Diffracted Channeling Radiation and Other Compound ... · Diffracted Channeling Radiation and Other...
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Diffracted Channeling Radiation and Other Compound Radiation Processes
Diffracted Channeling Radiation and Other Compound Radiation Processes
Hideo Nitta
Department of Physics
Tokyo Gakugei
University
Channeling 2008Erice, Italy
ContentsContents
•
Diffracted Channeling Radiation (DCR)
•
Diffracted Coherent Bremsstrahlung
(DCB)
•
CPR (PXR) by Neutral Particles
Fundamental processes of radiationFundamental processes of radiation
atom e-
photon
atom
e-
photon
1.Bremsstrahlung
2.Polarization radiation
in crystals:coherent bremsstrahlung (CB)channeling radiation (CR)
in crystals:“coherent polarization radiation” (CPR)others:transition rad., SP rad.,Cherenkov rad.
Bethe-Heitler
Amusia Phys.Rep. 162,249 (1988)
0 1 2 , ( , , )L L n n
photons from P and Q interfere constructively when:
Interference condition for CB and CPRInterference condition for CB and CPR
e-
L0
L
Φ
θ d
P
Q
radiation
PQ
sind
0 PQ cosL
PQ ,vT L cT
1
( cos )sin
c dn
vor
1
g v
cos“dispersion relation” of both CB and PXR
0 1 2 , ( , , )L L n n
e-
L0
Lθ
dP Q
radiation
2
T
0 PQ cosLPQ ,vT L cT
for θ=0:1
cosn 22
1
n
n
photons from P and Q interfere constructively when:
Interference condition for CRInterference condition for CR
1 (actually )
Diffracted Channeling Radiation (DCR)Diffracted Channeling Radiation (DCR)
Baryshevsky and Dubovskaya, J.Phys.C 16, 3663 (1983).General theory
Ikeda, Matsuda, Nitta, Ohtsuki, NIM B115, 380 (1996)Kinematical theory
Yabuki, Nitta, Ikeda, Ohtsuki, Phys.Rev.B 63, 174112 (2001).Dynamical theory
Korotchenko , Pivovarov, Tukhfatullin, NIM B (to appear).Detailed dynamical calculations for LiF crystal.
(and presentations given by above authors and Fiks in this conference.)
channeling radiation:
parametric x-ray radiation:
diffraction of channeling radiation:(use of channeling crystal itself as a monochromater)
Diffracted Channeling Radiation (DCR)Diffracted Channeling Radiation (DCR)
DCR as intense monochromatic x-ray source
~0.1photons/e-
large backgroundforward radiation
~10-5photons/e-
negligible backgroundemitted into a large angle
channeledelectron
θy
θx
2θB
diffracted radiation
chan
nel p
lane
diffraction planes
channelingradiation
Diffracted Channeling Radiation (DCR)Diffracted Channeling Radiation (DCR)
i fE E
2 2 4( ) ( ) p p E c m c, ,( ) pi f i fE E E
( ) p p gk
1 cos
g v
if v c
0 c c
Diffracted Channeling Radiation (DCR)Diffracted Channeling Radiation (DCR)
Frequency of DCR
Energy-momentum conservation:
( ) if i fE E
initial and final energy of the particle
Diffracted Channeling Radiation (DCR)Diffracted Channeling Radiation (DCR)
1 cos
g v
1 cos
g v
if
20
1 cos2
( )( 0)
if
if
PXR
CR
0 if
0g
Diffracted Channeling Radiation (DCR)Diffracted Channeling Radiation (DCR)
Radiation process and matrix elements
22 IF int Fw F H I
ˆ
A pinteHmc
( ) exp[ ( ) ] gk g
A r A k g ri c c
( ) 1( ) ( ) p rr isn
x z
y eL L
2ˆ( ) ( ) ( )
2 n n nV y y E ym
p
( )1( ) ( ) exp[ ( ) ] nn G y y
Gy
y C p i p G yL
Fermi’s golden rule:
The interaction Hamiltonian:
Bloch wave “photon”:
quantum states of channeled electron:
Diffracted Channeling Radiation (DCR)Diffracted Channeling Radiation (DCR)
DCR needs dynamical theory of diffraction
PXR: virtual photon diffraction (no divergence)
DCR: (virtual) CR diffraction (divergence occurs)
k,ω k v
k+g,ω* k gc
k,ω* kc
k+g,ω* k gc
2 02( )
g
g k k + gA Akinematical:
Diffracted Channeling Radiation (DCR)Diffracted Channeling Radiation (DCR)
( 0)
0
( ) ( )0
( 0)
ˆexp( ( ) )
ˆexp( )
gg
gg
p A k g r p p
p A k r p p
int
f i
f i
if if
F H Ie imce imc
M M
( )
( ) ( )1 ˆ( ) ( )
( )
g
k g k gg g
g
A v A
p p k
y y
if
i y i yf i y f iy
eMc
e e pm
Matrix elements
Diffracted Channeling Radiation (DCR)Diffracted Channeling Radiation (DCR)
intraband transition: i=f
form factor
( ) ( ) (( ) ) ( )
g g gA v k g p p k iiii y
eM Fc
( ) iqyii i iF q e
22
2 2 24 sin 4(1 ) 4(1 )
yxB
x y B v vPXR
dNd d dz c W W
2 22 2 2
2 2 2
1 ( )2
gv x y kin
g x y kin
PW
P
2 20 kin
Diffracted Channeling Radiation (DCR)Diffracted Channeling Radiation (DCR)
interband transition: i≠f
( ) ( ) ( ) ( ) ( )
g g g gk g A v A p kp if
f i y y ifeM y i ic
2 23 2 2 2
3 2 2 2
( )4 sin 4(1 ) 4(1 )
if
ByB if x y
x y BDCR
ydNd d dz c W W
if f iy y 2 212
g
g
PW R
P R2
202
1cot 2if ifx B y
B B
R
where
Diffracted Channeling Radiation (DCR)Diffracted Channeling Radiation (DCR)
Angular distribution of DCR and PXR
10MeV e-
→ Si(110)/ Si(111)
diffraction
202
cot
12
ifx B
B
ify
B
0W DCR peaks appear at
e-
monochrometer
detector
targetDCR
Diffracted Channeling Radiation (DCR)Diffracted Channeling Radiation (DCR)
Electron energy and DCR intensity
1 2
02
ifth g
B
0W if the electron energy is small,
is not satisfied.
DCR threshold
th where
Diffracted Coherent BremsstrahlungDiffracted Coherent Bremsstrahlung
“CB planes”
diffraction planes
electron
2θB
diffracted radiation
coherentbrems.
Diffracted Coherent Bremsstrahlung
(DCB)Diffracted Coherent Bremsstrahlung
(DCB)
1 cos
g v
( )1 cos
g h v
20
1 cos2
( )( 0)
h v
h v
PXR
CB
0h
0g
PXR emitted by Neutral ParticlesPXR emitted by Neutral Particles
Search for properties of neutrino
Majorana neutrino Dirac neutrino
mass, magnetic moment, …
Cherenkov radiation by neutrino
Grims
and Neufeld, Phys.Lett.B
315
(1993) 129.
Transition radiation by neutrino
Classical theory:
Sakuda, PRL 72
(1994) 804.
Quantum theory:
Sakuda
and Kurihara, PRL 74
(1995) 1284.
PR-type radiation by neutrino magnetic moment
PR-type radiation by neutrino magnetic moment
PXR by Neutral ParticlesPXR by Neutral Particles
Magnetic moment μ
Effective currenteff ( ) ( )c j r μ r
neutral particleat rest
Lorentz transformation-v
eff ( ) ( )c
t
j r μ r v
effective current due to magnetic moment
Classical electrodynamics
2
03 3 2 00064 /
( , )dI c
dd
g
gk k E k g
eff2( )
( , ) ( )i c
j k k μ k v
eff0 2 2 2
4*
( , )( , )
( / )ic c
j kE k
k
PXR by Neutral ParticlesPXR by Neutral Particles
Classical PXR formula
(Ter-Mikaelian)
32
3 2 2 20
2 22 22
22 2 2 200
14
3 2
1
gg
/
/
sin
cos / cos cos
/
B
B
B B x B y
x y
cdNd dz v
PXR by Neutral ParticlesPXR by Neutral Particles
Intensity of PXR from magnetic moment
2 2 22 2
2 22 2 2 200
2
4 1
gg
/ cos
sin /
eB B x y
Bx y
cdN ed dz c
cf. PXR for an electron (F-I formula):
PXR by Neutral ParticlesPXR by Neutral Particles
-4 -2 0 2 4
-4
-2
0
2
4
-4 -2 0 2 4
-4
-2
0
2
4
ΘB=20° ΘB=25° ΘB=30°
-4 -2 0 2 4
-4
-2
0
2
4
-4 -2 0 2 4
-4
-2
0
2
4
-4 -2 0 2 4
-4
-2
0
2
4
ΘB=34°
-4 -2 0 2 4
-4
-2
0
2
4
ΘB=35° ΘB=45°ΘB=38°ΘB=36°
-4 -2 0 2 4
-4
-2
0
2
4
-4 -2 0 2 4
-4
-2
0
2
4
Angular distribution of PXR by magnetic moment
PXR by Neutral ParticlesPXR by Neutral Particles
Comparison with electric-charge PXR
2
222ePXR
3 22PXR
2 2
/4 sin 1
//14 sin
B
B c
B BB
B
cecN
N ccc
c : Compton wavelengthB : Bohr magneton
2el4 6PXR
mgPXR
10 10B
NN
e30PXR
PXR
10NN
!!!
2 3/ ( ) 10E m c
10/ 10B
Quantum effect: radiation due to spin flip
int 2H F
2i
F A A
cf. TR (Sakuda and Kurihara 1995)
Analytical expression has been obtained for TR (Ueno and Nitta)
(numerical calculation)