Neutron and/or photon response of a TLD-albedo personal dosemeter on an ISO slab phantom

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Neutron and/or photon response of a TLD-albedo personal dosemeter on an ISO slab phantom Problem P4 Rick J Tanner National Radiological Protection Board Chilton, Didcot, Oxon OX11 0RQ, United Kingdom Intercomparison on the Usage of Computational Codes in Radiation Dosimetry Workshop in Bologna-Italy July 14-17 2003 P4: 1

Albedo dosemeters General features P4: 2

Albedo dosemeters: I Original concept from UKAEA in the 1960 s More than 30 years later still one of the most commonly used personal dosemeters Basic principle relies on the detection of neutrons moderated in the body Sensitive volume shielded from direct neutrons Use capture reactions for detection Shield using material with large thermal neutron capture cross-section P4: 3

Albedo dosemeters: II Albedo field has a strong thermalized component Capture reactions such as 6 Li(n, t) or 10 B(N, α) detect the backscattered field with good efficiency 6 Li(n, t) is particularly useful because LiF is commonly used for thermoluminescence detectors (TLDs) Shield from incident thermals using boron-loaded plastic holder or cadmium Can add an unshielded element to give additional information on field hardness P4: 4

Albedo dosemeters: III Natural lithium is 7.5% 6 Li, 92.5% 7 Li Typically β/γ TL-detectors 99.93% 7 Li Typically neutron TL-detectors 95.6% 6 Li Use four elements: two 7 Li enriched to give the photon response and two 6 Li enriched to give the neutron response Algorithm for dose equivalent involves subtraction of the low LET component and correction for field hardness P4: 5

Important capture cross-sections (JEF-PC) 10 5 10 4 10 3 10 B(n, α) Cross-section (barns) 10 2 10 1 10 0 10-1 6 Li(n, t) Cd(n, γ) 10-2 10-3 10-3 10-2 10-1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 Neutron energy (ev) P4: 6

6 Li cross-sections (JEF-PC) 10 4 10 3 6 Li(n, t) Cross-section (barns) 10 2 10 1 10 0 10-1 Elastic Total 10-2 6 Li(n, p) 10-3 10-3 10-2 10-1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 Neutron energy (ev) P4: 7

P4 Specification P4: 8

Problem Model the photon response using the absorbed dose to the TL-material. Assume light output is proportional to dose. Model the neutron response by counting 6 Li(n, t)α events. Assume that the neutron response is proportional to the number of capture reactions. Calculate the fraction of the neutron and photon response that is due to backscatter P4: 9

Irradiation conditions 30 cm x 30 cm plane parallel source located in a vacuum, incident normal to the front face of the phantom 30 cm x 30 cm x 15 cm ISO, water filled slab phantom (PMMA walls) Dosemeter mounted on the centre of the front face of the phantom P4: 10

Dosemeter Element 1 2 3 4 x-offset -0.75 cm +0.75 cm -0.75 cm +0.75 cm y-offset +1.75 cm +1.75 cm -1.75 cm -1.75 cm 6 Li (%) 95.6 0.07 95.6 0.07 7 Li (%) 4.4 99.93 4.4 99.93 ρ (g cm -3 ) 2.54 2.64 2.54 2.64 Front shielding Back shielding None none 4 mm boron loaded plastic plus 1 mm Al 2 mm boron loaded plastic 2 mm boron loaded plastic none 4 mm boron loaded plastic plus 1 mm Al none P4: 11

Dosemeter Water PMMA (Perspex) Aluminium LiF Boron loaded CH2 P4: 12

Slices through dosemeter back front Aluminium Boron loaded CH2 7 LiF 6 LiF P4: 13

Author s (normalization) solution: PHOTONS P4: 14

General Implied kerma approximation Calculation in vacuum Need air column for secondary charged particle build up Variable depth because of ranges of secondaries Diameter of column? Electron transport will produce significant differences where the ranges of the electrons are significant Rapid calculation 33 kev main problem because of poor penetration Little need for variance reduction Generally very good agreement: refer to paper for results P4: 15

Photon response: author 40 E1: 6 LiF, bare Response (MeV g -1 ) 10 E2: 7 LiF, bare E3: 6 LiF, H p (10) E4: 7 LiF, H p (10) 3 10 100 1000 Photon energy, E γ (kev) P4: 16

Author s (normalization) solution: NEUTRONS P4: 17

Normalization solution: neutrons MCNP-4C F4 tally, track-length estimate of fluence with FM card - pure 6 Li for tally only FM card: ρ atom V (i.e. atomic density of 6 Li multiplied by the volume of the element) Relevant data in MCNP Table 60: atomic density needs to be multiplied by 0.5 6 Li% ENDF/B-vi continuous cross-sections 40 cells, 41 surfaces, six materials S(α, β) for water, and used CH 2 for polymers P4: 18

Source neutrons (fixed CTME): analogue 20 Source neutrons (x10 6) 15 10 5 0 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy (MeV) P4: 19

Analogue, total response 10-3 Response per source neutron 10-4 10-5 10-6 10-7 10-8 10-9 E3: 6 LiF, albedo E1: 6 LiF, direct E4: 7 LiF, albedo E2: 7 LiF, direct 10-10 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) P4: 20

Analogue, backscatter 10-5 E3: 6 LiF, albedo Flagged response per source n 10-6 10-7 10-8 10-9 10-10 E1: 6 LiF, direct E4: 7 LiF, albedo E2: 7 LiF, direct 10-11 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) P4: 21

Normalization solution: VR Main problem is to get thermal neutrons back from the phantom, through boron-loaded plastic to the TL-element Introduced extra cells in the vacuum and phantom to increase the response Used energy dependent weight windows to allow high-energy neutrons to pass through the phantom but increase the number of lower energy neutrons WWE:n = 100 mev, 10 ev, 1 kev, 1 MeV, 10 MeV P4: 22

WWE, total response 10-3 10-4 E3: 6 LiF, albedo Response per source n 10-5 10-6 10-7 10-8 10-9 E1: 6 LiF, direct E4: 7 LiF, albedo E2: 7 LiF, direct 10-10 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) P4: 23

6 Li(n, t) and H p (10)/Φ 10-3 H p (10)/Φ 600 10-4 E3: 6 LiF, albedo 300 Response per source n 10-5 10-6 10-7 10-8 E1: 6 LiF, direct E4: 7 LiF, albedo E2: 7 LiF, direct 100 60 30 Hp (10)/Φ (psv cm2 ) 10-9 10 10-10 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) 6 P4: 24

H p (10) response 10 4 E3: 6 LiF, albedo 10 3 E1: 6 LiF, direct 6 Li(n, t) (µsv -1 ) 10 2 10 1 10 0 10-1 E4: 7 LiF, albedo E2: 7 LiF, direct 10-2 10-3 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) P4: 25

R direct ( 6 Li)/R albedo ( 6 Li) 1.00E+01 Neutron Energy (MeV) 1.00E+00 1.00E-01 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 Direct/Albedo P4: 26

Backscatter: cell flagging for phantom 10-4 E3: 6 LiF, albedo Flagged response per source n 10-5 10-6 10-7 10-8 10-9 E1: 6 LiF, direct E4: 7 LiF, albedo E2: 7 LiF, direct 10-10 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) P4: 27

Backscatter, normalized (flagging) E1: 6 LiF, direct Flagged response per source n 1.0 0.5 E2: 7 LiF, direct E3: 6 LiF, albedo E4: 7 LiF, albedo 0 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) P4: 28

Backscatter fraction (flagging) Flagged response/total Response 1.0 0.5 E4: 7 LiF, albedo E3: 6 LiF, albedo E2: 7 LiF, direct E1: 6 LiF, direct 0 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) P4: 29

BS fraction: flagging and voiding Backscatter response fraction 1.0 0.5 E4: 7 LiF, albedo E3: 6 LiF, albedo E2: 7 LiF, direct E1: 6 LiF, direct Voided phantom 0 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) P4: 30

Participants solutions P4: 31

Participants: codes 17 solutions 16 Monte Carlo 1 deterministic 15 participants transported photons 14 participants transported neutrons 13 solutions using MCNP family of codes 2 solutions using MCNPX One own code (photon only, but can transport n) One each TRIPOLI and PENELOPE P4: 32

Participants: origin 13 solutions from Europe 11 from EU France 4 UK 3 Austria, Greece, Italy Portugal 1 each 2 from Eastern Europe 3 from the US 1 from South America P4: 33

P4-A Comprehensive report Russian roulette to kill neutrons in the water Additional energy: 223 kev peak in the 6 Li(n, t) cross-section shows as an increase in the response more visible as smaller backscatter fraction Careful inspection of cross-sections FM problem Tally all (n, t) P4: 34

Normalized n response: P4-A Backscatter response fraction 10 4.0 1.0 E1: 6 LiF, direct E2: 7 LiF, direct E3: 6 LiF, albedo E4: 7 LiF, albedo 0.4 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) P4: 35

Normalized n response: P4-A. FM corrected 7 Li(n, t) Normalized response 10 5.0 1.0 E1: 6 LiF, direct E2: 7 LiF, direct E3: 6 LiF, albedo E4: 7 LiF, albedo 0.5 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) P4: 36

High energy LiF cross-sections (JEF-PC) 10 0 Q = -3.4 MeV Q = +4.8 MeV 10-1 Cross-section (barns) 10-2 10-3 6 Li Target 7 Li 19 F Reaction (n, p) (n, d) (n, t) (n, α) 10-4 1 2 3 4 5 7 10 20 Neutron energy (ev) P4: 37

Backscatter fraction: P4-A Normalized backscatter fraction 1.0 0.8 0.6 0.4 0.2 E1: 6 LiF, direct E2: 7 LiF, direct E3: 6 LiF, albedo E4: 7 LiF, albedo 0 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) P4: 38

With and without S(α, β) in PMMA: P4-A 1.1 S(α, β): (Water & PMMA)/Water 1.0 0.9 0.8 E1: 6 LiF, direct E2: 7 LiF, direct E3: 6 LiF, albedo E4: 7 LiF, albedo 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 1 Neutron energy, E n (MeV) P4: 39

Thorough report Analogue solution P4-B In air not vacuum: source 2.5 cm from phantom (1.71 cm from front of holder) No 7 Li(n, t) available, but subtracted 19 F(n,t) Initial problem with FM card: neglected cell volume. Later corrected. Tally all (n, t) 4x10 7 histories for all energies Backscatter by energy deposited & flux P4: 40

Normalized response: P4-B 25 20 15 Normalized response 10 7 5 3 2 E1: 6 LiF, direct E2: 7 LiF, direct E3: 6 LiF, albedo E4: 7 LiF, albedo 1.0 0.8 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) P4: 41

Backscatter from F6: P4-B 10 Normalized backscatter 1 0.1 E1: 6 LiF, direct E2: 7 LiF, direct E3: 6 LiF, albedo E4: 7 LiF, albedo 0.01 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 Neutron energy, E n (MeV) P4: 42

Backscatter from F4: P4-B 10.00 E1: 6Li, direct E3: 6Li, albedo E2: 7Li, direct E4: 7Li, lbedo Backscatter fraction 1.00 0.10 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 Neutron energy (MeV) P4: 43

P4-C No report Problem with 7 Li chips: results ~ factor of 10 4 too low 6 Li results ~ 0.4 but energy dependent difference Backscatter by phantom voiding, but not presented here because of problems with total response P4: 44

Normalized n response: P4-C 1.0000 0.5000 0.4500 0.1000 0.4000 E1: 6Li, direct 0.3500 Neutron response 0.0100 0.0010 E2: 7Li direct E3: 6li albedo E4: 7Li albedo Neutron response 0.3000 0.2500 0.2000 0.0001 0.1500 0.1000 E1: 6Li, direct E3: 6li albedo 0.0500 0.0000 0.0000 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 Neutron energy (MeV) Neutron energy (MeV) P4: 45

P4-D No report - late submission Problem with all data ~ factor 100-1000 low Energy dependent difference Backscatter not calculated P4: 46

Normalized n response: P4-D 8.00E-03 Neutron response 7.00E-03 6.00E-03 5.00E-03 4.00E-03 3.00E-03 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo 2.00E-03 1.00E-03 0.00E+00 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 Neutron Energy (MeV) P4: 47

P4-E No report, but input files and comprehensive data supplied Calculation analogue in provided input file Calculated induced photon signal in the chips (would be important in the real dosemeter) Backscatter by phantom voiding P4: 48

Normalized n results: P4-E 1.200 E 1: 6Li, direct 4.00 1.150 E 2: 7Li, Direct 3.50 Neutron Response 1.100 1.050 1.000 0.950 E 3: 6Li, Albedo E 4: 7Li, Albedo Backscatter fraction 3.00 2.50 2.00 1.50 1.00 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo 0.900 0.50 0.00 0.850-0.50 0.800 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 Neutron Energy (MeV) Neutron Energy (MeV) P4: 49

P4-F No report Large energy dependent errors P4: 50

1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 Results: P4-F 100.00 10.00 1.00 0.10 0.01 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo Neutron energy (MeV) P4: 51 Backscatter fraction 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 2.53E-08 1.00E-06 1.00E-05 1.00E-05 1000.000 100.000 10.000 1.000 0.100 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo Neutron energy (MeV) Neutron response 2.53E-08 1.00E-06

P4-G No report Very small statistical uncertainties: 0.3-2.7% Tripoli solution but very close agreement with normalization solution Did not calculate backscatter Only participant to request experimental data P4: 52

Normalized n response: P4-G 1.080 Normalized neutron response 1.060 1.040 1.020 1.000 0.980 0.960 0.940 0.920 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo 0.900 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 Neutron energy (MeV) P4: 53

P4-H Brief report - paper submitted with updated data Generally small statistical uncertainties: 1-3%, but larger for some results Close agreement with normalization solution Backscatter by voiding phantom P4: 54

2.00E+01 1.10 1.05 1.00 0.95 0.90 0.85 0.80 Normalized n response: P4-H 4.50 4.00 3.50 3.00 2.50 2.00 1.50 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo 1.00 0.50 0.00 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 Neutron energy (MeV) Neutron energy (MeV) P4: 55 Normalized neutron response Normalized backscatter fraction 2.53E-08 1.00E-06 1.00E-05

P4-J Provided report & input files Some significant statistical uncertainties Generally close agreement with normalization solution Backscatter by cell flagging S(α, β) for water only 15 million histories Analogue Pure 6 Li for tallies P4: 56

2.00E+01 Normalized n results: P4-J 1.800 1.600 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo 1.80 1.60 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo 1.40 1.20 1.00 Backscatter fraction 1.400 1.200 1.000 Neutron response 0.800 0.80 2.53E-08 1.00E-06 1.00E-05 1.00E-04 0.60 0.600 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 Neutron energy (MeV) Neutron energy (MeV) P4: 57

P4-K Provided short report & input files Backscatter by phantom voiding S(α, β) not used 15 million histories Used cell importances for variance reduction Pure 6 Li for tallies Used 6000.24y ENDF/B-V dosimetry cross-section P4: 58

2.00E+01 1.600 1.500 1.400 1.300 1.200 1.100 1.000 0.900 0.800 Normalized n results: P4-K E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo 2.00 1.80 1.60 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo 1.40 1.20 1.00 0.80 0.60 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 Neutron energy (MeV) Neutron energy (MeV) P4: 59 Neutron response Backscatter fraction 2.53E-08 1.00E-06 1.00E-05

P4-N Deterministic Backscatter not possible with deterministic method Provided short report Direct and adjoint Results for group energies Takes seconds to run Simplified geometry P4: 60

Normalized n results: P4-N Direct Adjoint 1.200 1.30 1.20 Neutron response 1.000 0.800 Neutron Response 1.10 1.00 0.90 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo 0.80 0.600 E 4: 7Li, Albedo 2.53E-08 1.00E-06 1.00E-05 1.00E-04 Neutron energy (MeV) 0.70 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 Neutron energy (MeV) P4: 61

P4-P Provided short report Backscatter by phantom voiding Very small statistical uncertainties P4: 62

100.000 10.000 1.000 0.100 Normalized n results: P4-P E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo 2.00 1.50 1.00 0.50 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo 0.00-0.50 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 Neutron energy (MeV) Neutron energy (MeV) P4: 63 Neutron response Backscatter fraction 2.53E-08 1.00E-06 1.00E-05

P4-R Provided short report - subject to thorough approval process Backscatter not calculated Beta-version of MCNP5 (no Doppler broadening) Used source biasing to improve statistics Mesh based weight windows for neutrons and photons Generally small statistical uncertainties Checked for convergence of results Energy dependent systematic difference compared to author P4: 64

Normalized neutron results: P4-R 180.000 Neutron response 160.000 140.000 120.000 100.000 80.000 60.000 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo 40.000 20.000 0.000 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 Neutron energy (MeV) P4: 65

P4-S Provided short report Backscatter by flagging Very small statistical uncertainties P4: 66

Normalized neutron results: P4-S 1.150 1.100 1.050 1.000 0.950 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo 1.40 1.30 1.20 1.10 1.00 0.90 0.80 E 1: 6Li, direct E 2: 7Li, Direct E 3: 6Li, Albedo E 4: 7Li, Albedo Neutron response Backscatter fraction 0.900 0.70 0.850 0.60 2.00E+01 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 2.00E+01 2.53E-08 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 Neutron energy (MeV) Neutron energy (MeV) P4: 67

Conclusions - neutrons I Several participants noted that they are not familiar with this type of dosemeter (nor is the author!) 1 participant comes from a laboratory that runs a TLDalbedo service others (including the author) come from laboratories that run β/γ TLD services Impressed by the quality of some of the reports Some late entries were clearly not given as much time as they otherwise would have received I have not interacted with the participants to give them a chance to submit revised data, although some authors did revise their data spontaneously P4: 68

Conclusions - neutrons II Some problems with tallying/scoring Some FM card values not calculated correctly Some participants tallied over LiF Others have errors that have not been explained Correct cross-section: 3006.60c or 3006.24y? Not very much use of variance reduction Statistical errors reported in almost all cases Some very large, energy dependent errors Deterministic calculation quickest and better than badly applied Monte Carlo P4: 69