1. Neutron and 9Li Background Calculations
Peter Fisher/Jon Link
Oct. 27, 2005
Peter Fisher - MIT

2. Checks on neutron background calculations
Outline
Previous results
Checks on neutron background calculations
9Li production: reinterpetation of Hagner experiment
Peter Fisher - MIT

3. Previous Results GEANT4 Calculation: 0.8 neutron/day at vessel
All neutrons originating from closer than 6 m are vetoed; high premium on veto efficiency
Peter Fisher - MIT

4. Simple Calculation (J. Link):
Pilcher-Hurwitz muon energy spectrum and angular distribution at 450 MWE
Based on Wang et al. neutron energy spectrum
MARS used to transport neutrons through rock (~150/ton/day in rock surrounding the detector)
0.93% survive passage through 1m of heavy concrete and 0.5 m mineral oil
20% of neutrons reaching vessel have 0.8<T<8 MeV
88% of neutrons reaching vessel have veto muon
0.47 unvetoed fast neutrons/day reaching the detector
Peter Fisher - MIT

5. 9Li (J. Link)
Scaled from KamLAND, 1.5 GeV tag on muons losing more than 1.5 GeV in the detector tags 85% of all 9Li
A 0.5 s veto would eliminate 85% of all 9Li decays, giving overall efficiency of 72% for getting rid of 9Li decays with 7% deadtime.
The Veto Working group has spent the last few months checking these calculations and understanding 9Li production.
Peter Fisher - MIT

6. Neutron background: comparison between hand calculation (Noel Stanton) and GEANT4 (Peter Fisher) for very specific muon source geometries located just outside the shield:
Line source
Sheet source
Peter Fisher - MIT

7. Unvetoed, 1<En<10 MeV* 101 86
Sheet
(x 10-6n/m)
Line
Unvetoed, 1<En<10 MeV*
101 86
Simple calculation
130
250
*Roughly 10% of neutrons have energies greater than 10 MeV
Intuitively, one would expect the number of neutrons form the line source to be greater than from the sheet. More work needs to be done.
Peter Fisher - MIT

8. Where do the neutrons come from?
Toy model spreadsheet calculation
(Spherical symmetry; point production of neutrons;
neutrons travel in straight lines; effective neutron attenuation lengths; H&P muons; Wang neutrons/muon)
Sources of neutrons (spherical geometry):
Fiducial volume, r=260 cm
Oil buffer, thickness 85 cm
Steel vessel, thickness 5.0 cm
CHESS shield, thickness 100 cm, “counters” on outside
Dolomite rock, starts 100 cm outside shield
Parameters: effective attenuation lengths in each medium; muon detection inefficiencies of “counters”, fiducial volume, oil buffer
Peter Fisher - MIT

9. Toy model: calculate neutrons/day into fiducial volume
Note: Fake IBD rate has further reduction factors, ~1/5
“Base” rate: contribution without shielding or tagging
“Mitigated” rate: includes passive shielding
Untagged rate: includes also muon tagging
The two examples below use extremes of  for oil; same tagging effic
We must understand effective  for H-rich stuff (oil, water) !
Peter Fisher - MIT

10. Toy model neutrons/day into fiducial volume (continued)
Examples below have optimistic  for oil, varying tagging efficiency
Looks like we want shield “counter” efficiency > 99%
Peter Fisher - MIT

11. 9Li Production m 9Li m n p 9Li 12C(n,n3p)9Li
Hagner et al. (Astropart. Phys. 14(2000)33 measured σ(μ+12C->9Li+X) assuming 9Li was produced directly in μ-nucleon interactions: m
9Li
However, it seems unlikely to produce 9Li directly for Eμ>10 GeV. From our studies, it appears the process looks like this: m
Deep inelastic
scattering n p
9Li
Neutrons are produced ~20 cm from muon axis.
12C(n,n3p)9Li
Peter Fisher - MIT

12. For the case of the multi-step process and, since the neutron energy spectrum is relatively independent of Em for Em>10 GeV, the production of 9Li breaks into two parts:
Production of neutrons by muons, the number of neutrons increases with muon energy but shape of neutron spectrum remains the same(peaks around 100 MeV)
Production of 9Li by neutrons (integral of s(12C(n,n3p)9Li) over neutron energy spectrum
Bottom line: if we determine #2 from 9Li production anywhere from a known muon source, we know it at any depth
Peter Fisher - MIT

13. If 9Li production is a multi-step process, what did Hagner measure anyway?
Hagner measured 9Li production in scintillator target cell from 190 GeV muons.
Result:
This is geometry dependent and hence not really a cross section! However, can use this to extract a cross section for 12C(n,n3p)9Li.
Peter Fisher - MIT

14. Calculations and measurements collected by Steve Dytman
Common thread:
All have approximately linear rise starting at 50 MeV and flattening at 100 MeV. Roughly, can think of single parameter: cross section at 100 MeV.
Peter Fisher - MIT

15. Analog of hagner setup using Braidwood GEANT4 MC. Rock
Use (100MeV)=0.2mb
20 million incident muons gives:
369 9Li events total
14 9Li events in target cell
47 9Li event in Z slice.
Number of events in target cell corresponds to =2.2 b consistent with Hagner
Using Hagner cross section would underestimate the total number of 9Li by a factor of three!
Rock
240 cm
Shield
100 cm
Vessel
Z slice
Buffer
88 cm 
Target Cell
Peter Fisher - MIT

16. Simple Calculation (Noel Stanton)
R(9Li)=(F *G * M) * f * n * <L> * 
Muon flux (P&H)
Neurons/muon/g/cm2 (Wang)
Detector mass
Takes into account rise in
Cross section from MeV
Target density
Attenuation weighted neutron
Pathlength (=69 cm)
Using 9Li rate from KamLAND, =0.64 mb
Applying to Braidwood gives a rate of 7/day
Peter Fisher - MIT

17. Conclusions
Given the limitations of the calculations (statistics for GEANT4 and approximations for simple calculation), the agreement for neutrons is reasonable. Results for the sheet source will be investigated further.
For 9Li, there is a factor of three difference in extracted cross section, again consistent with the limitations of the calculations. For purposes of future calculation, a cross section of (12C(n,n3p)9Li, En>100 MeV)=0.64 mb should be used. The Hagner cross section should not be used.
We plan to use our GEANT4 code to estimate the 9Li rate for Braidwood based on the cross section in Point 2. After that, we will retire our code and use RAT.
Peter Fisher - MIT

18. Conclusion (cont.)
Our next simulation task will be to validate RAT with previous results.
Noel Stanton has made a first cut at how measuring backgrounds in situ and we plan to use RAT to continue this study.
Peter Fisher - MIT