Shell Model in Complex Energy Plane Institute of Atomic Physics, Bucharest Resonances and virtual states: Berggren representa Shell model with resonances and virtual states Application: the structure of 11 Li N. Sandulescu Espace de Structure Nucleaire Theorique, Saclay **Similar work : N. Michel, W.Nazarewicz, M. Ploszajczak, K. Bennaceur,… *Collaborators : R.Id. Betan (Rosario) , R.J.Liotta (Stockholm), T. Vertse (Debrecen)
Shell Model in Complex Energy Plane. N. Sandulescu. Institute of Atomic Physics, Bucharest. Espace de Structure Nucleaire Theorique, Saclay. Resonances and virtual states: Berggren representation Shell model with resonances and virtual states Application: the structure of 11 Li. - PowerPoint PPT Presentation
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Shell Model in Complex Energy Plane
Institute of Atomic Physics, Bucharest
• Resonances and virtual states: Berggren representation
• Shell model with resonances and virtual states
• Application: the structure of 11Li
N. Sandulescu
Espace de Structure Nucleaire Theorique, Saclay
**Similar work: N. Michel, W.Nazarewicz, M. Ploszajczak, K. Bennaceur,…
*Collaborators: R.Id. Betan (Rosario) , R.J.Liotta (Stockholm), T. Vertse (Debrecen)
Resonances and virtual states
10Li
virtual stateresonances
9Li
Single-particle resonant states
79Ni
78Ni
Resonant states
Decaying state (Gamow,1928)
2En
nn iE
divergence !
« Capturing » state: tt *nn kk
tEi n
e ri ne
General defintion ( Siegert, 1939)
0),()](2)1(
[22
22
2
krurVh
M
r
llk
dr
dl
« Resonances »: out-going solutions
Time-reversed solutions : ),(~),( * rkurku nln
),( rku nl
0),()( lll OuWky
;)()(),( lllll IkyOkxrku
Resonant states
Poles of S-matrix
Re k
Im k• k-plane :
• energy plane: ;2
iE );(
222
2
M
M
2
ik
« resonance »
« anti-resonance »
« crazy »
« anti-bound » Re E
Gamow states : normalisation
• Bi-orthogonal set : ),( rku nl ),(),(~ * rkurku nn