J. Mass Spectrom. Soc. Jpn.

Vol. 57, No. 5, 2009

REVIEW /
 1  

Fundamentals of Mass Spectrometry
ῐBasic Explanation for Collisions in Mass Spectrometryῐ
Shigeo H6N6@6L6


Department of Chemistry, School of Science, Graduate School of

Science, Osaka Prefecture University, Sakai, JAPAN
Recent development in mass spectrometry has far-reaching e#ects not only in physical and chemical studies
of gaseous molecules and ions, but also in biological studies, including proteomics and metabolomics. In mass
spectrometry, collisions are very important elementary processes in ionization, collision-induced dissociation,and mobility, whose methods are useful for the development of proteomics and metabolomics. In the present
review, to understand the basis of collision, the concepts of center-of-mass system, laboratory system, crosssection, kinetic energy release, and impact parameter are explained. The cross sections, which provide themagnitude of elementary reactions, depend on reaction species, collision energies, and reaction processes. I haveattempted to present these dependences with the support of various examples.
(Received May 25, 2009; Accepted May 25, 2009)[+ N ^7) a$% (|/ AA

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E(Lab; fast)

m(VMvmῒ)22
m ῌῌ2EInc῎1/2 ῌ2(Mm)KER῎1/2῎2῏ ῏ (19)2 ῍῍ M ῏ ῍
mM(2EInc/M)1/2 1a (2(Mm)KER/mM)1/2

E·¸¹]9
º.
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Lab

 ^ m¶Cutp/

78 (E Lab)  (DELab)  (18)  (19) "M

ZMS


ELabDELab

4m(Mm)EInc KER῎1/2m
E »2ῌ
῏ (20)M Inc ῍M2º. ¢  ¼ m  Mm )½\T!
Fig. 4. 781H º. h¨M
ῐ 349 ῐCM¡£>78

S. Hayakawa

Fig. 5. efg) hi*c-D B1 [Huuo R!
 =R' Lab



   !

O2 D

4S' $ u>n,Kv> ef  @A "#$%&'  !
()

*+*,

% "%- %.' ()*- d /01

2$%34" M/EInc

 KER 563$%

KER8

EInc
d2
16m(M9m)

}~

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."O' (b)  4 

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?@AB1>H7."r ' $ >H" d 0EInc
ῌd29ῌm d ῎῎
16m(M9m) ῍ ῍M 0῏῏

KER8

!

5 keV

A 5 eV!# 100 u>D ,%7  90 uu

KER  8.2 eV

B1>n,

Kv> Dishing %4o|w$

(22)

%-

cd4' uoU4UV %uo>d@ = (KER)   90 u

 :EF  GH%GI !

7Zt=+>7.S$%
S' L )X (a)2% 10 uS' (a) o|"

D {O$%n-. KER #)X %a>>_-(21)

C -563412) .

5:)X B1ef  w D xyz. KER=d4)X Fig. 4 >n,Kv. %. H7

7'

:;

- H % O  H῍ % O῍ @A%-t=d@A

3'4S KER R>H7.UVW xyU4' $4 (21) 6U4Kv> KER R d>

2,O" KER R3>

>O$%n-S' :; 90 u@A :EF  GH%GI !

KER R>O" Dishing rM8100 u, m890 u, EInc85000 eV, KER8

B1 d   (Full Width at Half Maximum:

5 eV  (18) 6% (19) 6>J ,$%>K"
4595.4 eV % 4405.6 eV %34' $eV %."



CM

L4M4

FWHM) 3$%>K" GS

N 190%d4 KER R<=d4S' Fig. 5(a)KER O 5 eV K"P%H7.QR>.S' T ()*-%7

o| }~

!

?@A

"C - (22) 6 S KER R<=-.S%H7.Nr $%%.'88.11 u %.' L N 3.8 u %." %R LabB1 KER R>"OB1."O' T SB1>-

GH%GI UVW 3)X !
> M/EInc V$%>K"L4M4 91.91 u % 4.2Y %.' $$%O 

5. ῌ῏῎ῐ῍% KER % O 0.1Y K"P%H7Z.

! ll l @A x¡¢ \$S$%&' $ [H\$  ] x¡¢

H7dQR%-c,$% L ^>_`,%a>b1OO" 0.1Y^O 3Y >_`-S' $KER R [H Lab"Id.!

 c4  =O Lab

4 "`£> @A¤l H7d£>#¥¦O' !§$¨©%. "` \

.

 D

$"¤,d$¨eª&«,RO'll¬b ©%'­l()>*D,7®¯O /01 B13$%7$%&!§$¨ °+*D,> TP±²³´U'

4Kv.,p .SµS¶ ·¸¹¶º !,)X

Fig. 5 >efg) hi*jkc-C»' Fig. 6 n,Kv>¼ RInc

!, ?-

n-13), 14)' (a) % (b)  L

l (Incident Particle: Inc) %¼ RTar(½-.)-

lmD /01
ῌῌ

4M4 H2 % O2 @A

opqrs-\ H2 %l (Target: Tar) %] v !,)XC»'ῐ 350 ῐU

Fig. 6   RInc

R Tar 

!"#$%&'(PQOMN&op~ )* Z[-WCc"&Z[-W  

Cq

-

 )*+,-./01& 2345 6 

t& [ #~  A 6 !-378 9:-& Fig. 7 C6 Fig. 7(a)  ;<= >?-@A

3BCD 

RIncRTar -%E F7 6 -G;

BCH D 6 -5I%EJKW IIN &2:   W D - "Cc L -q



Cc

)*&ef 6 -LCD >? RIncRTar -MNBCDW& [D3H- '+qJKD - OMN+ p(RIncRTar)2 3 6 -

CW IOUT

[c" 6 q-{|&e+5I%E F7 -PQOMN2R7" 6 

f C Fig. 7(b)  q5<-3STU--)*+VW v XY3

= x -X-W I(x)   5DOMN+Z[A 6 \ ]^ ---_`a&2BH )* 

] 

-bD

c&d[c"C2-efK"3H6 -)*2 ./-W-t dI(x) + -W

I(x) -W D 5<= dx  - [& c fK" 601#5I%E-Fg3h  -OMNdI(x) cῌDῌI(x)ῌdx

Hij+ST3)*kl-mn&2:6 opq(Lab) rst (CM) r-uvwC9x

+yzst m &2:Z:{|}vD &C6
A# !

ῌ3-
dI(x)  I(x) +k¡¢£ D
¥¦ m

st

¢£xN¤C#-Wc [m] -¢£&2:- [ c+ [m2] -MN-¨&2: 7J 6

ef 6 -ef

-bDc&ef 3 A

§ dx

(23)

Fig. 7(b)  D dx + WJ© <=st

%EJKLCªH dx -«¬A -¦&OMN p(RIncRTar) PQc" ef H 6 Fig. 6 C p(RIncRTar)2 -OMN

D 6&­® Fig. 7(b) c"  -­-

2

BC +%E F7#PQc" - t Fgt dI(x)/I(x) + 

1 ¦-
ῌ1 MN ¯OMN s ¥m ¦ §°  D dx
2[mῌ2] &J©C±* PQc" «¬3# c

" 6
dI(x)
I(x)

sD dx- (24) & (23) ²c³
2-

 [ c HC

Fig. 6 vwCOMN (s) -bDcAC - [ cFig. 6. ¸x(24)

OMN s ´J3K3H µ¶D

6    ·JKL  Fig. 7(c) c"-)*-OMN

Fig. 7. PQOMN- [XC῍ 351 ῍

S. Hayakawa





 (24)  x0  !

'()

῏

IOUT
IIN

L " #$ % &



I
dI(x)
[loge I(x)]IOUTloge(IOUT/IIN)
IN
I(x)

῏

L

 *sD dx*sLD

(25)

0

(IOUT/IIN) + 1 ,-.

/

0-% loge(IOUT/IIN) +1

/  (25) 23 4 % &)
IOUT/IINexp(*sLD)
(26)

 56 78# s 9: ;<$ & s*

loge(IOUT/IIN)
loge(IIN/IOUT)LD
LD

44 %  !

Fig. 8. <¶® WXYFB=>?@AB(27)

L% =>?@3AB D CD

% sLD 0 tBfI 34 ] IIN ED IOUT FBGH I J% :<% IOUT/IIN NO+ (27) <

78# s 9: 4 I  KLM< ! < ,<23'3

NO P +Q% FBRS/9"

78# s  2b20ῌ20 m2 %  !  1.0

TU V% =>?@3ABNO P% WXYF

b10ῌ2 m ]I IOUT/IIN =>?@3AB

BZ[ IOUT/IIN NOGH$ 4 78#

 Fig. 8 <$ 3AB 2b1021 mῌ3

 K\<KLM<78#9: ]:<%

9:4^_` I 
a 6:



 0.67 -% k<C 1.0b10ῌ2 m, 25c

!



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+% (28) y& `  0.6   2 &V
106 i 1 de+fgdhV 1 <S 2 

de 1.0 Pa 5fgdh 105 i 16 I% CDjh 10l 4k 10l Z[] 4mn78#9: 

keV X  +%  1 de 

IOUT/IIN0.9

0  % loge(IOUT/IIN)*0.105,

% 100 eV   +% 3a 7: 78# 3b10ῌ20 m2%  !  2b

opgqrs^t` =>?@3AB D

10ῌ2 m ]I% CDjkFBv<>?@3AB 25c

ῌ1

23

D(mῌ3)

6.022b10 (mol )b1.0 (Pa)NAP

RT
8.3145 (JKῌ1 molῌ1)b298.15 (Kῌ1)

2.423b10

20

 MS/MS _`  loge(IIN/IOUT)0.105+& 9:

4

=>?@de9: 

CDjkFBv<

ῌ3

=



I OUT /I IN + 0.5 < (27) 3AB D +& ¡ % 4 <3/m(27) <4 /uC$ 78#9:

C/9:

loge(IIN/IOUT)
0.693

Ls
0.02 (m)b3b10ῌ20 (m2)
1.16b10ῌ21 (mῌ3)

D

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s
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LD
0.01 (m)b2.423b1020 (mῌ3)
4.34b10ῌ20 (m2)

4 de<N¢$  4.76 Pa   @£?¤=W¤kvw Bohr vw (5.29b10

ῌ11m) <x$% y^z{]8# (p(2r)2) + 8.8b10ῌ21 m2  MS/MS _ +4tBde 0-% 3`  4  k|w+ Bohr vw},-~fItB 0

 % 78# 10ῌ20 m2 tB 4

34

TU<+% ¥¦§¨t (lmean:

mean free path) ¥¦§¨©ª (tmean: mean free time) I% K\<78#+ 10ῌ20 m2 X/` 4

" <jk«$ ¥¦¬­ 0-% 78(26) + sLD .

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1
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(*sLD)2ῌῌῌ2!
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῍1*(sLD)

1(sLD)22lmean

(28)

1
sD"]% 4 lmean jk´B v

sLD . KL +% IOUT/IIN + D <y&<a$(29)µ 4<,-% 1 &"  tmean & ¡

῎ 352 ῎.

tmean

1
sDv  

"-./z$3d wlmno=

(30)



-./lmno={G

   ( )* (  +, '$ -./'012&) )* 34

lmno=|}"~%$ wlmn
o=#6&-./ !" "#$ %  &" ')*

0 ' C*%R$ *8 

-./

"!

70100 eVA&% lmno=2|}

'G6!-./'"!*&O%$ *5)* 67-./

70100 eV lmno=

'$ *86'01 9: & ;6 <=>66*&?"zOd"!$ C&#-./ #3 |} 10ῌ20 m2 (10ῌ16 cm2) .=='

2@#A 6 9:B @*&suvi#3&QW"!*& &6$ C D (EBF'G

#$HI6! 1 FJK@ '$ (24)L&L' 9:-./ IFormed

6. ῔ΐῒ῎῍ῑῌ῏ῐM&N OPL&6$dIFormed(x)I(x)sD dx
1 FJK()6 (31)

Fig. 10  K i 34&#

I(x) Q&" 0 %R L G$ *

R%6|} "!

$ +6&,-!"

&STPL&6$
IFormed(sLD)IIN(32)

$ .*&/'$
5 s ?¡¢& ;6

PV& (32) L QW$ *QW%R   /q£¤$'?"A9: '?"A &" XY, F(r) -$ *, A?"!*&O%$ 9: Z"

o=P¦

[\

1 FJKY A  ]+^=_`aB (32) Lbc

JK@3d6edf gh6

A

-.

¤¥ (r) |}*&lmn§¨/©ªnlmno= V(r)«*&#$ ¡¢ ]+0¬d&*­

Rd6,-%6! 0¬d&*­ §¨/©ªn
0 & §¨/©ªn PL*3d$

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r

V(r)

9: !&" i&-./
j

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(28) L IFormed(IINUIOUT)/IIN && (28) LQ 67

5 suv

8 p(RIncRTar)2 *3dR6!$

Fig. 9 8"k3d"!$ ghl

῍ F(R)dR(33)®

*8*¯&§¨/©ªn2 ¤¥ r

mno= p 34"9:-.

°|}±²=&6$ ¡¢/ @&!8qr#'$ 2 s Lab t& CM0¬d&*­%R1

tuv8 wlmno=x&y7v

RTar) b³G

Fig. 10.
Fig. 9. -./ 15)·OPU ¸
" 2¹ 15  Fig. 33 3º$»ῌ 353 ῌ¤¥ (R Inc´,AµOR6! 0¬¶

K i& · »  16) ÕA
10ῌ10 m·45¼½¸" 2¹ 16 3º$»

S. Hayakawa

noApqrABA

Table 1.

s (12,6)

-./
 ½

c [10῎10 m]

eLJ [meV]

He

2.57

0.93

Kr

3.59

14.9

CH4

3.81

12.8

2 : 

re [10῎10 m]

De [eV]

O2

1.21

6.6

O2

1.12

5.18

s (12,6)

noApqrA 0 2 : 4 ;  "#4 "!

   $ %& "! Fig. 11'( )*+, -./ 0
 RIncRTar

"  ! +, tm*9lm $&2$ 3&Morce D@AJK

re  De  |"< =>?@AB C456!
=>?@ABWaals DEF

G H G IAJK LM*9N (r)6O

C+ van der[\Fig. 10= ?+

 1N  "R Z!;dN (re)  N

 (rvre) ab" 2 O

<9#@AJ BA4

Table 2 )P @AJ

;dN"% 2 &noApqrA &% 1,000 &< @AJ# ;dN"# jfg

r῎12 P*9 lm)& LennardJones
DnoApqrA sK (12,6)P tm*9&yz#"ῌ '{*eP#!

(34)

V(r)uv=>?4R=!

"+




(a





BA ῍ (34) m4 r  *9 0  !+Zῌ
5}~A #U47;dNῌ c  2

q2e2
8pe0r4!!  a  #῍
&

2 2
aq2e2
 a  qeuv
4pe0 8pe0r4
32p2e02r4

uva ῌ ST5

Fig. 11 )P+,ῌ c  eLJ ῌ |}~A 0 47N"  lm )&  =>?+ r῎4 4 r῎12 PPwx

j



0 +,W"PR" c 12c 6
V(r)u4eLJ  v r r!

5¤*" fg

456 " d<'£EF GHGIAJ*9k"&9*9¡

W¢t4*9#"

s (12,6)r῎6 P 5 "j ¡ fg

d+Z1 R" NhAi j+Zj"%

U47;d!P @AJ]^_ `ab4cP!"de fg d 16) .

(35)

4BA Z 2 :   

1 P Q

T*U  'VUWX*9YZ !



N }~A&  a R(R" r῎6 P*9S

Fig. 10"

V(r)uDe exp[v2a(rvre)]v2De exp[va(rvre)]78   *95 :; !

 ;dN" &#! #RwP $1  0!

 " :"!

:e d RIncRTar  

456

 BAnoApqrA s

 R Inc R Tar !" #:G 

Table 2. @AJ

Fig. 11.

SI §¨ [J(36)?( e0 ¥¦
῎1

2

2

C m]

( 

" )© 4pe0ª?(._ a m3 *979#!"«#D*¬ «HA CGS §¨£­®!&9Y

Z cm3 §¨ ¯9#K 

6?

? +Oy4kU !"῍ # 6 :hAi  °±+Z²³ ´ µ* "«  U4 Table 1 )P῍ ! U")P+,ῌ c ¶·% 

῎10

 U45

+%U

6 ! U  %&e  gAA"$* r 4 10῎10 m §¨¨ $P (36) mlm

10

mgAA U45 eLJ  meV

 % e¸¹º»¼·354

 %&4 eV?(._ a 4 10῎30 m3

§

?-

V(r)

q1, r3.010(37)43.4 (10ῌ30 m3) (K)  aΐ
ῌ10

7.20aΐq2
r4

m   3.86 eV  ῑ (12,6) ! meV "#$% &' !()* eV ( +,-. / 0!1 (Ar)  aΐ $ 1.64 (10ῌ30 m3)
 K (23#*, 4 r2.010ῌ10 m  *"($ 0.73 eV  meV 567" /
89

:

;

$ r ῌ4

<4.=

,

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Fig. 13.  Ejk

 !>#,"*  + (5?,@ABC#/ +5D<4

+,-.

A

,

 ?E$FG(:,H*A.FI

f$tNO=

J(KLM / +P:J@ H +(5  NO PQ(R(?ST U8VWXVYZ[\  E NO /7. 

]^($_:?

I#E¤-(ui* /NO+, "   f:, !(5I#ghi Fig. 12 (jk l/ < $ ,.* :$m / O, ++ $J(¢iE £+K, `(a2P5D( bcd m :,de O/  E($ !¡(¢iE,#

  [X(I# E ¥Q PQ.¦/8Z

Fig. 13(l/ ?ST, 2pb db 0§(fiP89
, dq 0§(I#
2pr sin q dq

+mnG

P

1O=

2

;

E$/¨ I# PqIe$?ST

Fig. 13n( x o  / $ O .=p  fq r$

"# 6 * , ]^( H©(i / x osG

: :ª86 $ « " / 2q¬­2qE3

$t

/

y o  <  y 

u<!  y  ?ST U8VWXVYZ[\ vwx b+ b z{?]y"/ ]^?]y+$#|$

H*AGK%-/ +P

Q ?ST~& ' +$K(b 1 gh:T$ I02pb db/H#

:2q¬­3PT$ I0q(q)2p sin qdq/ 4²,5i**D¢³.=

q(q)

 e

()}AG(, , e()}" ,"A(38) j  ´E,¥Q=

G,(%-7:$ *A/ bcd m

K_

qJ * (LMi*#gh Fig. 12"s

5D( ?$t_ + / ]^($ I,+ ?ST b $: :"# 

QP]y  +$x,

ῒ

4p
0

2p

, 

b ῌdb῎sin q ῍dq῏(38)´.¦J dW(sin q dq d*) (¢iE )4 (rCl)  )}*P i+#:, ! I#

E$R/ + $E/J2q K_/

j 1O=

de()}AG,%-7* / b2 gh$ b1 )*(2q¬­3P/ IJ(¢ E q(q) + =D± q  q¯dq(, + b "#(5de)}A4K%iP,7I#P I0 ® :,f  b  b¯db
(°

2p

q(q, *)dWῒ

2p ("bO=  Rj /
2p

p

0

0

ῒ ῒ q(q, *) sin q dq d*

p
0

nD

/  ! $ 

῎sin q dq
ῒ sinb q ῌ῍dbdq῏pq(q) sin q dq2p0µῒ b db(39)

0IJ2G E  ´E ?ST´6¶ E  ´Et7i·8¸,*+
,-. / (39) j?³T b $ 9 Kl#
5D(I 1O " b  +j E

iK:I¹6;u /º¦I

EjkFig. 14l/ 2

:<S »iP4 RInc¯RTar  )}A CM ¼
e.=?! ½(I#
Fig. 12. de¼ I/ ?ST (b) )4
(rCl) IJ (q)STJ f $ Rj 1O=
ῐ 355 ῐ/ ?

b i ?e½(ie.=?!
/S. Hayakawa

Fig. 14. JKL½ῌb
῎
sin fῌ
῍(RIncRTar)῏,bῌ῎ (40)fsinῌ1῍(RIncRTar)῏ q 

Fig. 15. JKL)*)*+,'-.

 f 
b῎qp!2fp!2 sinῌ1ῌ
῍(RIncRTar)῏ q(q) 3\UQ3'V6 (41)

JKL)* (46) UQ3"'7#$"#$ (38) %&'( sin q '($
sin qsin (p!2f)sin 2f2 sin f cos f  ]7V65[TDU'^_3s2p)*+, b ' q '-. 

p

p

0

0

Inc

Tar

2

p

0

b
p!q῎
q῎
ῌp
sinῌ
῍ 2 ῏sin῍2 ! 2῏
RIncRTar
q῎
cosῌ
῍2῏

(RIncRTar)2
sin q dq4

ῑ q(q) sin q dq2p ῑ(R R )
2p
ῑ sin q dq
4

(42)p(RIncRTar)p(RIncRTar)2p[cos q]0
[2]
2
2
2


(43)

p(RIncRTar)2(47)(43) -./012343567 "-,

`aQb)* 6 cQbdefghijFig. 15 815 b/(RIncRTar) 9 1 :;)*1(<

8I5#W(klmnop'qlrnopI q  0  b/(RIncRTar) 9 1 :=7(' (41)  stu Fig. 16 783 vwgQb)*(x7>9?@4($ )*+, 0 3(ABCD))* QbJK'y5z{#$|'?@(}* p (180ῒ) '($E3FGH7Id~mn94 ?@()*+,op 

JKL)* RIncRTar M, (43) NOPQ3"'7#$ R
db
1
q῎
!
sinῌ
῍2῏dq
2
RIncRTar7 9" s)*+,op JKL'($ b7<7I

"'7($ 7( 51  I5(44)"'I9 Qb

MI<(<xB 7 I5  M@(< "56

RIncRTar
db
q῎
!
sinῌ
῍2῏
dq
2

"

 7<

b/R ' q '-. `'1 3\l7

RIncRTar
p
῎
!
sinῌ
῍2 !f῏2MI"''( "Qu7

RIncRTar

cos f
2

' )*+,P(719A (<'
(45)"H94 s)*+, db/dq 9 (38) 7S'PQTDU9V6

TDU q(q) 9¡?'(¡?'($ ¢'£¤s Fig. 16  qRainbow 81<7M3TDU9b ῌdb῎q(q)
sin q ῍dq῏`a¡?7((<9qRainbow ¥¦(§¨9©ª )*+,9#$I4(' 9 0 7('"H94 s"

(RIncRTar) sin f ῌ(RIncRTar) cos f῎῏
2 sin f cos * ῍
2(RIncRTar)2
4< )*+,9I4($rn9@6

()*+,b9«ª"'7( (¬9­(®¯°'<APQ(46)

TDU7-3±² sG9³7((46) 983#W7JKL)* PQTDU9

 E5 «ªefghij´ Sbµ¶·¸j q 7XY1(<Z¹9(' «ªn?@I´º»¼d9(7(< [TDU

ῐ 356 ῐ,-

Fig. 16. 9'9"%:;<=>uvT 

    !

"#$%&'()%& '$ *+,-./0!
()%&
8. ῒΐ῔῎῍ῑῌ῏ῐ
2 ,-  CM 1 2345 m !6"7

89:;<=> V(r) )?@AB$  789:;<=> V(r) "CDEF
GHIJ 4578KL,-MNOPQ r'' 789:;<=>RSTUEFC

Fig. 17.

H 4578'VWX5'YZ[\ r '[\"?]
78''x  y ' r  f f2

^ f _/'"`a
"z{\'|:;<=> V(r)  0 'CLab 1' CM 1,- 2 bc " CM 1!

dZEF"Uef2) 

gh &i x ' y jklY Fig. 17 mRJEr

 r ' f '' n_o pq xrr cos f 

yrr sin fr(48)

qstuv'pq'&

dy
dr
df
r
sin fxr cos f
dt
dt
dt

(49)

(10) q Zi

EF'&H

EF5 (L)})

EF5 [\

 EF5

<Q ( mr )

^ (df/dt) 

2

OPQ  pq"H6
Lrrmvrbmv0rmr2

dfdt

 L iZ (51) q df/dt $2

(52)

'

 pq 1 ῐῌdrdf῎2
rmῑ῍ cos fwr sin f
2
dt
dt ῏

Er

2

dr
df῎ῒ
xῌ
῍dt sin fxr cos f dt ῏ΐL2
1 ῌdr῎2xV(r)m῍ ῏ x2
dt
2mr2[\ (r) _EF

2

1 ῐῌdr῎df῎ῒmxr2ῌ
῍ dt ῏ΐ2 ῑ῍dt῏(51)& :;<=>" r  ?ST1
1 ῐῌdx῎2 ῌdy῎2ῒ
Tr
mv2r
m
x
2
2 ῑ῍ dt ῏ ῍ dt ῏ΐr

1 ῐῌdr῎2 2ῌdf῎2ῒ
mxr ῍ ῏ΐxV(r)2 ῑ῍dt῏dt

 r "()%& Z V(r) "  'pqfy$

2

1
mv02rTxV(r)2z{ EFh"

dx
dr
df
r
cos fwr sin f
,
dt
dt
dt

CM 1EF (T)pqK

N%'}~RH (E)

(50)

(53)

(1/2)m(dr/dt)2  n:;<=>'c '"$ n (53) q 2 ' 3 YZ pq
῔ 357 ῔

S. Hayakawa





VE# (E#ective)dfc 
VE#(r)

L2
Eb2
V(r)
2 V(r)
2mr
r2(L /2mr )((Eb /r )) 
2

2

2

(54)

(58)

qkr" f "' fCl "' 5"! Fig. 12 _! "

2

῍

b
dr
2
b2
V(r) r1d 2 dEr%& "'()t_Yu q  pd2fCl  9! (58) ^:v#
w_qkrG

rCl U"^:x ?

*+,-./0123,-./,-45

q 123 by() *+ E "z3 p^`!  L2 67 8 8"' 59!

T#$

l :;"<3 L2῏2l(l1) =5>&5

q(b, E)pd2

5
: Fig. 18 ? O2 ""

V(r) @! E500 eV, b0.1, 0.15, 0.20A10

῏10

 BC  #$m῎

r῏2 DE?"ῌH45IJK45῍
O" r῏4 "

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6L" r

0MN

(r) 

6

"PQ@ r῏2 "RS

rCl

῍

b
dr
2
b2
V(r) r1d 2 dEr

9. 

!

6"F VE# G

{

u



(59)

 

| }MN : }? 9! 1 O"~qjzF" O MN
6 O  MN

N

61?M

6 O!  !

 BTῌ () *+UB123 VW"X6! MN " =5UU5 O  -ῌ Fig. 18 ?Y5 "~!  Oj4 !  O J"Z[\῍ "Z" :#$] Y῍jMN(53) ^_ dr/dt :`T ab"^ 5
dr
c
dt

῍ 2Em ῍ 1d r d V(r)
E

(55)

2

"eMfg"h! iL
"!

MN

2

b

jG

r H45iL :o = p^:

qkrG

῍

b2
V(r)
1d 2 dEr(rCl: Closest) "  0 6 VWa"G kl4 -5 "Y5./ O"Y9=_"6kl4 -mn? (52) ^:!
r2
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b
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6 VWa"G kl_5

O5 8 B#$

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N+

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Y=

Langevin    J917)! z?x  x j%&
MN

(56)

~

6 "L¡4#G MN "j¢£ ~5"!

rCl p^:B?

6 O>4"./! MN

¤ (polarizability)  ¤

6"

 9! (36)^=B  ! p^b2
V(rCl)
1d
d
0
2
E
rCl

VPol(r)d

(57)

aq2e2
32p2e02r4(60)

r῏4 DE?"ῌ ¥¦ ῎§ ῎¨+ g9#(56) ^"  6:s? p"^ 5

G _¡4 iῌ ©ª" 6L
9«J

5῍ "

,-5'


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Stevenson 9ῌ N+ Gioumousis"¬518)῍ "­¡4 -"ῌ (54) ^" V(r)  (60) ^:®!? 
9p^=῍
VE#(r)

Eb2
Eb2
aq2e2
2 VPol(r)
2 drr
32p2e02r4(61)

 r῏4 "#?"ῌ () *+6L

UB123 b H -ῌ r῏2 "#?#$
@"¯,-4ῌ Fig. 18 "a_ 2 $"°± VE# "Y¤,²῍ "¤,:³=kl4 9ῌ M

"
N

6m´µ?

J

O9Y῍"
"! kG

>"¤,'#¡4¶:·¸¹?

9! N+ "x¸¹-
Fig. 18. "C() *+
ῌ 358 ῌ

6"!º"Z » -¼½Y

56

qe
ῑ aῒ 2pe
E
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p

(65)

0

BBlm Q.`a1b2c((65))*+,-. 88K 
1 PQ2 aῒ SI

N

sOr16.9

ῑ aῒE 10ῌ30 m3
sOr  10ῌ20 m2

Fig. 19. Q.`a1b2cR+,-.

1.0 keV

(61)

E







r

aq e
0
32p2e02E





2



 

0





(62)

! eV &|PQ2Ivw (63)Nvw

! /01234,

rCr

bCr
ῑ2

Avw¤hK

¦

§o

P
2 2

2

0

Fig. 19 J KLM5678

 ¢Avw xN|>?@ rReact 

rso vw ª«¬$vw| Fig. 18 Jlm*+,-.h! n[

|~PQ2

6S[\ rCr  " ]] ^_ 

I|&rso$ ;  WX Q.`a1b2cWX d­   !e fg()*+,-.

h!$5678NO;iRSkU JVlmn[ 01234, Eb

b2rReact2®

2n Yp $Z  !$ fg()*+,-.

bCr lZqV$ *+,n[~ b yo$

T bCr Kh!o$1 PQ2

vw xNbCr

`a1b2c (sOr)  (63)



Q.


P

§o

aq2e2
῎
32p e02ErReact2῏<¯vw°± (67)

2

(69)
(69)

h!K

A A   Kr vw

vw¦

rcl ῎4῎PprReact2ῌ1®ῌ῍ ῍rReact῏῏  !$  uA*+,-. ~;I()*+,-.yo$

(68)

bcl4 ῎
PprReact2ῌ1®
῍
4rReact4῏-. } n[ 01234, uA

A

aq2e2
32p e02ErReact2

r2

A

lZy*+,-. rsoi

vw xN  $ B ()*+,| (62)22sReactPpb2Ppῌ
῍rReact ®

  uAPQ2 Ivw xN 
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$5678 rs;ij RStU JVlm! Eb2 fgK

(67)

2

 © | ;

NO;PQ2 RSTU JVWX YZ5

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11. 

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-. $ ,"; Table 3 = p9 100 u 6
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Fig. 20  b) %&#!"#$

'"!() *+,%%
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 &#WX Y#$ ++#&a  (Demkov26) "N *\#$ Landau῏Zener῏ (84) Stüeckelberg E L(]%^EFm (V

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adiabaric    T % 0 &   U  0 

21)E2 Landau , Zener24)  Stüeckelberg25) 
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A#-"+_  

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+a

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Table 3 #de*CDEFGf g <#R$ ) *+ NV

+,-.   -. +!0©ª ^)K fg«¬h

CDEFG  2 h+,/% 01CDE ­®¯CV1i¯°6) ±²e ³CV

FGf% 0.03 eV 2# 100 u 6ijC)^D

DEFG 100 eV 2CDEFG#*CV|H% > +j#±·kV%+#

+ de e k3l4 >m50

 ./¸¹ KLj,'º0»-

῎ 361 ῎y.#$Q´µ $

¶~S. Hayakawa

   11)

   !"#$%

&'()*+,-,./0123456

12)

7 89:;<=34>?

13)

@ 


14)



15)

1) ABCDE FGHIJBKLMN O PQR ST(1999).
2) U V W X FY B Z J B Z  B  K L O P Q R S T(1972).
3) UVWX FJBKL O [\]^ ST (2007).
4) _`abc defgh FJBZBKL O ijkl
ST (1981).
5) m n o p F q I   G H r s t O u v ] ^ S T(2003).
6) wxyz FGHrs{|H O [\]^ ST (2004).
7) }~῎%bic  h FBKL6G
Hrs O ST1Hkl ST (1976); R. D. Levine andR. B. Bernstein, “Molecular Reaction Dynamics andChemical Reactivity,” Oxford University Press, NewYork (1987).
8) R. G. Cooks, J. H. Beynob, R. M. Caprioli, and G. R.
Lester, “Metastable Ion,” Elservier, Amsterdam (1973).
9) “Collision Spectroscopy,” ed. by R. G. Cooks, Plenum,
New York (1978).
10) K. L. Busch, G. L. Glish, and S. A. McLuckey, “MassSpectrometry/Mass Spectrometry Techniques and ap-

16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)

Keywords: Cross section, Scattering, Kinetic energy release,
Impact parameter, Semiclassical method 
1A B  l 0A/B

ῌ1kJῌmolJ

eV

plications of tandem mass Spectrometry,” VCH, NewYork (1988).
    D WX  J. Mass Spectrom. Soc. Jpn., 49, 144 (2001).
D. T. Terwillinger, J. H. Beynon, and R. G. Cooks, Proc. R.
Soc. A, 341, 135 (1974).
S. Hayakawa, Int. J. Mass Spectrom. Ion Process., 60, 251(1989).
S. Hayakawa, A. Matsumoto, M. Toshioka, and T. Sugiura, Rev. Sci. Instrum., 63, 1958 (1992).
A. von Engel, “Ionized Gases 2nd Ed.,” Oxford Univ.
Press, London (1965).
I. Kusunoki, Bull. Chem. Soc. Jpn., 44, 2067 (1971).
P. Langevin, Ann. Chim. Phys., Ser. 8, 5, 245 (1905).
G. Gioumousis and D. P. Stevenson, J. Chem. Phys., 29,294 (1958).
T. Koizumi, K. Okuno, N. Kobayashi, and Y. Kaneko, J.
Phys. Soc. Jpn., 52, 2650 (1982).
T. Su and M. T. Bowers, Int. J. Mass Spectrom. Ion Phys.,
12, 347 (1973).
H. S. W. Massey, Rep. Prog. Phys., 12, 248 (1949).
J. B. Hasted, “Physics of Atomic Collisions,” Butterworths, London (1964).
L. D. Landau, Phys. Z. Soviet Union, 2, 46 (1932).
C. Zener, Proc. Roy. Soc. A, 137, 696 (1932).
E. C. G. Stüeckelberg, Helv. Phys. Acta, 5, 370 (1932).
Y. N. Demkov, Sov. Phys. JETP, 18, 138 (1964).

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