1. M ULTIPLE S CATTERING CM34 @ RAL Timothy Carlisle 1

2. I NTRO. MICE performance predicted using the cooling formula (CF): G4MICE ≠ CF (see prev CMs) Simulation disagrees with C.F by up to 20%. MS calc. typically approx.: CF uses Rossi-Greisen (1941). Somewhat crude. Rutherford scattering law - simplest description of MS. 2 N

3. R UTHERFORD MS Rutherford  tends to infinity at θ=0 Apply limits:  Lower cut-off by Uncertainty Principle: (Thomas-Fermi model of the atom)  Upper by rel. size of nucleus: Integrate, giving : 3 Rutherford Form. I - with hard limits for scattering

4. D ERIVING THE PDG FORM 1941: Rossi-Greisen 1974 - PDG - log correction to R-G (by Highland) removes strong path length dep. * Z dep. remains however* PDG values for X 0 include e-  R-G implicitly incl. atomic e- scatters. However...  Heavy particle scatters off e- have a rel. small max. angle.  Limited by kinematics.  Not incl. by R-G/PDG 4 4 Definition of X 0 :  Log terms cancel..., substitute X 0 into diff. eqn. 

5. S CATTERING OFF A TOMIC ELECTRONS e- collisions are significant, increasingly at low Z. Include e- by using different limits for e- scatters.... integrate to get: However - Also need to include screening of the nuclear potential by e-s. Rutherford Form. II - with sep. hard limits for nuclear & electron scatters 5

6. A TOMIC S CREENING N e - screened nucleus Wenztel-Moliere Form. Atomic e-s reduce nuclear charge seen by muon. 1927: Wentzel assumed exponential scattering potential, used Born Approximation.  later corrected by Moliere 6 Integrate to get:

7. C OMPARISON OF F ORMULAE 7 Mean Sq. Angle of scattering / X 0 (Z). Muons at 200 MeV/c. electrons (W-M) Total – Wentzel-Moliere nuclei (W-M) Total – Rutherford w. hard limits PDG R-G

8. S IMULATION OF M ULTIPLE S CATTERING 8

9. S CATTERING IN SIMULATION CODE Geant4 : several different scattering models! Urban (default), Wentzel-VI & CoulombScattering model Compared with MuScat in *, Urban ‘ worst ’ of the 3. Urban used by LHC sim. exps., quoted as 1% precision. Used by MAUS – now builds with the latest version G4.9.5.p01. ELMS Uses knowledge of photoabsorption cooeffs to describe atomic structure. Only for LH 2, only useable through ICOOL at present... Can we build a Monte Carlo using the Wentzel-Moliere Z-section? 9 * Geant4 models for simulation of multiple scattering V N Ivanchenko et al 2010 J. Phys.: Conf. Ser. 219 032045 YES!

10. C OBB -C ARLISLE M ODEL New Monte Carlo Model, based on Wentzel-Moliere X-section Simulates muons fired through block of absorber material. Predicts. Integrate over angle and thickness Gives N nucleus & N electron scatters. E.g. for 10.9cm LH 2 ~ 36,000 scatters (total). Nuclear scattering angles distributed as: Integrate over angle, solve: Sum for all collisions = total scat. angle. Can compare with MuScat results... 10

11. M U S CAT A BSORBERS 11

12. C OMPARISON FOR 10.9 CM LH 2  2 ~12  2 ~15 vs. MuScat 12 Probability / radian Cobb-Carlisle Model MuScat ELMS Geant4.7.0p01

13.  2 ~130 vs. MuScat Probability / radian 13 C OMPARISON FOR 0.15 CM AL Cobb-Carlisle MuScat Geant4.7.0p01

14. Fe Al C Be 14 C OMPARISON WITH MUSCAT

15. MS MEASUREMENTS IN S TEP IV [CM32] Use MAUS to evolve tracks to downstream face of absorber. Use tracker hits as starting values. Scattering angle is the angle between two vectors. Model tracker resolution by smearing. Tracker code status? MICE Note #90 15

16. AFC + LH 2 Smear 10 20 30 40 50 60 70 80 No Smear 16

17. S UMMARY Longstanding disagreement between Geant4/ICOOL & CF. New Monte Carlo model. Simple, uses 4 parameters. Doesn’t incl. energy loss correlations (unlike ELMS). V. good agreement with LH 2, less so at higher Z. Unclear why! Thomas-Fermi model less accurate at low Z... Need to explain atomic structure better  encapsulated by. Eq. Emittance lower than CF, ~20% less for LH 2 – consistent with Geant4. New Geant4.9.5.p01 to be tested shortly. How close to MuScat? Step Length dependencies fixed? Step IV can & should measure MS. Complement MuScat measurements. Test of physics models. Resolution covered @ CM32 – to be revisited. 17

18. E XTRAS 18

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21. 21 1990 - Lynch & Dahl expression “much better approximation...agrees with Moliere scattering to 2% for all Z ”... Derivation / comparison with Highland / Moliere not supplied! doesn’t seem to have replaced Highland…

22. 22 G4MICE: Step IV 63mm LiH Note: known Step Length problems at 1mm, as used in these simulations [old Geant4 version].

23. 23  z LiH = 6.3 cm  z LH2 = 57.6 cm Note: known Step Length problems at 1mm, as used in these simulations [old Geant4 version].

24. E Q. E MITTANCE & S CATTERING A NGLE (S TEP L ENGTH ) Pencil beams sent through absorber block 24