Adil BahalimDavidson College

Dr. Joseph Natowitz (Advisor), Dr. Seweryn Kowalski (Mentor)Summer REU 2005 – TAMU Cyclotron Institute

Reconstruction Main hurdle is secondary decay

(intermediate mass fragments) which makes it difficult to reconstruct primary fragments

Antisymmetrized Molecular Dynamics (AMD) calculations used have shown to be good models for reconstruction

Mean multiplicities (obtained from experiment) and distributions widths (difficult to obtain) of LP’s are used as input parameters in GEMINI

GEMINI is a statistical modeling code that uses the Monte-Carlo method to simulate sequential binary decays of nuclei

Heavy Ion Collisions

Background

AMD Model Reconstruction

Figure 1. Immediately after the collision, the system undergoes a multifragmentation process. Primary fragments emerge from the projectile and target nuclei. These fragments separate and de-excite during secondary emission, decaying to secondary fragments while giving off light charged particles and neutrons.

Figure 2. In this previous study, AMD Model calculations were used to reconstruct simulated decays of several IMF’s. The filled stars represent the original parent nuclei. The open stars show the reconstructed parent nuclei. There is a good fit between the two, making this a reasonable model for reconstruction.

Simulated 1000 decay events for each nucleus from Z=3 to Z=40 with at least one from each:

Stability line (i.e. ~ Z = N) Proton-rich side (~ Z > N) Neutron-rich side (N > Z)

Excitation energies ranged from 2 to 5 MeV/amu in .5 MeV/amu increments

Assumed constant inverse level density parameter (8)

Procedure

Distribution Widths vs. Mean MultiplicitiesSimulation Data

Figure 3. A typical sample of data gathered by GEMINI of each of the light particles emitted during decay. These data were collected for the decay of the 95Zr.

Neutron Width vs. Mean Multiplicity Z=3 to Z=40

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M ean M ultiplicity

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Proton Width vs. Mean Multiplicity Z=3 to Z=40

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Deuteron Width vs. Mean Multiplicity Z=3 to Z=40

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Triton Width vs. Mean Multiplicity Z=3 to Z=40

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3Helium Width vs. Mean Multiplicity Z=3 to Z=40

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4Helium Width vs. Mean Multiplicity Z=3 to Z=40

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Mean Multiplicity

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Figure 4. Global plots of all series from Z=3 to Z=40 with excitation energies from 2.5 MeV/amu to 5 MeV/amu for each of the light particles emitted. Though on different scales, all plots show a positive trend as the mean multiplicities of the particles increase. 4He has a greater spread than the rest of the particles. A possible cause is the limitation of the computer code.

GEMINI Simulations

Conclusion

As expected, we found the relation between the mean multiplicities and distribution widths of the LCP’s and neutrons

These relations can be used as references to determine the distribution widths from the experimental data on mean multiplicities and implement them as input parameters for the reconstruction models

Results

Best Fit Function at Exc. Energy = 3 MeV/amu

Neutron Width vs. Mean Multiplicity at Exc Energy = 3 MeV/amu

y = 0.6065x0.3583

R2 = 0.9766

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M ean M ultiplicity

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Proton Width vs. Mean Multiplicity at Exc Energy = 3 MeV/amu

y = 0.6859x0.3549

R2 = 0.9192

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M ean M ultiplicity

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Deuteron Width vs. Mean Multiplicity at Exc Energy = 3 MeV/amu

y = 0.9245x0.5224

R2 = 0.9778

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M ean M ultiplicity

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Triton Width vs. Mean Multiplicity at Exc Energy = 3 MeV/amu

y = 0.9534x0.4914

R2 = 0.9989

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M ean M ultiplicity

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3Helium Width vs. Mean Multiplicity at Exc Energy = 3 MeV/amu

y = 0.9185x0.4813

R2 = 0.9976

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M ean M ultiplicity

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4Helium Width vs. Mean Multiplicity at Exc Energy = 3 MeV/amu

y = 0.9637x0.5068

R2 = 0.7343

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Figure 5. Width vs. Mean Multiplicity plots for each light particle for all nuclei simulations at an excitation energy of 3 MeV/amu. Power functions had the best fits to these plots. All fits, excluding 4He, have a correlation coefficient, R2, of greater than .90.

Neutron Power-Function Parameters A & B (y=AxB)

Figure 6. The graph on the right shows the values of the power-function fit parameter A at each of the excitation energies. The graph on the left shows the values for B. There is an almost linear trend for each parameter.

Proton Power Function Parameter A vs. EE

y = 0.016x + 0.6331

R2 = 0.7808

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Excitation Energy

Param

eter A

Proton Power Function Parameter B vs. EE

y = 0.014x + 0.3183

R2 = 0.8711

00.05

0.10.15

0.20.25

0.30.35

0.40.45

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Excitation Energy

Param

eter A

Using GEMINI to study multiplicity distributions of light charged particles and neutrons