A novel manifestation of α clustering discovered in 212Po
Alain Astier, CSNSM Orsay
212
84Po128
GANIL, March 26th, 2010
Outline
Introduction
« α-core» nuclear clusters
Electric dipole moment and asymmetric nuclear systems
Experimental details
Particular production of 212Po excited states
Analysis tools & Results
Unexpected states discovered, with surprising properties
Discussion
212Po
: a nucleus located at 4 nucleons or 1 alpha from 208Pb ?
Conclusions & Perspectives
Introduction: “α-core” nuclear clusters
Experimental evidence: rotational bands
8
Be
αα
16
O
12C
α
18
O
14C
α
20
Ne
16O
α
44
Ti
40Ca
α
W. von Oertzen et al., EPJ A 43 (2010) 17
Introduction: “α-core” nuclear clusters
CMasse =2 fm
8
CCharge =2 fm
Be
αα
D=0
18
16
CCharge =1.2 fm
O
12C
α
CMasse =1.1 fm
18
CCharge =1.2 fm
O
14C
α
D=0
+ enhanced E1
transitions in 18O
D=0.9 efm
“enhanced” E1’s
CCharge =1 fm
Ne
16O
α
D=0
W. von Oertzen et al., EPJ A 43 (2010) 17
CMasse =0.54 fm
CCharge =0.54 fm
44
O
“standard” E1’s
CMasse =1 fm
20
B(E1) (W.u.)
CMasse =1.2 fm
Ti
40Ca
α
Electric dipole moment:
D=0
D = e(r p − Z .Rc.m.) = e ZN  r p − rn
A 




Introduction: “α-core” nuclear clusters
Be
αα
16
O
12C
18
O
14C
α
20
Ne
16O
α
44
Ti
212
Po
D=0
α
40Ca
208Pb
D=0
D=0.9 efm
D=0
18
B(E1) (W.u.)
8
O
“enhanced” E1’s
“standard” E1’s
α
D=0
α
CMasse=0.17 fm
CCharge=0.21 fm
D=3.7 efm
Experimental evidence: ???
Rotation is quantically forbidden
Experimental conditions
Initial goal of the EB-02/17 experiment:
Study of high spin states of neutron-rich isotopes populated by fusion-fission
18O
8
226Th* → FF1* + FF2* + <4-6n>
(85 MeV) + 208
Pb
→
82
90
EUROBALL IV
(239 Ge)
Experimental conditions
18O
+ 208Pb → fission
~150 nuclei produced
Symmetric fission around Z=45
Experimental conditions
Initial goal of the EB-02/17 experiment:
Study of high spin states of neutron-rich isotopes populated by fusion-fission
18O
8
226Th* → FF1* + FF2* + <4-6n>
(85 MeV) + 208
Pb
→
82
90
~150 nuclei produced
Symmetric fission around Z=45
EUROBALL IV
(239 Ge)
Energy of 85 MeV for 18O beam chosen in order to induce a “cold” fission
σf ~ 100 mb, Ibeam ~ 5 pnA,
~ 104 fissions/s in the target
Thick Pb target (100 mg/cm2) γ emitted by stopped nuclei
~ 4x109 events with fold ≥ 3 recorded in 10 days
A very successful experiment : 14 articles published up to now !
The “bonus”: 212Po in the data
Total projection:
212Po
γ-rays, among those of 150 other nuclei…
405
(4+ → 2+)
727
(2+ → 0+)
Production of 212Po
Fusion-fission was not the only exit channel of the reaction.
The following transfer reaction also occurred:
208Pb
18O, 14C) 212Po
(
82
126
84
128
Estimation of 212Po production:
σ ~ 10-20 mb
212
Po
However, several parameters are not known exactly:
Beam fully stopped in the target
Energy: BCoulomb ≤ E(18O) ≤ 85 MeV
γ multiplicity (212Po) << γ multiplicity (FF)
EB Trigger (fold ≥ 3) not optimized for 212Po
Analysis tools
γ coincidences
“1 gate” spectrum (727 keV):
405
6+
4+
2+
223
405
727
0+
223
Analysis tools
γ coincidences
“1 gate” spectrum (727 keV):
6+
4+
2+
223
405
727
0+
223
rather selective…
405
but a lot of FF contaminants…
212Po
117Cd
+ 104Mo
112Pd + 108Ru
106Ru + 113,114Pd
98Zr
Analysis tools
γ coincidences
“2 gates” spectrum (727 & 405 keV):
223
6+
4+
2+
223
405
727
0+
Analysis tools
γ coincidences
“2 gates” spectrum (727 & 405 keV): only composed of 212Po γ rays
223
6+
4+
2+
223
405
727
0+
212Po
212Po
level scheme: before
212Po
☺ γ-γ-γ coincidences
level scheme: now
☺ γ angular distributions
☺ γ-γ angular correlations
50 γ rays added
35 new states, some of them extremely interesting:
They decay by a very enhanced E1 (with ∆I=0) transition
The starting point: The 780 keV line is Doppler-shifted
727 keV
780 keV
Consequences:
(>90°)
(~90°)
(<90°)
1) 212Po recoils along the beam direction.
2) The lifetime of the emitting state is very
short: it is definitely shorter than the
stopping time of 212Po in the lead target
(1.4 ps).
The starting point: The 780 keV line is Doppler-shifted
Consequences:
1) 212Po recoils along the beam direction.
Eγ = Eγ0 [1+ v/c cos(θ)]
2) The lifetime of the emitting state is very
short: it is definitely shorter than the
stopping time of 212Po in the lead target
(1.4 ps).
Eγ0=780.4 keV
v/c=1%
3) The reaction is a transfer reaction, with a
back-scattered carbon residue.
208Pb(18O,14C)212Po
Kinematics
Carbon is mainly detected at backward angles for energies
close to the Coulomb barrier
Polonium is therefore emitted forwards
Kinematics
O
H. Bohn et al., Z. Phys. A 302 (1981) 51
208Pb
(mg/cm2)
18O
energy
N
Measures
(MeV)
C
48
75
(pulsed)
γ-γ coincidences
1.1
79
(pulsed)
α-γ coincidences
(6+→4+)
(4+→2+)
(2+→0+)
0.9
69, 72.5 ejectile (151°≤θ≤166°)-γ
76.6, 75 coincidences
81.6
212Po
Analysis tools
Angular distributions
Angular distributions extracted versus the beam axis
Ge
Eγ
θ
Eγ multipolarity determined from N(θ)
(Euroball → 13 values of θ ranging between 15° and 163°)
beam
For less intense γ rays:
quadrupolar
(I+2 → I)
RADO=N(39.3°)/N(76.6°)
<θ(T+C)>
dipolar
(I+1 → I)
<θ(Q)>
Confirmation of the symmetry
about the beam axis
Analysis tools
Angular distributions
Eγ (keV)
coef. a2
Nature
Spins
727
+0.16(4)
∆I=2, quadrupole (E2)
2+ → 0+
405
+0.20(4)
∆I=2, quadrupole (E2)
4+ → 2+
223
+0.18(4)
∆I=2, quadrupole (E2)
6+ → 4+
357
+0.24(4)
∆I=2, quadrupole (E2)
10+ → 8+
577
-0.25(5)
∆I=1, dipole (E1)
11- → 10+
868
+0.18(6)
∆I=2, quadrupole (E2)
12+ → 10+
466
-0.5(1)
∆I=1, dipole (M1)
4(-) → 3(-)
587
-0.23(8)
∆I=1, dipole (M1)
7(-) → 6-
718
-0.29(5)
∆I=1, dipole (M1)
9(-) → 8-
1020
-0.28(8)
∆I=1, dipole (E1)
7(-) → 6+
276
+0.29(6)
∆I=0, dipole (E1)
8- → 8+
432
+0.27(7)
∆I=0, dipole (E1)
6- → 6+
661
+0.26(9)
∆I=0, dipole (E1)
6- → 6+
In agreement with
previous assignments
Unexpected states !
Lifetime evidence
All E1 (∆I=0) γ transitions discovered in 212Po have a particular profile:
a “stopped” component and a “in flight” component.
<90°
~90°
432
276
>90°
661
633
398
780
Analysis tools
3- Lifetime measurements
It is then possible to extract the
lifetime of the corresponding states
with the Doppler Shift Attenuation
Method, with 2 inputs:
- The kinematics is given by the profile
of the 780 keV line, which is entirely
emitted in-flight.
- The slowing down of
the lead target.
212Po
nuclei in
Lifetime measurements
Results
All measured lifetimes are in the range [0.1-0.6] ps.
The other states, for which the decaying γ transition is too weak to be analyzed, have
necessarily a lifetime ≤ 1.4 ps, corresponding to the stopping time of polonium in the
target.
Conclusion
The corresponding B(E1) transition rates are
huge
:
Up to 1000 times the values of typical B(E1)’s generated by only one nucleon !
Lifetime measurements
212
Results
O
B(E1) (W.u.)
18
All measured lifetimes are in the range [0.1-0.6] ps.
Po
The other states, for which the decaying γ transition is too weak to be analyzed, have
necessarily a lifetime ≤ 1.4 ps, corresponding to the stopping time of polonium in the
target.
Conclusion
The corresponding B(E1) transition rates are
huge
:
Up to 1000 times the values of typical B(E1)’s generated by only one nucleon !
Main structures observed in 212Po
The same basic structure is observed
3 times in the 212Po level scheme.
It is built upon each I+ yrast state
(I=4, 6, 8), and is composed of:
Two I- states which decay towards
the I+ yrast state via an enhanced E1.
One (I+1)- state decaying towards
the I+ and (I+2)+ yrast states, the two
I- states, and the lowest (I+2)- state.
Two (I+1)+ states which decay
towards the (I+1)- state via an
enhanced E1.
Discussion
The shell model should be well suitable to describe the first excited states of 212Po,
by considering the excitations of 4 nucleons outside the doubly magic 208Pb core.
82
126
Discussion
The shell model should be well suitable to describe the first excited states of 212Po,
by considering the excitations of 4 nucleons outside the doubly magic 208Pb core.
212Po
ground state:
[π(h9/2)2 ν(g9/2)2] 0+
i13/2
f7/2
j15/2
i11/2
h9/2
g9/2
82
126
π
ν
208Pb
212Po
and the shell model interpretation
i13/2
f7/2
h9/2
82
π
126
j15/2
i11/2
g9/2
ν
π(hi)
π(hf)
πh2
(cœur)
(2π)
ν(gj)
ν(gj)
ν(gi)
ν(gi)
νg2
νg2
(2π 2ν)
(2ν)
212Po
and the shell model interpretation
The 212Po description by the shell model works relatively well :
☺ The excitation energies of yrast states are reproduced
However it is not completely satisfactory, calculations fail to reproduce by more than an order of
magnitude the experimental values:
B(E2)’s (measured for the 6+ et 8+ states)
212Po
and the shell model interpretation
The 212Po description by the shell model works relatively well :
☺ The excitation energies of yrast states are reproduced
However it is not completely satisfactory, calculations fail to reproduce by more than an order of
magnitude the experimental values:
B(E2)’s (measured for the 6+ et 8+ states)
α decay of the ground state
α decay of the 212Po ground state
The half-life of the 212Po ground state is shorter than expected by the systematics
Hindrance Factor (N=128)
N=128
90Th
88Ra
86Rn
84Po
1.4
1.8
2.2
2.3
T1/2 should be larger
(expected: HF(212Po)~2.6)
log10 T1/2 = a E α-1/2 + b
(Geiger-Nuttall)
Sign of α preformation in 212Po
212Po
and the shell model interpretation
The 212Po description by the shell model works relatively well :
☺ The excitation energies of yrast states are reproduced
However it is not completely satisfactory, calculations fail to reproduce by more than an order of
magnitude the experimental values:
B(E2)’s (measured for the 6+ et 8+ states)
α decay of the ground state
the new states -with non-natural parity(4-, 6-, 8-) cannot be explained
212Po
and the “α-208Pb” cluster model
In such a model, the 212Po nucleus is
only described by the α-208Pb
structure.
The potential is phenomenological
(square well, modified WoodsSaxon…), or obtained by a double
folding procedure (i.e. from the real
part of the optical potential which is
used to describe the α-208Pb
scattering).
Free parameters are needed in order
to better reproduce the excitation
energies of yrast states of 212Po.
212Po
and the “α-208Pb” cluster model
☺ α decay of the ground state
☺ B(E2)’s
yrast energies
4-, 6-, 8- states ?
212Po
with a “shell + cluster” hybrid model
30% of α in the ground state
What about the excited states ?
Discussion of the new states discovered in 212Po
The excited states of polonium 212 present two facets:
“shell model” and α-208Pb cluster structure
ψtot (Iπ ) = a ψSM (Iπ ) + b ψcluster(Iπ )
Physical hypothesis: The large electric dipole moment established in this work is due to the
oscillation motion of the α-core distance around its equilibrium position.
Hcluster =
Hα(r) + Hdipole(d)
Central potential (3 dimensions)
→ Solution : χπ’α (I)
(spin I, parity π’=(-1)I )
208Pb
α
α
208Pb
Double well (Right & Left), 1 dimension
(the dipole moment)
→ 2 solutions (for each well) : ϕ0 et ϕ1
parity not defined
After parity projection:
ϕ±0,1 = 1/√2 (ϕ
ϕRight0,1 ± ϕLeft0,1 )
Discussion of the new states discovered in 212Po
The excited states of polonium 212 present two facets:
“shell model” and α-208Pb cluster structure
ψtot (Iπ ) = a ψSM (Iπ ) + b ψcluster(Iπ )
ψcluster 0,1 (Iπ ) = χπ’α (I) ⊗ ϕ±0,1
(π’=±π)
For each I, one get 2 states with π = + and 2 states with π = –
The mixing with the “shell model” part is only possible between states of
natural parity.
The cluster states with non-natural parity cannot mix with the “shell model”
states, they remain pure α-208Pb states.
Main structures observed in 212Po: Interpretation
α-208Pb
α-208Pb
ν(g9/2)
2
⊗ 3-(210Po)
& α-208Pb
ν(g9/2)
2
& α-208Pb
Conclusion
212Po
: almost considered as a textbook example in nuclear physics…
Yrast states relatively well described by the shell model, by considering the excitations
of 4 nucleons outside the doubly magic 208Pb core.
…up to now !
Unexpected states (by shell model) discovered at low excitation energy (non natural
parity, decay via dipole electric γ transition with huge B(E1) transition probability) in the
study of the 208Pb(18O,14C)212Po transfer reaction, performed with the Euroball 4
multidetector and the Vivitron accelerator.
212Po can (and must) be also considered as α-208Pb
Difference from light nuclei: no collective rotation of the system.
The states discovered in 212Po are interpreted as due to the oscillation motion of the αcore distance around its equilibrium position.
They are pure cluster states!
Perspectives
Manifestation of the α vibration in other α–core nuclei?
Prerequisite: a heavy magic core
208Pb+α
= 212Po
132Sn+α
= 136Te
100Sn+α
= 104Te
N=Z nuclei: no electric dipole moment…
Vibration of a small nucleus heavier than an α?
208Pb+8Be
= 216Rn Q ~ +17 MeV
Theory
Towards a better understanding/description of the phenomenon
Values of the excitation energies for these states
B(E1)’s
Collaboration
Alain Astier, Marie-Geneviève Porquet
CSNSM Orsay
Pavel Petkov
IRNNE Sofia
Doru Delion
IFIN-HH Bucarest
Peter Schuck
IPN Orsay
Thanks to all colleagues involved in the EB-02/17 Euroball experiment,
which was initially devoted to the study of fission fragments…
References
+ (much) more information in the next paper submitted to EPJ A
Thank you for your attention !
p
208Pb
n
p
n
208Pb
α