plaques de carbonecollimation

guidage magn´etique

plaques de carbone collimation

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drevTr}Z{k´¼;gT;}Txq)=mglqfk_dfgB}A~xq)>´}Tfm»qf}T~r}?o_}ZèmTwx

r 0

}Trd)¹

ozmFu ~{

ijmoiB{o

kËqr}

o} }jilqf}T{;mk_=mp|qSmqfk_ xo{~;kzyx{}~}iB}Bq¼qf}MdrevT¼}

drAA}T|q

=mgBqrkzyx{}O}Bdrq]~g%empOs

I = 4π

3 r ₀ ³ .

^m ^| ^¸ ^¾^K+}

o}Oièvmp;e=mgBqfky|{}

ok|qrgTrk_}T{]~}OiB}Bq¼qf}O~k_drqrrk_{~qfk_W}Td¼q1mpo_¼dQs

in = 2 3 µ 0

= µ 0

4π 2 r ³ ₀

I

¸ ¾ º'}

ko¬#k_}T|qQs

W _hf ^c = µ 0

4π 2µ B

~

. 2 r ₀ ³

I

¸ ¾ }

I

gBqSmp|q1{~}jilqf}T{1iBd¼qSmp|q

eh}T{~q1ehdr}Tdèmdr}Td¼qf¼}Tk_u~r}QozmDgTgTfmo_kqfgZ~{er

o_T;};s

I = M I .

⁼

z

¸ ¾ }

}Bqumpo_}T;}T|qQs

W _hf ^c = µ 0

4π 2µ B

S z

~

. 2

r ³ ₀ M I

¸ ¾ M9}

ÉËmoiB{o_dW»mk_|qf}Bm|qMo}TdMgTo_gT;}T|qrd~} =mpqrrkiB} ~} iB}BqehgTèmqf}T{umpdozm umdr}

~}Td;gBqèmpqrdDÉ4{oZk_}Td

| k l m, ε i

^9Í

ε

}Td¼q;o_}Z¼}y|{mp|qfky|{}Wmdrdr#iBk_gmp{§drek_§~}

oçgTo_}jilqf¼

¾hÈ

mMs

h k l m, ε | W _hf ^c | k ⁰ l ⁰ m ⁰ , ε ⁰ i = µ ₀ 4π

2µ _B M _I

~ h ε | S _z | ε ⁰ i

× 2 r ³ ₀

Z

r<r 0

d ³ r ϕ ^∗ _klm (r)ϕ k ⁰ l ⁰ m ⁰ (r)

^| ^¸ ^¾^¶p}

ç1»Yótìéöö_ô`ù®ùÎô3ÿ)ô

a 0 = _αm ^~ _ep _c

v é]êkô`ï

m ep = _m ^m _e ^e _+M ^M ^p _p

ù®é÷jé{ô¯ì{ë`ú)ÿ)íÎð7ôjúÿc{(ð{üc÷uô3¼ú4ô`ÿEõ¬ïeòì{ö

öì{òð{òkó(ë`ùÎôcïð7ì{òkóôeð

α = _4πε ^q ^e ² ₀ _~ _c = _~ ^e ² _c

ù®é¯ïeòkóoðéóð7ôVú)ôCð7ì7ÿ)ïðñÿ4ì{ôVîó4ôVò½òkóéö_ò{ë

e ² ≡ 4πε ^q ² ^e 0

¸LK

mk_dr~d]=mk_|qr}Tmxqqf}T~r}

r 0

x}T¼dTgTrs

r lim 0 → 0

2 r ³ ₀

Z

r<r 0

d ³ r ϕ ^∗ _klm (r)ϕ k ⁰ l ⁰ m ⁰ (r) = 2 r ₀ ³

4π

3 r ³ ₀ ϕ ^∗ _klm (0)ϕ k ⁰ l ⁰ m ⁰ (0)

= 8π

3 ϕ ^∗ _klm (0)ϕ k ⁰ l ⁰ m ⁰ (0)

^| ^¸ ^¾^bp}

}B~gj~{~k_q]o}#er}Tdrdrk#{qr}Tr;}%~}OiBxqSmilqQs

W _hf ^c = µ 0

4π 8π

3 I . 2µ B

~

δ(r)

^| ^¸ ^¾^µj¹p}

ÏjÁ]À;Á{Ï ÆjÄVÉ;ÃÉgÈÊeËÇÇnpoPV2ÆIÃ0ÈÇÆäåÆÉ@^Æ!ÃsÑ Ê

t¢{?~qr}Tk_AonmId¼qf¼{uilqf{¼}Mv|w#eh}T]u}W#}oglqSmq

µBd}Qk_oc{~d;dr{Û;qA=mpk|qr}Tmp|q»~}

~kzmLmpo_kdr}T

W _hf ^c

umdozm?Z{oqfk_eo_kiBk_qrgQiBrr}Tdrehuump|qf}

¾hÈ

m s

I = g p

µ n

~

@ | ¸ ¾

µµ)}

9Í

}Td¼q]o_}%drek_W~{erqf

µ n = ^q ^p ^~ _2M _p

o}%»mLgBqfW~}

vc{uiBo_gGmk_r}%}Bq

g p

o_}aømilqr}T{

mu#gQ~{Merqf

¾uÂ

}TdgTo_gT;}T|qrd#}%=mpqrrkiB}O~{Mqr}Tr;}%~}OiB|qSmilq]djgTiBrkx}T|q]~uiAs

h 1s | W _hf ^c | 1s i = A h m s ⁰ , m I ⁰ |

.

| m s , m I i

^| ^¸ ^¾^µj¸9}

mTx}jiAs

A = µ 0

4π 8π

3 2µ B

~ g p µ n

~ h l = 0, m l = 0 | δ(

) | l = 0, m l = 0 i

^| ^¸ ^¾^µKp}

mMs

h l = 0, m l = 0 | δ(

) | l = 0, m l = 0 i = 1

4π | R 10 (0) | ²

^| ^¸ ^¾^µBº'}

9Í

R 10 (r)

}BdrqOozmMeum¼qrk_};èm~knmpo_}=~}Aonm ´uilqrk®¬u~}»~};ogBqèmpq2´uumA}T|qSmpo~~gT}

em%s

R 10 (r) = 2

a ^3/2 ₀ e ^−r/a ⁰

^| ^¸ ^¾^µ ^}

kmpo_}T;}T|qQs

A = 4 3 g _p m e

M p

m _e c ² α ⁴

1 + m e

M p

−3 1

~ ²

| ¸ ¾µ }

t¢{~knmmpo_kdr}ToçehgTfmpqr}T{

.

^F yx{khmpeempèm(¨zq4umpd'ogTy|{mpqrk_

| ¸ ¾

µG¸9}»iB;ehdf}

o}Bd=~}T{ §A;}B|qfd»iBk_gBqfky|{}BdD~}drek§}T ehdèm|q

=

+

^FK¾Â ^m mpdf}~qr}T{}}Td¼q

´r;gT} ~}Tdy|{mqf¼}TdMgBqèmpqrd

| S = 1/2, I = 1/2, F m F i

^mTx}ji ^|

F = 0, m F = 0

^}=}lq

F = 1, m _F = − 1, 0, 1

^} ^¾ Ê6r}T»mry|{mxqyx{}

.

= 1

2 (

² −

² )

^| ^¸ ^¾^µ4M_}

¸pº ÉÑvmpekqfr}Q¸ Å]mjwW~} }T=mièvW~{erqf

o}Bdmo_}T{¼d]erer}Bd]}O~gBeh}Tu~}T|qy|{}O~}

F

}Bqmo_}T|qOs

~ ² 2

F (F + 1) − 3 2

| ¸ ¾ µT¶+}

È ~qrk}TxqMmpk_drk1~}T{ §k_}Gmp{ ~}d¼qf¼{uilqf{~r}vxw#eh}T`u}®s6{ gBqSmq= ~ggTgTrg

F = 0, m _F = 0

^}}Bq){ dr}jiBu

F = 1, m _F = − 1, 0, 1

}1#ggT~gTrgZqfrk_dank_d

¾/Â

gjijm q

v|w#eh}T]uW}Td¼qmo_¼d#g%em%s

∆E _hf ⁰ = A ~ ² 2

1(1 + 1) − 3 2

+ 3

2 = A ~ ²

^| ^¸ ^¾^µb+}

É4}Bq]gjijmp¼qgT}TcgBqfky|{}Qmeeh}To_gOdrgTempèmqfk_v|w#eh}T]u}O~}t}Tr;k;©¸~µªñdjgTiBrkq~ui;s

E ^F = 4 3 g p

m e

M p

m e c ² α ⁴

1 + m e

M p

− 3

| ¸ ¾

¸¹+}

ÏjÁ]À;ÁÜ º%Ë;ÃÃÆU8ÈÊeËÇÝåÆËÊtÆIÑáÉYUÌn

m1iBr¼}jilqfk_A~}

}T»mièv©÷¸¸ªiBdrk_drqr}

iBdrkz~gBr}TKozmdrqrr{uilqr{r}Ñkxqf}Tr}Ë~{?e¼qr

P~guk_q mpkdrkxo};ømilqf}B{~};´r;}»mLgBqfky|{}

ρ m (r)

}lqo_};ømilqf}T{¢~};´r;}gTo_}jilqf¼kzyx{}

ρ _e (r)

qr}To_dy|{};s

M ~ I = g p

µ _p

~ Iρ ~ m (r)

^}Bq

q p = qρ e (r)

^| ^¸ ^¾^¸#µ4}

mj}jiAs

Z

ρ _m (r)d ³ r = Z

ρ _e (r)d ³ r = 1

^| ^¸ ^¾^¸¸p}

ÊK df{kmxqAo_}MDB;}Mièv~}T;k_}T;}T|qAy|{}Me~rgjiBgj~}B;;}T|q

§m¼rkx}

o}~er}Tdrdrk_

iB¼rkgB}Q~}%ozmN´rP{o}O~}2}TrAk

| ¸ ¾

¸¹p}°s

∆E hf = B ~ ²

^| ^¸ ^¾^¸LK+}

9Í©s

B = µ 0

4π 8π

3 2g p

µ B µ n

~ ² Z

d ³ r | ϕ(r) | ² ρ m (r)

^| ^¸ ^¾^¸pº+}

9Í

ϕ(r)

r}Te¼gTdf}B|qf}%ozm¬´uilqfk_W/~}%dSmpddrek_W~{{~x}To/gBqSmq´uumA}T|qSmpoñ/r~r}

TgTrIe¼}Tmp|q?}Til;e~qr} o}#qf}Tdrk_ dfeumpqrknmpo} ~} ozmièvmpc}M~{ erqf

¾ Ï

oÑ{d?r}Td¼qr}

~gBqf}T¼;k_}T]iB}Bqrqr}a´uilqfk_

ÏjÁ]À;ÁHß @^Ë;Ç/U8ÈÊeËÇÝå¬ØHËÇåÆÉUAË;ÃÃsÊeâ;Ä!Æ

Ã]{dmo_o_d }Tdrdèmjw}TM/}~erk_;}B onm´uilqfk_!/u~}I;~kugT} }B ´ilqfk_ ~}Ionm

´uilqfk_¿/~}»~}AoçgBqSmq2´um;}B|qSmpo~};omqf;};/v|w#~r_T~};~qr}T{}»mdOo_};ijmd

/{ w|m{ ~}ifvm`}WgTo}Tilqfrky|{}ehuilqf{}To_o_}

Ã]{dDm²ú}jilqr}TrdD~ui{ k_u~kiB}

p

qf{~qf}»y|{mp|qfkqfg;df};èmpeeh¼qSmp|qZm{¿ijmdOeúuilqr{}To

o_}TdPy|{mp|qfkqfgTdQdèmpdQk_u~kiB}»df};rgngTr}T|q

m{d¼w#d¼qrT;}MiBAer}Tmp|q;{ erqf mTx}ji {}il}T¼qSmpk_}M}#qf}T~dfk_§dremqfkzmo_}

1k_drkËo}Td

ehqr}T|qfk_}To_dÑ/k_|qr}Tèmilqfk_ É4{o_Pk_}T}}T|qrr}]ogTo_}jilqrr=}Bq4o_}e~rqr»dr|qÑ~gTd4emps

V ^p (r) = − e ² r

| ¸ ¾¸ }

V (r) = − e ²

Z ρ e (r ⁰ )

| r − r ⁰ | d ³ r ⁰

^| ^¸ ^¾^¸ ^}

ÊK {#qfk_ok_dèmxqËo}TdÑere¼kgBqrgTdc~}1ozmt´uilqfk_M~}a¡°¼}T}T

G k (r)

^~}1oçehgTfmpqr}T{

∆ − k ²

xk_mp}~}%a}

Weh}B{~q]gjiBrk_r}%o_}Td]~}T{ Mgjy|{mqfk_d]k_|qrgfmo_}Tddf{~k_mp|qf}TdOs

ϕ(r) = 2m ep

~ ² Z

d ³ r ⁰ G k ⁰ (r − r ⁰ )V (r ⁰ )ϕ(r ⁰ )

^| ^¸ ^¾^¸9M_}

ϕ ^p (r) = 2m ep

~ ² Z

d ³ r ⁰ G k (r − r ⁰ )V ^p (r ⁰ )ϕ ^p (r ⁰ )

^| ^¸ ^¾^¸¶p}

mTx}jiAs

k =

p 2m _ep ( − E ₀ )

~

}lq

k ⁰ =

p 2m _ep ( − E ₀ ⁰ )

~

¸ ¾

¸Lb+}

9Í

E 0

¼}Tdre

E ⁰ ₀

}}Td¼q°ogT~}Tck}?~{kx}Gmp{>nuump;}TxqSmpoKmd1oç÷mee¼4#k»mpqrk /f~¼}

TgTr)dèmdKerk_df}Ë}T;iB;e~qf}

¼}Tdfe

mT}jiËerk_dr}c}T;il;e#qf})}~}co}k²ú}Bq~}Ëo_{;}#{Aw|m{

Ê6uèmpeeh}To_~dy|{}

G k (r)

}Bdrqcqf}To_o_}Qy|{};s

(∆ − k ² )G k (r) = δ(r)

^| ^¸ ^¾^K¹+}

Â m mprkzmqfk_ ~}ogB}Tck}~}ogBqSmq

µBd}A~}omqf;}/v|w#¼9T}ok_gT}

o}²¬}BqD~}

xo{~;}=~{©erqf¿}Td¼qOqrrTd2ømk_o_} [

¾ñÏ

o}Td¼qP~ui;o_gkqfk_;}=~}»iBdfk~gT¼}TPy|{}

G k ⁰ (r) ' G k (r)

^¾ ^}1T;} ^ý umpdÑo_}°ijmpoiB{oú~}1ok|qrgèmo_}°meempèmpk_dfdèmp|qËumd4oçgjy|{mqfk_

| ¸ ¾

¸9M_}6

eh}T{~q)¼}T;eozmiB}B

ϕ(r)

^emp

ϕ ^p (r)

^¾ Ê6dr{~drqrèmTwmp|q%mpord°ogjy|{mqfk_

| ¸ ¾

¸¶+}]~}

| ¸ ¾

¸pM_}

~qrk_}T|qQs

ϕ(r) ' ϕ ^p (r) + 2m ep

~ ² Z

d ³ r ⁰ G k (r − r ⁰ ) (V (r ⁰ ) − V ^p (r ⁰ )) ϕ ^p (r ⁰ )

^| ^¸ ^¾^K~µ4}

iB;;}

G k (r − r ⁰ ) = − _4π ¹ ^e ^−k|r−r _| _r ₋ _r 0 | ^0|

}BqMy|{}onm®~k²úgT¼}TuiB}I}T|qrr}

V (r)

^}Bq

V ^p (r)

^}Td¼q

kAeh qSmp|qf}1y|{mp{=xk_dfk_m}°~k_r}jiSqc~}1orkk}

Deh}T{~qÑgjiBrk_r}

}TD~}°iBdrkz~gTfmxqcy|{}

o}Bdqf}T¼;}Td]#;k_mp|qfd]umdok_|qfgkfmo_}Q~}%ogjyx{mpqrk

| ¸ ¾ Kµ4}°s

ϕ(r) ' ϕ ^p (r) + 2m ep e ² 4π ~ ² ϕ ^p (0)

Z d ³ r ⁰

Z ρ e (u)

| r ⁰ − u | d ³ u − 1 r ⁰

1 | r − r ⁰ |

| ¸ ¾ K¸p}

}T{~qfk_o_kdèmp|q]onmZr}Tozmpqrk

| ¸ ¾

¸¸p}ÑiB}Bqrqr}%gjy|{mqfk_df}%A}Bq]dr{d]ozmNn¼;};s

ϕ(r) ' ϕ ^p (r)+ 2m ep e ² 4π ~ ² ϕ ^p (0)

Z Z

d ³ u d ³ r ⁰

1 | r − r ⁰ |

1 | r ⁰ − u | − 1 r ⁰

ρ e (u)

^| ^¸ ^¾^K9Kp}

t /ó^ô|Í_ô]ð}v4ù®é;êéÌì7íéðñíÎòkó^ì{ô`ùéðñíêkôgú4ô

E 0

ôoðIú)òkó)ó4ë]ôYö_éÌì

δE 0

E 0 = ⁴ ₅ ( a ^r ⁰ 0 ) ²

ò½

r 0

ôðIùÎôYìé|{òkóú)ÿ^ö)ì7òÌð7òkó

Î./óöì{ô`óéókð

r 0 ∼ 1F = 10 ⁻¹⁵ m

v4òkóð{ì{òkÿ4êô

δE 0

E 0 ∼ 2, 8.10 ⁻¹⁰

¸ ÉÑvmpekqfr}Q¸ Å]mjwW~} }T=mièvW~{erqf

oçk_|qfgèmqfk_dr{

r ⁰

~}Qmo_rd s s

ϕ(r) ' ϕ ^p (r) + m _ep e ²

~ ² ϕ ^p (0) Z

d ³ u (r − | u − r | ) ρ e (u)

^| ^¸ ^¾^Kº+}

] ~gBx}To_eeh}T;}T|qDo_k_;k_qrgImp{ er}B;k}B=f~r}~}

ϕ ^p (r)

^mp{ k_drkm}I~}Woç¼kk_}

eh}Tr;}lq/gjilrk_r}O/mperTd

| ¸ ¾µ }°s

ϕ ^p (r) = ϕ ^p (r) ' ϕ ^p (0) + ∂ϕ ^p

∂r

0 r = ϕ ^p (0)

1 − e ² m ep

~ ² r

| ¸ ¾K }

drkqQs

ϕ(r) ' ϕ ^p (0)

1 − m ep e ²

~ ² Z

d ³ u | u − r | ρ e (u)

| ¸ ¾K }

ÏjÁ]À;ÁÏ ÐBÉoËÇÝåÆËÊ2Æ@ÑáÉrUÌn

}'qf}T¼;}Ñ~}Ë#rk_qr}Ë~}4o}~e¼}Tdrdrk

| ¸ ¾K

}ñmeempèm(¨q6iBozmpk¼}T;}T|qKiB;;}4ozmiBrr}jiSqfk_

ok_gT}

o}qf}Tdrk_Odremqfkzmo_}'~}ozmc~k_drqrrk_{~qfk_QgBo}jilqrr=mgBqrkzyx{}'~{Oerqf

Ê6%{~qfk_o_kdèmp|q

onm¬´rZ{o_}

| ¸ ¾

¸pº+}ÑW~qfk_}T|qOs

∆E _hf ' ∆E ^F

1 − 2 m ep e ²

~ ² Z Z

d ³ r d ³ u | u − r | ρ _e (u)ρ _m (r)

| ¸ ¾ KpM9}

t¢drdOs

ρ em (r) = Z

d ³ u ρ e (r − u)ρ m (u)

^| ^¸ ^¾^K¶p}

É4}1er~{k_qc~}°il|o_{~qfk_ }T|qrr}1o_}ømilqf}T{Ë~}´¼;}1gTo_}jilqrrky|{}°}BqÑ=mglqfky|{}°}Bdrq

meeh}Bog2ómilqr}T{]~}a´r;})gTo_}jilqf¼=mgBqfky|{}

¾hÈ

m?k_}TWd}%s

Z

d ³ rρ em (r) = Z Z

d ³ rd ³ u ρ e (r − u)ρ m (u) = 1

^| ^¸ ^¾^K9bp}

ÊKD}k²ú}jilqr{mxqËo_}1ièvmps}TA}T|qË~}mprkzmo_}Td

r ⁰ = u − r

^}Bq

s = u + r

umpdÑok_|qrgfmo_}

~}Dogjy|{mqfk_

| ¸ ¾

K+M_}%®eh}T{~q?;}Bq¼qfr}=ozmdrgTempèmqfk_ vxw#eh}T`u}D~}DoçgBqSmqNnum;}TxqSmpo

dr{dozmN´r;}As

∆E hf ' ∆E ^F

1 − 2 m ep e ²

~ ² R p

= ∆E ^F 1 + δ ^Zemach

| ¸ ¾ º¹+}

mj}jiAs

δ ^Zemach = − 2αm ep c ² R p

¸ ¾ ºµ)}

9Í©s

R _p = Z

d ³ r ⁰ r ⁰ ρ _em (r ⁰ )

^| ^¸ ^¾^ºx¸p}

R p

}Td¼q%o_}

ìèápÛx×pðÚxÝÑ ÝlÞ»áxæSä

~{ e¼qr

tKr}T;k_}T)A;}B|q%~}AdèmD~kd¼qrrk_{~qfk_ gTo_}jilqf¼L

=mgBqrkzyx{}

k_o~gBqr}Tr;k_}Ëo}qf}Tdrk_?dfeumpqfkzmpo}c~}TdKevgT;T}TdKgTo_}jilqf¼=mgBqfky|{}Td'mp{

dr}TkW~{e¼qf

»Yóéô`óô|Í9ôeðrÒ

1 2π

R d ³ r ⁰ _| _r ₋ ¹ _r 0 |

1 | r ⁰ − u | − r ¹ ⁰

= r − | u − r |

¸9M

<#" $%6[&)GI=@"

mI~gBqf}T¼;k_mpqrk§~}Mozmdrqrr{uilqr{r} k_|qf}T¼}~{erqfempdrdr}Mem?ozm iBmpkdrdèmpuiB}

~}»oç}Tdr}TZo_}D#}TdP;;}TxqfdP~}TdP~k_drqrrk_{~qfk_dPgTo_}jilqf¼kzyx{}TdP}BqP=mgBqfky|{}Td

¾¢Â

}»èmTwx

}T»mièv }Td¼q»oç{ ~}iB}Td»;;}T|qrd

¾Â

}~ehgTrk_}TuiB}#}A}Tdf{~r}~{ ozmP dfv~knq=umd

oçv|w~~¼9T}P{~kzy|{~}milqf{~}Too_}T;}Txq»}T§iB{rd»m{ t4

Ï ý

~kq;eh}TrA}Bqrqf¼}MempA}~}T;eo_}

~}?#gBqf}T¼;k~}T1}T|qf¼}?m{~qrr}Po_}ZfmjwI~}Zièvmpc}?~{e¼qrIy|{k ilr¼}TdrehuIm{er}TAk}T

;;}T|q]~}%dèmA~k_d¼qfrk_{~qrkWgTo_}jilqrrky|{}

6D¹6 ÓÔ¥´:T»P¼ <¿®8;:<¾¤¿ ½ µ83¤¬¾¤¿ » Õ>»j¼ 8 C¯

ÏjÁ{ÏjÁ]À @^ËVÃsÑæÓÖeÉgÈÊeË;ÇÖV2ÆIÃ'ÈÓ^ÃsÞÉgÈÊ1×ÆÒå^Æ

∆E _hf ^th

kÑo}#er}Tdrdrk

| ¸ ¾ º¹p}P~}

∆E _hf

^;}Bq?}T gB#k~}TuiB} o_} }Øo_}M~} ozmd¼qfr{uiSqf{r}Dk_|qf}Br}

~{ erqf

}TZ}T{MumpdcozmQdrqrr{uilqr{r}°vxw#eh}T`u}

t6o_{dce¼gjiBk_dfgB;}T|q

koú}Td¼qcehdrdrko_}%~}°A}Bqrqf¼}

∆E hf

∆E _hf ^th = E ^F 1 + δ ^QED + δ ^Zemach + δ ^recoil + δ ^pol + δ ^hvp

| ¸ ¾ º9K+}

ÊK§eo_{d»~}Monm iBr¼}jilqfk_

δ ^Zemach

^o_k_gT} ^ozm d¼qf¼{uilqf{~r}Mkxqf}Tr~}W~{§e¼qr

§~kd]

qfk_s{}Meo_{drk_}T{rd;m{~qrr}TdZqf}T¼;}Td

δ ^QED

}Td¼qAozmiB¼r}jilqrk§meeh¼qfgB}Memp?ogTo}jiSqfr#w#m4

;ky|{}Oy|{mp|qfky|{}

1{ Me¼}T;k_}Trdr~r}Td}T

α

^ý

δ ^QED

ªs

δ ^QED = a e + 3

2 α ² + α ² (log 2 − 5

2 ) − 8α ³

3π log α(log α − log 4 + 281

480 ) + 17.676 × α ³ π + . . .

| ¸ ¾ ºº'}

9Í

a e

}TdrqKo_}ËA;}B|qK=m~gBqfky|{}mpr=mpo~~}ËogTo_}jilqrr

δ ^pol

erG#k_}T|q6~}Ëozm1#w#mp;ky|{}

kxqf}T¼}#{ e¼qr }lq=eh}T{~q#Bqf¼}WgBmo_{gT}}B {~qfk_o_kdèmp|q=o}Td=~gT}Td=~qf}T{}Bd=emp=~}Td

}~ehgT¼k}Tuil}TdZ~}=~k²¬{drk_¿k_gTonmpd¼qfky|{}TdPdr{Q~}TdPe¼qrd

δ ^hvp

~gjilrkqPo}TdQ}k²ú}BqrdPo_k_gTd?mp{

kxqf}Tfmilqrkd;´¼qf}Td'm{;dr}Tk_»~{;e~rqf

}Bdfdr}T|qrk}Boo_}T;}Txq'ozm)ehonmprk_dèmqfk_»~{A#k~})}

Ê6 u

δ ^recoil

iBuiB}Tr}?o}Td)}k²ú}Bqfd%~}?r}jiB{oK}lq%}Tsoh}?qf{d)o}Td°qf}T¼;}Td%~gTeh}Tuump|qO~{ èmpeeh q

~}%=mpdrdf}Td

m e /m p

<#" $%6[&)GI=@"'0

µ ¾

t¢{Ñ~}BdÑèmpkdrdË~}°iB;A#~kqfg1/gjiB¼k_qr{r}

{dcmTxdÑ{~qrko_k_dfg1o_}1d¼w#d¼qrT;}1/{~k

qrgTd

~ = c = 1

^¾

¸ ¾

É4}»~gB}To_eeh}TA}T|qQeh}T¼qr{rmqfkË~}

∆E _hf ^th

}Bdrq%mozmpo_}=yx{mp{ e¼}T;k_}TrdOf#r}Td }T

α

^¾ Ê6I}k²ú}Bq

mp{ f~r}Bd)eo_{d)gTo_}BxgTd

o_}Td)}k²ú}Bqfd)~}?d¼qrr{uilqr{r}Z}Bq%iB}T{ o_kgBd

ozm

Ç)Ê'}Ñdr}%;gTozmps}Txq

o_}Td~k_d¼qfk_s{}T#}B#k_}T|q1mo_rdkAehdrdrk_o}

¾Â

d¼qf¼{uilqf{¼}=k_|qf}T¼}D~{®e¼qf

ªËm;xqfrg=y|{}=o}~er}Tdrdrk_ ~}

¸¶ ÉÑvmpekqfr}Q¸ Å]mjwW~} }T=mièvW~{erqf

δ ^Zemach

}Td¼q1mpo_¼dQs

δ ^Zemach = − 1.0152 × 2α m ep R p

¸ ¾º }

ÏjÁ{ÏjÁ{Ï Ù ÃsåÃÆIÅ åÆ â;ÃÉÇåÆ@Ó^ÃBÆ\ÈBÊeÇ/UAÆIÃ'ÈÊñÈÓå^Æ@Å

o/}Td¼q]k_|qfgT¼}Tdrdèm|q]/}m;k_}Tcoçr~r}O~}aèmpu~}T{]#}Oièvmil{~}Bdcqf}TrA}Td]iBk·~}Tdrdf{~d

}Bq~}1ergjiBk_dr}TËo_}TdËkiB}T¼qfkqr{u~}Tdy|{kúo_}T{rdËdrxq]mpdrdr#iBk_gT}Td

¾~Â

}BdËrgTdr{oqSmqfdc~})iB}Bq¼qf}%mpmpo_w#dr}

dr|qËe¼gTdr}T|qfgTdcumpdËo_}Td#}T{ De¼}T;k_Tr}TdciBo_}Tdc~{DqSmpo_}Gm{

| ¸ ¾

µ)}r}Bonmqfkx}Td

oç÷mpqrA}

/v|w#~r_T~}

Ç1{}Toy|{}Td=ergjiBk_drkd=df{»o_}Td»mo_}T{¼d y|{}Woç§qfr{~x}umpdDiB}WqSmpo_}Gm{

;gTrkqf}B|qc/Bqf¼}%mpeeh qfgT}Td

ÉÑdrkz~gBrdÑqf{~qc/mphrDo_}1qf}T¼;}°~}u}T¼;k

E ^F

^¾Â ^kiB}T]

qfkqf{u~}°mpdfdriBk_gT}1}Td¼qÑ}Tdrdr}T|qrk}To_o_}T;}T|qÑo_kgB})mp{ »kiB}T¼qfkqr{u~}TdÑdr{

m e

^ý

m p

^ý

µ p

}Bq

α

^¾ PmperTd

¹µPee

Ê6 iB}Zy|{kKiluiB}T¼}

δ ^QED

^ý ^oçkuil}T¼qfkqf{~}?e¼#k_}T|q)~}Td qf}T¼;}Td6»iTmoiB{o_gTd'/f~¼}dr{ehgT¼k_}T{

K°}T

α

^¾xÈ Aeh}T{~q}Td¼qfk_;}T6y|{}Boo_}c}Tdrq6k´gTrk_}T{¼}

¹ ¾

¹¹~µËee ©¸ºLª

°mpdiB}ÑqSmpo_}Gm{

{d~~d6onmmo_}T{6~}Ëozm°iB|qrrk_{~qfk_Aok_gT}

onm

d¼qfr{uilqr{r}°k_|qr}Tr})~{Me¼qr

δ ^rigid

^¾ ÊKsomp|qo_}TdiBrr}Tilqfk_d

δ ^Zemach

^}Bq

δ ^recoil

^ý }To_o})}Bdrq

~qr}T{}

em qfk_~}Bd~~gT}Td]erGx}Tmp|q/}#ehgTrk_}TuiB}Td~}Q~k²¬{~dfk_gBonmpd¼qfky|{}Odr{]~}Td

erqfd

¾úÂ

}Qqr}Tr;}P~}P¼}jiB{o

δ ^recoil

k_o¢}Tdrq°~}Pof#r}

¶»ee~

¾hÂ

mAmpo}B{°~}

δ ^pol

^ý ^µ ^¾ ^ee~ ^ý ^}Bqoçk_uiB}T¼qrk_qr{u~}?mpdfdriBkgB}

ý ¹ ¾ ee~

|q1glqfg

ijmoiB{o_gT}Tdhmp{d¼qfG

ÝBÜËáÙ_ô

©÷¸9M)ª

emp¼qfk_]~}O~gT}Bd}#ehgTrk_;}T|qèmo_}Td]dr{ozm?ehozmrk_dèmpko_kqfg

~{Merqf

Ê6u

eh}T{~q¼}T=mpfy|{}Tcy|{}°onmZiBr¼}jilqfk_Mo_k_gT}

ozmPehozm¼kdèmqfk_W~{ #k~}

δ ^hvp ∼ 10 ⁻ ⁸

qw#~r_T~} qw~#r_T}%Z{ky|{}

mpo}B{

uil}T¼qfkqf{~}

mo_}T{

uiB}T¼qrk_qr{u~}

E ^F

^µTºµj¶ ^¾^¶º ^½ ^{q^} ^¹ ^¾^¹µ)ee ^µj¶¸ ^¾^ºº9KA;} ^Î ^¹ ^¾^µ%ee

δ ^QED 1.13 10 ⁻ ³ < 0.001 10 ⁻ ⁶ 1.13 10 ⁻ ³ 10 ⁻ ⁶

δ ^rigid 39 10 ⁻ ⁶ 2 10 ⁻ ⁶ 7.5 10 ⁻ ³ 0.1 10 ⁻ ³

δ ^recoil 6 10 ⁻⁶ 10 ⁻⁸ 1, 7 10 ⁻³ 10 ⁻⁶

δ ^pol 1.4 10 ⁻ ⁶ 0.6 10 ⁻ ⁶ 0.46 10 ⁻ ³ 0.08 10 ⁻ ³ δ ^hvp 10 ⁻ ⁸ 10 ⁻ ⁹ 0.02 10 ⁻ ³ 0.002 10 ⁻ ³

Ú+O

¸ ¾µ

ÓÜÛáÙ_ÝSØ#ìZÝBÜå´ðúæèÝlìlÜøåóÜøØuÚxÝ?æf×pìlìfÝSâòàu×ð¬ÚxápðÜòÝZÚxÝèâPÚpåÝ¨lìfÝlðÜ´â%Ü·ÝlìSÞ=ÝSâPæè×pðÜóìlåSlØápðuÜßÞ

Þ?Øu×pðuå7·lØuÝGô

(1

^Þ»Ý4Û

' 2.41798836 10 ⁵

^à=áãâ

)

^ô

ÏjÁ{ÏjÁÜ ä ÊeÖeÉÇ

Ã]{dPeh{~dQqf{~q?/÷mhf¿r}T»mry|{}TZyx{}Di}Td¼qPo}»qr}Tr;}DiTmoiB{o_gDempPogTo_}jilqf¼L

#w#mp;ky|{}Ay|{mxqfky|{}Ay|{k6iB|qrrk_{}Ao_}?eo_{d

onmDd¼qrr{uilqf{~r}?v|weh}T`u}

É4}TozmDgBqSmp|q

onm

iBAemfmk_dr #k¼}jilqf}=}T|qf¼}=onmmo_}T{P}~ehgT¼kA}T|qSmpo_} ~}Dogjijm q?vxw#eh}T`u

∆E _hf ^exp

^}BqZonm

mpo_}T{OqfvgTrky|{}

∆E _hf ^th

}»eh}Tr;}lqPempdZ~};qf}Td¼qf}TOonm mpo_kz~kqrgD~{®~gBx}To_eeh}T;}T|qPeh}T]

qf{¼mpqrkñ~}

δ ^QED

^¾ Ê6D}k²ú}Bq

{dc~gj~{k_drd~}TdË¼gTdr{o_qèmpqrdËe¼gjiBgj~}Txqfdcy|{}°okuiB}B¼qfkqf{u~}

¸Lb

mdrdr#ilkgT}

oç}Tdr}TZo_}O~}Td1mp{~qf¼}TdiBr¼}jilqfk_~d

∼ 10 ⁻ ⁶

}4}Td¼q]h}Gmp{uiB{eWeo_{dèmpu~}Oy|{}

onm ergjilkdrk_ ~qr}T{}mj}jio_}TdDijmpoiB{odD~}

Ç)Ê'}

∼ 10 ⁻⁹

^} ^¾ ^ÊK ^em qfkiB{o_k}B

i}Td¼q=o_}

qf}T¼;}

δ ^rigid

y|{kúmpeeh qf}]onm%eo_{dèmpu~}k_;ergTiBkdrk_Dumpd4o_}TdÑiTmoiB{o_d4qrvgTrky|{}Td

É4}Bqrqr}

kiB}T¼qrk_qr{u~}1}Td¼qÑ}Tdrdf}B|qfk_}To_o}TA}T|qÑok_gT}

ozm%mo_}T{Ñ~{=èmTwxD~}

}T=mièv yx{k

il;A}{d

mo_o_d4o}]xk_Ëm{=empèmèmpev}1dr{kmp|q

}Td¼qÑeumdÑiB{}°~}»mk_Tr}]qrvgT¼kzyx{}

;k_}T{

5 %

^¾ t{Ëqr}Td¼qf}TËo})ijmoiB{o~}

Ç)Ê'}

k_o!ømp{u~èmpkq]~k_dfehdr}T~}%~gT}TdcqrrTdce~rgjiBk_dr}Td

dr{]iB}Ofmjw

¾hÈ

eh{¼èmpk_q1mp{drdfkñiB;empr}To_}Td]rgTdr{oqSmqfd}~ehgTrk_;}TxqSmp{ }BqqfvgB¼kzy|{}Bd

~qr}T{d]dr{~}Td]d¼w#d¼qfT;}Tdvxw~~r_gB Zò#}TdnrAgTd]eum]~}T{ Memp¼qfkiB{o_}Td]ehuilqr{}To_o}Td~g

eh{ #{}Td~} d¼qf¼{uilqf{¼} k_|qr}Tr}

gBqrg ;}TgB} df{~ o} P{k_{

d¼w#d¼qfT;}2n¼;gOem]{WZ{Wehdrkqfk

µ ⁺

}Bq{WgTo}jiSqfr

¾Â

mAiB;emfmk_dr#k¼}jilqf}Pmj}ji

o}Bd4rgTdr{oqSmqfd4}~ehgT¼kA}T|qSmp{ »~qf}T{d4emp

k_{

ÝBÜáÙ

onm

Ç)Ê'}¢{dfy|{

{}%ergjilkdrk_#}

0.5 10 ⁻ ⁷

^¾

emp¼qrk)#}AiB}Bd%iBdrkz~gBèmpqrk_d

{dOmTxd%m#e~qrg?{qf{~qOmp{~qfr}Zehk_|q%~}Z{}Ms

drk4ok_uiB}T qfkqf{u~}=dr{

δ ^rigid

}=eh}TrA}BqZeumdZ~}»qr}Td¼qf}TQogTo_}jilqrr#w#mp;kzyx{} y|{mp|qfky|{}

ozm

ergjilkdrk_~qr}T{}Pdr{1o_}Td)m{#qfr}Td°iB|qrrk_{~qfk_~d°eú}B{~q°{d°eh}Br;}Bq¼qfr}Z¬}#qrèmpk¼}Z~}Pozm

Dans le document Transfert de charge muonique (Page 21-44)

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