Generalized Faddeev equations in the AGS
form for deuteron-induced reactions
ECT*, Trento-2016
T. V. Nhan Hao, C. A. Bertulani, Shubhchintak
Texas AM University-Commerce
A. M. Mukhamedzhanov
Texas AM University-College Station
Outline

Introduction

Generalized Faddeev-AGS equations
 Born-Coulomb
 Microscopic

approximation
optical potential
Conclusion and Perspectives
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Introduction
(d,p) reactions off heavy targets at low energies < 50 MeV/A
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Neutron transfer
Proton transfer
-
+
Direct
+
Elastic
Exchange
+
Elastic
+
Two-potential formula
Screening and Renormalization




Mainz-Bonn-Tübingen group: Alt, Grassberger, Sandhas, and Ziegelmann
Graz group: Zankel
Texas A&M group: Akram, and Sattarov
Lisbon group: Deltuva (now in Vilnius), and Fonseca
 Most advanced screening techniques to the date
 Realistic N-N potentials
 Non-local energy dependence phenomenological optical potential
 Fast convergence compared with previous works
Alt et al., PRC 17, (1978)
Alt et al., PRC 21, 1733 (1980)
Deltuva et al., PRC 71, 054005 (2005)
Deltuva et al., PRC 80, 064002 (2009)
Deltuva et al., PRC 79, 021602(R) (2009)
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Screening and Renormalization
Upadhyay et al., PRC 85, 054621, (2012)
Ch. Elster’s talk, Ruhr-Universitat Bochum, July 1-3, (2013)
AGS equations on the way to the heavier target
Alt et al., PRC 21, 1733 (1980)
Mukhamedzhanov et al., PRC 86, 034001, (2012)
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without numerical applications
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Born-Coulomb approximation
Neutron transfer
Exchange
Off-shell Coulomb scattering amplitude
Born-Coulomb approximation
good for d(p,d)p
Koh et al. Czech. J. Phys. B 32, 311 (1982)
Alt et al. J. Phys. B 28, 5137 (1995)
Alt et al. PRA 54, 4091 (1996)
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Preliminary Results
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Preliminary Results
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Preliminary Results
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Preliminary Results
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NA optical model potential
 Phenomenological
•
•
•
F. G. Perey, and H. Buck, Nucl. Phys 32, 353 (1962)
A. J. Koning, and J. P. Delaroche, Nucl. Phys. A 713, 231 (2003)
M. H. Mahzoon et al., PRL 112, 162503 (2014)
 Microscopic
 nuclear structure approaches
• N. Vinh Mau et al., Nucl. Phys. A 257, (1976)
• V. Bernard, and N. Van Giai, Nucl. Phys. A 327, (1979)
• G. Blanchon et al., Phys. Rev. C 91, 014612, (2015)
• K. Mizuyama, and K. Ogata, Phys. Rev. C 86, 041603(R) (2012)
• T. V. Nhan Hao, B. M. Loc, N. H. Phuc, Phys. Rev. C 92, 014605 (2015)
• G. P. A. Nobre et al., Phys. Rev. C 84, 064609 (2011)
 nuclear matter approaches
• M. Dupuis et al., Phys. Rev. C 73, 014605 (2006)
•
M. Toyokama et al., Phys. Rev. C 92, 024618 (2015)
 combination nuclear matter and structures approaches
• V. V. Pilipenko et al., Phys. Rev. C 81, 044614 (2010)
 Faddeev RPA
• S. J. Waldecker et al., Phys. Rev. C 84, 034616 (2011)
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Generate the microscopic optical potential
HF-RPA
PVC
 0+,1-,2+,3-,4+,5 E<50 MeV
T. V. Nhan Hao et al. PRC 92, 014605 (2015)
Skyrme interaction
MOP
CROSS
SECTIONS
Without ad hoc
Non-local, energy
adjusted parameters
dependent, self-consistent
G. Colo et al. PRC 82, 064307 (2010)
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Core excitation-Collective motions
GMR
GDR
GQR
T. V. Nhan Hao et al. PRC 92, 014605 (2015)
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Core excitation-Cross sections
T. V. Nhan Hao et al. PRC 92, 014605 (2015)
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Preliminary Results
T. V. Nhan Hao et al. in preparation
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Preliminary Results
T. V. Nhan Hao et al. in preparation
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Preliminary Results
T. V. Nhan Hao et al. in preparation
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Preliminary Results
T. V. Nhan Hao et al. in preparation
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Conclusions and Perspectives

AGS equations in Coulomb basis avoids introducing
screening and renormalization technique

Full-Coulomb T matrix should be used for the heavy
targets

MOP is the bridge between the nuclear structure and
nuclear reaction. It reduces the model dependence and
increases the predictive power of the nuclear reactions

Possibility of using the MOP for (d,p) reactions off heavy
targets at low-energy
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ISPUN17 (https://ispun.vn/)

Halong City, Vietnam, September 25 – 30, 2017

CEA, CNRS, RIKEN, GSI, INST, VINATOM

Nuclear Structure, Nuclear Reaction, Nuclear Astrophysics, Nuclear
Facilities
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Backup
ISPUN14
T. V. Nhan Hao
10/07/2014
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AGS equations
3-body Hamiltonian
AGS equations
Screening and Renormalization
Alt et al. Nucl. Phys. B 2, 167 (1967)
Alt et al. PRC 17, 1981 (1978)
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T. V. Nhan Hao
October 2, 2016
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Screening and Renormalization technique
Alt et al. PRC 17, 1981 (1978)
ECT*, Trento
T. V. Nhan Hao
October 2, 2016
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Coulomb + short-range potential scattering of 2-charged
particles
Total short-range interaction
Using two-potential formula
where
and
with
For on-shell values of momenta
Full amplitude for on-shell values of momentum
AGS equations for short-range + screened Coulomb potential
for 3-particles
3-body AGS equations
Neutron transfer
Proton transfer
-
+
Direct
+
Elastic
Exchange
+
Elastic
+
Renormalized pole diagram
Exchange
Pole diagram
Mukhamedzhanov et al., PRC 86, 034001, (2012)
AGS equations on the way to the heavier target
Screened Coulomb
Coulomb interaction can be treated exactly
No Coulomb screening
(d,p) reactions off heavy targets
2-charged particles scattering
Pure Coulomb potential
Transition operator
Off-shell scattering states
Highly singular kernel for on-shell values
Screened Coulomb potential
Violent oscillations for on-shell
and
when
Renormalization
3
Neutron transfer
Proton transfer
-
+
Direct
+
Two-potential formula
Elastic
Exchange
+
Elastic
+
Separable potential
Preliminary Results
ECT*, Trento
T. V. Nhan Hao
October 2, 2016
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2-charged particles scattering
Screened Coulomb potential
Violent oscillations for on-shell
when
Renormalization
ECT*, Trento
T. V. Nhan Hao
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Nuclear collective motions
College of Education
T. V. Nhan Hao
16/October/2015
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