Математические модели физических процессов «Реакция деления ядер. 
Жизненный цикл нейтронов»

??? ???-???

???

???? 33.

??? ??? ??? ???

«??? ??? … ??? ??? ???»

???

20021. ??? ??? ???

1.1 ??? ??? ???

? ??? ???,? ??? ??? ??? ??? ???? … ?? ??? ??? ??? ??? ??? ??? 30% ??? ??? … ??? ???, ??? ??? ??? ???? ???? ???? ??? ??? ??? ?? … ??? ??? ??? ??? ??? ??? ??? ??? ?? ??? (??? ???)? ??? ??? (??? ??? ??? ???). ??? ??? ??? ???? ???, ??? ?? ??? …

??? ?? ???? ???, ??? ??? ??? ??? ???, ??? ???? ??? ??? ???? ??? ??? ??? … ???, ??? ??? ??? ??? ??? ??? ??? ??? ??? … ??? ??? ??? ??? ???? ???? ??? E₁? ??? ??? ??? ??? ??? ???? ??? E₂ (E₁ > E₂).? ??? ??? ??? ??? ?? ??? ???, ?? ??? ??? ??? ??? ???, ?? ??? ??? ??? ??? ???? ??? E' (E' > E₁). ??? ??? ??? ??? ??? ??? ??? ??? ??? ??? …

1.2 ??? ??? ??? ???, ??? ???

??? ??? ??? ??? ??? ??? … ??? — ??? ??? ??? ??? ??? (??? ???). ??? ??? ???? ??? ??? ??? ??? … ??? ??? ??? ??? ??? ???? ??? ??? …

??? ??? ??? ??? ??? ??? ??? ??? ??? ??? ??? … ??? ??? ??? ??? ??? ??? — ??? ??? ??? ??? ??? ???,? ? ??? ?? ??? ??? ??? ??? …

??? ??? ??? ??? ??? ??? ??? ??? ???, ??? ?? ?? ??? ??? ???? ??? ??? ???? ??? … ??? ??? ??? ??? ??? ??? ??? ??? ??? … ??? ??? ??? ??? ???, ??? ??? ??? ???? ???? ??? 2,5 ?? ??? ??? ??? … ??? ??? ??? ??? ?? ??? ??? ???,? ??? ??? ??? … ??? ??? ??? ??? ??? ??? ??? ???, ??? ?? ??? ?? ??? ?? ??? ???, ??? ??? ?? ??? ??? ??? ???? ??? …

2. ??? ???? ??? ???, ??? ??? …

2.1. ??? ???? ??? ??? ??? ???? ???

? ???? ??? ??? ???, ??? ??? ??? ??? ??? ??? … ???, ??? ??? ???? ??? ??? ??? ??? ???? ??? ??? ??? ??? ??? ??? …

? ??? ??? ??? ??? ??? ??? ??? ???? ??? ???, ??? ??? ?? ??? ??? — ??? ??? ???, ??? ??? ??? (???)? ??? …

??? (fission).

n A ??? (capture).

??? (scattaring).

??? ??? ??? ??? ??? ???, ??? ??? ??? ???? ??? ??? ??? ??? ??? ?? … ??? ??? ??? ??? ??? ??? ??? (???) …

2.2. ??? ??? ??? ???

??? ??? ???, ??? N_? ???, ?? ??? ??? ??? ??? ?? ??? v? ??? n.

??? ??? ??? ??? ??? ??? …

??? ??? ??? ??? R, ???

R = N_? (1).

= n v — ??? ??? ???, — ??? ??? … ???? ??? (1? = 10^-24 ??²).

??? ??? ??? (1) ??? ??? ??? ??? ???:

R_f = N_{? f} — ??? ???

Rc = N_{? c} — ??? ??? ???

R_s = N_{? s} — ??? ???

_total = _f + _c+ _s

??? ???, ??? ??? ??? ??? ??? ??? ?? ??? ??? ???? ?? ??? … ??? ??? ??? ??? (E_?) ??? ???,? ??? ??? ??? ??? ??? E_?. ? ???? ??? ??? ??? ??? ??? ?? ??? ???: ??? ??? ???, ??? E < 0,625 ??; ??? ??? ??? ??? ??? ???, ??? 0,625 ?? < E < 0.1 ???; ??? ??? ???, ??? E > 0.1 ???;

2.3 ??? ??? ???? ??? ???

??? ??? ??? ??? ??? ??? ??? — ??? (???)? ???, ? ??? ???? ??? ??? ??? — ??? ??? ???, ??? ??? ??? ??? ??? …

2.3.1 ??? ???

??? ??? ??? ??? ???: ??? ???, ??? ??? ??? ??? ??? ??? ???? ??? ?? ??? ??? ???? ??? ???, ??? ??? ??? ??? ??? ??? ?? ??? ??? ???? ??? ???? ??? -…

E₀ A E₁

n A.

n E₂

n.

n A A₊₁

A.

??? ???, ??? ??? ??? ??? ??? ??? ??? ??? ??? ??? ??? (E_??? 0,1 ???),? ?? ??? ??? ??? ??? ??? ??? …

??? ??? ???? ??? ??? ??? ???, ??? ??? ?? ??? ??? ??? ??? ???? …? ??? ???-??? ??? ??? ???? ??? ???, …

2.3.2 ??? ??? (???)

??? ??? ??? ??? ???? ??? ???, ??? ??? ??? ??? ?? ???? ??? …

n A A₊₁

A₊₁

? ??? ??? ??? ?? ??? … _c ??? ?? ??? ???? ?? ??? ??? A.? ??? ??? ??? ??? ??? ??? _c(E) ??? ??? ??? ??? v (??? ??? ??? ?? E). ??? ??? ??? ??? ??? ??? ???,? ??? _c ??? ??? ???? …

2.4 ??? ??? ???

??? ??? ??? ??? ??? ??. ??? ??? ??? ??? ??? ???:

2.4.1 ??? ??? ??? ???

n.

A_{1 ???}

n A A_{+1 ???}

n n A_{2 ???}

n.

??? ??? ??? ??? ??? ??? ??? ?? ??? ??? (???) ??? ??? ??? ??? (??? ??? ??? ???) ???? 95/140. ???, ??? ??? ??? — ??? ??? … ??? ?? ??? ??? ??? ???: U²³⁵, Pu²³⁹, Pu²⁴¹ (? ??? ??? ??? U²³⁵, ??? ???? ??? U²³⁸ ??? 0.714%). ??? ???, ???, ??? ???, ??? ??? ??? … ??? ???, ??? ?? ??? ?? ??? ???, ??? ??? ??? ??? ??? ?? ??? …

2.4.2 ??? ??? ??? ???

??? ??? ??? ??? …

??? E_??? = 0.025 ?? — ??? ??? ??? ??? ??? 20⁰ ?. ??? E_???= 200 …

2.4.3 ??? …

… 2 … 3.

… 1.

??? _f(E) ??? ??? ??? ???, ??? ?? ??? E^-½ ??? ??? … ??? ?? ??? ??? ??? ??? ??? _f(E) = E^-½, ?? ??? ??? f (E) = _f E^½ ??? U²³⁵? ??? ??? ???_, ??? ?? … 1 ??? ??? ???, ??? ??? … ??? ?? ??? ??? ??? ??? ??? ?? … 1 ???,? ???? ??? E = 0,3 ??.

?? … 2 ??? ??? ??? _f? _total ?? E? ??? ??? ??? ??? ??? ???? ??? … ?? … 3 ??? ??? ??? ??? ??? U²³⁸, ?? ??? ???, ??? ??? ??? ??? ??? ??? ??? ??? (E_??? > 1). ??? ??? ??? ??? ??? ??? ??? ??? ?? ??? …

2.4.4 ??? ???

??? ??? ?? ??? ??? ???, ??? ??? ??? ??? ??? ??? ??? ??? -???, -??? ???, -??? ???, ??? ???? …? ??? ??? ??? ??? ??? ??? ??? ??? ??? … ??? ??? ???? ??? ??? ??? ??? ??? _f. ??? ??? ??? ?? ??? ??? ??? ???? ??? ???? ??? … ??? ??? ??? ??? ??? (??? ?? 0,5 ?? 15 ???), ??? ??? ??? ??? … ??? U²³⁵ ??? ??? ??? ??? ??? ??? 1.93 …

? ??? ??? ??? ??? ??? ??? ??? ??? ??? ??? ??? (?? ??? ??? ??? ???), ???? ???, ??? ??? ??? ?? ?? ??? (??? ??? ??? ??? ??? ??? ???).

2.4.5 ??? ???

??? ??? ??? ???, ??? ?? ???? ??? ??? ??? ??? ??? … ?? ???, ??? ??? ?? ??? ??? ??? ??? ??? (??? ???),? ? ??? ??? ??? ??? ??? … ??? ??? ??? ??? ?? ??? … ??? ??? ??? ??? ?? 6 ??? ?? ??? ???: T — ??? ??? ??? ???, _i — ??? ??? ??? ??? ??? ??? ???, _i/ - ??? ??? ??? ??? ??? ???, E — ??? ??? ??? …

? ??? ??? ??? ??? ??? ??? ??? ??? U²³⁵

? ???:

N_??? / (N_??? + N_???) = = 0.0065; T_??? 13 …; T_??? 0.001 …

?? ??? ?? ??? ??? ??? ??? ???? ???? ??? ??? ??? ???? ??? ??? …

3. ??? ??? ???

3.1 ??? ??? ???

? ??? ??? ??? ???? ??? 2.5 … ??? ??? ??? ??? ??? ???, ??? ??? ??? ???,? ??? ??? ??? ??? ??? ??? … ??? ??? ??? ??? ??? ??? ??? ??? ??? ???? ??? ??? ?? ??? ??? …? ??? ?? ??? ??? ???, ??? ???? ???, ??? ??? ??? …

??? ??? ?? ???? ??? ??? ???, ??? ??? ??? ??? ??? ??? ???? ?? ?? ??? ??? (??? ??? ??? ??? ??? ??? ??? ???). ??? ???, ??? ?? ??? ??? ???, ??? ??? U²³⁸, ??? U²³⁵. ??? ??? ??? ??? ??? ???, ??? ??? ??? ??? — ???? …

3.2 ??? ??? ??? ???

??? ???, ??? ??? ??? ??? …

3.2.1 ??? ??? ?? ??? ???

???? ??? ??? N ??? ???, ??? ??? ???? ??? ???,? ??? ???? ? ??? U²³⁸, ?? ?? ??? ??? ??? ??? ??? ??? ??? (1 ???) ??? ??? ??? ???? ??? ??? ??? … ??? ??? ?? ??? ??? ??? ??? …

??? ??? ?? ??? ??? — ??? ??? ??? ??? ??? ??? U²³⁸ ?? ??? ??? ??? (???? ??? ??? ??? U²³⁵).