1. 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

2. Eikonal Waves k k’k’   E << E,  << 1 radian, v V(r) rb z Breakup (Knockout) Reactions

3. (a) Diffraction Dissociation: (Elastic breakup) Breakup amplitude: to state k (b) Stripping: (Inelastic breakup) bnbn bCbC z C survives, n absorbed

4. 4 Momentum Distribution 60 MeV/nucleon S n = 0.504 MeV One neutron-removal

5. Medium effects in  NN (Pauli Exclusion) Bethe – Goldstone equation 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)  pp : proton-proton collision cross-section

6. 11 Be + 9 Be  10 Be + 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%. S n =0.504 MeV weakly bound Low Energy: Karakoc, Bertulani, arXiv:1201.3677

7. 23 Al + 12 C  22 Mg + X @ 50 MeV/u Karakoc, Bertulani, arXiv:1201.3677Data: Banu et al, PRC 84, 015803 (2011) Low Energy: S p =0.141MeV weakly bound The Coulomb corrections change the cross-sections by about 16% but, medium corrections has an effect which is almost 21%.

8. 15 O + 9 Be  14 N + 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: S p =7.29 MeV Karakoc, Bertulani, arXiv:1201.3677

9. 17 C + 12 C  16 B + 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%. S p =23.0 MeV tightly bound Low Energy: Karakoc, Bertulani, arXiv:1201.3677

10. 17 C + Y  16 B + X @ E (MeV/u) different targets, Y different energies, E Karakoc, Bertulani, arXiv:1201.3677 solid : with Coulomb dashed: without Coulomb Low Energy (Coulomb):

11. Karakoc, Bertulani, arXiv:1201.3677 Low Energy (Coulomb): S p =23.0 MeV tightly bound S p =0.141MeV weakly bound

12. Karakoc, Bertulani, arXiv:1201.3677 Low Energy (Medium): S p =0.141MeV S p =23.0 MeV S p =7.29 MeV S p =0.504MeV

13. 24 O + 12 C  23 O + 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 S n =3.61(27) MeV High Energy:

14. 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!