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Transcript Slide 1

Why an optical model ?
N body problem
A1 nucleons
A2 nucleons
H E
for each nucleon
N=A1+A2 equations to solve....
Optical model
all the interactions between the nucleons are replaced
by an average and central interaction V(r)
between the projectile and the target
References:
one body problem
2
H
V
2
a particle with a mass is in a potential well
V(r) which replaces all the interactions between
the different nucleons.
P. E. Hodgson, The nucleon optical potential, Clarendon Press, 1994
G. R. Satchler, Direct nuclear reactions, Oxford University Press, New York, 1983
:reduced mass of the system
Optical potential
The optical model used to describe the interaction between two nuclei is inspired by the
optical phenomena.
imaginary
V(r) = U(r) + i W(r)
real part
imaginary part
represents the elastic scattering
to take into account the others
reactions which can occured
reflexion of the incident wave
simulates the loss of flux due to no
elastic collisions
absorption of the incident wave
V(r) = U(r) + iW(r) + Vso(r) + Vc(r)
spin-orbite
Coulomb
Phenomenogical optical potential
U(r) = Uv f(r)
W(r) = Ws g(r) + Wv f(r)
g ( r ) 4a
Woods- Saxon
f (r )
1
f ( r )
r
1 e (r R) / a
R: potential radius
a: potential diffusness
elastic scattering data: parametrization of Uv, Ws, Wv, av, aWs, aWv, R, Vso
p-nucleus, n-nucleus interaction: parametrization CH89 from Varner et al.
nucleus-nucleus interaction: not general parametrization
a projectile on a reduced number of target or limitation in energy.
parameters adjusted case by case
150 MeV
d/d (mb/sr)
6He(p,p)6He
nuclei in their ground sates !!!!
cm (deg)
Microscopic optical potential
rt
rpt
Ot
p
rp
Op
p
r
Target
Projectile
effective nucleon-nucleon force
Folding
U (r )
3
3
(
r
)
(
r
)
(
r
)
d
r
d
p p t t tp p rt
densities : microscopic or macroscopic densities
Link with ABLA
The decay width for evaporation:
max
Eimf
E max
partner
0
0
capt
imf ( Eimf ) partner ( E partner )
dEimf dE partner
c (E)
E = Eimf + Epartner + Q + - B
Now: a real potential is used to describe the transmission probability of particles
Kildir et al., PRC 51, 1873 (1995)
another possibility to calculate capture: optical potentials
(nuclei not in their groundstates)
Aleksandra