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 conditions on 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 recognition Critical behavior Symmetry energy Isoscaling Infinite systems (NS matter) Topology, g(r), The role of coulomb Intermezzo 2D system Lennard Jones + Coulomb Lennard Jones and the one pasta cell, the infinite Cluster,etc Illinois potential Nuclear Matter NS Matter
The model and finite nuclei
According to original work
Flat CC, etc
From nuclei to N Stars
(or Debye) “ “
...
Pasta ! Gnocchi Spaghetti Lasagna
(related to lindemann coefficient)
X=0.3 =0.1 0 Fragment Size Distriubution
How to use the Euler number with “pasta” shapes?
The role of coulomb with 0 α 1 We analyze the behavior of a system driven by:
The role of coulomb This suggests that there is pasta even without Coulomb! =1 (circles) =0 (squares)
Intermezzo : what is the role of Coulomb? Lennard Jones + Coulomb Illinois potential is rather complicated because :
Lennard Jones +coulomb no bump! as increases
The role of coulomb N=800
no bump, still get ‘pasta’
Cluster recognition in this case: MST with LRPBC Single cell analysis “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 cluster 2 dimensions “no coulomb”
In 3 dimensions, no coulomb 1 structure per cell
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 conditions and 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 Surfaces
1 sphere 1 cylinder 1 slab
Nuclear Matter CMD
Back to CMD B1=SCB B2=BCCB B3=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 =0.04 T=0.001 =20 =15 =10 =8
If we vary the Temperature….
We now calculate de Lindemann coefficient
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)
T=4.5 MeV MSTE(rc=5.4)
The effect of the cell geometry We now evaluate the effect of using different geometries of the Primitive cell used in the simulation
ρ=0.08 fm -3 A=1728 A=4096
Conclusions Systems with competing interactions undergo “pasta” formation at Low temperatures Systems with hc + attractive interactions (i.e. LJ) display “1 per cell pasta” at Low Temperatures This systems can be properly described by Minkowsky functionals Correlation functions Fragments 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 T 0MeV When fragments are properly identified, a line of power law is detected
71 Thank you