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ALPHA AND LAMDA MODEL

α & λ MODEL

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CHOOSE TAMPER MATERIAL; "DU" OR "WC"

Tamper WC :

TAMPER RADIUS: \[REGION[d7c409e0cd5945509a1e123c97ddb16f]]\

R.T 21.21 cm * :

DEFINE SOME UNITS

AMU 1.66 1027 -^* kg * :

1 eV * 1.602 1019 -^* J *

1 MeV * 1.602 1013 -^* J *

Avogadro's Number

N.A 6.022 1023^* 1 mol / *

Ton.TNT 4.2 109^* J * :

KT 1000 Ton.TNT * :

CORE DEFINITION

HEU 235U PERCENT: \[REGION[ee5d80608d224c02b46b1fbc905fb865]]\

HEU% 80 :

HEUMASS 65.8 kg * :

M.core HEUMASS HEU% 100 / * : 52.640 kg *

GRAM MOLECULAR WEIGHT OF 235U: \[REGION[030ac39937c445e5971bc1bfa63e3a99]]\

U235.gmw 235 g * :

MolesU235.kg kg U235.gmw / : mol 4.255 1 mol / *

NumberAtomsU235.kg MolesU235.kg N.A * : 2.563 1024^* 1 mol / *

DATA MANHATTAN DATA Sheet1 A1:E6 importData.XLSX :

ρ DATA 22 el g cm 3^/ * : g cm 3^/ 18.710

DATA ELEMENT r (gm/cm3) lf (cm) lt (cm) n U235 1.871 101^* 1.689 101^* 3.596 2.637 Pu239 1.560 101^* 1.414 101^* 4.108 3.172 DU 1.895 101^* 0.000 4.342 0.000 WC 1.480 101^* 0.000 3.159 0.000 0.000 0.000 0.000 0.000 0.000 65 mat

ρ.DU DATA 42 el g cm 3^/ * : g cm 3^/ 18.950

ρ.WC DATA 52 el g cm 3^/ * : g cm 3^/ 14.800

λ.f DATA 23 el g cm 3^/ * : g cm 3^/ 1.689 101^*

λ.TampDU DATA 44 el g cm 3^/ * : g cm 3^/ 4.342

ν DATA 25 el : 2.637

λ.t DATA 24 el g cm 3^/ * : g cm 3^/ 3.596

λ.TampWC DATA 54 el g cm 3^/ * : g cm 3^/ 3.159

NOW DEFINE λs IN TERMS OF NUCLEAR CROSS SECTION AND NUCLEI NUMBER DENSITY

A 235.04 g mol / * :

n ρ N.A * A / : cm 3 -^4.794 1022^*

σ.f 1.235 barn * :

λ.f 1 n σ.f * / : 0.169 m *

σ.el 4.566 barn * :

σ.t σ.f σ.el + :

λ.t 1 n σ.t * / : 3.596 102 -^* m *

A.WC 195.85 g mol / * :

n.WC ρ.WC N.A * A.WC / : cm 3 -^4.551 1022^*

σ.elWC 6.857 barn * :

λ.TampWC 1 n.WC σ.elWC * / : 0.032 m *

M.core 52.640 kg *

R.c 3 M.core * 4 π * ρ * / 3 nthroot : cm 8.76

M.Tamper 43 / π * ρ.WC * R.T 3^R.c 3^- (* : 549.88 kg *

NOW LET THE RADII OF THE CORE AND TAMPER EXPAND BY Δr

maxk 20 :

k 1 maxk range :

Δr 0.01 cm * :

Rexp R.c k 1 - (Δr * + :

Rexp max cm 8.95

RTexp R.T k Δr * + :

RTexp max cm 21.41

ρexp 3 M.core * 4 π * / Rexp (3 -^* vectorize :

nexp ρexp N.A * A / :

ρTexp 3 M.Tamper * 4 π * RTexp 3^Rexp 3^- (* / vectorize :

nTexp ρTexp N.A * A.WC / :

λf 1 σ.f nexp * / vectorize :

λt 1 σ.t nexp * / vectorize :

λT 1 σ.elWC nTexp * / vectorize :

Λ λT λt / vectorize :

λT max λT min / 1.02

α f1 e 23 α * λT λf * / sqrt * R.c R.T - (*^vectorize :

α f2 3 ν α - 1 - (* λf λt * / sqrt R.c * 3 ν α - 1 - (* λf λt * / sqrt R.c * cot * 1 - Λ 3 α * λT λf * / sqrt R.c * 1 - (* - R.T 23 / λT * 3 α * λT λf * / sqrt R.T * 1 - (* + / vectorize :

α f3 3 ν α - 1 - (* λf λt * / sqrt R.c * 3 ν α - 1 - (* λf λt * / sqrt R.c * cot * 1 - Λ 3 α * λT λf * / sqrt R.c * 1 + (* + R.T 23 / λT * 3 α * λT λf * / sqrt R.T * 1 + (* - / vectorize :

α F α f1 α f2 * α f3 - vectorize :

Ans α F α solve 2 el vectorize :

α Ans :

r Rexp :

slope α maxk el α 1 el - r maxk el cm / r 1 el cm / - / : 0.378 -

αfit slope r r 1 el - cm / (* α 1 el + :

α 0.485 0.481 0.477 0.473 0.469 0.466 0.462 0.458 0.454 0.450 0.447 0.443 0.439 0.435 0.432 0.428 0.424 0.420 0.417 0.413 201 mat

r cm 8.758 8.768 8.778 8.788 8.798 8.808 8.818 8.828 8.838 8.848 8.858 8.868 8.878 8.888 8.898 8.908 8.918 8.928 8.938 8.948 201 mat

αfit 0.485 0.481 0.477 0.473 0.470 0.466 0.462 0.458 0.454 0.451 0.447 0.443 0.439 0.436 0.432 0.428 0.424 0.420 0.417 0.413 201 mat

r k el cm 8.7576 8.7676 8.7776 8.7876 8.7976 8.8076 8.8176 8.8276 8.8376 8.8476 8.8576 8.8676 8.8776 8.8876 8.8976 8.9076 8.9176 8.9276 8.9376 8.9476 201 mat

α k el 0.485 0.481 0.477 0.473 0.469 0.466 0.462 0.458 0.454 0.450 0.447 0.443 0.439 0.435 0.432 0.428 0.424 0.420 0.417 0.413 201 mat

alpha r cm / α augment :

alpha