1. Form factor studies for analyses of transfer reactions
Alain Gillibert (CEA/IRFU/SPhN)
Work in progress
Ph.D Thesis, F. Flavigny
PRL 110, (2013) Wood-Saxon form factors
ab initio form factors
A. Gillibert ECT Trento June 2016
test

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What we would like to measure and discuss….
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What we have access to…
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(e,e’p)
Study of
proton-hole states
validity and limit of a mean-field description
effect of nuclear correlations
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9. Shell occupancies in stable nuclei
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10. A. Gillibert ECT Trento June 2016
Unstable nuclei Direct reactions
Major assumption : separation of structure inputs and reaction mechanism
What is done
Measurement σexp i->f
calculation with a reaction model σsp (nlj)
Ratio (C2S )exp a σexp i->f / σsp (nlj)
comparaison to structure model (C2S )th
Need for consistency between structure and reaction model
A. Gillibert ECT Trento June 2016

11. Nucleon removal from exotic nuclei
≈ 700 MeV/u
C. Rodriguez-Tajes et al., Phys.Rev. C 82, (2010)
10C 120 MeV/u
G. Grinyer et al., Phys.Rev.Lett. 106, (2011)
LBL Bevalac 2.1 GeV/n, 1.7 GeV/n
D.L. Olson, Phys. Rev. C 28 (1983) 1602; D.L. Olson, Phys. Rev. C 24 (1981) 1529
A. Gillibert ECT Trento June 2016

12. Stripping cross sections at intermediate energies
Projectile energy large enough to consider
that the intrinsic degrees of freedom are frozen
Probability to
leave the core intact
Probability to
remove the nucleon A
A-1
NN cross section
Core density
No explicit treatment of core excitations
A. Gillibert ECT Trento June 2016

13. Nucleon removal from exotic nuclei
ΔS = |Sn – Sp | (MeV)
Intermediate-energy knockout
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B.P. Kay et al., PRL (2013 )
ΔS (MeV) = |Sp – Sn|
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Question
Are Reduction Factors from knockout (<100 MeV/u) and transfer consistent ?
Experiment and data
One-nucleon knockout from 14O, 16C at intermediate energy (NSCL, MSU)
F. Flavigny, et al., PRL (2012)
One-nucleon transfer from 14O 18 MeV/u at SPIRAL, GANIL
F. Flavigny, et al., PRL (2013)
Perform a consistent analysis on the same nucleus with same form factor
Advantage of 14O
Large value ΔS = 18.6 MeV
Beam intensity high enough for (d,3H) (d,3He) transfer measurements
Closed sub-shell nucleus with data available for 16,18O
A. Gillibert ECT Trento June 2016

16. Ion Source Primary beam : 16O 95 A.MeV, 1.4 kW SPIRAL Target
GANIL SPIRAL1 14O 18 MeV/nucleon, 18Ne
VAMOS
CSS1
CSS2
SPIRAL Target
CIME
Primary beam :
16O 95 A.MeV, 1.4 kW
Ion Source
MUST2
Beam : 14O8+
pure
18.1 A.MeV
~ pps
A. Gillibert ECT Trento June 2016

17. Fully exclusive measurement
Experimental Setup
Fully exclusive measurement
SPIRAL Beam intensity: pure, pps
CD2 targets: 0.5,1.5 and 8.5 mg.cm-2
Reactions: (d,d), (d,3H) and (d,3He)
MUST2 array 10x10 cm2 300μm DSSSD + SiLi or CsI
VAMOS spectrometer in dispersive mode
A. Gillibert ECT Trento June 2016

18. One-neutron pickup channel One-proton pickup channel
Experimental data set
Elastic channel
One-neutron pickup channel
[M. Gaillard et al., Nucl. Phys. A 119, 161 (1968)]
One-proton pickup channel
Published Data on 16O and 18O
[V. Bechtold et al., Phys. Lett. B 72,169 (1977)]
[M. Gaillard et al., Nucl. Phys. A 119, 161 (1968)]
[D. Hartwig et al., Z. Phys. 246, 418 (1971)]
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Reaction Framework
Input Potential:
14O+ 2H
Folding of a nucleon-nucleus optical potential over the deuteron wave function; complex potential lv, lw
A.J. Koning et J.P. Delaroche, NPA 713, 231 (2003)
Validated on elastic data
Output potentials:
13O + 3H and 13N + 3He
Global potential
 D. Y. Pang et al., PRC 79, (2009)
 C. M. Perey and F. G. Perey, ADNDT 17,17,1 (1976)
Form factors:
<14O | 13O + n> and <14O | 13N + p>
Two prescriptions:
Woods Saxon, Hartree Fock constrained
Ab-initio overlap (SCGF)
Coupling scheme
Coupled Reaction Channel analysis (CRC)
Coupled discretized continuum channel
(CDCC) for deuteron breakup
13N+3He
13O+3H
14O+2H
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Elastic scattering 14O + 2H
Energy resolution 720 keV
Angular resolution 0.2 °
Ed (MeV)
Θlab (deg)
13N + 3He
13O + 3H
14O + 2H
λV = 1.1 , λW = 0.8
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Elastic scattering 13N + 3He, 13O + 3H
Global potentials
C.M. Perey, ADNDT 17, 1(1976)
D.Y. Pang, Phys. Rev. C 79, (2009)
12C + 40 MeV DWBA
12C + 17 MeV
Need for a better local potential for exit channel
A. Gillibert ECT Trento June 2016
test

23. Test Case : stable 16O data in direct kinematics
C2Sexp = 0,93 (9)
rrms from M. Leuschner et al., PRC 49, 955 (1994)
Form factors
X Standard arbitrary value:
(r0 , a0) : (1.25 fm , 0.65 fm)
rrms from 16O(e,e’p)15Ngs :
rrms = 2,943 fm
WS parameters to reproduce rrms and Sp:
r0 = 1.46 fm
a0 = 0.65 fm
Single-particle HF w.f. with Sly4 interaction:
rrms(HF) = 2,95 fm
Data points from :
[V. Bechtold et al., Phys. Lett. B 72,169 (1977)]
[M. Gaillard et al., Nucl. Phys. A 119, 161 (1968)]
A. Gillibert ECT Trento June 2016

24. 14,16O Wood Saxon Form factor
16O (e,e’p) 15N
0.00 MeV 1/2- (p1/2) RRMS = 2.943(30) fm
M. Leuschner et al., Phys. Rev. C 49 (1994) 955
16O HFB calculation SLy 4 interaction
RRMS( p1/2) = 2.95 fm ro = 1.46 fm ao = 0.65 fm
14O HFB calculation SLy 4 interaction
RRMS( p1/2) = 3.03 fm ro = 1.12 fm
RRMS( p3/2) = 2.77 fm ro = 1.23 fm
RRMS( p3/2) = 2.69 fm ro = 1.40 fm
δ (RMS)  δ ro
16O
p1/2
p3/2    
14O
A. Gillibert ECT Trento June 2016

25. 14O results (Wood Saxon form factor)
C2Sexp strongly depends on radii
Ex: DC2S/C2S ≈ 6 Drrms/ rrms
Δℓ = 1
Δℓ = 1
A. Gillibert ECT Trento June 2016

26. Dependence of C2Sexp on r0
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27. Dependence of C2Sexp on r0
14O(d,t) r0 = 1.4 fm C2Sexp ≈ 1.3
r0 = 1.25 fm C2Sexp ≈ 2.1
11% change 60% change
A. Gillibert ECT Trento June 2016

28. J. Vernotte et al., NP A571 (1994) 1 (d, 3He)
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29. Results with WS overlap functions
δ (RMS)  δro  box
Error bars due to exp. Uncertainties
OFs : WS (HFB constrained)
C2Sth: Shell model with WBT interaction
sth(q) = C2Sth ssp(q)
48 analysis:
2 sets of C2Sth:
- WBT Interaction 0p shell + 2ħΩ
- Utsuno int. 0p1s0d space
3 HF calculations for radii
8 combinations of optical potentials
for entrance and exit channels
c2min
Exp. Error
(1 set)
Systematic error
from 48 data sets
Rs = a . DS + b
a = (24)(12) MeV-1
b = Rs(0) = 0.538(28)(18)
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Ab initio form factor
Ab-inito SFth and overlaps ( from C. Barbieri and A. Cipollone)
Single-particle Green’s function (third order diagrammatic construction method)
Chiral two-body + three-body interactions (cutoff l=1.88 fm-1)
sth(q) = C2Sth ssp(q)
All microscopic OFs rescaled by the same factor to account for the differences
of predicted and experimental rms radius of 16O one phenomenological correction
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Notch test
Notch test
Gaussian shape added to the radial shape
Effect on the fitted cs (dσ/dΩ)pert
[(dσ/dΩ)pert – (dσ/dΩ)unpert]2
[(dσ/dΩ)unpert]2
c2 =
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[(dσ/dΩ)pert – (dσ/dΩ)unpert]2
[(dσ/dΩ)unpert]2
c2 =
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Notch test
16O O
SCGF form factor, A. Cipolonne et al.,
Wood Saxon form factor
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Result overview
Rs = a . DS + b
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Summary
Transfer experiment 14O(d,3H) (d,3He) ΔS =37 MeV
Rs = α ΔS + β α ≈ 0
To be confirmed with other nuclei 18Ne
Improvement of the exit channel potential
Test of ab initio overlap functions (SCGF, next NCSM)
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Thank you!
F. Flavigny, S. Boissinot, A. Corsi, A. G., V. Lapoux, L. Nalpas, A.Obertelli, E.C. Pollacco,
A. Signoracci, CEA Saclay
D. Beaumel, S. Giron, J. Guillot, F. Hammache, B. Lecron, A. Matta, Morfouace, N. de Séreville, IPN Orsay
B. Bastin, G. Burgunder, A. Lemasson, R. Raabe, M. Rejmund, A. Shrivastava, GANIL Caen
J. Gibelin, LPC Caen
N. Keeley, NCNR Warsaw
C. Barbieri, A. Cippolone, U. Of Surrey
P. Navratil, Triumf
A. Gillibert ECT Trento June 2016

37. Ab initio form factor : Notch test
<14O | 13O + n >
[(dσ/dΩ)pert – (dσ/dΩ)unpert]2
[(dσ/dΩ)unpert]2
c2 =
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EDSSSD (MeV)
ToF (a.u.)
ΔEDSSSD (MeV)
ESiLi (MeV)
MUST VAMOS
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14O(d,3H)13O
E* (MeV)
Et (MeV)
lab (deg)
MUST2+VAMOS
MUST2 alone
Δℓ = 1
3/2-
1/2-
(3/2-)
Expt.
SP-SM
2750
4210
6020
7853
5408
=1.2MeV
Sp = 1516 keV
13O
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40. A. Gillibert ECT Trento June 2016
14O(d,3He)13N
1/2-
3/2-
Expt.
SP-SM
2365
3502
3547
3643
Sp = 1944 keV
13N
1/2+
5/2+
Δℓ = 1
E3He (MeV)
Θlab (deg)
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42. Parallel-momentum distributions
Loosely-bound nucleon
Deeply-bound nucleon
F. Flavigny et al., PRL (2012)
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44. One-nucleon removal from 14O and 16C at the NSCL
16C beam at 70 MeV/nucleon
14O beam at 53 MeV/nucleon
A. Gillibert ECT Trento June 2016

45. Rs: comparison to existing data
s(16C-1n)= 80(7) mb
s(14O-1p)= 64(6) mb
s(16C-1p)= 15(1) mb
s(14O-1n)= 14(1) mb
= |Sn – Sp | (MeV)
A. Gillibert ECT Trento June 2016

46. Dissipative processes ?
1p knock-out 16C
1/2+ 3/2- 1/2- states in 15B
Dissipative processes
5/2-, 7/2-
16C
F. Flavigny et al., PRL (2012)
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47. A. Gillibert ECT Trento June 2016
High-momentum cutoff
ef =0
ef= kinetic energy of the fragments (nucleon + target) in the lab. frame
Momentum threshold (CUT) for ef =0
A. Bonaccorso, Phys. Rev. C 60, (1999). dp
“barely visible” effect in published data
A. Gade et al., PRC 71, (2005).
A. Gade et al., PRC 77, (2008).
G. Grinyer et al., PRL 106, (2011).
70 MeV/u
85 MeV/u
80 MeV/u
120 MeV/u
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48. A. Gillibert ECT Trento June 2016
14O (p,d) 13O @ 51 MeV/u
Expt points from D. Suzuki et al., EPJA (2012)
Wood-Saxon form factor
C2Sexp from 14O(d,3H)13O
A. Gillibert ECT Trento June 2016