle

Helmholtz- spulenpaar

Kühl- falle Recycling

Magnet

% 2*

/

2# /

, ((

6 "

*

2 -2-

, (( , 2 %

,

+ + 7

#

2 ,2" "

! / /0 "" "8 1 1 0"83

" - , -

#" ) 2

! !" $+4$'/2$ %$/ &4.$00$

) 7, ! 0"8*%

6

2 1.&8!&* ! ! 3 2 "+

12 %2 2-3 ( 1

2

10

^{*, 3 !( "}

% 2 2

+

$

%

,&

& !

& #

$

$

$

# #

, )

/

$

) 1+

! 23

x

^"

z

^{"8 /, 2 7 "}

% #

$ , #

$ + 2(" %0 3"

- + ((

, # ! 2 (( ("

(( !

+ 2" %"

6

+ 1/ 13

/( % % 22

! ! 0$2,&()$( &(% :1(%$%2()&()$(

3 ! (

%2 "

#

* 12$ %2 32 ! "

0 1 + 12*3 * "

32

7 . "

# 0, "

/"01"

13 ' "! "+ ( 3 ,,"

+

~v(~r)

⁺

p(~r)

^+"

Rubidium

Magnet- feld

Einlass

Auslass Laser

Temperatur T

0

x y

z

% 2 -

#

#

/

,&

$

1!#

2

^#%

10

^{#3 !}

13

$

x

^#

1 , #

&

$

% ' -

3%

,

x

^{#% #&}

)

&)

$

z

^#

ρ gas (~r)

⁺

13 -, $

T (~r)

13 +

γ p (~r)

^{% #"}

*

13 # #

S z (~r)

^"

129

^{) "!}

I z (~r)

²

+ , 0 3 22

% ( 1

∂ t ≡ _∂t ^∂

^{3 ' 2}

', 2 " , %

/"1 1 8 3

+ , 2 7

, % # (( , 1"

* 3

6

#

10 − 15

^{8 (}

% ! 2 0

+ ,

8 ', 2

( . +

8 7, -, , -, "

, . % %2

4&

S z

I z

# 1#* +

z

8(

#" + # *3& * *&+ & *

x

8+# &63

+

/ ) !.

$ , , 2

"%% #

" 8 "

' "! "+ ,,

7 +

ρ gas (T ) ∂ t ~v + ρ gas (T ) (~v · ∇ ~ )~v =

− ∇ ~ p + ( ∇ ~ η(T )) ( ∇ · ~ ~v) + η(T ) ∆~v − (ρ gas (T ) − ρ 0 ) g 0 e ˆ z

12 23

∂ t ρ gas (T ) + ∇ ~ (ρ gas (T ) ~v) = 0

^{12 -3}

/

~v

^{+ +}

η

" , 7, , -

+

,

ρ _gas

^{+ %,}

$

T

^{) +}

ρ 0

&

$

T 0

2

g 0

"

z

^{"% "#}

2

0 ' "! "+ + 7"

, ! , 2 (

6

! $

%

6

%

, 2 8 +

$ , +

ρ gas (T ) = p 0 (x He M He + x Xe M Xe + x N 2 M N 2 ) 1 R gas T

123

x i

% +

i M i

8 2

p 0

" + 1

0, 5

1

^{8 3}

R gas

+ 2 ) +

1" "-"+ 3 1 " "-",

/ ) !. +

3 ,

+

1%

^{% +}

2

# #+ 3 # , #*#+ *+3*" #& %& &# +

7

"&+# &#

95%

, ##+* # +" , ##"

% (( , + 1

~v = 0

^{3 11}

132 % ! ( 8 (( "

,

6

/"01" , 2 0

/"01" ""

6

%

!3

p _aus = const = 0

%3 2 % " !3

"!3 ,

v _x (r) = v ₀ 1 − r

R zyl

2 !

123

r

⁽⁽

R zyl

# (( 2

v 0

!3 ((

1, 5

^{" + +2}

# ', 0 2

7 !3 " (( "

*3

, , 2% ', "

%

129

^{) "! %}

% % * )

!3 " ( 2

% .2 %2

-, , +

-, ' "! "+ 2

-, , 7 $

T

ρ _gas (T ) c _p (~v · ∇ ~ )T = − κ(T ) ∆T + Q

¹²³

c _p

^{+ 1}

98%

^/

1%

⁾

1%

^{!.3 -, ,}

$

6

,

+

$ %2 %2

κ

^-,"

, + + / )

8#8,&+** +* "# ## 3 #+

+* # 2*#&# 4#& #+# && #&

& + + #+ '8 #& ## &# 48

** 6&" &&*# # *6& ##" ## # , # *#+

2*#*#+* '& ##

!. %, $

T

^,

1 + 1 2 +332 $ ! "

-, ! -, 2

-,

Q

^{% * "}

#

Q = hν l n Rb γ p (~r) γ sd,Rb

γ p (~r) + γ sd,Rb

.

¹²³

% -, "

hν l

% # 7

n Rb

% # ! *

γ p

2 # * 3

, % + #"

3

γ _sd,Rb

^{! ! 3}

γ p

2/

σ = 1

2

2 ++2

# -, 0 +(

-, ,

κ glas

1

= 1, 16

^{->1 , 3 6, 3}

d glas

1

= 1, 7

^{8 3}

κ n ˆ · ∇ ~ T = κ _glas

d glas

(T − T 0 ).

¹²⁺³

/

T 0

$ & # 2

$$

!

P Xe

P Rb

8

200

^{! 2 #}

#""

S z

2 " &

< S ˆ z >

129

^{) ",}

I z

1

< I ˆ z >

^{3 % +}

− D Rb (T (~r))∆S z (~r) + ~v(~r) · ∇ ~ S z (~r) = γ p (~r) ( 1

2 − S z (~r)) − γ sd,Rb S z (~r)

¹²³

− D Xe (T (~r))∆I z (~r) + ~v(~r) · ∇ ~ I z (~r) = γ se (S z (~r) − I z (~r)) − γ sd,Xe I z (~r).

¹²³

/

D Rb

D Xe

, . "

#" ) / 1

95%

^{+ "}

32

γ p

# * #"

4

. 1 +

γ sd,Rb

2

γ sd,Xe

7, #">

129

^{) "!"}

3 - # 2

! #""

129

^{) ",}

!

γ se

2

( ( 3 #

+

γ _sd,Rb = κ _Rb n _Rb + κ _Xe n _Xe + κ _N 2 n _N 2 + κ _He n _He + γ _trap + γ _se

^12*3

•

^2/

κ i

, "

, !3 # #" ) "

!." / $

n i

2 , -

3 $ %2 % %2 2

•

γ trap

#

/ 1 22 # "

+

# 2 ) 7 , 3

+ !. "

# #

2 # /"

1 !. 1 3

-

+ +*

γ trap = 33000

⁻¹ 3

3 + 0, 0075 p N ² [Pa] .

¹²²³

0

33000

⁻¹

⁸

+2

8

6

% ,"

"0 / 1 1 + 2+32-

/ 1 * , .

%

6

!. 1/ 13 2

•

^{./ ! #"}

""

129

^{) ",}

+

γ se = n Rb



 h σ se v i + k se,He

n He

+ k se,Xe

n Xe

1 + 0, 275 _n ^{n N2}

Xe



 ,

^12-3

h σ se v i

^{! , !3}

, ,

k se,He

k se,Xe

8 !"

! 27" "-"8 )

, !. ( '

$ 2

•

^{/ #}

¹²⁹

^{) "!}

$

! "

)

γ sd,Xe = κ Xe−Xe n Xe .

^{12 3}

!

κ Xe−Xe

,

5 · 10 ⁻⁶

⁻¹

⁻¹

2

1, 86 · 10 ^{− 31}

³ s ^{− 1}

^{2% +}

! %, .

+

)

γ sd,Xe

+

2 · 10 ^{− 3}

^{− 1}

^{,2 % $}

2 − 4

^{+3 "}

! "0

, , 2

•

^{8 / #}

! !3 - 2 -,

- " #

0"8"! # "

2 0 #""

# ,

2/

# + 2

6

2 7 "

, 2 #"

! - .,

.

D Rb

γ p

2 % 0

D Rb (T (~r)) ∇ S z (~r) = − S z (~r) r 1

2 γ p (~r) D Rb (T (~r))

^{12 3}

)

6

# )

D _Xe (T (~r)) ∇ I _z (~r) = − I _z (~r) r 1

2 γ _se D _Xe (T (~r)) .

^{12 3}

/" "! 1 )

# !3

- 2 # "

, 0 - ' "

! + 2

# %&&#& * *3&# #+

*#" & ( 3* *3&*6 +&6##8

$

7 % # ! "

&

~r

^{* , "}

+

++ +-

∂ x γ p (~r) = − β γ p (~r) n Rb

1 − σ γ p (~r) γ sd,Rb + γ p (~r)

.

^{12 3}

+ # 1$ "

n _Rb

^{3 * 3 %}

# 1 0 7 ,

γ p

γ sd,Rb

3 2

σ

1

^{, 2! * % " "}

7 ! 2 "

6

0

β

³

* " 1- ,

λ l = 794, 8

^*

δλ l = 1, 5

⁰

δν l

3 #"

1 0

δν Rb

3

β = 2 √

π ln 2 r _e f λ ² _l w ⁰ (r, s) δλ l

12 +3

r e

"

f ≈ 1/3

^&,

#" "* 1 %

6

32

w

^,

7 , *

r

^{1 * # 3}

7 0 3 ,

s

^!

w = w ⁰ + iw ⁰⁰ = exp ln 2 (r + is) ² √

ln 2 (r + is)

12 3

s = 2 ν l − ν Rb,D1

δν l

12 3

r = δν _Rb,D1 δν l

.

^{12 *3}

/ % !

- ( , 2

6

#

δν _Rb

⁰

w ⁰

β

^{% 6 2}

% * 1

x las = 0

²

x las = l

³

β

^{( * "}

! 1 % , %

( 3 "

hν _l

*

w laser

γ p (x las = l) = β w laser

A _laser · hν _l .

^{12 23}