ISOVECTOR EXCITATIONS OF sd-SHELL NUCLEI IN THE PARTICLE-CORE COUPLING

VERSION OF SHELL MODEL

N.G. GoncharovaSkobelzyn Institute of Nuclear Physics,

Moscow State University

50 YEARS of MultiparticleShell Model (MSM)

G.E.Brown,M.Bolsterly,Phys.Rev.Lett.3(1959)472

Beyond particle-hole doorway basis

• Expanded basis →

,2 2

2

( );

( ..).

ph p h ph phononV V F

f C

int 2 2 ,2 2 ....ph p h ph p hV V V V

Particle Core Coupling Shell Model

, ,

( , ) ( , , )i f

JT f f JT i i f JT i i fi j j

F q J T O J T j O i j C f J j T

'

'

'

' '

( ),,

( ),

( ), ',

( ),

1

1

( ' ' ') ( ) : ,

( ' ' ') ( ' ' ') : ,

J ji i i

J j

J jf f f

J j

i iA

A f f

J T C

J T

J E T nlj J T

J E T n l j J T

2 ,ii

i

SC

S Connection with direct

reaction spectroscopy

Form factors of Electroexcitation

Matrix elements of Hamiltonian

( ' )ij j c ij ijH E E V

(1) (2)ij f fV J V J

Nuclear photo- and electroexcitation

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

max 2 212 2 2

1

, ( ) 2 1J

el magT EJ MJ i f J i f J i

J

F q F F J J T J J T J

( ) .J

J J JB j qr Y

Spin currents contributions to MR

Orbital currents contributions to MR

1 1 1 1, .mag elJ J J J J J J JT A A B T A B B

( ) , J

J J JA j qr Y

Summed squared form factors

32S(γ,p)

Exp:В.Варламов и др ЯФ.т.28 (1978)590

E, MeV

mb

Spectroscopy of pickup reactions on 18O and 22Ne

18O 22Ne

• PCC SM -IzvRAN,72(2008)

18O(γ,n)

O-18 (γ,n)/Exp.J.H. Kelley ea, Nucl. Phys.A564,1 (1993)/

E1 resonances at photopoint in 22Ne

Exp: V.V.Varlamov, M.E.Stepanov, BRAS Physics 64 (2000) №3

σ, mb

E, MeV

10 12 14 16 18 20 22 24 26 28 30

0.0

10.0

20.0

30.0

27Al+γ → 26Al+n

26Al (T=0) 26Al (T=1)

27Al+γ → 26Al+n

Exp: M.N.Thompson et al // Nucl. Phys.1965.V. 64.P.486.

Dynamic deformations in 27Al photodisintegration

• 27Al+γ → 26Al+n 27Al+γ → 26Mg+p

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

Spin- and orbital currents interference in E1 1p shell form factors

At q~0.5÷0.6 Fm-1

FE1(p3/2-1d5/2) ~0 /HOWF/

1( ) 0EF q

Interference of spin- and orbital currents contributions into MR

• Exp:E1 in 12C(e,e’) / Mainz,MAMI A,1988/: Calc. PCCSM

E1 in sd-shell nuclei electroexcitations

Nuclear Orbital M2 CurrentOrbital M2 TWIST Mode: Orbital current has oppositesignes in the upper and lower semispheres.The current vanishes at

Z=0

2

2, 2 2

2 Ji

Mag j i j

eT j qr

q

(e,e’) excitation ~Spin +orbital(twist) modes

(p,p’) excitations –SPIN part onlyComparison of (e,e’) and (p,p’) reveals ORBITAL TWIST M2-

ORBITAL (TWIST) M2 MODE in the transitions from sd-shell

1d5/2-1f7/2

-0,05

0

0,05

0,1

0,15

0 0,5 1 1,5 2 2,5

q, Fm-1

TM2

A1+A3

B2

M2

1d3/2-1f5/2

-0,05

0

0,05

0,1

0,15

0 0,5 1 1,5 2 2,5

q, Fm-1

TM2

A1+A3

B2

M2

1 1

M2 in 32S

Experiment: S-DALINAC 1997 (Emax=14 MeV)

E, MeV

F2 105

8.00 12.00 16.00 20.00

0.000.501.001.502.002.50

S-320.7 g free

8.00 12.00 16.00 20.00

0.0

4.0

8.0

12.0

16.0

S-32F2 106

q = 0.6 fm-1

Spin and orbital currents in M2 32S

E, MeV

F

g=0.7g free q = 0.6 fm-1

q-dependence of M2 peaks

M6 stretched states in sd shell

• Spin current contributions only:

1 1

1

1 11

.

( 6 )

1{ ( .

2 2 1

magJM J J J

magJM J

A JM

j J i J i ji

T A A B

T M A

iq Jj qr

M J

M6 in sd-shell nuclei : 28Si

E, MeV

2

102

F2 102 q = 1.8 Fm-1

S.Yen, T.E.Drake et al., Phys.Lett.B289, 22(1992)

M6 in Ca-40

M6 in sd-shell nuclei : 32S

Exp.: Clausen B.L et al , Phys.Rev.C48, 1632(1993).

PCCSM, NG,Phys.At.Nucl.(2009)#10

Summary

• The deviation of (A) nucleus from closed shells or subshells reveals in a wide range of energy distribution for ”hole” among the (A-1) nuclei states. In the PCC version of SM these distributions are taken into account in microscopic description of multipole resonances 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 q≈2 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.