Compton Photon CalorimeterGregg Franklin, B. QuinnCarnegie Mellon

Design Considerations• Light Yield and Photoelectrons• Detector Geometry, EGS Simulations, Linearity• Decay time• Crystal Properties

,

,

energy of bin i

mean photoelectrons per photon of energy

=mean number of photons of energy

pe i i iphotonenergybin

i

i i

i i

n N E

where

E

E

N E

First, write mean total photoelectrons as:

Calculate contribution of finite photoelectrons per MeV energy deposited

(integrated flux) x (Compton cross section d/dE) x (bin size)

• Light yield and Photoelectrons

22i ii

22i ii

-( ) / 2-(N ) / 2pe i

-( / ) /(2 / N )-(N ) / 2

Prob(n , E ) e e

e e (using N )

i pe ii

pe i i ii

E n EN

n E ENi

2 2 2,

1= (1+ ) n i i i ii

E N E

max 2

0,

max

0

11

E

n sumEsum

Esum pe

dNdE E

dE EdNE n dE EdE

Probability of getting npe photoelectrons from Compton Photons of energy Ei

photonsphotonsgiving npe photoelectrons

Convolution of two gaussians gives variance for npe,i:

If energy independent, error on summed energy is: Finite photoelectronterm small ifEmax large

Measured Energy Deposited (MeV)

20 MeV

5 MeV

1MeV

Measured energy deposited for1 Mev, 5 MeV, and 20 MeV energy deposions

Photoelectrons not a big issue for integrated energy

BUT: Electron tagged data may be easier to analyze with more photoelectrons

+Other calibration issues?

Simulation includes onlyphotoelectron statistics andPMT gain variance

• Detector Geometry, EGS Simulations, Linearity

EGS simulation by Brian Quinn

12.75 MeV photons

ISaint-Gobain“BrilLanCe 380”LaBr3(Cd)

Density: 5.29 g/cm3

1 inch diam.4 inch thick(~ 5.3 rad lengths)

Energy Deposited

511 keVescape peaks

Infinite slab still looses energy due to backscattering

Finite slab energy loss goes up with photon energy

Linearity improves with thickness,but is it important? 4 inches

5 MeV

25 MeV

1% change inanalyzing power

1 MeV

Analyzing Power of summed Deposited Energy as function of Deposited Energy Threshold

% change in Analyzing Power

1.5%

3.0%

EDep Thresh.

EDep Thresh.

• Decay Time Consideration

Why not use BGO (decay time ~300 nS)?• Bremstrahlung

• If ~10 kHz and “deadtime” 3* 300 ns, get 1% deadtime• Other

• Coincidence and singles data• Electronics set up for ~100 nS gate• Larger background from tails

Prefer faster decay time (50 ns?)

PbWO4 BGO GSO CeF3BriLanCe

380PreLude

420

Density

(6/cm3)8.30 7.13 6.70 6.16 5.29 7.1

Rad Length

(cm)0.90 1.12 1.39 1.68 ~1.9 1.2

Moliere Radius

(cm)2.0 2.3 2.4 2.6 ? ?

Decay time

(ns)50 300 56:600 30 16 41

Light output

(% NaI)0.4% 9% 45% 6.6% 165% 84%

photoelectrons

(# / MeV)8 170 850 125 3150 1600

$$$

4 in max

Natural

decay

• Crystal Properties

Need to settle on crystal (at least for test)

Test FADC algorithm at CMU this summer• Gated and integrating modes (simulate summing algorithm)• Does ADC sum represent #photoelectrons?

• Test resolution on sources• Need to slow down signal?• Possibly clip large pulses?

Better linearity simulations• GEANT4 (Optimization by Guido, some work at CMU)

This summer