nuclear pasta ?
DESCRIPTION
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 all pasta ?. Are both pasta?. What is nuclear Pasta? - PowerPoint PPT PresentationTRANSCRIPT
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