Смелов В.В. Лекции по теории переноса нейтронов

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aaueaa

nepexenaoal)

naer

g (E, E',

00')

g (e, o',

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= 7 X(e, v').

(21.17)

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(21.16)

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xanecrae

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nocnpoaasenea

ypanneaae

(21.7) B

saepre-

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nepexeaaoa

E=v

2/2.

I1cnOJIh3yH

paseacraa

(21.16) H

(21.17),

nOCJIe

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onepauaa

noaysaea

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+OVCP+

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(21.18)

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naparparpa

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qaCTO

npeaedperaror, CqHT3S1 v

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(v=

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235U),

3 X-

<pyHKUHeH

O,lI,HOH

nepexeaaoa

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<pyHKUHH

X C ,lI,OCTa-

TOlIHOH

TOqHOCThlO

3nnpOK~HMHpyeTcSI

<j>OpMyJIOH [1]:

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=0,4840

exp(

- v

/2)

shv

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exp

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V2E].

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aHaJIHTHqeCKOe

BhIpa2KeHHe

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pacceaaaa

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MO~eJIH

ynpyroro

pacceanas

6y,neT

nOJIyqeHO

·B

CJIe,nYlOmeM

naparpatpe.

150

(22.1)

§ 22.

CbYHKl.\HSI

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HeHTpOH+51,npO

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ynpyrax

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H,llpaMH

aTO-

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orpaHHlIHMCH

paCCeHBalOIII.eW

cpenon, COCTOSImeH HS

snep

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copTa.

PacnpOCTpaHeHHe

pesyJIbTaTOB

cnylIaH

cpe,llbI,

COCTOSlIII.eH

113

anep

HeCKOJIbKHX

3neMeHTOB,

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sarpynaenaa.

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npencroar

HCnOJIb30BaTb

nne

CHCTeMbI

-DTClIeTa:

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cacrexy

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ClIHTaeTCH

51,npO-MHllIeHb,

a BO

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cpensr.

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roro

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lITO

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aoro

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oripaayror

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BHellIHHX

CHJI;

2) K

CHCTeMe

HeHTpoH+H,llpO

npHJIO}KHMbI

3aKOHbI

coxpaneaas

HMnyJIbCa

KHHeTHlJeCKOH

3HeprHH

(ynpyroe

pacceaaae);

pacceanae

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cHCTeMe

KOOp,llHHaT

r - panayc-sexrop

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HeHTpOHa;

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uenrpa

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_ 1

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+Mdro)

dt-l+M

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6yKBOH

CKOpOCTH

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L, a

6yKBOH

B CH-

crexe

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Toro,

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qaCTHU

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xopomo

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<l>opMyJIa

(22.2)

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L H C

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a V

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•

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pona

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rennoaax

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151

(22.4)

(22.5)

-(22.6)

,.B'

J(aJIbHeHWeM

6YJleM

CtIHTaTb,

lITO

CKOpOCTb

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e.B

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ero

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sepea

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M. .

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naa

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coynapenas

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CKOpOCTb

azipa B

CHCTeMe

panna

HyJIIO:

v'o=O. C

ytIeTOM

.3TOrO

q>OpMyJIbI

(22.1) nonyaaex

c=v'/

+M)

(22.3)

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nanee,

BOCnOJIb30BaTbCH

epOpMyJIOH

(22.2)

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2 = v

+Mv

saKOH

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3TH

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qTO

0==0.

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{a,

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aexropos

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V - vv cqs 0 V t

rne

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pacceaaas

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nOJIyqeHHbIH

pe-

ayJlhT3T

,BO

sropoe

paneacrao

(22.5),

JIerKO

npHXOJI.HM

K cnenyioniexy

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peaynsrary:

M + 1 v. M

-1

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=-------

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v·

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JII06bIM

npe-

.n.e..nax '[0,

n].

rorna

<pOpMyJIbI (22.6)

cnenyer,

'tITO

II'llH

38,llaHHOM

sexrope

H. MO.nYJIb

'BeKTOpa

v OJ:(H03HaQHO onpeneaea 6b1Tb He MO:>KeT. A HMeHHO,

ero

MO,nYJIb

3aBHCHT

Toro,

KaKHM

OKa3aJlCSI

yron

paccesaas

60.

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HeOJlH03Ha1lHOCTb CKOpOCTH v

pacceaaaoro

HeHTpOHaCJIe.llyeT

aenocpen-

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caMOM

.n.ene,

3Ta

CHCTeMa COCTOHT H3 xenspex CKaJISlp-

HblX

yp.a~BHeHJfii,

COJlep*HT

meers

'HeH3BeCTHbIX

- 3TO Tl).H 'KOMTIOHeHTbI CKOPOCTH v

TpH

KOM;nOHeHTbI OKOpOCTH

Vo.

TaxHM

o6pa30M,

CHCTeMa (22.5) aeaoonpenenena

nOT6MY

O,n'H03H8t1HOTO peIlIe'HHSI

HMeTb

MO}KeT.

C~{(;>POCTb

~u.eHTpaHHePUJiH

v c

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axra

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CAApoM,

noroxy

HeT

·HY)K)I.~

crxesars

13Ty

CKOpOCTb

IllTp:HXOM.

152

(22.7)

(22.9)

Ilonyrao

4>OpM.yJtOH

(22.6)

yMecTHo

nOJIytI.lnb

tPoPMyJIy·K

JlJlH

cos

xoropas

_T~K~e

norpeoyerca

-B ,naJIbHeAweM.

YtIHTbIO(1H

KO'JIJIH-

aeapaocrs

BeKTOpoBV

if:

[CM.

1(22.3)], H3

fPOpMyJIbI

(22.2)

XOJ(HM

= (v - v

V - v

)c= v

- 2vv

cosO.+v

•

Ilpaayio

·tIaCTb

sroro

paBeHCTBa

aerxo

npeoopaaoaars

OCHOBe

epop-

MyJI

(22.3) .H (;22.6) H

yCTaHoBHTb,

lITO

l;-l+M

•

Kcrarn,

conOCTaBJIeH:HH

epQtpMyJI

(22.7) 11 (122.4); caenyer,

tIro

CHCTexe

C B

pesyasrare

coynapeaas

a6!COJIIOT'HaH

BeJlijttJaHa

S·~KTO,

CKopoCTHHeHTpoHa

coxpaasercs

(MeHHeTICH

TOJIbKO

aanpasaeaae

CKOpOCTH).

3aMeQaH,

H·aKOHeu,

tIro

aexropu

S' H V

'KOJlJIHHeapHhI---.

STO czrenyer H3

paseacrs

'(22.3) H (22.4), -

CHOBa

epOpMyJIhl

(22.2)

HaXO,lI.HM

= (V

+ S,

vc+~)=v2c+2vcecos6+~2.

(22.8)

MO,nYJIb

sexropa

vv,

onpenenax

(22.3), a S ·,llaeTCH

<pOpMyJIOH

(22.7).

BHTore

cos

6 H3

paseacraa

;(22.8)

Bblpa3HTcSI

«popMe

(1 +M)2 [ ( o

)1]

COS 0= 1- 2M 1- .

lila

<pOpMyJIbli(22.9)

cnenyer,

liTO:

UpH

-«CKOJIb3HmeM;»

coynapeaaa

;(16==0)

-MOJlYJIb .CIKOpOCTH

HeH-

TpoHa

CHCTeMe

MeHsIeTCH

(vlv'=l);,

II-pH

«JI060BOM»

coynapeana

;(-8==1&)

MOJJ.YJIb CKOpO'CTH aefirpo-

CHCTeMe

npHHHMaeT

aaaxeasuree

lB03MO)K'HbIX

3HaqeHHH

[vjv'=(M-I)

I(M+I)].

TaKHM

06pa30M,

JIa60paTopHOH

cHCTeMe.

CKOpOCTb

HeHTpOHa

nocae

coynapeaas

MO)KeTnpeBbIlIIaTb

CKOpOCtH

coynapeaas

'MOJKeT

faa'

HCKJIlOqeHHeM

CJIyqaH

sonopona,

xorna

M=l)

CTaTb

CKOJIh.yrOJllIO

MaJIOH,

[(M

.1)j(M

+I)]o'<

v~o'.

(22.10)

06paTHMcH

Tenepb

K BbIBO.n:y

<pyHKUHH

pacceaaas

st».

o',

gO'),

Qn.pe.n:eJIeHHOH

paaeacraox

(21.2). Tlpeacne scero

HanOMHHM,

xro

B -

CHCTeMe

L C

noxoursro

3TOH

<pyHKUHH

Be-po.5ITHOCTb

nonaaaaaa

HeHTpOHa

!IoCJIe

CTOJIKHOBeHHH B

3JIeMeHTapHbIM

rrysox (dvdQ)v,o.Aa-

eTCH

BblpaiKeHHeM

g (e,

o',

00')

IdvdQ

(22.11.)

ECJIH

CHCTeMe

BBeCTH

crpepanecxae

xcopnaaarsr,

cBH3a~

BeK-

TOpOM

(pHC.

27,

L),

dQ=sin!8

od'i'

H ssrpaaceaae (22.11)

nepen.HlIIeTCH

BH,ne

g(v, o',

cos6G)ldvsin.O.d6od~l.

153.

Haxoaeu,

0603HaQHB

'COS

J..t

3anHIIIeM

BepOHTHOCTb

norranaaas

HeHTpOHa

06j]:aCTh

dvdJ..todnIJ

aane

g(v, v',

JLo)ldvdfJ'odtl.

(22.12)

<PyHKnHIO

g(v,

o',

J..to)

6Y,lleM

nozryvars

ocaose

asorpomroro

3aKOHa

pacceaaas

HeHTpOHOB

CHCTeMe

(rpersa

ranoreaa).

ECJIH'

0603HatIHTb

di»

3JIeMeHTapHbIH

TeJI~CHhIH

yrOJI

CHCTeMe

C, TO sepo-

HTHOCTb

nonanaaaa

HeHTpOHa

Bnero

nOCJIe

pacceanas

pasna

Idt»

1/41t.

CHCTeMe

BBe,lleM

TaKJKe

ctpepasecxae

KOOp,llHHaTbI,

CBH3aB

H'X

BeKTo'pO'M

v',

KOJIJIHHeapHbIM

nexropy 6'

(CM.

pac,

27,

C).

1130-

PHC.

27. Jlaooparopnaa L H

HHepUHaJlbHaH

C CHCTeMbI KoopJJ.HHaT

TponHhIH

38KOH

pacceanas

dO)

1/41£

npeoripasyerca

npa

3TOM

38KOH

pacnpeneaeaas

yraax

8 H

1J':

Idm

1/41t

===

sin

dOd~

1/41t,

rae,

OqeBHJlHO,

Id'¢

1/21t

3aKOH

pacnpeneneaaa

JIy

'1';

sin8ldOl/2-3aKoH

pacnpenenenaa

yrJIy

33KOH

pacnpeneaeaas

yrJIy

CHCTeMe

JIerKO

npeoopaso-

B8Tb

'KOH

pacnpeneneaaa

'CKOPOCTSl/M v

CHCTeMe

L),

eCJI'H

BOCnOJIb30BaTbCH

<l>OpMyJIOH

·(22.9).

,llH<I><f>epeHUHpySl

paseacrso

(22.9),

arore

HMeeM

Si~91d61

t:>1

v~2Idvl.

(22.13)

BbIpa1KeHHe

(22.13)

npe){CT8BJISleT

C060H

nepenopxapoaxy

nJIOTHOCTH

BepoHTHoCTH

npa

nepexone OT e K v - B

TOM)Ke

acnexre,

K8K

.9TO

6bIJIO

C,lI.eJlaIHO

npa

BbIBO,lI.e <f>OpMyJIbI

(2·1.14).

MTaK,

3aKOH

pacnpene-

.1JeH'HSI

pacceHBIII·Hx'CH

HeH'TpoHOB

a3HMYT8JIbHOMY

yrJIy

1J'

CKOPO-

CTHM

HMeeT

BH.n

+M)2

v I

door'}

O~,h~2.

M-I

47tM v'

1t,

M +1o

o ·

(22.14)

'~pa3bI

THna

«BepOHTHOCTb

nOna.u.aHHH

HeHTpOHa

B 06J1aCTb

dvd~od~

yroJl

dID,

B 3J1eMeHT

dJ,to

H T.

,ll.)>>

HOCHT YCJIOBBbIH

xapaxrep

03HaQalOT

enonanaaae» He

HeHTpOU3,

aero

'TIapaMeTpOB

v H O. .

154

,[lJISI

npespameaas

,llByxMepHorO

3aKOHa

pacnpenenenaa

(22.14)

TpexMepHhIH

(22:12)

HyJKHO

yMHOJKHTb

(22.14)

BepoHTHoCTb

no-

nanaaas

HeHTpoHa

.9JIeMeHT

aJlo oxono

3HalJeHHSI

Jlo

npa

yCJIOBHH,

tITO

HeHTpOH

nonan B

06JIaCTh

dvd'¢

OKOJIO ·v 'R 'i'.

BBHAY

«}KeCTKO:H»

o,nH03HalJHOH

CBSl3H v C Jlo I[CM. (22.6)] aarepecyiomyio

Hac

ycaosnyro

BepOSlTHOCTb

cnenyer

aanacars

nOMoIUblO

r6-<pyHKuHH

[7]:

a(Mi

-".)ld

....

(22.15)

YMH01KaSl

(22.14)

(22.1.5) H conOCTaBJISISI

nonYlJeHHbIH

pesynsrar

c (22.12),

aaxonaa

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