Potential Approach to Scattering of Exotic Nuclei Goncharov S.A.
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Potential Approach to Scattering of Exotic Nuclei Goncharov S.A.
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Transcript of Potential Approach to Scattering of Exotic Nuclei Goncharov S.A.
Optical Model
Potential approach: effective potential conception
)()(]2
[ )()(22
rr uuU
0)( modeleffH
P→ single elastic channel
QP
PPmodel
)]()()([00 AAaamodel xxu rA
),( rxUKHH rineff
Potential approach: effective potential conception
Mean Field Potential (“MFP”)
)( UVU PP
Dynamic Polarization Potential (“DPP”)
QPQQ
PQ VH
VU)(
1)( )(
Dispersive Relation
a
p
A
t
ptvV1 1
EErrW
EdrrVP ),,(1
),,(
0000 AaAaFPP VVV A
)(Im)(Re UWUVP
Phenomenological (Woods-Saxon)Phenomenological (Woods-Saxon)Optical Model PotentialOptical Model Potential
f (x) = ( ex + 1 ) -1 ,
xi = ( r – Ri ) / ai (i=V,W,D)
)()(
4)()()( rVdx
xdfWixiWfxVfrU Coul
D
DDWV
Semi-microscopic (or semi-phenomenological) approachSemi-microscopic (or semi-phenomenological) approach
Folding Model
Microscopic calculation of the mean field potential
,
)()()()(
)()(
21,
21
1,0
rrrr AT
aT
DcT
DT
T
DT
D
sgddrV
rVrV
ip
in
i
ip
in
i
1
0
+ Phenomenological construction of DPP
EDF VVV
Microscopic calculation of the mean field potential +
“SNKE” – single nucleon knock-out exchange approximation
Exchange effects – Khoa-Knyazkov SNKE Procedure
Semi-microscopic approachSemi-microscopic approach
K(r)ssrrsrrrr
isgddrV A
TaT
EcT
ET exp),(),()()( 2211
,21
)(2
2 rr(r)2CVV )(-EK
pt
E
ptptptvvAv P̂ˆˆˆˆ
Microscopic calculation of the mean field potential
,
EDF VVV
Effective nucleon-nucleon interaction
s = rp - rt + r
a
p
A
t
ptvV1 1
T
t
T
ppt
ten
Tptpt
so
T
S
t
S
pS
c
STsT
CT
sTpt
Ssgsgsgv
sgvv
)ˆ(ˆ)()()(),(ˆ
)(),(ˆˆ1,0
sSLps
ps
rtps aA
Aapppp
2
1
“M3Y”
zc=zso=1, zten=s2 (m=c,so,ten , n =D,E)
)()/Y()()(3
1
,, szRsiGsgm
ii
nm
ST
nm
ST
xex x /)Y(
tptppt
tpsptpt
iiiiii
S σσσσ
σσ
sss
psSL
ˆˆ3)ˆ(ˆ
)(2
1
,τ,σ,1 1100
Semi-microscopic approachSemi-microscopic approach Microscopic calculation of the mean field potential
Imaginary part of DPP (“absorptive potential”)
),(),(),( riWrVrU P
Semi-microscopic approachSemi-microscopic approach
D
DDW dx
xdfWixiWfErW
)(4)(),(
W(E), WD(E), α(Е), β(Е) – free for all energies
Construction of DPP
Real part of DPP (“dispersive correction”)
rW , aW , rD, aD – free but the same for all energies
D
DWP dx
xdfxfrV
)((E))((E)E),(
Microscopic calculations → rather qualitative information about different processes contributions in particular energy regions
Phenomenological construction of DPP is still topical
Since wide-used version of the semi-microscopic approach
)(),()(),(Re rVNrVrVrU FFPF EE
)()1)((),( rVNrV FFP EE
Semi-microscopic approachSemi-microscopic approach
D
DDW
D
DWF dx
xdfWxfWi
dxxdf
xfrVrU)(
(E)4)((E))(
(E))((E))()(
Semi-microscopic Dispersive Optical Model Potential
• More flexible form but less number of parameters, less ambiguity • Explicit account for the dispersive relations• Explicit energy and radial dependences of DPP, the role of the DPP contribution
)()()( ImRe rViNNrU F
6Li Density: by Zhukov et al.(“DZ”) 12C Density from: Sorensen & Winter (“SW”)
Semi-microscopic Dispersive Optical Model Potential As Applied To
6Li+12C Elastic Scattering
Experimental data set: Elab= 30, 60, 90, 99, 156, 210 and 318 Mev
JV(E)=Jfold(E)+JP(E)
drrruJu2)(
6He Density: by Zhukov et al.(“DZ”) 12C Density from: Sorensen&Winter (“SW”)
Semi-microscopic Dispersive Optical Model Potential As Applied To
Evaluations of 6He+12C Elastic Scattering
6Li & 6He Density: by Zhukov et al.(“DZ”) 4He Density: gaussian
Semi-microscopic Dispersive Optical Model Potential As Applied To
4He+6Li & 6He+4He Elastic Scattering
Experimental data set: E4He = 36.6, 50.4, 59.2, 104 & 166 Mev
E6He = 151 Mev (Ter-Akopyan et al.)
Semi-microscopic Dispersive Optical Model Potential As Applied To
4He+6Li & 6He+4He Elastic Scattering
Analysis of experimental data: E4He = 104 Mev & E6He = 151 Mev
3He, 3H Density: by Efros et al.
Comparative Analysis of Data Sets:3He+14C at Elab= 72 MeV (Ecm=59 MeV) & 14C+3H at Elab= 334MeV
Semi-microscopic Dispersive Optical Model Potential As Applied To
Isospin Effects in Elastic Scattering
Vi3He – Vi
3H
Semi-microscopic Dispersive Optical Model Potential As Applied To
Density Model Effects
Comparative Evaluations of 6He+3He & 6He+3H Elastic Scattering
“DZ” – solid“2pF” - dush
1– 3He 2 – 3H
)()(
)()()(
21
21
1– 3He 2 – 3H
Semi-microscopic Dispersive Optical Model Potential As Applied To
Density Model Effects
Comparative Evaluations of 8He+3He & 8He+3H Elastic Scattering
)()(
)()()(
21
21
1 – 3He2 – 3H)()(
)()()(
21
21
Semi-microscopic Dispersive Optical Model Potential As Applied To
Density Model Effects
Comparative Evaluations of 8B+3He & 8B+3H Elastic Scattering
