Methods of excitation: nuclear reactions

Electromagnetic excitation

208Pb beam

238U target

energy of gamma radiation (keV)

log

(inte

nsity

)

r

r

d

Electric fields of multipoles

In general the electric potential due toan arbitrary charge distribution is

'

'

'

d

rr

rrU p

expansion

',',12

4'

'

1 *

01

m

mm YY

r

r

rr

special case: electric monopole

4

1',',0 0000 YYm

rrr

1

'

1

r

r

d

Electric fields of multipoles

In general the electric potential due toan arbitrary charge distribution is

homogenous charge distribution

special case: electric monopole '''sin''1

4

3 230

dddrrrR

eZrU

'

'

d

r

rrU p

304

3'

R

eZrp

43

1

4

3 30

30

R

rR

eZrU

r

eZ

Electric field lines of two interacting charges

Monopole

dipole quadrupole octopole

2

1U

rr 1

Ur

r 3

1U

rr 4

1U

rr

Monopole, dipole, quadrupole, ...

Monopole, dipole, quadrupole, ...

r

r

d

Electric fields of multipoles

In general the electric potential due toan arbitrary charge distribution is

'

'

'

d

rr

rrU p

expansion

',',12

4'

'

1 *

01

m

mm YY

r

r

rr

special case: electric quadrupole matrixelement

'',''', ** dYrrmM mp

2

20*

4

3,2

ReZ

mM

multipole moments

B(E2)-value: 2,2);2(

mMiiiffffi

f

KMImMKMIIIEB

mMYr

rU m

m

m

,2,1

5

4 *,23

2

2

special case: electric quadrupole potential