Физика столкновений ультрарелятивистских ядер (экспериментальные закономерности). Коротких В.Л. - 84 стр.

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σ
in
(pA) = 2π
Z
bdb(1 − e
−σ
in
AT (b)
).
T (b) =
Z
dzρ(x, y, z), b = (x, y).
ρ(r) =
ρ
0
1 + e
(r−R
A
)/d
.
σ
in
(pA)
d
2
P
A
(b)
d
2
b
= (1 − e
−σ
in
AT (b)
).
(1 −e
−σ
in
AT (b)
)
e
−σ
in
AT (b)
b (1 − e
−σ
in
AT (b)
)
AT (b)
ν
p
ν
(b) = C
A
ν
[σ
in
T (b)]
ν
(1 − σ
in
T (b))
A−ν
.
A
X
ν=1
p
ν
(b) = 1 −[1 − σ
in
T (b)]
A
|
A>>1
≈ (1 − e
−σ
in
AT (b)
).
ν
”
“ N
A
coll
hN
A
coll
(b)i =
σ
in
AT (b)
(1 − e
−σ
in
AT (b)
)
.
  Çäåñü â çíàìåíàòåëå ñòîèò ïîëíîå ñå÷åíèå íåóïðóãîãî âçàè-
ìîäåéñòâèÿ ïðîòîíà ñ ÿäðîì
                                 Z
                  σin(pA) = 2π       bdb(1 − e−σin AT (b) ).        (21)
   Ôóíêöèÿ ÿäåðíîé òîëùèíû, ââåäåííàÿ â ìîäåëè                  ëàóáåðà
[126℄,               Z
              T (b) = dzρ(x, y, z), b = (x, y).                     (22)
çàâèñèò îò ïëîòíîñòè ÿäðà, îáû÷íî çàäàâàåìîé äëÿ òÿæåëûõ
ÿäåð â îðìå Ôåðìè-ïëîòíîñòè
                                ρ0
                    ρ(r) =                .          (23)
                           1 + e(r−RA )/d
   Ïåðåïèøåì îðìóëó (20) â âèäå
                         d2PA (b)
                 σin(pA)    2
                                  = (1 − e−σin AT (b) ).    (24)
                           db
è ïîÿñíèì èçè÷åñêèé ñìûñë âûðàæåíèÿ (1 − e−σin AT (b) ). Çäåñü
e−σin AT (b)  âåðîÿòíîñòü ïðîòîíó ïðîëåòåòü ñ ïðèöåëüíûì ïà-
ðàìåòðîì b áåç âçàèìîäåéñòâèÿ, (1 − e−σin AT (b) )  âåðîÿòíîñòü
ïðîëåòåòü, âçàèìîäåéñòâóÿ ñ òîëùèíîé ÿäðà AT (b).
   Ïîëåçíî ââåñòè âåðîÿòíîñòü ν íåóïðóãèõ âçàèìîäåéñòâèé íóê-
ëîíà ïðè ïðîõîæäåíèè òîëùèíû ÿäðà
               pν (b) = CνA[σinT (b)]ν (1 − σinT (b))A−ν .          (25)
  Ñóììà ïî âñåì íåóïðóãèì ñòîëêíîâåíèÿì ïðèâîäèò ê âûðà-
æåíèþ (24)
    A
         pν (b) = 1 − [1 − σinT (b)]A |A>>1≈ (1 − e−σin AT (b) ).   (26)
    X

   ν=1

  Çíàÿ âåðîÿòíîñòü ν âçàèìîäåéñòâèé (25), ïîëó÷èì ñðåäíåå
÷èñëî íåóïðóãèõ ñòîëêíîâåíèé íóêëîíà ñ ÿäðîì À ( ÷èñëî áè-
                                                    ”
íàðíûõ ñòîëêíîâåíèé “ ) Ncoll
                            A
                               ïðè çàäàííîì ïðèöåëüíîì ïàðà-
ìåòðå
                   A             σinAT (b)
                hNcoll (b)i =                     .     (27)
                              (1 − e−σin AT (b) )
                                     83

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