Transcript Synthetic Paths to the Heaviest Elements W. Loveland Oregon State University Corvallis, OR 97331 USA.

Synthetic Paths to the
Heaviest Elements
W. Loveland
Oregon State University
Corvallis, OR 97331 USA
Production of Heavy Elements in
Complete Fusion Reactions
where
• We need to know three spin-dependent quantities: (a) the
capture cross section, (b) the fusion probability and (c) the
survival probability, and their isospin dependence
How well can we describe
observations?
Let’s look at this more carefully
Despite correctly predicting σEVR correctly, , the
values of PCN (and Wsur )differ significantly
ANU estimate is 0.01
A Primer on Capture Cross
Sections
• For heavy systems, this means a fission
cross section.
• Capture cross sections are “barrier
crossing cross sections”
• The “barrier” is the interaction barrier
not the fusion barrier
 capture   fusion fission   quasifissi on
Models for capture cross sections
• Improved isospin dependent QMD model
(Bian, et al, NPA 829, 1 (2009))
• Modified semi-empirical Swiatecki et al
model (PRC 74, 014602 (2005), K.
Siwek-Wilczynska, 2009))
• Coupled channels calculations, such as
those at http://nrv.jinr.ru/nrv/
• Skyrme energy density functional
approach (PRC 74 044604)
• DNS model
How successful are the models?
Conclusions
• For the 50-150 “calibration” reactions, we
know capture cross sections within 50%
• We know interaction barriers within 20%
• For the heavy element synthesis reactions,
we know the capture cross sections within
a factor of 2.
• The “coupled channels” calculations (such
as Zagrebaev) do the best overall job of
describing capture cross sections.
What about Wsur?
• Well-established formalism for
calculations
• Principal uncertainty is the values of the
fission barrier heights.
• Best calculations for SHE show an
average discrepancy between data and
theory to be 0.4 MeV, with largest
error being 1.0 MeV.
Calculation of Wsur
 n
 Pxn ( E*)  

i 1  n   f
imax  x
Wsur



 i , E*
Γn/Γf evaluated from Vandenbosch and Huizenga expression
Γ (E* )
4A2/3(E*  B )
1/2
 *
1/2 
n CN 
CN
n

e
xp(2a
E

B
  E*  B


1/ 2
CN
n
f
*
1/2
*

 CN

Γ (E
) k 2a
ECN  B f
1

f CN




k=9.8 MeV
1/2 
 
)
 

a=A/12 MeV-1
Bn, Bf from Möller et al., (ADNDT 39,213; 59, 185)
a = a ê1+ d E 1- exp(-g E) ú
E
êë
úû
g = 0.061
é
ù
Collective enhancement of the level density
Deformation dependence of the collective enhancement
Energy dependence of the collective enhancement
E* behavior of Bf
Pei, et al. PRL 102, 192501 (2009)
How well can we calculate Wsur?
• We took a group (~75 ) heavy element
synthesis reactions where Z1Z2 < 1000
(ZCN =98-108) and compared the
calculated and measured values of σEVR.
• The average ratio of
(measured/calculated) cross sections
was 6.5. We conclude that we know
Wsur within a factor of 3.
What about PCN?
• This is the most difficult quantity to
estimate or measure.
• There are a limited number of
measurements of PCN.
How do you measure PCN?
•
σfission =σfusion-fission + σquasifission
• Width of the mass distributions (Itkis et al.) One
assumes fusion-fission gives symmetric mass
distributions while quasifission gives asymmetric mass
distributions. This is problematic in some situations
32S
+
232Th
How do you measure PCN?
• Angular distribution method (Back)
• Fusion-fission is assumed to be
described by the ordinary transition
state model of fission angular
distributions while quasifission is
described by a strongly fore-aft peaked
distribution.
ANU approach to measuring PCN(fissility)
J max
s EVR (Ec.m. ) = å s capture (Ec.m., J)PCN (Ec.m., J)Wsur (Ec.m., J)
J =0
s EVR =
s EVR (Ec.m. )
p 2
Consider a set of reactions of differing asymmetry that produce the same CN
Consider the cases where the E* is high enough that PCN is independent of E*.
Assume all relevant partial waves are “saturated” and that Wsur is then
independent of entrance channel.
Sample Data
Excitation Energy Dependence of PCN
Zagrebaev and Greiner
PCN ( E*, J ) 
0
PCN
*
 E B*  Eint
(J ) 
1  exp




PCN (E*)
PCN results
PCN (fissility)
Hot fusion systematics
E*=35 MeV
48Ca
+X
Hot fusion predictions
•
•
•
•
•
249Bk(48Ca,3n)294117
σEVR=1 pb.
249Bk(50Ti,4n)295119 σ
EVR=0.07 pb.
248Cm(54Cr,4n)302120 σ
EVR=0.02 pb.
244Pu(58Fe,4n)302120 σ
EVR=0.006 pb.
238U(64Ni,3n)302120 σ
EVR=0.004 pb.
Based upon MNMS masses
Damped Collisions—A new path to
the superheavy nuclei?
• Zagrebaev and Greiner have predicted that damped
collisions (such as 232Th + 250Cf, 238U+238U,
238U+248Cm) might produce new n-rich isotopes of
Cn.
• Surrogate for this reaction is 160Gd + 184W.
Because of difficulties in studying the damped
collisions of the heaviest nuclei, it has been
suggested to study this surrogate reaction.
Why use RNBs for producing new
heavy nuclei?
•
Longer half-lives of products enable more detailed atomic
physics and chemical studies.
•
Lowered fusion barrier due to n-rich projectiles allows
lower E*.
Higher survival probabilities for n-rich products.
•
Applying what we know about
the synthesis of the heaviest
nuclei to the problem of
making new heavy nuclei with
radioactive nuclear beams
Calculational Model For RIBInduced Reactions
RIA/SPIRAL2/FRIB…Beam List
•All “stable” targets
•Fusion Probability
•Survival Probability
Yield in atoms/day
What RIBs are likely to be most useful in the short term?
Cold fusion
New elements from RIB facilities
(LOL)
Atomic Physics and Chemistry of
the Transactinides
>5 atom/day list
 264Rf
 265Db
 268Sg
 267Bh
252Cf(16C,4n)
249Bk(20O,4n)
252Cf(20O,4n)
252Cf(21F,6n)
What kind of reactions with RNBs
are used to form n-rich nuclei?
Reactants
Products
FRIB Beam
Intensity (p/s)
Production
Rate
(atoms/day)
26Ne
+
248Cm
271Sg
+ 4n
2.2 x 106
0.004
30Mg
+
244Pu
270Sg
+ 4n
7.1 x 106
1
29Mg
+
244Pu
269Sg
+ 4n
3.6 x 107
0.2
20O
+
252Cf
268Sg
+ 4n
1.5 x 108
5
23Ne
+
248Cm
267Sg
+ 4n
1.6 x 108
1
Targeted Radioactive Beams
• Consider a typical targeted set of
radioactive beams, 46-48K.
Reaction
Beam
Intensity
(p/s)
Cross
Section
(pb)
Atoms/day
248Cm(48Ca,4n)
3x1012
3.3
1
248Cm(46K,4n)
5.3x108
1.8
1x10-4
248Cm(47K,4n)
3.5x108
3.8
1.4x10-4
248Cm(48K,4n)
3.5x106
6
2.2x10-6
Conclusions
• RNBs offer unique opportunities to explore
the physics and chemistry of n-rich heavy
nuclei
• There are short term and long term
opportunities
• RNBs are not a path to new chemical elements
• RNB research can help us to understand the
isospin dependence of fundamental quantities
in heavy element science.
The Future
• New directions in synthesizing heavy nuclei
can be pursued to make n-rich heavy nuclei
with transfer reactions and reactions with
radioactive beams.
• There is work to be done to understand
the physics of the fusion reactions used to
date.
• Heavy element synthesis studies remain a
laboratory for studying nuclei, their
structure and reactions at the limits of
stability.