a classical mechanics study of isoscalingscoccola/iguazu/ntd/05_ntd5-lopez.pdf · p-n stability...
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A classical mechanicsstudy of isoscaling
Isoscaling is studied using classical molecular dynamicssimulations of several reactions at various energies.
Isoscaling at different stages of the reaction wascalculated and the validity of the isoscaling power law
was estimated.
Copyright, 1996 © Dale Carnegie & Associates, Inc.
Jorge A. LópezUniversity of Texas at El Paso
OutlineOutline• P-N Stability, Isoscaling, etc.
• Latino Model
• Energy dependence of isoscaling (at long times)
• Time evolution of isoscaling
• Isoscaling and reaction dynamics
• Conclusions
PP--N stabilityN stabilityCoulomb repulsion – nuclear attraction Stability
(between protons) (between p-p, pn, and nn)
Number of protons ~ number of neutrons
Spherical symmetry
N~Z
N~1.4 Z
???
???
What if N is
different from P?
N-P ratio – who cares?
It pays to study it!
How to study it: disrupt stabilityHow to study it: disrupt stabilityNuclear reactions:
Start with a nucleus with a fixed N-P
ratio
Shoot a particle to form a compound
nucleus
Let it decay, final nucleus will have a different N-P ratio
During its short life, use final nucleus for
experiments, etc.
How to study it: disrupt stabilityHow to study it: disrupt stabilityAnother type of reactions:
Start with two nucleus with a fixed
N-P ratio
Again, use final nucleus for
experiments, etc.
Create a collisions to form a compound
nucleus
Let them decay, final nuclei will have a different N-P ratio
IsoscalingIsoscaling, a N, a N--P ratio effectP ratio effectPerform a heavy ion
reaction leading to fragmentation
Repeat many times and count number of fragments of each size
Repeat experiments with similar nuclei with other N-P ratio and compare
IsoscalingIsoscaling, a N, a N--P ratio effectP ratio effectRepeat experiments with similar nuclei with other N-P ratio and compare
A bit of theory to explain A bit of theory to explain isoscalingisoscalingFrom a presentation of C.O. DorsoFrom a presentation of C.O. Dorso
How to study How to study isoscalingisoscalingUse molecular dynamics to simulate nuclei and make collisions with them
Repeat many times varying the nuclei and their relative energies
Collect information and produce the isoscalingratio at different times
Conclude something, publish it, get famous, be happy
Latino: Latino: molecular dynamics + fragment recognition
Potential:Potential:
Now use model to study isoscalingNow use model to study isoscaling
•• Solve equation of motion (Solve equation of motion (VerletVerlet))
•• Recognize clusters (MSE)Recognize clusters (MSE)
•• Track evolutions in spaceTrack evolutions in space--timetime
•• Determine mass distributionsDetermine mass distributions
•• Determine caloric curvesDetermine caloric curves•• Determine critical phenomenaDetermine critical phenomena
Isoscaling and EnergyIsoscaling and Energy
Determine if isoscaling exist for all energies, Determine if isoscaling exist for all energies, track behavior of track behavior of αα and and ββ
•• 4040Ca+Ca+4040Ca, Ca, 4040Ca+Ca+4848Ca, Ca, 5252Ca+Ca+5252CaCa•• E= 20, 25, 35, 45, 65, 85 E= 20, 25, 35, 45, 65, 85 MeVMeV/A/A•• 2000 collisions per case2000 collisions per case•• Calculate Calculate
at asymptotic times (5000 fm/c) at asymptotic times (5000 fm/c)
•• Fit to Fit to
40Ca - 48Ca at 35 MeV/A at 1250 fm/c
•• Isoscaling exists:Isoscaling exists:Isoscaling at Isoscaling at asymptotiaasymptotia
Isoscaling exists at long timesIsoscaling exists at long times
Asymptotic (t=5000 fm/c)
α and βhave a smooth
dependence on energy
Isoscaling and energyIsoscaling and energy
Compare Compare 4040Ca Ca –– 4848Ca at 35 Ca at 35 MeVMeV/A /A
AMDAMD--V: V: αα=1.03, =1.03, ββ=1.22 Latino: =1.22 Latino: αα=1.07, =1.07, ββ=1.22=1.22
•• Isoscaling exists for all reactions at all energies:Isoscaling exists for all reactions at all energies:
Isoscaling and TimeIsoscaling and Time
Determine if isoscaling exist at all times, track behavior of α and β
•• 4040Ca+Ca+4040Ca, Ca, 4040Ca+Ca+4848Ca, Ca, 5252Ca+Ca+5252CaCa•• t = 75, 125, t = 75, 125, …… , 5000 fm/c, 5000 fm/c•• 2000 collisions per case2000 collisions per case•• Calculate Calculate
•• Fit to Fit to
Isoscaling at early times
Isoscaling exists since early in the reaction
40Ca - 48Ca at 35 MeV/A at
125 fm/c
Isoscaling at Isoscaling at very very early timesearly times
Isoscaling exists since very early in the reaction
40Ca - 48Ca at 35 MeV/A at
75 fm/c
α and β have a smooth
time evolution
40Ca - 48Ca at 35 MeV/A
Evolution of IsoscalingEvolution of Isoscaling
Isoscaling exists from impact and survives collisionIsoscaling exists from impact and survives collision
•• Isoscaling exists for all times:Isoscaling exists for all times:
Isoscaling and reaction dynamics
Try to link isoscaling (α and β) to the reaction
• Expected:
• Track T, mass, KE, radial velocity oflargest fragment
• For Fermi gas:
Isoscaling and reaction dynamics
Black: 40Ca Red: 48Ca
at 35 MeV/A
Compression-Expansion
30% in ΔT
μ varies during reaction => α and β cannot be linked to specific μ or T
Isoscaling and reaction dynamicsIsoscaling and reaction dynamics
μ varies during reaction => α and β cannot be linked to specific μ or T
Isoscaling cannot reflect thermodynamic conditions of a single time
ConclusionsConclusions√ Latino produces isoscaling
Not a quantum effect
√ Isoscaling is seen at all energiesNot specific to late decay modes
√ Isoscaling is seen at all timesCan be formed in and out of equilibriumIs cumulative, i.e. it has contributions from different times
√ Isoscaling not linked to reaction variablesDoes it reflect specific values of μp, μp, T, etc.?
√ Isoscaling is probably linked to “fair sampling”See our next paper
¡¡Gracias!Gracias!
Submitted to PRC Submitted to PRC –– and still fighting the referee!!!and still fighting the referee!!!
¡¡Gracias!Gracias!
Jorge A. LópezUniversity of Texas at El Paso
jorgelopez@utep.edu
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