ELDM def( ) = ES 0( ) BS def( ) −1+ 2x BC def( ) −1( )[ ]BS def( ) = ES def( )

ES 0( ), BC def( ) = EC def( )

EC 0( )

x =EC 0( )2ES 0( )

=Z 2 / AZ 2 / A( )

crit

≈Z2

50A

Deformed liquid drop (Bohr & Wheeler, 1939)

fission of nuclear droplet

x: fissility parameter

The nuclear droplet stays stable and spherical for x<1. For x>1, it fissions immediately. For 238U, x=0.8

Realistic calculations Nature 409, 785 (2001)

• All elements heavier than A=110-120 are fission unstable!• But… the fission process is fairly unimportant for nuclei with A<230. Why?

https://www.youtube.com/watch?v=mBdVK4cqiFs

Fact Check

240Pu

Realistic calculations

136 140 144 148 152 156 160 16410-9

10-4

101

106

1011

1016

1021

1026

Status: 6.3.2012

N = 162

N = 152

Hs

SgRfNo

Fm

Cf

Cm

Pu

U

T sf /

sNeutron number

238U lives 4.5 billion years 250No fissions after 4.2 µs

EM fission of RNBs at GSI, E*~11 MeV K-H Schmidt et al., NPA 665, 221 (2000)

TKE

deformation

180Tl

QEC

Bf

180Hg

• 2 step process: β+/EC decay of a parent 180Tl nucleus populates an excited state in the 180Hg daughter, which then might fission (in competition with the γ decay to the g.s.)

• Low-energy fission! (E*<QEC=10.8 MeV) • 10 cases know so far (neutron-def. Uranium region)

γ

γ

γ

β+/EC

β+/EC

Curious Fission of 180Hg

Phys. Rev. Lett. 105, 252502 (2010); Rev. Mod. Phys. 85 1541 (2013)

•  Before the ISOLDE experiment: expected SYMMETRIC split in two semi-magic 90Zr

•  The most probable fission fragments are 100Ru (N=56,Z=44) and 80Kr (N=44,Z=36)

http://www.nature.com/news/2010/101201/full/news.2010.642.html

Fission pathways...

WKB:

multidimensional space of collective parameters

collective inertia (mass parameter)

The action has to be minimized!

Fission half-lives: depend on potential, friction, and inertia terms

100 200 300

-5

0

5

10

out

Pot

entia

l ene

rgy

(MeV

)

in

scission

Quadrupole moment (b)

E0

collective actionminimization

LangevinWKB

stochasticdynamics

WKB:

multidimensional space of collective parameters

collective inertia (mass parameter)

The action has to be minimized!

Fission half-lives: depend on potential, friction, and inertia terms

Phys. Rev. C 80, 014309 (2009) Phys. Rev. C 90 061304(R) (2014)

Quality  Input  

Numerical  Techniques  

Large-­‐scale  Simula9ons  on  Leadership-­‐class  Computers  

Dynamics  

Low-energy fission: theoretical strategy

PRC 78, 014318 (2008)

PRC 84, 054321(2011)

PRC 80, 014309 (2009) Confronta9on  with  experiment;  predic9ons  

PRC 80, 014309 (2009)

PRC 85, 024304 (2012)

https://people.nscl.msu.edu/~witek/Talks/Fission-JINA.pptx http://science.energy.gov/ascr/highlights/2015/ascr-2015-08-a/