Лекции по основам кинематики элементарных процессов. Строковский Е.А. - 281 стр.

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E
∗
µ
E
∗
µ
− p
∗
µ
p
∗
µ
s m
2
i
λ
t
min
≈−
µ
2
M
2
− m
2
2
s
2
+ ... .
l =
k
f
+ k
i
k
f
+ k
i
, m =
k
f
− k
i
k
f
− k
i
, n =
k
i
× k
f
k
i
× k
f
,
k
i
k
f
l m n
l = m × n , m = n × l , n = l × m .
l = m × n
m × n =
k
f
− k
i
k
f
− k
i
×
k
i
× k
f
k
i
× k
f
=
k
f
× [k
i
× k
f
] − k
i
× [k
i
× k
f
]
k
f
− k
i
·
k
i
× k
f
.
a × [b ×c]=
b (ac) − c (ab)
k
f
× [k
i
× k
f
]=k
i
(k
f
k
f
) − k
f
(k
f
k
i
)=k
i
− k
f
cos θ,
k
i
× [k
i
× k
f
]=k
i
(k
i
k
f
) − k
f
(k
i
k
i
)=k
i
cos θ − k
f
,
k
f
× [k
i
× k
f
] − k
i
× [k
i
× k
f
]=(k
i
+ k
f
)(1− cos θ) ,
θ k
f
k
i
k
f
− k
i
·
k
i
× k
f
=sinθ
2(1− cos θ)=2cos
θ
2
(1 − cos θ) ,
m × n =
k
i
+ k
f
2cosθ/2
.
.    Eµ∗ E  ∗µ − pµ∗ p µ∗  F"+"EG   F"+"!G0 1
s  m2i 0 2    λ C C 1   0 1/
        ?
                                                2
                                  µ2 M 2 − m 2
                       tmin ≈ −
                                       s2
                                                     + ... .           F"+"+G
   ;
   FG .                         1           
2    F"E"G?
                    kf + ki         k − ki           k × kf
             l =           , m=  f              i      
                                   kf − ki  , n = ki × kf  ,
                    kf + ki 

2 ki  kf     0 1    1 
       0    F 0
     G
     /     0     l0 m  n    5
 9 ?
                   l=m×n , m=n×l , n=l×m .

.               1  20   l = m × n
               kf − ki     k × kf     k × [ki × kf ] − ki × [ki × kf ]
    m × n =          × i
                        
                                    = f
                                   
                                                              
                                           kf − ki  · ki × kf      .
               kf − ki     ki × kf

H    O 1   1                        a × [b × c] =
b (ac) − c (ab)?

        kf × [ki × kf ] = ki (kf kf ) − kf (kf ki ) = ki − kf cos θ ,
        ki × [ki × kf ] = ki (ki kf ) − kf (ki ki ) = ki cos θ − kf ,
        kf × [ki × kf ] − ki × [ki × kf ] = (ki + kf ) (1 − cos θ) ,

2     θ  2  C     kf  ki 
      I 1      ?
                                                         θ
      kf − ki  · ki × kf  = sin θ   2 (1 − cos θ) = 2 cos (1 − cos θ) ,
                                                             2
      0
                                         ki + kf
                              m×n=                 .
                                         2 cos θ/2

                                         ,"

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