Mapping timescales of quasifission
Dr. Elizabeth Williams, Australian National UniversityHumboldt Kolleg, ECT*, Trento, Italia, 1 September 2015
E. Williams, Humboldt Kolleg, 1 September 2015
Outline
Quasifission and superheavy element formation
ANU’s quasifission mapping program
New technique: High angular momentum mass angle distributions
E. Williams, Humboldt Kolleg, 1 September 2015
40Ca
Quasifission238U
TDHF calculation of 40Ca+238U reaction (Cedric Simenel, Aditya Wakhle)
E. Williams, Humboldt Kolleg, 1 September 2015
Quasifission: PCN = 1 - PQF
The ANU Quasifission Program
Aims to examine the dependence of quasifission probability and characteristics on collision variables (related to PCN):
• Compound nucleus fissility (Z2/A);
• Coulomb repulsion in the entrance channel (Z1Z2);
• Angular momentum;
• Nuclear structure of the colliding nuclei:o deformation (alignment with projectile)o closed shells (magic numbers) in the colliding nuclei
E. Williams, Humboldt Kolleg, 1 September
2015
Aim of the ANU Quasifission Program
Ultimate goal: Reliable model including all relevant physics to predict PCN
Model should allow direct comparison to experimental data
Model should predict quasifission probability, since PCN = 1 – PQF
E. Williams, Humboldt Kolleg, 1 September
2015
Means of creating this model
Start with experimental data
Define smooth trends in quasifission dynamics Fissility Coulomb repulsion Angular momentum
Then take into account the influence of shell effects on quasifission outcomes Magicity Collective structure Valence nucleon number
Work closely with theorists to develop models that provide insight into the physics driving quasifission probabilities E. Williams, Humboldt Kolleg, 1
September 2015
Means of creating this model
Start with experimental data
Define smooth trends in quasifission dynamics Fissility Coulomb repulsion Angular momentum
Then take into account the influence of shell effects on quasifission outcomes Magicity Collective structure Valence nucleon number
Work closely with theorists to develop models that provide insight into the physics driving quasifission probabilities E. Williams, Humboldt Kolleg, 1
September 2015
E.
Wil
liam
s,
Hu
mb
ol
dt
Koll
eg
, 1
Sep
tem
ber
20
15The MAD Map
Identifying smooth trends in quasifission dynamics
How do we identify smooth trends in quasifission dynamics experimentally?
• Minimize shell effects – high E*
• Minimize effects of angular momentum – low E/Vb
• Compromise: choose E/Vb = 1.05-1.10o Effects of spherical magic numbers
attenuated by E*
o Effects of deformation alignment averaged out
o Angular momentum not too high (but still relevant to SHE production)
E. Williams, Humboldt Kolleg, 1 September
2015
E. Williams, Humboldt Kolleg, 1 September
2015
The MAD Map
R. du Rietz, E. Williams et al.,
PRC 88 (2013) 054618
Z = 6 Z = 28Projectile Z
Z = 82
Z = 92
Z = 102
Z = 112
Com
pound n
ucl
eus
ZTa
rget
Z
Hg
No
Ti
0
45
90
135
180
0 0.5 1MR
q (d
eg.)
q
(deg
.)
0
0.5
1
0 20 40 60 80Time
MR
04590
135180
0 20 40 60 80Time
q (d
eg.)
Miminal mass-angle correlationStrong mass-angle correlation
160o
20o Scission
R. Bock et al., NP A388 (1982)
334
J. Toke et al., NP A440 (1985)
327
W.Q. Shen at al., PRC 36 (1987)
115
B.B. Back et al., PRC 53 (1996)
1734
10 20 30 40
10 20 30 40
MADs: Mass equilibration and rotation
Slide courtesy of D. J. Hinde
Quasisim: A simple Monte Carlo model for quasifission timescales
Ingredients:
Reaction timescale determined by:• Angular velocity ω = L/I
Angular momentum L moment of inertia I
• Center-of-mass scattering angle θc.m.
• θi,f: ½ Coulomb deflection angles for the initial and final trajectories
Angle of rotation of the dinuclear system during reaction: Δθ = π-θi-θf-θc.m
trxn = Δθ/ω
Mass equilibration: 1-exp(trxn / τm), τm ~ 5.2 zs
[1] J. Tōke et al. Nucl. Phys. A 440, 327 (1985)[2] R. du Rietz et al. PRL 106, 052601 (2011)
E. Williams, Humboldt Kolleg, 1 September
2015
QF Timescales
<t> 5x10-21s <t> 10x10-21s <t> >> 10x10-
21s
186W
Experimental MAD
Simulated MAD
R. du Rietz et al. PRL 106 (2011)
052701 MAD1 MAD2 MAD3
E. Williams, Humboldt Kolleg, 1 September 2015
MAD Classes: Distinguishing features
Class Mass distribution Mass-angle correlation?
MAD 1 (<τ> < 5 zs)
Minimum at Mr=0.5 Yes
MAD 2 (<τ> ~ 10 zs)
Maximum at Mr=0.5;
Significantly wider than that predicted
for fusion-fission
Yes
MAD 3 (<τ> >> 10 zs)
Maximum at Mr=0.5; may be
slightly wider than that predicted for
fusion-fusion
No
For MAD class 3, quasifission can be identified using other observations (e.g. angular anisotropies in comparison to Standard Model predictions).
Class 1
Class 2Class 3MADs for reactions in this energy regime (E/VB ~ 1.05 – 1.10) show a smooth evolution from long to short timescales as a function of entrance channel parameters.
Primarily fusion-fission
E. Williams, Humboldt Kolleg, 1 September
2015
Class 1
Class 2Class 3MADs for reactions in this energy regime (E/VB ~ 1.05 – 1.10) show a smooth evolution from long to short timescales as a function of entrance channel parameters.
Based on entrance channel quantities (charge product, effective fissility, etc.) and compound nucleus properties, can we predict which MAD class a given reaction is likely to conform with?
Primarily fusion-fission
E. Williams, Humboldt Kolleg, 1 September
2015
R. du Rietz, E. Williams et al., PRC 88 (2013) 054618
Smooth trends: Coulomb repulsion
Smooth trends: Fissility
W. J. Swiatecki, Phys. Scr. 24, 113 (1981)
Compound nucleus fissility
Effective fissility
R. du Rietz, E. Williams et al., PRC 88 (2013) 054618
Smooth trends: Fissility
E. Williams, Humboldt Kolleg, 1 September 2015
What conclusions can we draw from the MAD Map?
Using ZpZt and ZCN, or Xeff and XCN, we can roughly estimate the average timescale of a given reaction at ~1.05-1.10 VB.
We can use the same parameters to determine whether quasifission is likely to dominate in a given reaction in this energy range.
We have observed a smooth evolution in the MADs as a function of two categories of reaction parameters; this smooth evolution provides a first test of future dynamic models of reactions.
E.
Wil
liam
s,
Hu
mb
ol
dt
Koll
eg
, 1
Sep
tem
ber
20
15
Mapping MADs for high angular momentum collisionsA new method of extracting more from experimental data
Means of creating this model
Start with experimental data
Define smooth trends in quasifission dynamics Fissility Coulomb repulsion
Angular momentum
Then take into account the influence of shell effects on quasifission outcomes Magicity Collective structure Valence nucleon number
Work closely with theorists to develop models that provide insight into the physics driving quasifission probabilities E. Williams, Humboldt Kolleg, 1
September 2015
MAD Map
E. Williams, Humboldt Kolleg, 1 September 2015
The angular momentum degree of freedom
This is a difficult thing to study directly:
Each observation represents the sum of many reaction outcomes, reflecting the angular momentum distribution of the reaction in question.
We cannot select out reactions corresponding to a single angular momentum (L) value.
But can we restrict the angular momentum range we examine, using observations from complementary reactions?
E. Williams, Humboldt Kolleg, 1 September 2015
Complementary reactions
We’ll define complementary reactions based on fusion angular momentum distributions.
0 20 40 60 800
2
4
6
8CCFULL [1]No couplinga = 1 fmr0 = 1 fmVB reproduced
52Cr + 198Pt (Elab = 264.8 MeV; E*=42.9 MeV)
[1] K. Hagino, N. Rowley, and A.T. Kruppa, Comp. Phys. Comm. 123 (1999) 143
E. Williams, Humboldt Kolleg, 1 September 2015
Complementary reactions
We’ll define complementary reactions based on fusion angular momentum distributions.
CCFULL [1]No couplinga = 1 fmr0 = 1 fmVB reproduced
52Cr + 198Pt (Elab = 264.8 MeV; E*=42.9 MeV)
[1] K. Hagino, N. Rowley, and A.T. Kruppa, Comp. Phys. Comm. 123 (1999) 143
0 20 40 60 800
2
4
6
8
54Cr + 196Pt (Elab = 272.2 MeV; E*=42.3 MeV)
E. Williams, Humboldt Kolleg, 1 September 2015
Complementary reactions
We’ll define complementary reactions based on fusion angular momentum distributions.
CCFULL [1]No couplinga = 1 fmr0 = 1 fmVB reproduced
52Cr + 198Pt (Elab = 264.8 MeV; E*=42.9 MeV)
[1] K. Hagino, N. Rowley, and A.T. Kruppa, Comp. Phys. Comm. 123 (1999) 143
0 20 40 60 800
2
4
6
854Cr + 196Pt (Elab = 272.2 MeV; E*=42.3 MeV)
Complementary reactions
E. Williams, Humboldt Kolleg, 1 September
2015
52Cr + 198Pt (Elab = 264.8 MeV; E*=42.9 MeV)
[1] K. Hagino, N. Rowley, and A.T. Kruppa, Comp. Phys. Comm. 123 (1999) 143
0 20 40 60 800
2
4
6
8
54Cr + 196Pt (Elab = 272.2 MeV; E*=42.3 MeV)
0 20 40 60 800
400
800
1200
Complementary reactions
E. Williams, Humboldt Kolleg, 1 September
2015
52Cr + 198Pt (Elab = 264.8 MeV; E*=42.9 MeV)
[1] K. Hagino, N. Rowley, and A.T. Kruppa, Comp. Phys. Comm. 123 (1999) 143
54Cr + 196Pt (Elab = 272.2 MeV; E*=42.3 MeV)
0 20 40 60 800
400
800
1200
Complementary reactions
E. Williams, Humboldt Kolleg, 1 September 2015
54Cr + 196Pt 250Nb; E*~42.6 MeV
0 20 40 60 800
400
800
1200
0 20 40 60 800
400
800
1200
Subtract the two complementary distributions to isolate the high angular momentum component:
52Cr + 198Pt (Elab = 264.8 MeV; E*=42.9 MeV)54Cr + 196Pt (Elab = 272.2 MeV; E*=42.3 MeV)
Class 1
Class 2Class 3
Primarily fusion-fission
E. Williams, Humboldt Kolleg, 1 September
2015 Cr
Pt
Complementary reaction:- Same reaction
(and therefore, same CN), different E*.
- Same CN and E*, different projectile / target combinations leading to the same MAD class.
E. Williams, Humboldt Kolleg, 1 September 2015
High angular momentum MAD
How can we use this concept to extract high angular momentum MADs?
52C
r +
19
8Pt
(Ela
b =
26
4.8
MeV
)54C
r +
196P
t (E
lab =
272.2
MeV
)
E. Williams, Humboldt Kolleg, 1 September 2015
High angular momentum MAD
MA
D1
: 52C
r +
19
8Pt
(Ela
b =
26
4.8
MeV
)M
AD
2:
54C
r +
196P
t (E
lab =
272.2
MeV
)
MAD 2’ - MAD 1’ = ΔMAD
High angular momentum MAD
E. Williams, Humboldt Kolleg, 1 September 2015
0 20 40 60 800
400
800
1200
High angular momentum MAD
Correspondingangular momentum
distribution
54Cr + 196Pt 250Nb; E*~42.6 MeV
Cr + Pt reaction energies
E. Williams, Humboldt Kolleg, 1 September
2015
ANU 14UD tandem accelerator + LINAC + CUBE
CUBE
CN Reaction Elab (MeV)
E/VB E* (MeV)
250Nb
52Cr + 198Pt
264.84 1.03 42.9
54Cr + 196Pt
272.15 1.06 42.3
52Cr + 198Pt
272.67 1.06 49.1
54Cr + 196Pt
278.22 1.08 47.0
52Cr + 198Pt
276.85 1.08 52.4
54Cr + 196Pt
284.29 1.10 51.8
52Cr + 198Pt
282.85 1.10 57.2
54Cr + 196Pt
288.68 1.12 55.2
Preliminary
Mass-Angle Distributions (elastics / recoils excluded)
E. Williams, Humboldt Kolleg, 1 September 2015
Preliminary
Loss of efficiency due to pulse height in back detector X-position delay line
Detector effects
E. Williams, Humboldt Kolleg, 1 September 2015
Preliminary
Loss of efficiency due to pulse height in back detector X-position delay line
Exclusion of events due to poor front detector timing resolution
Detector effects
E. Williams, Humboldt Kolleg, 1 September 2015
Preliminary
Mass-Angle Distributions (elastics / recoils excluded)
E. Williams, Humboldt Kolleg, 1 September 2015
Preliminary
CCFULL (no coupling, a = 1 fm, r0 = 1 fm, VB reproduced)K. Hagino, N. Rowley, and A.T. Kruppa, Comp. Phys. Comm. 123 (1999) 143
High Angular Momentum Mass-Angle Distributions
0 20 40 60 80 100
0
500
1000
1500
What can we learn from this?
E. Williams, Humboldt Kolleg, 1 September 2015
A first estimate of timescales
Ingredients:
Reaction timescale determined by:• Angular velocity ω = L/I
Angular momentum L moment of inertia I
• Center-of-mass scattering angle θc.m.
• θi,f: ½ Coulomb deflection angles for the initial and final trajectories
Angle of rotation of the dinuclear system during reaction: Δθ = π-θi-θf-θc.m
trxn = Δθ/ω
Mass equilibration: 1-exp(trxn / τm), τm ~ 5.2 zs
[1] J. Tōke et al. Nucl. Phys. A 440, 327 (1985)[2] R. du Rietz et al. PRL 106, 052601 (2011)
E. Williams, Humboldt Kolleg, 1 September
2015
Preliminary
45 55 65 75 850
5
10
15
Tim
e [z
s]
Moment of inertia –TDHF (tip collision):K. Vo-Phuok
E. Williams, Humboldt Kolleg, 1 September 2015
Cr + Pt: Summary of findings
Preliminary
• High angular momentum mass angle distributions have been extracted for reactions leading to 250No
• Simple model suggests quasifission timescales decrease with increasing angular momentum
• Next steps: Improve the model, cross check with TDHF Apply method more broadly
E. Williams, Humboldt Kolleg, 1 September 2015
Means of creating this model
Start with experimental data
Define smooth trends in quasifission dynamics Fissility Coulomb repulsion
Angular momentum
Then take into account the influence of shell effects on quasifission outcomes Magicity Collective structure Valence nucleon number
Work closely with theorists to develop models that provide insight into the physics driving quasifission probabilities E. Williams, Humboldt Kolleg, 1
September 2015
MAD Map
High angular momentum MADs
0.5 0.6 0.7 0.80.75
0.80
0.85
0.90
0.95
Ca+Pb Simenel et al.Cr+W Hammerton et al.
Xeff
XC
.N.
Entrance channel magicity, isospin: C. Simenel et al., PLB 710 (2012) 607N/Z ratio: K. Hammerton et al., PRC 91 (2015) 041602Shell effects: G. Mohanto et al., ANU, in preparation
Additional measurements
E. Williams, Humboldt Kolleg, 1 September 2015
Collaborators
Heavy Ion Accelerator Facility (HIAF)
E. Williams, D.J. Hinde, C. Simenel, M. Dasgupta, A. Wakhle, I.P. Carter, K.J. Cook, D.Y. Jeung, D.H. Luong, G. Mohanto, C.S. Palshetkar, E. Prasad, D.C. Rafferty and R. du Rietz (ANU)
The ANU Accelerator and Technical Staff
Research made possible by the Australian Research Council Grants and Fellowships DP110102858, DP110102879, DP130101569, FL110100098, FT120100760, and DE140100784.
Thank you!
Thank you!
E. Williams, Humboldt Kolleg, 1 September 2015
E. Williams, Humboldt Kolleg, 1 September 2015
ANU Experiments
Hinde et al., PRC 53 (1996) 1290 Rafiei et al., PRC 77 (2008) 024606 Thomas et al., PRC 77 (2008) 034610 Hinde et al., PRL 100 (2008) 202701 Hinde et al., PRL 101 (2008) 092701 du Rietz et al., PRL 106 (2011) 052701 Lin et al., PRC 85 (2012) 014611 Simenel et al., PLB 710 (2012) 607 Williams et al., PRC 88 (2013) 034611 du Rietz et al., PRC 88 (2013) 054618 Wakhle et al., PRL 113 (2014) 182502
Designed to study two-body fission.
• Composed of two large-area multiwire proportional counters (MWPC).
• MWPCs are position sensitive in X,Y coordinates.
• Position resolution: ~ 1mm
• Relative positions of the MWPCs can be adjusted to suit the experimental aims.
• Pulsed beam allows time-of-flight measurement.
• Resolution ~1 ns
• Angular coverage ~ 1.2π sr
Hinde et al., PRC 53 (1996) 1290
Rafiei et al., PRC 77 (2008)
024606
Thomas et al., PRC 77 (2008)
034610
Williams 50
The ANU CUBE detector
Hinde et al., PRC 53 (1996) 1290
Rafiei et al., PRC 77 (2008) 024606
Thomas et al., PRC 77 (2008) 034610
Position and time-of-flight information provide:- scattering angle θC.M. in the
center of mass frame,
- differential cross sections, and
- angular anisotropies.
Williams
The ANU CUBE detector
51
V1
V2
V1cm
V2cm
Hinde et al., PRC 53 (1996) 1290
Rafiei et al., PRC 77 (2008) 024606
Thomas et al., PRC 77 (2008) 034610
Kinematic coincidence:Position and time-of-flight information allow us to determine the mass ratio MR of the two fission fragments:
MR1 = AF1/(AF1+AF2)
= V2cm/(V1cm+V2cm)
Williams
The ANU CUBE detector
52
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