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Mesut Karakoç
May 31st, 2012
TAMU-Commerce & Akdeniz U. - Turkey
Collaborators:
Carlos Bertulani (TAMU-Commerce)
Adriana Banu (James Madison U.)
Livius Trache (Texas A&M University)
Coulomb distortion and medium corrections in nucleon-removal reactions
Eikonal Waves
k
k’q
DE << E, q << 1 radian ,
rkbr ieS )(
')'(exp
)(
dzVv
i
eS i
r
b b
v V(r)
r bz
1Ψ/Ψ2
'' z
br
EV2
2
2
Breakup (Knockout) Reactions
(a) Diffraction Dissociation: (Elastic breakup)
kBreakup amplitude: to state
2
000
2
0.. )( nCnCdisdif SSSSdbb
k
(b) Stripping: (Inelastic breakup)
bnbC
z
22)(1)( nnCC SS bb
C survives, n absorbed
2
0
22
0 1)( nCstrip SSd bb
4
Momentum Distribution
11 9 10Be Be Be X 60 MeV/nucleon
Sn = 0.504 MeV
One neutron-removal
Medium effects in sNN (Pauli Exclusion) Effective two-nucleon interaction in infinite nuclear matter (Bethe – Goldstone equation): Solutions for the equation:
1 - Geometric approximation
2 - Brueckner theory
3 – Phenomenological app.
Bertulani, Phys. Rep. (1991), JPG 27, L67 (2001)
Bertulani, De Conti, PRC 81, 064603 (2010)
spp : proton-proton collision
cross-section
11Be + 9Be 10Be + X @ 60 MeV/u
Data: T. Aumann et al, PRL 84, 35 (2000)
The Coulomb corrections change the cross-sections by about 0.03% but, medium corrections has a huge effect which is almost 52%.
Sn=0.504 MeV weakly bound
Low Energy:
Karakoc, Bertulani, arXiv:1201.3677
23Al + 12C 22Mg + X @ 50 MeV/u
Karakoc, Bertulani, arXiv:1201.3677Data: Banu et al, PRC 84, 015803 (2011)
Low Energy:
Sp=0.141MeV weakly bound
41+¿¿
42+¿¿
21+¿ ¿
0❑+¿¿
The Coulomb corrections change the cross-sections by about 16% but, medium corrections has an effect which is almost 21%.
15O + 9Be 14N + X @ 56 MeV/u
Data: H. Jeppesen et al, NPA 739, 57 (2004)
The Coulomb corrections change the cross-sections by about 5% but, medium corrections has an effect which is almost 18%.
Low Energy:
Sp=7.29 MeV
Karakoc, Bertulani, arXiv:1201.3677
17C + 12C 16B + X @ 35 MeV/u
Data: Lecouey et al, PLB 672, 6 (2009)
Medium corrections change the cross-sections by about 5% but, the Coulomb corrections has a huge effect which is almost 60%.
Sp=23.0 MeV tightly bound
Low Energy:
Karakoc, Bertulani, arXiv:1201.3677
17C + Y 16B + X @ E (MeV/u)
different targets, Y
different energies, E
Karakoc, Bertulani, arXiv:1201.3677
solid : with Coulombdashed: without Coulomb
Low Energy (Coulomb):
Karakoc, Bertulani, arXiv:1201.3677
Low Energy (Coulomb):
Sp=23.0 MeV tightly bound
Sp=0.141MeV weakly bound
Karakoc, Bertulani, arXiv:1201.3677
Low Energy (Medium):
Sp=0.141MeV
Sp=23.0 MeV
Sp=7.29 MeV
Sp=0.504MeV
24O + 12C 23O + X @ 920 MeV/u
Data: Kanungo et al, PRL 102, 152501 (2009)
Brueckner calculations are limited by the pion production threshold, and should only be valid for projectile nucleon energies below 300 MeV/u.
Karakoc, Bertulani, arXiv:1201.3677
Sn=3.61(27) MeV
High Energy:
Conclusions:
Medium corrections for the nucleon-nucleon cross sections and Coulomb distortion, modify appreciably the nucleon knockout cross sections.
As expected on physics grounds, these corrections are shown to be larger for experiments at lower energies, around 50 MeV/nucleon.
Future:
To take in to account higher order corrections, CDCC (Continuum Discretized Coupled Channels) is the next step!
THANK YOU!