Probing nuclear potential with reactions
description
Transcript of Probing nuclear potential with reactions
![Page 1: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/1.jpg)
Probing nuclear potential with
reactions
Krzysztof Rusek Heavy Ion Laboratory, University of Warsaw,
www.slcj.uw.edu.plThe Andrzej Soltan Institute for Nuclear Studies,
www.ipj.gov.pl
![Page 2: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/2.jpg)
Going out of the valley of stability
Can we use the standard form of effective nucleus-nucleus potential?
Magic numbers are no longer magic
Nuclear halos
Importance of three-body forces
Granulation of nuclear matter
etc.
![Page 3: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/3.jpg)
Effective nucleus-nucleus potential
V = Vo + iW
Vo :
W = 0.5 Vo
G.R. Satchler, W.G. Love, Phys.Rep. 55 (1979)183
![Page 4: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/4.jpg)
Elastic scattering
Deviation from Rutherford c.s. at very forward angles
6Li + 208Pb
6He + 208Pb
Y. Kucuk, N. Keeley PRC 79 067601 (2009)
![Page 5: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/5.jpg)
Elastic scattering
Structure effects important!
L. Acosta et al. EPJ A in print
↑
↓
![Page 6: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/6.jpg)
Complete fusion
R
V
![Page 7: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/7.jpg)
Complete fusion
Supression above the Coulomb barrierL.R. Gasques et al. PRC79 (2009) 034605
![Page 8: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/8.jpg)
Complete fusion
Enhancement below the Coulomb barrier
S.M. Lukyanov et al. PLB 670 (2009) 321
↑
![Page 9: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/9.jpg)
The method (continuum-discretized coupled-channels)
[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)
... . . . . . . . . . . . . . . . . . . . . . .
Φ(r,R) = ψg.s.(r)χel(R) + ψ1exc(r)χinel(R) + ..
![Page 10: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/10.jpg)
The method at work
Structure of 6He is ”reflected” in elastic scattering close to the barrier
K. R. PRC72, 037603↓
![Page 11: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/11.jpg)
The concept of DPP(dynamic polarization potential)
local, L-dependent DPPs, many methods to derive L-independent DPP.
If the method is working well, results (σel ) should be close to CDCC
V = Vo + iW + DPP
Method 1: inversion S → VIP method of R.S. MackintoshReview of IP method: V.I. Kukulin and R.S.Mackintosh, J. Phys. G: Nucl. Part. Review of IP method: V.I. Kukulin and R.S.Mackintosh, J. Phys. G: Nucl. Part. Phys. Phys. 3030, R1 (2004) , R1 (2004)
Method 2: „trivially equivalent potential”
[T + Vo + i W + DPP] χel(R) = E χel(R)
χel(R) from CDCC calculations
![Page 12: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/12.jpg)
Case 1 – 4He + 238U
Solid, dashed – CDCC, Dotted – OM+DPP
Strong repulsion at the surface is due to nuclear interactions (absorption)
![Page 13: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/13.jpg)
Case 1 – 4He + 238U
Solid, dashed – CC, Dotted – OM+DPP
Strong repulsion at the surface is due to nuclear interactions (absorption)
Exp. data of Budzanowski et al., PL 11 (1964) 74
![Page 14: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/14.jpg)
Solid – CDCC, dashed – OM+DPP
Case 2 – 7Li + 208Pb
Coupling with unbound states generates similar DPP as with bound state
Exp. data Keeley et al., NPA 571 (1994) 326
![Page 15: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/15.jpg)
Case 3 – 6He + 208Pb
Long range attraction due to dipole polarizability
Contiunnum dominated by L=1 states
Exp. data A. Sanchez-Benitez et al., NPA803 (2008) 30
![Page 16: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/16.jpg)
Similar tendency – repulsion at the surface and long range attraction reflecting dipole couplings with the continuum
Conclusion
![Page 17: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/17.jpg)
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]
Parametrization
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
![Page 18: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/18.jpg)
V = Vo + i W + DPP
Explanation of all the effects observed for el. scatt. and fusion.
Consequences
![Page 19: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/19.jpg)
Prediction for fusion barrier distribution – shifts it to higher energies and make broader
Consequences
K. Zerva et al., PRC80(2009)017601
6Li + 28Si
![Page 20: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/20.jpg)
Recipe
V = Vo + iW + DPP
Vo – from densities
W – a half of V0
DPP – coupling with direct
reaction channels
![Page 21: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/21.jpg)
Parametrization
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
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
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
α + 238U
7Li + 208Pb
6He + 208Pb
![Page 22: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/22.jpg)
CYCLOTRON
PET QCC H E M I S T R Y
QC
Pro
d.
Pro
d.
CYCLOTRON
GDR
EXPERIMENTAL HALL
SEPARATORICARE
BIOLOGY
CUDAC
K = 160
EAGLE
Energies 2 ÷10 MeV/A
Ions 10B ÷ 40Ar
![Page 23: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/23.jpg)
Potential from transfer reaction analysis
Probability: potential a + A
+ structure
+ potential b + B
a + A
B + b
![Page 24: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/24.jpg)
10B + 7Li → 8Be + 9Be
A.T. Rudchik et al. PRC 79 054609 (2009)
![Page 25: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/25.jpg)
The method (continuum-discretized coupled-channels)
[T + εi – E + <ψi(r)IV(r,R)Iψi(r)>] χi(R) =
<ψi(r)IV(r,R)Iψk(r)> χk(R)
Φ(r,R) = ψ1(r)χ1(R) + ψ2(r)χ2(R) + …..
prof. G. Rawitscher
![Page 26: Probing nuclear potential with reactions](https://reader030.fdocuments.net/reader030/viewer/2022033102/56814e83550346895dbc1f93/html5/thumbnails/26.jpg)
Input parameters
- Structure of the projectile(wave functions)
- Fragment – target interactions
No free parameters