ISOVECTOR EXCITATIONS OF sd-SHELL NUCLEI IN THE PARTICLE-CORE COUPLING VERSION OF SHELL MODEL
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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
( ) , JJ 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, MeV10 12 14 16 18 20 22 24 26 28 30
0.0
10.0
20.0
30.0
27Al+γ → 26Al+n26Al (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 22 Ji
Mag j i jeT j qrq
(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
16.0S-32
F2 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 J j qrM 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.