Slides - 11th International Spring Seminar on Nuclear Physics

Walking at the dripline
Walking at the dripline
Angela Bonaccorso
INFN, Sez. di Pisa
11th INTERNATIONAL SPRING SEMINAR ON NUCLEAR PHYSICS
SHELL MODEL AND NUCLEAR STRUCTURE:
achievements of the past two decades
in honor of Aldo Covello
Ischia, May 12-16, 2014
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
1 / 42
Ouverture
Entering the world of exotic nuclei: probing the unbound.
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
2 / 42
Ouverture
Entering the world of exotic nuclei: probing the unbound.
• Is there a life beyond the
dripline?
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
3 / 42
Ouverture
Entering the world of exotic nuclei: probing the unbound.
• Is there a life beyond the
dripline?
• Extend our understanding of the
residual nuclear force.
• Check the limits of validity of
structure models such as the
SHELL MODEL
• In practice AFA this talk is
concerned: try do do
spectroscopy in extreme
conditions.
• Challenges in reaction theory.
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
4 / 42
Ouverture
The rˆole of Reaction Theory
This week we have seen once again that exotic nuclei can be studied by
very sophisticated structure models and extremely complex experiments
with relatively ”simple” interpretations.
Which is the rˆole of Reaction Theory and how simple and/or
”complicated” does it need to be or can we allow it to be?
• Understand the reaction mechanisms.
• Suggest for the best observable to be measured and used in the data
analysis (in view of the reduced intensity of RB).
• Accuracy of methods and numerical implementations.
• The 13 Be puzzle: or of the ”sometime” elusive 1/2+ state in Be isotopes
• Beyond the proton drip line
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
5 / 42
Fragmentation
Fragmentation reaction (coincidence)
Let us start with a two neutron halo nucleus like
11 Li
or
14 Be
∗ ∗ ∗ (+)
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
6 / 42
Fragmentation
Fragmentation (10 Li best example)
GSI, H. Simon et al. NPA791 (2007) 267; G. Blanchon et al. NPA791 (2007) 303
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
7 / 42
Fragmentation
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
8 / 42
Fragmentation
14
... an open question
Be structure
The ground state of 14 Be has spin J π = 0+ . In a simple model assuming
two neutrons added to a 12 Be core in its ground state the wave function is:
|14 Be >= [b1 (2s1/2 )2 + b2 (1p1/2 )2 + b3 (1d5/2 )2 ] ⊗ |12 Be, 0+ >
Then the bound neutron can be in a 2s, 1p1/2 or 1d5/2 state. However,
the situation is much more complicated and in particular the calculations
of Tarutina, Thompson and Tostevin show that there is a large component
(2s1/2 , 1d5/2 ) ⊗ |12 Be, 2+ > with the core in its low energy 2+ state which
can modify the neutron distribution.
In a fragmentation reaction will all these components suddenly become
unbound?
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
9 / 42
Fragmentation
13
... an open question
Be experimentally
It is experimentally proved that
• 13 Be is not bound
• 5/2+ resonance at around 2MeV
• S2n (14 Be) =1.34±0.11MeV
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
10 / 42
13
Be and 14 Be problem
Fragmentation: (13 Be puzzle)
(a)
Figure :
(b)
(a) LPC & GANIL, Lecouey, Orr et al. 2002.
(b) G. Randisi, N. Orr et al. Phys. Rev. C 89, 034320
⊗
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
11 / 42
13
Be and 14 Be problem
Figure : (a) GSI, H. Simon et al.
NPA791 (2007) 267.
Angela Bonaccorso (INFN, Sez. di Pisa)
Figure : (b) G.Blanchon et al. NPA784
(2007) 49.
Walking at the dripline
Ischia2014
12 / 42
13
Be and 14 Be problem
Figure : (b) RIKEN, Y. Kondo et al. PLB690 (2010) 245; G. Blanchon, private
communication.
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
13 / 42
13
Be and 14 Be problem
Theoretical models (structure)
• Generator coordinate model (Descouvemont)
• Lagrangian mesh calculation (Baye)
• Fadeev calculation (Zhukov and Thompson)
• Macroscopic model with deformation (Tarutina, Thompson, Tostevin)
• RPA particle-particle (Pacheco and Vinh Mau, Blanchon et al.)
• Antisymmetrized molecular dynamics (Y. Kanada-En’Yo)
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
14 / 42
The ”sometime” elusive 1/2+ state in Be isotopes
The ”sometime” elusive 1/2+ state in Be isotopes
The 1/2+ state in 9 Be
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
15 / 42
The ”sometime” elusive 1/2+ state in Be isotopes
A virtual state or a resonance?
PRC89, 027301, 2014
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
16 / 42
The ”sometime” elusive 1/2+ state in Be isotopes
The 1/2+ state in
10 Be:
Angela Bonaccorso (INFN, Sez. di Pisa)
deformation, strength fragmentation effects.
Walking at the dripline
Ischia2014
17 / 42
The ”sometime” elusive 1/2+ state in Be isotopes
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, Sez. di Pisa)
Walking at the dripline
Ischia2014
18 / 42
The ”sometime” elusive 1/2+ state in Be isotopes
Resonances
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
19 / 42
The ”sometime” elusive 1/2+ state in Be isotopes
Bound states in the DOM (R.J. Charity, private communication)
DOM: C. Mahaux and R. Sartor, Adv. Nucl. Phys. 20, 1 (1991).
R. J. Charity, L. G. Sobotka, and W. H. Dickhoff, Phys. Rev. Lett. 97, 162503
(2006).
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
20 / 42
The ”sometime” elusive 1/2+ state in Be isotopes
The 1/2+ state in
11 Be
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
21 / 42
The ”sometime” elusive 1/2+ state in Be isotopes
11 Be
→
10 Be
+n,
data from N. Fukuda, et al., Phys. Rev. C 70 (2004) 054606, potential from P. Capel, D. Baye,
Phys. Rev. C 70 (2004) )064605.
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
22 / 42
The ”sometime” elusive 1/2+ state in Be isotopes
The 1/2+ state in
12 Be
S. D. Pain et al.,PRL96, 032502, (2006)
A. Navin et al.,PRL85, 266, (2000)
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
23 / 42
The ”sometime” elusive 1/2+ state in Be isotopes
The 1/2+ state in
13 Be
G. Randisi et al., PRC 89, 034320, (2014)
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
24 / 42
The ”sometime” elusive 1/2+ state in Be isotopes
G. Randisi et al., PRC 89, 034320, (2014)
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
25 / 42
The ”sometime” elusive 1/2+ state in Be isotopes
N=9 effective particle energies
S. Bedoor et al.
→ my correction
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
25 / 42
Formalism
Here we go...
A consistent formalism for all previous reaction mechanisms
The core-target movement is treated in a semiclassic way, but
neutron-target and/or neutron-core in a full QM treatment.
AB and DM Brink, PRC38, 1776 (1988), PRC43, 299 (1991), PRC44, 1559 (1991).
dσ
= C 2S
dεf
∞
Z
dbc
0
dP−n (bc )
Pct (bc ),
dεf
⊗
Use of the simple parametrization
Pct (bc ) = |Sct |2 = e (− ln 2exp[(Rs −bc )/a]) ,
1/3
Rs ≈ rs (Ap
1/3
+ At )
rs ≈ 1.4fm
’strong absorption radius’.
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
26 / 42
Fragmentation
Fragmentation of a 2n- or 1n-halo nucleus
Inelastic-like∗ excitations can be described by the first order time
dependent perturbation theory amplitude:
Z
1 ∞
Afi =
dthψf (t)|V2 (r − R(t))|ψi (t)i
i~ −∞
Z ∞
≈
dzφ∗f (bc , 0, z)φi (bc , 0, z)e −iqz
(1)
−∞
∗
This method has the advantage that different potentials can be used for the
determination of ψi and ψf , thus strictly speaking these are not inelastic-like
processes but breakup with ”final-state” n-core interaction effect. After breakup
the 12 Be core is probably different than ” 12 Be-inside-14 Be”, cf. S. Ilieva et al,
NPA 875 (2012) 8.
Which components of the initial wave function show up in the continuum??
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
27 / 42
Fragmentation
Final continuum wave functions
(∗)
Final continuum state:
i (+)
(−)
φlf (r) = Cf k (hlf (kr ) − S¯lf hlf (kr ))Ylf ,mf (Ωf ),
2
S¯lf (εf ) is an optical model (n-core in fragmentation reactions, n-target in
knockout reactions) S-matrix.
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
28 / 42
Fragmentation
Determination of the bound and unbound
S-matrix) states.
U(r ) = VWS + δV
δV (r ) = 16α
e 2(r −R)/a
(1 + e (r −R)/a )4
Angela Bonaccorso (INFN, Sez. di Pisa)
(via optical model n-core
VWS = Woods-Saxon + Spin orbit
δV = Correction to the potential
originated from p.v. coupling or
deformation effects (N. Vinh Mau and J.
C. Pacheco, NPA607 (1996) 163)
Walking at the dripline
Ischia2014
29 / 42
Fragmentation
12
Be and
14
Be in pp-RPA: inversion (B), non inversion (A)
G. Blanchon et al. , PRC 82, 034313 (2010)
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
30 / 42
Fragmentation
Strength of every transition
Dependence on the scattering length of the final s-state
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
31 / 42
Fragmentation
Information about the ’mother’ nucleus
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
32 / 42
Outlooks
Outlook I
• There are very good indications that in the 13 Be spectrum the shell
ordering is 2s, p1/2 and d5/2 with a shell inversion. The s-state has a
large spread with a scattering length of as =-0.8fm.
• We look forward to other reaction calculations besides ours.
• More measurements of other observables.
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
33 / 42
Beyond the drip line
Proton unbound nuclei via invariant mass method
Interest: Two-proton radioactivity vs. 2n-halo by isospin symmetry
5
He, 6 He,8 He,12 Be and IMME
Proton unbound nuclei 6Li ..
P
α before
after: α+p
5Li
α vz
T
6Li,7Be,9C,13O
.
CM .
T+1
studied by knockout of a deeply bound neutron:
R. J. Charity & HiRA collabora5on Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
34 / 42
Beyond the drip line
Data: R. J. Charity and the HiRA collabora7on, preliminary. Calcula7ons: G. Salvioni & AB 8000
9
6
5
Counts
(a) Be( Li, Li)X
6000
E/A = 36.6 MeV
5
4000
p+
Lig.s.
2000
0
0
2
4
Counts
6
9
10000
(b) Be(7Be,6Be)X
E/A = 65.2 MeV
6
5000
0
0
2
4
6
250
9
9
8
(c) Be( C, C)X
200
Counts
2p+
Beg.s.
E/A = 63.8 MeV
150
8
100
Cg.s.
4p+
50
0
−2
0
2
Counts
4
9
13
12
(d) Be( O, O)X
60
E/A = 28.5 MeV
40
12
10
Og.s. 2p+ C
20
0
0
2
4
E* [MeV]
Angela Bonaccorso (INFN, Sez. di Pisa)
6
Walking at the dripline
Ischia2014
35 / 42
Beyond the drip line
Structure inputs: Shell model and ”ab initio” Variational
MonteCarlo
SFSM 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, Sez. di Pisa)
Walking at the dripline
Ischia2014
36 / 42
Beyond the drip line
Einc
A.MeV
σexp
mb
σ−n
mb
σ−p
mb
σ−nnop
mb
rs
fm
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, Sez. di Pisa)
Walking at the dripline
Ischia2014
37 / 42
Conclusions
Past-Present-Future
Possible experimental developments:
• Projectile-fragmentation...perhaps one the most interesting
experiment to make...and interpret? Can enlighten different channels
and reaction mechanisms.
• Elastic scattering experiments and or total reaction cross section
measurements: they can tell us about the typical interaction
distances.
• The past has been characterized by studies at high incident energy
and for weakly bound projectiles. In the future more and more
strongly bound nuclei will be studied at lower energies at ISOL-type
facilities.
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
38 / 42
Conclusions
Some of my co-authors, in historical order:
D. M. Brink
N. Vinh Mau
G. Blanchon
G. F. Bertsch
A. Garc´ıa-Camacho
Ravinder Kumar
R. J. Charity and the HiRA collaboration
G. Salvioni
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
39 / 42
Conclusions
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
40 / 42
Backslides
TC
Transfer to the continuum for knockout reactions
First 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 2
dP−n (bc )
dεf
=
≈
(2)
R(t) = bc + vt
1 m
1
Σm |Afi |2
3
2
8π ~ kf 2li + 1 i
4π
Σj (2jf + 1)(|1 − S¯jf |2 + 1 − |S¯jf |2 )F,
2kf2 f
φf see (∗)
F = (1 + Flf ,li ,jf ,ji )Blf ,li
Angela Bonaccorso (INFN, Sez. di Pisa)
Blf ,li =
Walking at the dripline
1
kf
e −2ηbc
|Ci |2
Mlf li
2
4π mv
2ηbc
Ischia2014
41 / 42
Backslides
Kinematics
Kinematics
From Eq.2 by the change of variables dtdxdydz → dxdydzdz 0
0
e −i(ωt−mvz/~) → e −ik1 z e ik2 z neutron energies to neutron parallel momenta
with respect to core
εf − εi − 12 mv 2
k1 =
;
~v
to target
k2 =
εf − εi + 21 mv 2
;
~v
to core parallel momentum
q
q
P// =
Er2 − Mr2 = (Tr + Mr )2 − Mr2
q
=
(Tp + εi − εf )2 + 2Mr (Tp + εi − εf ),
(3)
breakup threshold at εf = 0
++∗∗
Angela Bonaccorso (INFN, Sez. di Pisa)
Walking at the dripline
Ischia2014
42 / 42

Download Report