Opportunities for statistical methods in nuclear reactions: Streamlining calibrations and improving sensitivity

Crab Nebula, HST Image IV Proj Targ V‖V‖ ~v p ~ ½v p V⊥V⊥ Supernova Mass: 4.6 ± 1.8 M ⊙. (~9.2x10 30 kg) Temperature: 100 GigaKelvin IV Source ‘femtonova’ Mass: amu (~3.3x kg) Temperature: 100 GigaKelvin Nuclear Reaction from Heavy Ion Collision

TAMU Cyclotron Institute

Heavy Ion Reactions Projectile Target - stationary Impact Parameter (b) Large b, forward focused, few fragments Peripheral

Heavy Ion Reactions Projectile Target Impact Parameter (b) b~0, still somewhat forward focused, many fragments Central

Heavy Ion Reactions Projectile Target Impact Parameter (b) Mid b, forward focused, range of fragment multiplicity Mid-Peripheral

Heavy Ion Reactions : what we observe Each detected event (1-30 particles/event) ….hundreds of millions of events

Example problems that better algorithms might solve: Particle Identification, Calibration, Position – Can take years to process these plots by hand  Functional Data Clustering Online/offline analog signal analysis  Neural network Signal Dimensionality Reduction  Sliced Inverse Regression Spectra fitting – Error estimates are very large, could improve confidence in the uniqueness of the result

What is NIMROD? Large, multi-detector array for observing reactions between massive targets and projectiles – Total of 228 detector modules arranged in 14 annular rings 2-3 detectors/module – Projectile energies ranging from 20MeV to 4GeV – Measure 10s of fragments for each nucleus-nucleus collision Example Detector Module ΔEΔE E

DetNum1, ΔE1, E1 DetNum2, ΔE2, E2 DetNum3, ΔE3, E3 DetNum4, ΔE4, E4 DetNum5, ΔE5, E5... up to 20 or 30 DetNum1, ΔE1, E1 DetNum2, ΔE2, E2 DetNum3, ΔE3, E3 DetNum4, ΔE4, E4 DetNum5, ΔE5, E5... up to 20 or 30 Event 1 Event 2 DetNum1, ΔE1, E1 DetNum2, ΔE2, E2 DetNum3, ΔE3, E3 DetNum4, ΔE4, E4 DetNum5, ΔE5, E5... up to 20 or 30 Event s of millions of events Z1, A1, E1, θ1, φ1 Z2, A2, E2, θ2, φ2 Z3, A3, E3, θ3, φ3 Z4, A4, E4, θ4, φ4 Z5, A5, E5, θ5, φ5... up to 20 or 30 Z1, A1, E1, θ1, φ1 Z2, A2, E2, θ2, φ2 Z3, A3, E3, θ3, φ3 Z4, A4, E4, θ4, φ4 Z5, A5, E5, θ5, φ5... up to 20 or 30 Z1, A1, E1, θ1, φ1 Z2, A2, E2, θ2, φ2 Z3, A3, E3, θ3, φ3 Z4, A4, E4, θ4, φ4 Z5, A5, E5, θ5, φ5... up to 20 or 30

FAUST  68 Si-CsI(Tl) Telescopes  Dual-Axis Duolateral Silicons – Improve Angular Resolution – Uniform resistance – Charge-splitting – Position resolution <200 μm E ΔEDΔED ΔELΔEL ΔERΔER ΔEUΔEU

DetNum1, ΔEL1, ΔER1, ΔEU1, ΔED1, E1 DetNum2, ΔEL2, ΔER2, ΔEU2, ΔED2, E2 DetNum3, ΔEL3, ΔER3, ΔEU3, ΔED3, E3 DetNum4, ΔEL4, ΔER4, ΔEU4, ΔED4, E4 DetNum5, ΔEL5, ΔER5, ΔEU5, ΔED5, E5... up to 20 or 30 Event 1 Event 2 Event s of millions of events Z1, A1, E1, θ1, φ1 Z2, A2, E2, θ2, φ2 Z3, A3, E3, θ3, φ3 Z4, A4, E4, θ4, φ4 Z5, A5, E5, θ5, φ5... up to 20 or 30 DetNum1, ΔEL1, ΔER1, ΔEU1, ΔED1, E1 DetNum2, ΔEL2, ΔER2, ΔEU2, ΔED2, E2 DetNum3, ΔEL3, ΔER3, ΔEU3, ΔED3, E3 DetNum4, ΔEL4, ΔER4, ΔEU4, ΔED4, E4 DetNum5, ΔEL5, ΔER5, ΔEU5, ΔED5, E5... up to 20 or 30 Z1, A1, E1, θ1, φ1 Z2, A2, E2, θ2, φ2 Z3, A3, E3, θ3, φ3 Z4, A4, E4, θ4, φ4 Z5, A5, E5, θ5, φ5... up to 20 or 30 DetNum1, ΔEL1, ΔER1, ΔEU1, ΔED1, E1 DetNum2, ΔEL2, ΔER2, ΔEU2, ΔED2, E2 DetNum3, ΔEL3, ΔER3, ΔEU3, ΔED3, E3 DetNum4, ΔEL4, ΔER4, ΔEU4, ΔED4, E4 DetNum5, ΔEL5, ΔER5, ΔEU5, ΔED5, E5... up to 20 or 30 Z1, A1, E1, θ1, φ1 Z2, A2, E2, θ2, φ2 Z3, A3, E3, θ3, φ3 Z4, A4, E4, θ4, φ4 Z5, A5, E5, θ5, φ5... up to 20 or 30

Particle Identification Plot combinations of detectors in modules Example Detector Module ΔEΔE E CsI (E) Si (ΔE) vs CsI (E) Si (ΔE) vs Si (ΔE)

Particle Identification Plot combinations of detectors in modules Place points along each major line, by hand E ΔE Example Detector Module ΔEΔE E

Particle Identification Plot combinations of detectors in modules Place points along each major line, by hand Use points to straighten the lines, project onto x-axis – Identify Z,A of particle Be, B, C, …

Energy Calibration: FAUST Each line corresponds to a constant Energy Ohm’s Law Front 1 Front 2

Energy Calibration: FAUST

Position Calibration: FAUST

15 MeV/u alpha + collimated Au (1mm) Degrees of Freedom: 3 Position 3 Rotation 2 Stretching

DetNum1, ΔE1, E1 DetNum2, ΔE2, E2 DetNum3, ΔE3, E3 DetNum4, ΔE4, E4 DetNum5, ΔE5, E5... up to 20 or 30 DetNum1, ΔE1, E1 DetNum2, ΔE2, E2 DetNum3, ΔE3, E3 DetNum4, ΔE4, E4 DetNum5, ΔE5, E5... up to 20 or 30 Event 1 Event 2 DetNum1, ΔE1, E1 DetNum2, ΔE2, E2 DetNum3, ΔE3, E3 DetNum4, ΔE4, E4 DetNum5, ΔE5, E5... up to 20 or 30 Event s of millions of events Z1, A1, E1, θ1, φ1 Z2, A2, E2, θ2, φ2 Z3, A3, E3, θ3, φ3 Z4, A4, E4, θ4, φ4 Z5, A5, E5, θ5, φ5... up to 20 or 30 Z1, A1, E1, θ1, φ1 Z2, A2, E2, θ2, φ2 Z3, A3, E3, θ3, φ3 Z4, A4, E4, θ4, φ4 Z5, A5, E5, θ5, φ5... up to 20 or 30 Z1, A1, E1, θ1, φ1 Z2, A2, E2, θ2, φ2 Z3, A3, E3, θ3, φ3 Z4, A4, E4, θ4, φ4 Z5, A5, E5, θ5, φ5... up to 20 or 30 E*, E rel, Q shape, T, τ equila, ρ, flow,...

Sliced Inverse Regression Key ingredients of a model  subtle effect on several individual observables SIR method can reduce this to a large effect in a combined observable P. Cammarata et al. Nuclear Instruments and Methods in Physics Research A 761, 1 (2014)

Machine Learning – Analog Signal Analysis Particle ID using Fast-Slow relies on somewhat arbitrary integration limits Machine learning / neural networks analysis of the full digitized pulse should provide better resolution Online (real time) decisions based on pulse features can drastically reduce IO and storage requirements Scintillation Light (arb units) Time (ns)

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