# Presentation: 641990

## Fission-fragment properties in a microscopic approach

**Walid Younes**

**This work performed under the auspices of the U.S. department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344**

## The program in broad strokes

- Based on highly successful program at BIII
- Fully microscopic, quantum-mechanical, dynamical, self-consistent description of fission
- Only phenomenological input is effective NN interaction

**Physical Sciences Directorate - N Division**

| What | When | How |
| --- | --- | --- |
| Statics | Now | HFB w/ Gogny force |
| Low-E dynamics | Next | TDGCM |
| Mid-E dynamics | Future | TDGCM + 2qp, 4qp |
| High-E dynamics | Future | TDGCM at finite temp |

## Basic framework: Statics

**Basic framework: Statics**

- Challenges
- Definition of scission (by neck size, Eint, ...)
- Speed/accuracy of calculations ( 2-center basis)
- Choice of appropriate collective coordinates
- Delicacy/Difficulty of approach to scission

## Current work: hot-scission configurations for 240Pu 

- Hot fission  e.g., 239Pu(nth,f)
- Non-trivial boundary
- Painstaking lines of calcs, each based on previous one, until scission
- Last pre-scission point,  frag props (use new collective Coords)
- Defines landscape for dynamic calcs

**Physical Sciences Directorate - N Division**

## Behavior at scission for symmetric vs. asymmetric fission

**Physical Sciences Directorate - N Division**

**Gradual**
**approach**

## Behavior at scission for symmetric vs. asymmetric fission

**Physical Sciences Directorate - N Division**

**Gradual**
**approach**

**Sudden**
**break**

## A more controlled approach to scission: constraining the neck

**Physical Sciences Directorate - N Division**

- New coll. Coord: Q20,Q30,QN now constrained
- Near symmetry (Q30 = 10 b3/2), along scission line
- Abrupt drop from QN = 3 to 2
- Near most likely fission (Q30 = 55 b3/2), along scission line
- Gentler drop from QN = 1.5 to 1

## Calculation of fragment properties

- Method 1 (quick-and-dirty)
- Identify point where neck is thinnest
- Integrate particle densities left and right
-  Fragment properties
- Method 2 (more accurate)
- Identify sp wave functions with left or right frag
-  Left- and right-frag Slater determinants
- Integrate particle, energy densities for each determinant
-  Fragment properties

**Physical Sciences Directorate - N Division**

**Method 2 is better by far, now applying it to latest calcs**

## Prediction of the fragment mass and charge

**Physical Sciences Directorate - N Division**

- Afrag, Zfrag from integral of particle densities
- Compared to UCD prediction (not a fit!)
- Good agreement
- From effective NN int., micro calc “knows” where to break 240Pu at scission

## Prediction of the fragment quadrupole moment

**Physical Sciences Directorate - N Division**

- Q20 more sensitive to config at scission
- “jitter” in calcs due to difficulty in pinpointing scission
- Nevertheless, a trend emerges
- Peak near symm
- Dip near Afrag ~ 134

## Prediction of the total fragment kinetic energy

**Physical Sciences Directorate - N Division**

- TKE data disagree in symmetric limit
- TKE calc does not include pre-scission energy
- “jitter” due to poor id of scission config
- However
- Calcs are in the ballpark
- Reproduce drop in TKE near symmetry

## Earlier results from analysis of microscopic excitation energies

**Physical Sciences Directorate - N Division**

- Very stringent test
- Ex = integral of energy densities, =Ex/(Bn+Kn)
- Calcs at vanishing neck
- “error” bars from QN=0.1-0.3 (other form of jitter)
- Overall a bit low (but missing pre-scission E)
- But
- Trends near A = 130 dip well reproduced
- In the ballpark

**Now revisiting with new HFB calcs, more careful analysis of E****int**

## Conclusion

- Reached scission in 240Pu  hot scission line in Q20-Q30
- Very promising results, especially on TKE and (A), but fluctuations due to poor identification of scission configurations
- Next: careful analysis of Eint between fragments
- Reduce jitter/uncertainties
- Next: careful look at pre-scission energies
- Far better estimates of KE(A), Ex(A), (A)

**Physical Sciences Directorate - N Division**

## Behavior of the deformation energies at scission

**Physical Sciences Directorate - N Division**

- Larger drop near symmetric fission
- ~ 48 MeV at symmetric
- Suggests Q20, Q30 may not be best coll. coords to home in on scission configuration

## Behavior of the neck at scission

**Physical Sciences Directorate - N Division**

- QN measures particles in neck region
- Drops by at least factor of 10 at scission
- Better candidate for coll. coord near scission

## Current work: limitations of one-center basis

- Unphysical tails persist due to one-center basis:
- Meant for density concentrated near *z*=0
- Parameter *b* can be chosen to optimize neck or frags, not both
- Consequences:
- fragments never fully separated
-  identification of scission configs is uncertain
- Careful analysis needed to reduce tails, extract energies

**Physical Sciences Directorate - N Division**

**Need two-center-basis**

## Going to higher energies: validity of adiabatic approximation

**Going to higher energies: validity of adiabatic approximation**

- Ex < 1.8 MeV  no coupling to intrinsic excitations
- 1.8 MeV < Ex < 3.6 MeV  no 0-to-2 qp coupling from HFB, weak coupling from GCM via Q
- Ex >> 3.6 MeV (e.g., 5 MeV)  strong 0qp-4qp coupling possible  not adiabatic
- The more coll. d.o.f., the less the need for extra qp excitations

**240****Pu, most likely path to fission**

**Shape-dep. Pairing gaps from HFB**

## The Gogny effective interaction

**The Gogny effective interaction**

- Free parameters adjusted to properties of
- 16O, 90Zr, infinite nuclear matter, even-odd E in Sn (quenched), and fission barrier in 240Pu
- Effective int is the _only_ phenomenological input to the microscopic theory of fission

** ****parameters fixed a priori**
** ****if failure to reproduce data**
** ****can’t tweak interaction parameters**
** ******** ****look for unjustified simplification**
** ******** ****restore missing physics**

## Past successes

**Past successes**

**Predicts/explains cold & hot fission**

**Predicts realistic**
**Fission times**

**Predicts ****238****U(********,f) TKE to 6%**

**Reproduces yields for ****238****U(********,f)**

**Goutte et al., PRC 71 , 024316  (2005)**

**Berger et al.**
**NPA 502, 85 (1989)**
**CPC 63, 365 (1991)**

## Results for 240P(nth,f) hot fission: Total kinetic energies

**Results for ****240****P(n****th****,f) hot fission: Total kinetic energies**

- Some variance in data near symmetric limit
- Comparing calculated _min_ (hot) to measured _avg_ (hot to cold)
- Calcs agree well with data
- Perhaps a bit low in symmetric limit
- A bit high elsewhere
- Large errors for very asymmetric shape

**Notes:**
And these are the calculations, with error bars
Remember that what we calculate is for hot fission, which by definition produces the minimum kinetic energy possible.  By contrast, the measurement is an average over all fission modes, hot to cold
As a result, our points should be a bit below the data, but not too far below
Overall, we agree well with the data, although
We may be a bit low in the symmetric limit
And probably a bit high everywhere else
Also, the results for the most asymmetric split we calculated carries large uncertainties
Still, this is very good for a parameterless calculation