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