Nuclear Pasta ?C.O.Dorso (UBA, Universidad de Buenos Aires)

in collaboration with

P. Gimenez Molinelli (UBA)P.Alcain (UBA)J. Nichols (UBA)&J. Lopez(UTEP)

IWNDT 2013

In Honor of

Prof. J. Natowitz

Are both pasta?Are all pasta ?

What is nuclear Pasta?

What is the effect of periodic boundary conditionson the morphology of the system?

What is the role of Coulomb?

What is the role of the Debye screening length on the scale of heterogeneities?

Neutron Star

The model used(Illinois potential) Finite systems

Fragment recognitionCritical behaviorSymmetry energyIsoscalingInfinite systems

(NS matter)

Topology, g(r), The role of coulomb

Intermezzo

2D systemLennard Jones + CoulombLennard Jones and the one pasta cell , the infinite Cluster,etc

Illinois potential

Nuclear MatterNS Matter

The model and finite nuclei

According to original work

Flat CC

, etc

From nuclei to N Stars

(or Debye)

“

“

...

Pasta !Gno

cch

i

Spag

hett

i

Lasa

gna

(related to lindemann coefficient)

X=0.3

=0.10

Fragment Size Distriubution

How to use the Euler number with “pasta” shapes?

The role of coulomb

),,(),,(),,( jiijCouljiijPandhajiij rVrVrV

with

0 α 1

We analyze the behavior of a system driven by:

The role of coulomb

This suggests that there is pastaeven without Coulomb!

=1 (circles)

=0 (squares)

Intermezzo : what is the role of Coulomb?

Lennard Jones + Coulomb

Illinois potential is rather complicated because :

ccaaaccrrrnp rrrrVrrrrVrV /exp/exp/exp/exp)(

ccnn rrrrVrV /exp/exp)( 000

r

vrrrrrVrV cccpp

exp/exp/exp)( 000

Lennard Jones +coulomb

no bump!

as increases

r

vrrr

VrV c

exp)(612

0

The role of coulomb

N=800

no bump, still get ‘pasta’

Cluster recognition in this case:

MST with LRPBC

Single cellanalysis

“Clusters”In the cell(finite)

10 objects

Building the “big” fragments

Infinite

Cluster

Detected

If T>0 apply MSTE to MST Clusters

no bump, still get ‘pasta’

Trivial infinite cluster2 dimensions “no coulomb”

In 3 dimensions, no coulomb

1 structure percell

In the absence of coulomb we still get “Pasta” but just one structure per cell

The scale is fixed by the cell

When coulomb is switched on and is above the “critical value” we get “True Pasta”, multiple structures per cell

The scale is fixed by the potential

Finite size, periodic boundary conditionsand the appearance of “Pasta” without Coulomb

The system is finite but not too small, particles interact by a short range potential

Given a configuration we can write

surfbulk EEE

Surfaces

1 sphere

1 cylinder 1 slab

Nuclear Matter CMD

Back to CMD

B1=SCBB2=BCCBB3=Diam.B

Nuclear Matter

Illinois Potential Medium

Nuclear Matter

Illinois Potential Medium

Low T structures

Nuclear Matter

Illinois Potential Stiff

Nuclear Matter

MINI CONCLUSION

Same as in 2D Lennard Jones for < c

Without Coulomb (i.e. Nuclear Matter)

all of the “Nuclear Potentials” Display

“1 cell Pasta”

Illinois potential + screened Coulomb NS Matter?

We now explore:

The effect of varying

The effect of varying the temperature

Clusters as a function of T

As before we fix the density and then we vary in order to see at which point the solution goes to a single structure per cell

=0.04T=0.001

=20 =15 =10

=8

If we vary theTemperature….

We now calculate de Lindemann coefficient

i

iL N

r

a

2

´

1

Clusters in 3D with T

T=0.0001

T=0.8

MSTE (rc=3.0)

MSTE(rc=5.4)

MST (rc=3.0) MST (rc=540)

2.2

exp)( 0

sqsf

T=4.5 MeVMSTE(rc=5.4)

The effect of the cell geometry

We now evaluate the effect of using different geometries of thePrimitive cell used in the simulation

ρ=0.08 fm-3 A=1728

A=4096

Conclusions

Systems with competing interactions undergo “pasta” formation atLow temperatures

Systems with hc + attractive interactions (i.e. LJ) display “1 per cell pasta” at Low Temperatures

This systems can be properly described byMinkowsky functionalsCorrelation functionsFragments mass distributions

When the long range part of the potential is of the form Coulomb+Debye screening there is a c such that below it, the systems moves into the “1 per cell pasta” regime

A jump in energy when increasing T associated with morphological change has been detected, Also in the Lindemann coefficient

Fragments are to be recognized using MST+Reconstruction at T0MeV

When fragments are properly identified, a line of power law is detected

71

Thank you