Diffracted Channeling Radiation and Other Compound ... · Diffracted Channeling Radiation and Other...

$: Diffracted Channeling Radiation and Other Compound ... · Diffracted Channeling Radiation and Other Compound Radiation Processes ... 16, 3663 (1983). General theory. Ikeda, ... PXR:$
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)


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


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


Frequency of DCR

Energy-momentum conservation:

( ) if i fE E

initial and final energy of the particle


1 cos

g v

1 cos

g v

if

20

1 cos2

( )( 0)

if

if

PXR

CR

0 if

0g


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:


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:


( 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


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


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


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


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


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


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):


-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


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)

SummarySummary

•

Diffracted channeling radiation (DCR)

•

Diffracted coherent bremsstrahlung

(DCB)

•

A neutral particle with magnetic moment may emits PXR as well as TR.

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