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-

SD-

..


Particle Core Coupling (PCC) version of the Shell Model
· i,

J Ti =

(J ' ), j



C

(J ' ), j i

(J ' E ' T ')

A -1

в (nlj): Ji , Ti

Si Ci Si

J f, Tf =

(J ' ), j'





(J ' ), j ' f

(J ' E ' T ')

A -1

в (n ' l ' j') : J f , Tf


Matrix elements of Hamiltonian

H ij = (E '+ j + E c ) ij + Vi

j

V= ij


Nuclear photo- and electroexcitations
d( e, e) d
4 2 q 2 q 2 4M 2 = 4 FL ( q, ) + 2 + tg FT ( q, 2q 2 R q
-1 Jmax

2 FT ( q) = ( 2Ji +1)


J =1

{

Jf TJel (q) Ji

2

+ Jf TJmag (q) Ji

2

}

)

=

Jmax

(
J =1

2 2 FEJ + FMJ

)


Summed squared form factors: electroexcitation of sd-shell nuclei

Photopoint :

q = E

exc

0.1 В 0.2 Fm

-1

1 resonances in sd-shell nuclei: E1, M2, E3, M4, E5, M6


Spectroscopy of pickup reactions on

18O


E1 in

18O

at photopoint

1d 1d 1d 18O(
/2

5/ 2 5/ 2 5/ 2

1f 1f

7/2 /2

2 p3

5/ 2

1 p3 / 2 2 s1 1 p3 / 2 1d 1 p3 / 2 1d

,n)

3/ 2 5/ 2

U.Kneissl ea // Nucl.Phys.A272,125 (1976)


Spectroscopy of pickup reactions on

22

Ne


E1 in

22

Ne at photopoint
Si Ci Si

22Ne(

,n)

V.V.Varlamov, M.E.Stepanov MSU-INP,1999


E1 in 24Mg at photopoint
F2 в 102 0.40

a

0.30 0.20 0.10 0.00 15.00
20.0 10.0 0.0 15.00
Exp: Ishkhanov B.S. ea.,
Nucl. Phys.A186 (1972) 438

30.0 , mb

20.00

25.00

30.00

35.00 b

P.M. Endt, Nucl.Phys.A521(1990)1

20.00

25.00

30.00

35.00


E1 in 26Mg at photopoint
F2 в 10
2

0.80 0.40 0.00 10.00
, mb

a

20.00

30.00

40.00

40.0 20.0 0.0

c

10.00

20.00

30.00
E, MeV

40.00

Exp (c): (, n)+(, n+p)+(, 2n) Fultz S.C. et al., Phys. Rev. C4 (1971) 149


27

Al+ 26Al+n

Exp: M.N.Thompson et al // Nucl. Phys. 64 (1965)486




27Al

·

27

Al+ 26Al+n

27

Al+ 26Mg+p

H. RЖpke, P.M.Endt // Nucl. Phys. A632(1998)173.



32

S(d,3He)31P

32S(d,3He)31P; *- 31P J.Vernotte et al,Nucl.Phys.A655(1999)415


E1 excitations

32

S

PCC version of SM

Exp: B.S.ISHKHANOV et al,2002.



34S(p,d)33

S


34

S ­ photoneutron reaction


E1 excitation of

48Ca


Excitation and disintegration of (isospin factors)

48Ca


48

Ca ( , n )

O'Keefe G.J. , Thompson M.N. et al // Nucl.Phys.A469(1987) 239


48

Ca ( , p)

O'Keefe G.J. , Thompson M.N. et al // Nucl.Phys.A469(1987) 239


E1 resonances in (e.e')
Spin- and orbital currents interference in E1 sd-shell form factors


For E1 transitions

1Lj

=L+1/ 2

1(L +1)

j =L+3/ 2

maxima of C1 form factors (a) are near minima of E1 form factors(b)


F2(q) for E1 transitions


MJ
F
2 MJmax

max

excitations
2 22 2J

bq Jf O (q) Ji =Cвq exp(- ) J 2

qmax =

2J b


MJmax (stretched states)

Spin current contributions only


M6 in sd-shell nuclei : 28Si
q = 1.8 Fm-1

Endt P.M. Nucl. Phys. A 310 (1978) S.Yen,ea,Phys.Lett.B289, 22(1992): 6- T=1 at 14.32 MeV E, MeV


M6 in sd-shell nuclei :

32S

Exp q = 1.8 Fm Exp.: Clausen B.L et al , Phys.Rev.C48, 1632(1993).
-1


M6 in Ca-40


M2 resonances
Spin- an orbital currents in M2 excitations


Nuclear Orbital M2 Current
Orbital M2 TWIST Mode: Orbital current has opposite signes in the upper and lower semispheres. The current vanishes at Z=0
(e,e') excitation ~Spin

+orbital(twist) modes (p,p') excitations ­SPIN part only Comparison of (e,e') and (p,p') reveals ORBITAL TWIST M2mag

T2

2ei j2 ( qrj ) 2 ( i ) в j q

(

J =2

)


M2 in 32S(e,e')
q = 0.6 fm-1 F2 в 10
5

2.50 2.00 1.50 1.00 0.50 0.00

0.7 g free

S-32

8.00

12.00

16.00

20.00

F2 в 10

6

16.0 12.0 8.0 4.0 0.0 8.00 12.00 16.00 20.00

S-32

Experiment: S-DALINAC (Emax=14 MeV)

E, MeV


Spin and orbital currents in M2 32S
F

E, MeV


q-dependence of M2 peaks


Summary
· In the PCC version of SM distributions of the "hole" among the (A-1) nuclei states are taken into account in microscopic description of multipole resonances in sdshell nuclei using spectroscopy of pick-up reactions. · The energy spread of final nuclei states is the main origin of the multipole resonances fragmentation in open shell nuclei. Comparison of PCC SM results with experimental data on MR confirms the validity of this approach for a range of momentum transfer from "photopoint" up to q2 Fm-1. · The assumption that some very valuable information on MR in excited deformed nucleus is embedded in direct reactions spectroscopy data proved to be right.