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!