Transcript Reakcje z lekkimi, slabo zwiazanymi jądrami

Probing nuclear potential with
reactions
Krzysztof Rusek
Heavy Ion Laboratory, University of Warsaw,
www.slcj.uw.edu.pl
The Andrzej Soltan Institute for Nuclear Studies,
www.ipj.gov.pl
Going out of the valley of stability
Magic numbers are no longer magic
Nuclear halos
Importance of three-body forces
Granulation of nuclear matter
etc.
Can we use the standard form of effective nucleusnucleus potential?
Effective nucleus-nucleus
potential
G.R. Satchler, W.G. Love, Phys.Rep. 55 (1979)183
V = Vo + iW
Vo :
W = 0.5 Vo
Elastic scattering
6Li
+ 208Pb
6He
+ 208Pb
Y. Kucuk, N. Keeley PRC 79 067601
(2009)
Deviation from Rutherford c.s. at very forward angles
Elastic scattering
↓
↑
L. Acosta et al. EPJ A in print
Structure effects important!
Complete fusion
V
R
Complete fusion
Supression above the Coulomb barrier
L.R. Gasques et al. PRC79
(2009) 034605
Complete fusion
↑
S.M. Lukyanov et al. PLB 670
(2009) 321
Enhancement below the Coulomb barrier
The method
(continuum-discretized coupled-channels)
Φ(r,R) = ψg.s.(r)χel(R) + ψ1exc(r)χinel(R) + ..
[T + εg.s. – E + <ψg.s.(r)I V(r,R) Iψg.s.(r)>] χel(R)
= <ψg.s.(r)IV(r,R)Iψinel.(r)> χinel(R)
... . . . . . . . . . . . . . . . . . . . . . .
The method at work
↓
K. R. PRC72, 037603
Structure of 6He is ”reflected” in elastic scattering close to the barrier
The concept of DPP
(dynamic polarization potential)
V =
Vo + iW + DPP
Method 1: inversion S → V
IP method of R.S. Mackintosh
Review of IP method: V.I. Kukulin and R.S.Mackintosh, J. Phys. G: Nucl. Part.
Phys. 30, R1 (2004)
Method 2: „trivially equivalent potential”
[T + Vo + i W + DPP] χel(R) = E χel(R)
χel(R) from CDCC calculations
local, L-dependent DPPs, many methods to derive L-independent DPP.
If the method is working well, results (σel ) should be close to CDCC
Case 1 – 4He + 238U
Solid, dashed – CDCC, Dotted – OM+DPP
Strong repulsion at the surface is due to nuclear interactions (absorption)
Case 1 – 4He + 238U
Exp. data of Budzanowski et al.,
PL 11 (1964) 74
Solid, dashed – CC, Dotted – OM+DPP
Strong repulsion at the surface is due to nuclear interactions (absorption)
Case 2 – 7Li + 208Pb
Exp. data Keeley et al., NPA 571
(1994) 326
Solid – CDCC, dashed – OM+DPP
Coupling with unbound states generates similar DPP as with bound state
Case 3 – 6He + 208Pb
Exp. data A. Sanchez-Benitez et
al., NPA803 (2008) 30
Long range attraction
due to dipole
polarizability
Contiunnum
dominated by L=1
states
Conclusion
Similar tendency –
repulsion at the
surface and long
range attraction
reflecting dipole
couplings with the
continuum
Parametrization
DPPreal = V1 df/dR + V2 g(R)
DPPimag = W1 df/dR + W2 g(R)
f(R) = [1+exp(R-R0,i)/a1]
g(R) = [1+exp(R-R0,i)/a2]
V1
/W1
V2
/W2
Ro,i
a1
a2
6.5
0.20
10.3
0.80
6.0
imag 6.5
0.35
9.8
0.50
3.0
real
Consequences
V = Vo + i W + DPP
Explanation of all the
effects observed for el.
scatt. and fusion.
Consequences
Prediction for
fusion barrier
distribution – shifts
it to higher
energies and
make broader
6Li
+ 28Si
K. Zerva et al., PRC80(2009)017601
Recipe
V = Vo + iW + DPP
Vo – from densities
W – a half of V0
DPP – coupling with direct
reaction channels
Parametrization
α + 238U
V1 /W1
V2 /W2
Ro,i
a1
a2
real
6.5
0.18
8.2
0.55
2.8
imag
0.3
0.18
10.8
0.55
3.0
7Li
+ 208Pb
V1 /W1
V2 /W2
Ro,i
a1
a2
real
6.5
0.05
10.05
0.50
3.0
imag
0.0
6.0
10.30
-
0.40
6He
+ 208Pb
V1 /W1
V2 /W2
Ro,i
a1
a2
real
6.5
0.20
10.3
0.80
6.0
imag
6.5
0.35
9.8
0.50
3.0
CHEMISTRY
QC
Prod.
Prod.
PET
CYCLOTRON
EXPERIMENTAL HALL
ICARE
EAGLE
SEPARATOR
GDR
CUDAC
BIOLOGY
Energies 2 ÷10 MeV/A
Ions 10B ÷ 40Ar
CYCLOTRON
K = 160
QC
Potential from transfer
reaction analysis
B+b
a+A
Probability: potential a + A
+ structure
+ potential b + B
10B
+ 7Li → 8Be + 9Be
A.T. Rudchik et al. PRC 79 054609 (2009)
The method
(continuum-discretized coupled-channels)
prof. G. Rawitscher
Φ(r,R) = ψ1(r)χ1(R) + ψ2(r)χ2(R) + …..
[T + εi – E + <ψi(r)IV(r,R)Iψi(r)>] χi(R) =
<ψi(r)IV(r,R)Iψk(r)> χk(R)
Input parameters
- Structure of the projectile
(wave functions)
- Fragment – target interactions
No free parameters