Reaction Dynamics for Light Dripline Nuclei
Phys. Scr. T152 (2013) 014019

Angela Bonaccorso
INFN
Sezione di Pisa

Advances in Radioactive Isotope Science(ARIS2014)
Tokyo, Japan, June 1th- 6th, 2014

Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
ARIS2014
0140191 / 25OuvertureEntering the world of exotic nuclei: probing the unboundby walking at the drip line.
• Is there a life beyond thedripline?
• How can we discover it without

getting lost?
• Extend our understanding of theresidual nuclear force.
• Check the limits of validity ofstructure models such as theSHELL MODEL or ”ab initio”
models.
• Challenges in breakup reaction

theory.
Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Dynamics of light exotic nuclei

BreakupAngela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Formalism

Here we go...

A consistent formalism for all breakup reaction mechanisms
The core-target movement is treated in a semiclassical way, but
neutron-target and/or neutron-core with a full QM method.
AB and DM Brink, PRC38, 1776 (1988), PRC43, 299 (1991), PRC44, 1559 (1991).
Early eikonal model: I. Tanihata, Prog. Part. Nucl. Phys. 35, 505 (1995), halo-core decoupling.

dσ= C 2SdξZ ∞dP−n (bc )Pct (bc ),dξqalso ANC = C 2 SCi2dbc0⊗

ξ → εf , kz , P//

Use of the simple parametrization
Pct (bc ) = |Sct |2 = e (− ln 2exp[(Rs −bc )/a]) ,1/3Rs ≈ rs (Ap1/3+ At )rs ≈ 1.4fm’strong absorption radius’Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Formalism

TC

Transfer to the continuum: from resonances to knockout
reactionsFirst order time dependent perturbation theory amplitude: ∗∗Z
1 ∞Afi =dt < φf (r)|V (r)|φi (r − R(t)) > e −i(ωt−mvz/~)i~ −∞ω = εi − εf + 21 mv 2dP−n (bc )
dεf=
≈(1)

R(t) = bc + vt

1 m1Σm |Afi |28π 3 ~2 kf 2li + 1 i
4πΣj (2jf + 1)(|1 − S̄jf |2 + 1 − |S̄jf |2 )F,2kf2 f

φf see (∗)
F = (1 + Flf ,li ,jf ,ji )Blf ,li



−2ηbc
1kf
2e
Blf ,li =|C|Mlf lii
4π mv 22ηbc

Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Formalism

TC

Final continuum wave functions(∗)
Final continuum state:i (+)(−)φlf (r) = Cf k (hlf (kr ) − S̄lf hlf (kr ))Ylf ,mf (Ωf ),2S̄lf (εf ) is an optical model (n-core in fragmentation reactions, n-target inknockout reactions) S-matrix.

Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Examples1313

Be puzzle

Be puzzle or of the ”elusive 1/2+ state in Be isotopes
Our	  level	  sequence	  2s1/2	  	  	  	  a_s=-­‐0.8fm	  1p1/2	  1d5/2	  	  G.	  Blanchon	  et	  al.	  	  PRC82,	  034313	  NPA	  A	  784	  (2007)	  49	  Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Examplesn-target optical potential: AB, F. Carstoiu, PRC61, 034605 (2000)

n-9 Be optical potential: A.B & R.J. Charity, PRC89, 024619 (2014),
data from https://www-nds.iaea.org/exfor/exfor.htm(∗)

Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Examples

Incident energy dependence

knockout	  Resonances,	  trojan	  horse	  3data p reaction
data n reaction
data total
data elastic
react eik
elastic eik
tot eikσ(barn)

2

1
1.0

1.0

1.0

0.8

0.8

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

04

06

8

1020

0.2

3540

45

40
E_lab(MeV)

50

60

75

80

80

85

90

Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Examples

Incident energy dependence

Transfer to 10 Be resonances: missing mass experiment.
Paper in preparation	  Diana	  Carbone,	  AB,	  Mariangela	  Bondì,	  F.	  Cappuzzello,	  M	  Cavallaro	  et	  al.	  MAGNEX	  Collabora>on:	  1n	  and	  2n	  transfer	  experimental	  campaign	  	  91716	  O	  has	  a	  degenerate	  gs	  (1d5/2,2s1/2)	  10917	  O	  has	  5/2+	  gs	  and	  1/2+	  ﬁrst	  excited	  	  state	  at	  E*=0.87MeV	  8Be(n,nn) Be

96Be(n,_) He
1n break-up calculation

Posi>on	  and	  widths	  of	  p1/2	  and	  d5/2	  resonances	  in	  10Be	  perfectly	  reproduced	  +7.37 (3 ) + 7.54 (2 )+2

9.27* + 9.4*

3.37*

7.37* + 7.54*-g.s.*

9.27 (4 ) + 9.4 (2 )-+3.37 (2 )3dm/dEx (mb/MeV)

18Be( O, O) Be @ 84 MeV
3°< elab < 10°++g.s. (0 )-5.96 (2 ) + 6.26 (2 )410-20246 S S 8Sn_10

12

14

16

182n

Ex (MeV)Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Examples

Kinematics

Kinematics
From Eq.1 ∗∗ by the change of variables dtdxdydz → dxdydzdz 00e −i(ωt−mvz/~) → e −ik1 z e ik2 z neutron energies to neutron parallel momenta
with respect to core
εf − εi − 12 mv 2k1 =;~v
to targetk2 =εf − εi + 21 mv 2;~v

to core parallel momentumqq
P// =Er2 − Mr2 = (Tr + Mr )2 − Mr2q=(Tp + εi − εf )2 + 2Mr (Tp + εi − εf ),(2)breakup threshold at εf = 0++∗∗
Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Kinematical effects

Asymmetric spectra

Example ”deformation” effects due to n-target interaction and kinematical cut-off.
F. Flavigny, A. Obertelli, AB et al., PRL 108, 252501 (2012).

∗∗Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Kinematical effects

Asymmetric spectra

Asymmetries at high incident energy 
  !"#$%!

     !
     

 

     

 

  

 





  
 






 

 

Data	  courtesy	  of	  A.	  Gade	  Calcula3ons	  G.	  Salvioni	  	  MSc	  Thesis	  in	  prepara3on.	  
28S	  (-­‐1n)	  80.7	  d5/2+d3/2	  	  28S	  (-­‐1p)	  s1/2+d3/2	  A.MeV	  24Si(-­‐1p)	  d5/2	  85.3	  A.MeV	  34Ar	  (-­‐1n)	  s1/2	  gs	  	  70	  A.MeV	  34Ar	  (-­‐1n)	  d3/2+d5/2	        





     

 









 



Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Kinematical effects

Phase space effectOrigin of kinematical cut-off (phase space) and deformation effects
PRC60(1999) 054604,PRC44(1991) 1559,AB and GF Bertsch, PRC63(2001) 044604, F. Flavigny, A. Obertelli, AB et al., PRL108, 252501 (2012).

(+)

Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Connecting reaction with structure. Ex: reduction of spectr. fact.

Removal of a deeply bound n/p while the weakly bound p/n is un-touched ∗Knock	  out	  from	  a	  deeply	  bound	  state	  x	  . .	

bc	  T	  before	  .	

.	 .	

13O	  14O	  Core	  .
Tvz	   z	  a0er	  Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Connecting reaction with structure. Ex: reduction of spectr. fact.
reaction

Sn
[MeV]

Sp
[MeV]

Einc
[A.MeV]

(m)

σ exp
[mb]

9 C →8 C

14.25
19.3
17.01
15.74
21.56
21.54
21.09
21.28
5.66
23.18
17.06
18.42
18.86

1.3
1.3
1.51
2.3
2.42
2.49
3.3
4.01
4.43
4.63

63.8
7028.5
66.4
65.1
80.7
85.3
116.2
36.6
53

4.66

70

3.
5
2.5
9
10.4
11.9
9.8
23.4
38.1
14
4.7
3.2
4.9

10.68
10.25
14.0
15.04
16.29
17.28
19.5
8.02
8.56
7.53
8.54
11.82

5.6
7.3

65.2
70.2

28.1
7.7
33.7

8.86

62.8

36

18.64

70

36 Ca →35 Ca
13 O →12 O
33 Cl →32 Cl
32 Ar →31 Ar
28 S →27 S
24 Si →23 Si
10 C →9 C
6 Li →5 Li
14 O →13 O
34 Ar →33 Ar

7 Be →6 Be
57 Ni →56 Ni

32 S →31 S

46 Ar →45 Ar

34 Si →33 Si

10 Be →9 Be15 C →14 C

16 C →15 C

6.81
1.22
7.31
8.21
8.23
4.25
4.99

18.74
73.4
19.64
22.33

77.8

118.5
21.08

71.2
103

22.56

75

61.9
3.6
67
41
15

∆S = |Sn − Sp | ≈ 10 − 20MeV

σ = C 2SZ ∞dbc P−n (bc )(1 − P−p (bc ))Pct (bc )0e −P−p ≈ 1 − P−p (bc )DPP from phase shift, AB, F. Carstoiu, NPA706, (2002) -typically∼10% reduction in the cross sections.

69.5
100.8
27.4
6.5
5.5
36.5
46

Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Connecting reaction with structure. Ex: reduction of spectr. fact.

Absolute cross sections

σ=R∆S = |Sn − Sp | ≈ 10 − 20MeVdξ dσdξ

Ratiosσexp /σTheo
have been used to validate spectroscopic factors C2 S (=2j+1, in the IPM ) forsingle particle orbitals from shell model or ”ab initio” calculations, whenavailable. This is similar to what has traditionally been done for transfer.
However in transfer the core-target interaction is treated almost exactly
thanks to optical potentials fitted to the elastic scattering.
C. Barbieri PRL103, 202502 (2009)

Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Connecting reaction with structure. Ex: reduction of spectr. fact.

∆S = |Sn − Sp | ≈ 10 − 20MeV

neutron & proton → transfer vs breakup F. Flavigny et al., PRL110 ,122503 (2013)

Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Beyond the drip line

Proton unbound nuclei via invariant mass method
Interest: Two-proton radioactivity vs. 2n-halo by isospin symmetry
5He, 6 He,8 He,12 Be and IMME

Proton	  unbound	  nuclei	  6Li	  ..

Pα	  beforeafter: α+p5Liα	  vzT.

CM	  .

T+1

6Li,7Be,9C,13O studied by knockout of a deeply bound neutron:

R.	  J.	  Charity	  &	  HiRA	  collabora5on	  Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Beyond the drip line

Data:	  R.	  J.	  Charity	  and	  the	  HiRA	  	  collabora7on,	  preliminary.	  Calcula7ons:	  G.	  Salvioni	  &	  AB	  	  8000

965Counts(a) Be( Li, Li)X6000

E/A = 36.6 MeV
54000

Lig.s. A p+_

2000
02

469(b) Be(7Be,6Be)XCounts010000E/A = 65.2 MeV
65000

002

Beg.s. A 2p+_46250

9200

Counts98(c) Be( C, C)X
E/A = 63.8 MeV

150

8100

Cg.s. A 4p+_50
0−20Counts

2491312(d) Be( O, O)X60

E/A = 28.5 MeV401210Og.s.A2p+ C

200024E* [MeV]

6Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Beyond the drip line

Structure inputs: Shell model and ”ab initio” Variational
MonteCarloSFSM by Mihai Horoi, private communication.
SFVMC from R. Wiringa website http://www.phy.anl.gov/theory/research/overlap/,
ANCVMC from Kenneth M. Nollett and R. B. Wiringa, PRC83, 041001(R) (2011).

Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Beyond the drip line

EincA.MeV

σexpmb

σ−nmb

σ−pmb

σ−nnopmb

rsfm

h6 Li|5 Lii

36.6

38.1

44.53

47.41

38.5

1.53

h7 Be|6 Bei

65.2

28.1

34.14

15.22

27.5

1.38

h9 C |8 C i

63.8

3.

h9 C |8 BIAS i
h9 Li|8 LiIAS i
h13 O|12 Oi

64.4

1.24

28.5

2.5

9.8...
1.47
3.9

1.57(-1pCB )19.3 (22.3)

4.48

2.32(-1pCB )
1.9

3.6

1.4
1.59
1.4
1.4
1.5(-1pCB ) direct proton Coulomb breakup

Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Conclusions• Inclusive breakup reactions are dominated by final state interaction with thetarget at small incident energy: use as surrogate reaction• At intermediate incident energy: strong interplay between projectile andtarget characteristics: ”deformed’ momentum distributions and cutoff
effects. PROTON TARGET? see A. Obertelli and T. Aumann talks• .... by the valence particle projectile momentum distribution at high incident
energy: information on angular momentum of the initial state and possible
dynamical core-target excitations• Coincidence experiments of breakup particle experiments (using invariant
mass method ) are more INdependent on incident energy but possible
dependence on the initial state: necessity to link with methods discussed
above and angular correlation of the decaying particles... : one the mostinteresting experiment to make...and interpret? Can enlighten different
channels and reaction mechanisms.
• IN ADDITION• Elastic scattering experiments and or total reaction cross section
measurements: they can tell us about the typical interaction distances andhelp fixing the optical potentials.
• In the future more and more strongly bound nuclei will be studied at lower
energies at ISOL-type facilities. In Europe: HI-Isolde, SPES, Spiral2,EURISOL (?).
Angela Bonaccorso (INFN Sezione di Pisa) Reaction Dynamics for Light Dripline Nuclei Phys. Scr. T152 (2013)
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Conclusions

Some of my co-authors and collaborators in historicalorder.
D. M. Brink
N. Vinh Mau
G. BlanchonF. Carstoiu
G. F. Bertsch
Ravinder Kumar
MAGNEX collaboration at INFN-LNS
F. Flavigny, A. Obertelli
R. J. Charity
G. Salvioni... see his talk at DREB2014 in Darmstadt

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Conclusions

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