shift in n=2 muonium. The muonium atom is a hydrogen-like ..... t h e. o r b i t a l. e l e c t r o n . Since the charge of the u+. i s i d e n t i c a l t o t h a t o f. t h e ... B o h r ' s. c r i t e r i a. s h o u l d have energies and radii p B o h r. (. Z a. ) 2. 2. E. = -.
MEASUREMENT OF THE LAMB S H I F T IN MUONIUM
by CHARLES ALAN FRY
A THESIS SUBMITTED IN P A R T I A L FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
i THE FACULTY OF GRADUATE STUDIES Department of
We a c c e p t
Physics
t h i s t h e s i s as
to the required
conforming
standard
THE UNIVERSITY OF B R I T I S H COLUMBIA A u g u s t , 1985
©
C h a r l e s A l a n F r y , 1985
In p r e s e n t i n g
t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of
requirements f o r an advanced degree a t the
the
University
o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it
f r e e l y a v a i l a b l e f o r reference
and
study.
I further
agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may
be granted by the head o f
department o r by h i s o r her r e p r e s e n t a t i v e s .
my
It is
understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain
s h a l l not be allowed without my
permission.
Department of The U n i v e r s i t y o f B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date
/HI i
written
Abstract This thesis describes the f i r s t shift
in
n=2
bound s t a t e believed of
muonium.
of
to
two
The muonium
leptons
atom i s a h y d r o g e n - l i k e both
(u e~), +
of
which
be p o i n t - l i k e p a r t i c l e s . The p o i n t - l i k e
the constituent
uncertainty
m e a s u r e m e n t o f t h e Lamb
of
particles
the
simplifies
application
of quantum
(QED) t o t h e c a l c u l a t i o n
o f t h e Lamb s h i f t
atom.
t h e Lamb s h i f t
Measurements
of
and
are nature
reduces
the
electrodynamics in
the
i n hydrogen
muonium disagree
w i t h t h e p r e d i c t i o n s o f t h e o r y by a few s t a n d a r d d e v i a t i o n s ; however,
theoretical
predictions
also
o t h e r , p a r t l y because of d i f f i c u l t i e s treatment muonium the
of t h e proton
system
hydrogen
associated
the
will
be
t o t h o s e a l r e a d y made i n
a v a l u a b l e t e s t o f QED. The
present experiment
i s not intended t o t e s t
investigation
the
of
with
s t r u c t u r e . Thus a m e a s u r e m e n t i n t h e
of s i m i l a r p r e c i s i o n system
d i s a g r e e w i t h each
methods
QED.
It
i s an
and t e c h n i q u e s n e c e s s a r y t o
i
surmount
the
difficulties
The
available
presented
by
the
nature
of
I muonium. 10 ° + 1
first Lamb
number
of
muonium a t o m s i s a b o u t
t i m e s l e s s t h a n t h a t o f h y d r o g e n u s e d by Lamb measurement. shift
statistical were f o u n d
10701If
The MHz.
v a l u e o b t a i n e d f o r t h e n=2 The
a t t h e 68% c o n f i d e n c e to contribute a further
uncertainty level.
in his muonium
quoted
Systematic
2 MHz u n c e r t a i n t y .
is
effects
Table 1 .
1
1.1
The
1.2
H i s t o r i c a l
Muonium
Atom
1
P e r s p e c t i v e
1.2.1
Lamb's
1.2.2
The
3
Experiments
Race
between
Present S t a t u s and Experiment
of
6
Theory
the
Lamb
and
Experiment
S h i f t
8
C a l c u l a t i o n 9
1.4
O u t l i n e
of
the
T h e s i s
12
The
Muonium
Energy
L e v e l s
15
2.1
Symmetry
2.2
The
2.3
S e p a r a t i o n
2.4
N o n - r a d i a t i v e
2 . 5
3.
Contents
I n t r o d u c t i o n
1.3
2.
of
15
E i g e n s t a t e s of
of
the
F,
ny,
Center
and
J, of
Mass
L
16
M o t i o n
17
C o r r e c t i o n s
19
2.4.1
C o r r e c t i o n s
to
the
Fine
2 . 4 . 2
C o r r e c t i o n s
to
the
H y p e r f i n e
2 . 4 . 3
R e c o i l
R a d i a t i v e
s t r u c t u r e s t r u c t u r e
C o r r e c t i o n s
19 . . . . 2 1 22
C o r r e c t i o n s
25
2.5.1
S e l f - e n e r g y
25
2 . 5 . 2
Magnetic
28
2 . 5 . 3
Vacuum
P o l a r i z a t i o n
2 . 5 . 4
Higher
Order
the
29
C a l c u l a t i o n s
32
The
Formation
3.1
G e n e r a l
C o n s i d e r a t i o n s
35
3 . 2
Methods
of
35
3 . 3
The
3.4
S l o w i n g
2s
Muonium
Forming
F o i l
S h i f t
C o r r e c t i o n s
Summary
of
Lamb
B i n d i n g
28
2 . 6
Beam
of
Moment
Muonium
I n t e r a c t i o n
Muons
35
37 40
i i i
3.5
3.6
3.7 4.
5.
6.
The
S t a t i s t i c a l
P r o p e r t i e s
a
Degrader
50
3.5.1
Momentum
S t r a g g l i n g
50
3 . 5 . 2
M u l t i p l e
S c a t t e r i n g
51
Monte C a r l o Muon Beam . . .
S i m u l a t i o n
of
M o d e r a t i o n
of
the 52
Summary
58
R a d i o - f r e q u e n c y T r a n s i t i o n 4.1
The
4.2
Approximate
Time
E x c i t a t i o n
of
the
Lamb
s h i f t 59
Dependent
S c h r o d i n g e r
Equation
59
S o l u t i o n
61
4.2.1
DC
Stark
e f f e c t
64
4 . 2 . 2
AC
Stark
S h i f t
64
4 . 2 . 3
E f f e c t
D e s c r i p t i o n Procedure
of
of
the
the
2p
3 /
,
2
s t a t e
Apparatus
65
and
E x p e r i m e n t a l 66
5.1
Vacuum
5.2
S c i n t i l l a t i o n
5.3
N e u t r a l
5.4
RF
5.5
The
5.6
Data
A c q u i s i t i o n
5.7
Beam
Parameters
Data
of
System
66 Counters
P r o d u c t i o n
66
F o i l
68
Region Quench
R e d u c t i o n
70 Region
and
and and
and
M i c r o C h a n n e l Event
P l a t e s
73
T r i g g e r
E x p e r i m e n t a l
76
Rates
78
A n a l y s i s
82
6.1
Timing
82
6.2
N o r m a l i z a t i o n
92
6 . 3
Form
6.4
The
6 . 5
S y s t e m a t i c Measurement
of
the
Resonance
F i t t i n g
Procedure
Curve
U n c e r t a i n t i e s
92 95 i n
the
Lamb
S h i f t 96
iv
6 . 6
6.7 7.
6.5.1
RF
6 . 5 . 2
N o n - l i n e a r i t y
6 . 5 . 3
Alignment
6 . 5 . 4
V e l o c i t y
6 . 5 . 5
N o r m a l i z a t i o n
Other
E f f e c t s
6.6.1
T r a n s v e r s e
6 . 6 . 2
RF
6 . 6 . 3
Magnetic
Summary
Power
of
of
. . 9 6
t h e RF
t h e
RF
Power
Region
L e v e l
a n d t h e
103 Beam
. . 1 0 3
D i s t r i b u t i o n
104
U n c e r t a i n t y
104 105
Stark
of
U n c e r t a i n t y
Doppler
S h i f t
(Time
D i l a t i o n )
.105
s h i f t
105
F i e l d s
106
U n c e r t a i n t i e s
and S y s t e m a t i c
E f f e c t s
106
C o n c l u s i o n 7.1
108
Comparison Measurement
w i t h
t h e
L i m i t a t i o n s
7.3
New Methods Measurement
7.4
P o s s i b l e
of
t h e
Present
f o r
a
Measurement
of
P i o n i urn Summary
Lamb
S h i f t 108
7.2
7.5
Other
Technique Muonium
t h e
n=2
Lamb
110 Lamb
S h i f t . . . 1 1 2
S h i f t
i n
.• of
1 15
R e s u l t s
116
REFERENCES APPENDIX
118 A:
POISSON
THE
MAXIMUM
LIKELIHOOD
PROCESS
TECHNIQUE
FOR
A 123
v
List
of F i g u r e s page
Figure
1.1: S c h e m a t i c
o f t h e Muonium E n e r g y
Figure 1.2: S c h e m a t i c o f t h e a p p a r a t u s u s e d experiments Figure
Levels i n Lamb's
2 first 7
1.3: The L a y o u t o f t h e E x p e r i m e n t a l A r e a s a t TRIUMF. 13
Figure 2.1: Some Lamb s h i f t
Feynman d i a g r a m s w h i c h c o n t r i b u t e t o t h e 26
Figure 3.1: The n e u t r a l f r a c t i o n a n d r e l a t i v e p o p u l a t i o n i n various states f o r a beam o f positively charged particles emerging from a foil as a f u n c t i o n of velocity. 38 Figure 3.2: dp/dx f o r a l u m i n u m a s c a l c u l a t e d u s i n g e q u a t i o n 3.5 43 F i g u r e 3.3: Muon v e l o c i t y a s a f u n c t i o n o f p a t h l e n g t h aluminum degrader
i n an 45
Figure 3.4: P r o t o n v e l o c i t y a s a f u n c t i o n o f p a t h l e n g t h i n an a l u m i n u m d e g r a d e r . 46 Figure 3.5: Number o f p a r t i c l e s a v a i l a b l e f r o m t h e M13 beam l i n e a t TRIUMF a s a f u n c t i o n o f momentum p e r uk o f p r i m a r y p r o t o n c u r r e n t a t 500 MeV 48 F i g u r e 3.6: M o n t e C a r l o r e s u l t s f o r t h e f r a c t i o n o f a muon beam s t o p p i n g i n an a l u m i n u m d e g r a d e r a n d t h e n e u t r a l f r a c t i o n a s a f u n c t i o n o f i n c i d e n t momentum 54 F i g u r e 3.7: M o n t e C a r l o r e s u l t s f o r t h e f r a c t i o n o f t h e beam emerging from t h e degrader w i t h momentum less than 2 MeV/c a s a f u n c t i o n o f t h e i n c i d e n t muon momentum. ...55 F i g u r e 3.8: C o m p a r i s o n o f t h e Monte C a r l o results with e x p e r i m e n t f o r t h e number o f p a r t i c l e s e m e r g i n g f r o m t h e f o i l w i t h momentum l e s s t h a n 2 MeV/c a s a f u n c t i o n of i n c i d e n t momentum 57 Figure
5.1: A s c h e m a t i c d i a g r a m o f t h e a p p a r a t u s
67
Figure
5.2: The RF t r a n s m i s s i o n
71
Figure
5.3: The RF s y s t e m
l i n e arrangement
72
F i g u r e 5.4: The e l e c t r i c f i e l d i n t h e q u e n c h r e g i o n . V i e w i s from the s i d e a t the v e r t i c a l midplane 74 vi
F i g u r e 5.5: E f f i c i e n c y o f c h a n n e l e l e c t r o n m u l t i p l i e r s a s a f u n c t i o n o f wave l e n g t h . 75 F i g u r e 5.6: T y p i c a l c i r c u i t used t o run plate. Specific values of the capacitances depend on the size micro-channel p l a t e s F i g u r e 5.7: S i m p l i f i e d data a c q u i s i t i o n Figure
diagram
a micro-channel r e s i s t a n c e s and and kind of 77
of the e l e c t r o n i c
logic
5.8: The M13 beam l i n e a t TRIUMF
for 79 80
F i g u r e 6.1: A t y p i c a l t i m e - o f - f l i g h t h i s t o g r a m f o r p a r t i c l e s t r a v e l l i n g b e t w e e n t h e i n c i d e n t s c i n t i l l a t o r a n d MCP B. 84 F i g u r e 6.2: E v e n t s a s a f u n c t i o n o f t i m e - o f - f l i g h t a n d time of d e t e c t i o n o f a Lyman-a p h o t o n . See t e x t f o r m e a n i n g s o f a , b, c 85 F i g u r e 6.3: The t i m i n g c u t s on t h e e v e n t s o f F i g u r e text)
6.2 ( s e e 86
Figure 6.4: Events a s a f u n c t i o n o f 1/0 a n d t i m e i n t h e quench r e g i o n ( i . e . time of d e t e c t i o n o f t h e Lyman-a photon less t h e time of e n t r y i n t o t h e quench r e g i o n ) . 88 Figure 6.5: 2s muonium d e t e c t e d a s a f u n c t i o n o f v e l o c i t y . The e f f e c t o f t i m i n g c r i t e r i a f o r e n t r y i n t o t h e q u e n c h region i s i l l u s t r a t e d 89 F i g u r e 6.6: 2s muonium d e t e c t e d a s a f u n c t i o n o f t i m e from entry into t h e q u e n c h r e g i o n t o e m i t a Lyman-a p h o t o n . The e f f e c t o f v e l o c i t y r e q u i r e m e n t s i s i l l u s t r a t e d . ..90 Figure 6.7: The d a t a p o i n t s a n d b e s t f i t r e s o n a n c e a f u n c t i o n o f a p p l i e d RF power a n d f r e q u e n c y F i g u r e 6.8: The b e s t f i t r e s o n a n c e power l e v e l s a t which data circles a r e an independent (see t e x t ) Figure and
c u r v e shown f o r t h e t h r e e was a c q u i r e d . . The open t e s t of the n o r m a l i z a t i o n 98
6.9: x contours for variation the signal i n t e n s i t y , a 2
o f t h e Lamb s h i f t S 100
Figure 6.10: x contours for variation of i n t e n s i t y , a and background i n t e n s i t y , b 2
curve as 97
the
signal 101
F i g u r e 7 . 1 : The d a t a o b t a i n e d by B a d e r s t a c h e r et al. f o r t h e Lamb s h i f t t r a n s i t i o n a n d a s c h e m a t i c o f t h e a p p a r a t u s used 1 09 VI1
List
of T a b l e s page
Table 2.1: V a r i o u s c o n t r i b u t i o n s h y d r o g e n a n d muonium T a b l e 2.2: Lamb s h i f t
calculation
to
results
the
Lamb
shift in 33
f r o m T a b l e 2.1..34
T a b l e 5.1: Summary o f m a t e r i a l s p r e s e n t i n t h e p a t h muon beam T a b l e 6.1: The o b s e r v e d numbers of counts s i g n a l s u s e d t o d e t e r m i n e t h e Lamb s h i f t
and
of t h e 69
normalized 91
T a b l e 6.2: The r e s u l t s o f v a r i o u s f i t s t o t h e resonance d a t a , i n w h i c h d i f f e r e n t p a r a m e t e r s have b e e n a l l o w e d t o vary. L i n e I I I i s the the quoted result f o r t h e Lamb shift 1 00 T a b l e 6.3: Summary o f t h e v a r i o u s c o n t r i b u t i o n s s y s t e m a t i c u n c e r t a i n t y o f t h e Lamb s h i f t
viii
to the 103
Acknowledgements This
experiment
successful wish t o
without
thank
manpower
my
and
thesis
could
collaborators
necessary
attention
have
to
run
the
who
helped
experiments
to
detail
in
provide
t o Rob K i e f l
the
the
very
inception
measure the Lamb s h i f t , success
of
the
of
the
Bailey,
experiment.
Gord
for h i s
f i n a l design of the Warren,
experimental program to
was i n l a r g e part r e p o n s i b l e f o r the I a l s o l e a r n e d , r e c e i v e d much
encouragement, and gained i n s i g h t John
the
over the many
apparatus. The encouragement and a s s i s t a n c e of John from
been
the a s s i s t a n c e of a great many people. I
weeks of d a t a - t a k i n g . I owe many thanks careful
not
Giles,
from
conversations
with
Glen M a r s h a l l , and A r t O l i n f o r
which I am very g r a t e f u l . Tim M i l e s deserves
thanks
for his
a s s i s t a n c e , above and beyond the c a l l of duty, with the data acquisition
system.
corrections
and
I
very
much
appreciate
many
suggestions of J e s s Brewer i n c o r p o r a t e d i n
the f i n a l d r a f t of the t h e s i s , as w e l l enthusiasm,
the
and e f f o r t
h i s generosity,
over the past few years as one of the
c o - s u p e r v i s o r s of my work. F i n a l l y , most h e a r t f e l t thanks
as
I
wish
to
express
my
to C h r i s Oram, with whom I worked most
c l o s e l y over the course of the experimental program, f o r h i s guidance,
a s s i s t a n c e , and f r i e n d s h i p .
ix
1 . INTRODUCTION
1.1
T H E MUONIUM ATOM
The
muonium
very
much
some
In
l i k e
1836
almost
atom the
t i m e s
c a s e
of
a p p r o x i m a t e l y
207
Since
the
p r o t o n , the as
the
hydrogen
times
atom.
i s The
which t h i s
i s
l e v e l of
the of
u
i s
of
muon
a
i s to
s i m p l i f i e s
p r o t o n ,
S,
be
a
the
i n
for
a n c
the
Lamb
muon
the
i s
over
p r o t o n
motion
must of
1
a
The
to
be
the
e x p l a i n e d
mass
between
the
magnetic
1.1
shows e x c i t e d
between energy
v a l u e
of
the
of
the
the
Lamb
n o t a t i o n . u n l i k e r a d i u s
the of
of
l e s s
p a i d muon
to
p r o t o n ,
about
1
fm;
muonium
s t r u c t u r e .
times be
that
f i r s t
average
e
treatment
1836/207
a t t e n t i o n
n
Lamb's
m a t h e m a t i c a l of
t
p a r t i c l e ,
out
i d e n t i c a l
d i f f e r e n c e
s h i f t .
f o l l o w i n g
spread
*
of
the
of
and
muon
e l e c t r o n .
F i g u r e
ground
an
of
can
reduced
t h r e e .
energy
2s^^
almost
magnitudes
the
to
as
o r b i t s .
p o s i t i v e
i d e n t i c a l
of
a c t s
o r b i t a l
i s
b e i n g
e l e c t r o n a
the
the
f a c t o r
The
i s
It
p r o t o n ,
e l e c t r o n ,
d i f f e r e n c e s
r e l a t i v e
unknowns
more of
the
p o i n t - l i k e
the
the
because
of
the
c a l l e d by
known
+
diagram
denoted
e f f e c t s
the
and
muonium.
i s
c i r c u m v e n t s hand,
of
p a r t i c l e s .
the
the
n u c l e u s
mass
d i f f e r e n c e s
energy
s h i f t
which
the
Most
muonium
energy
s t a t e s
the
e l e c t r o s t a t i c a l l y
i s
a p p r o x i m a t e l y
2 p ^ 2
than
the
two
which
atom
moments,
average
i n
of
of
from
(n=2)
atom
around
muonium
and
s t a t e
system
massive
n u c l e u s
hydrogen
the
bound
charge
hydrogen a r i s i n g
a
more
s t a t i o n a r y
the
i s
On
and
the
other
massive
than
the
c a l c u l a t i o n
(nucleus)
in
a
L
2P3/2
—r 10,922 MHz
I
F i g u r e 1.1:
2
74 MHz 1 *
Schematic of the Muonium Energy
Levels
3
d e s c r i p t i o n
of
1.2
HISTORICAL
In
t h e
of
r e v e a l e d t h e
part
atoms,
t h e
Balmer
that
not
r a d i a t e
the
o r b i t
c o n s t a n t ,
e n e r g i e s
s o l a r
that
c e n t u r y ,
i n
t h e
f i r s t
of
Bohr
i t s
l a b o r a t o r y ,
(Bohr, i n
a
momentum
i n t e g r a l
had
e x p l a n a t i o n
1913,
1914).
He
Coulomb
f i e l d
d i d
and
l e n g t h
number
s a t i s f y i n g
s p e c t r o s c o p y
s u c c e s s f u l
o r b i t i n g
of
an
o r b i t s
and
The
product
and
p
n i n e t e e n t h
e l e c t r o n
the
The
the
was
equaled
h.
atom.
s e r i e s .
an
i f
of
both
o b s e r v a t i o n s
proposed
have
muonium
PERSPECTIVE
l a t t e r
hydrogen
of
t h e
t h e
times
B o h r ' s
of
P l a n c k ' s
c r i t e r i a
should
r a d i i
Bohr
E
(
=
Z
a
)
2
2
-
mc 2 n
n
;
2
a
2
=
— a Z
n
0
. . . ( 1 . 1 ) r e l a t i v e
t o
the
energy
1/137.03604(11) v a l u e s
of
today
v a l u e s
Bohr of
energy,
n=1
i s
known
s u b s c r i p t
r a t h e r
(n=l)
u s i n g
•
e
2
Data
t h e a s
/ 2 a
0
h c
than
Taking
z e r o , t h e
t h e
a / 4 * a
0
that
a r e
2
and
t h e
number
or
.
Rydberg
eV
or
The i s
mass on
r e s t
R
e l e c t r o n
=
a l l
i n f i n i t e l y
a t
Rydberg
1
a
accepted
t a k e s
the
Bohr
m a s s
the
n
the
free
where
e l e c t r o n
e l e c t r o n
of
mass
=13.6058
r e s t ,
l a b e l l i n g free
reduced mass
The
value
i n f i n i t e
a t
MeV/c
c o n s t a n t
1984).
a b s o l u t e
i n f i n i t e
•
e l e c t r o n
.5110034(14)
i n d i c a t e s
t h e
free
Group,
t h e
than
a
s t r u c t u r e
g r e a t e r
z e r o
used
0
m =
o r b i t s .
z e r o
'R
f i n e
( P a r t i c l e
i n t e g e r many
t h e
and
of
0
a s
energy
f o r
,
the
where
mass,
f i r s t
3 . 2 8 9 8 5 - 1 0
m,
Bohr
denoted
by
9
the
i s
r a d i u s a
MHz
0
.
It
4 is
l a r g e compared t o t h e p r o t o n s i z e ,
50000 fm. T h e B o h r e n e r g y d i f f e r e n c e s the few
observed parts
wavelengths
energy r e l a t i o n
the
solution electron
(Schrodinger,
1926)
( 1 . 1 ) on a f i r m e r of
that
a differential
Bohr
had
included
the
three
showed t h a t n,
a n g u l a r momentum ranges
deriving
i t from
e q u a t i o n f o r t h e motion of This
made
n a t u r a l l y l e d to the
to "quantize" solution
value
should
of
the
t h e energy
also
naturally
principal
be n s t a t e s , d i f f e r i n g
where t h e " o r b i t a l "
through integers
n states associated
t h e Bohr
d i m e n s i o n a l nature of t h e r e a l
f o r each
there
next placed
basis,
l e v e l s of t h e atom. S c h r o d i n g e r ' s
number
with
of t h e Balmer s e r i e s t o w i t h i n a
i n a Coulomb f i e l d .
assumptions
and
were i n a g r e e m e n t
i n 10,000.
Schrodinger
the
being of the order of
problem quantum
in orbital
quantum
number
/
0 , 1 , 2 , . . . ( n - 1 ) . The e n e r g i e s o f t h e
with each v a l u e of n s t i l l
exhibited
no
d e p e n d e n c e o n / a l t h o u g h i t was e x p e c t e d t h a t a
relativistic
treatment of t h e problem should break the n - f o l d
degeneracy.
It
was
also
known by t h i s t i m e t h a t
the electron
" s p i n " a n d h a d a m a g n e t i c moment a s s o c i a t e d Attempts (Dirac,
to find a relativistic 1927) p r o p o s e d t h e
explained
the
successfully or the
"fine
predicted
spin.
equation f a i l e d u n t i l
Dirac
of
the
"Dirac spin
the previously
equation"
which
o f t h e e l e c t r o n and
observed
"splittings"
s t r u c t u r e " of the Balmer s e r i e s as consequences of
electron
effects.
presence
the
famous
with
possessed
spin
magnetic
The e l e c t r o n
moment
and
of
relativistic
s p i n a n g u l a r momentum stf = K/2 s h o u l d
5 combine with the o r b i t a l angular total given
angular by
Dirac twice
momentum
|/±s |. One
theory
was
the value
electron
where the allowed
that
t h e r e f o r e behaves
momentum with
the
the
fine
/=1
magnetically
of the e l e c t r o n as
spectroscopy
structure
r e s o l u t i o n to observe that the predicted
by
of
hydrogen
the
Dirac
equation.
of the 2 5 ^ 2
to
the
2p y 1
electronic
2
and
binding
able
energy
Only
nuclear
in
the
25^2
wavefunctions
relative do
Coulomb
potential
distances.
Uhling
(Uhling,
1 935)
[reduced] had
e x p l a i n the
of the wrong s i g n and required
shift.
In
i f the
at
short
a l r e a d y proposed
p o l a r i z a t i o n of the D i r a c vacuum around a e f f e c t was
the
significant
t h e r e f o r e the proposed r e d u c t i o n c o u l d occur modified
be
s t a t e were
overlap;
were
less
could
state
have
to
Pasternack
10% of the f i n e s t r u c t u r e i n t e r v a l state.
be
enough
i n t e r v a l s were s l i g h t l y
explained
reduced by about
a
state
with
observations
the
should
was
(Pasternack,1938) proposed t h a t the if
the
state.
2
By the e a r l y 1930's atomic
those
exactly
c a s e s : y=/+s=0+l/2 f o r the 2 5 ^ 2
and y=/-s=1-1/2 f o r the 2 p ^
than
the
electron
energy of a s t a t e with j=\/2
f o r the two
measure
are
i n a c l a s s i c a l model.
motion a s s o c i a t e d with the
in nature and
l i k e o r b i t a l angular
identical
of j
that the s p i n magnetic moment has
were d i s t r i b u t e d i d e n t i c a l l y
so
values
single
i t would have i f the charge and mass of
is orbital
whole
a
of the most dramatic p r e d i c t i o n s of
T h i s means that angular spin
momentum to give
charge,
but
the the
of too small a magnitude to 1947
Lamb
(Lamb,
1947)
6 explain
the
reported
required
shift.
h i s observation
In
1947
MHz" u s i n g a m i c r o w a v e t e c h n i q u e .
the
same
Bethe
successful
calculation
difference,
obtaining
1040
(Bethe,
of a
the shift
MHz due t o t h e i n t e r a c t i o n
vacuum
1.2.1
On t h e way home 1947)
25^2
made
-
the
Pi/2
2
from first
energy
of t h e 2 5 ^ 2 s t a t e of about of
the
electron
with
the
LAMB'S EXPERIMENTS
follows The
the
(see Figure
hot
oven
atoms
through
velocities
principle
1 . 2 ) . H y d r o g e n was p r e p a r e d
were a l l o w e d a
o f t h e Lamb e x p e r i m e n t s was a s
small
on t h e o r d e r
probability first
of
as
the
s t a b l e as they
hole.
Travelling
o f 10* m/s t h e y
hand,
2p-states.
being
c o u l d r a p i d l y (T a b o u t
metastable,
the emission stream
thermal
were bombarded
with
so a s t o maximize t h e
the 2s-states
The p - s t a t e s h o w e v e r were n o t 1.6 n s ) r e t u r n t o t h e
o f a Lyman-a p h o t o n
d i p o l e t r a n s i t i o n . The were
with
(n=2). T h i s would p o p u l a t e
g r o u n d s t a t e by e m i s s i o n electric
oven.
e x c i t i n g atoms f r o m t h e g r o u n d s t a t e t o t h e
excited state
well
i n an
t o escape i n a s t r e a m from t h e
a beam o f e l e c t r o n s w h i c h was a d j u s t e d
The
1947)
field.
Briefly,
as
(Lamb,
o f an e n e r g y d i f f e r e n c e o f " a b o u t
1000
meeting,
Lamb
2s
states,
( 1 2 2 nm) v i a an on
t h e dominant d e - e x c i t a t i o n
o f two p h o t o n s (T a b o u t
1/7 o f a
o f atoms p a s s e d t h r o u g h a microwave
r e g i o n and f i n a l l y
the
struck a detector
which
other process
second).
interaction
registered
the
7
F i g u r e 1.2: Schematic of the a p p a r a t u s used i n Lamb's f i r s t experiments.
8
current
o f atoms i n e x c i t e d s t a t e s ,
consisting
1
mainly
of
a t o m s i n t h e 2s s t a t e . I f t h e m i c r o w a v e s were o f t h e c o r r e c t f r e q u e n c y t o e x c i t e t r a n s i t i o n s b e t w e e n t h e 2s^^ levels,
a n d were o f s u f f i c i e n t
power d e n s i t y ,
2s atoms w o u l d be t r a n s f e r r e d t o t h e and
de-excite
before
striking
r e g i s t e r e d by t h e d e t e c t o r At
that
required was
difficult
Lamb
microwaves of the frequency
generate
a
level
and
variable
of
power
required
i n a magnetic 2
1
2
1 /
/2
through t h e a p p l i e d microwave frequency,
By
but i t
frequency
h i s co-workers solved
s o a s t o sweep t h e 2 s y ~ P
reduction
The c u r r e n t
w o u l d be r e d u c e d .
t h e microwave r e g i o n
varied
detector.
2p-levels
1000 MHz) was n o t d i f f i c u l t
a constant
experiment. placing
to
the metastable
short-lived
the
generating
(approximately
maintaining
be
time,
a n d 2-g>^^
f o r the
t h e p r o b l e m by
field e n e r
z
s h i f t
=
0 . 8 6 2 ( 12)
by
fin
0.102
MHz,
to
Lamb
v a l u e
i n
F=0
to
l i f e t i m e
of
the
2 p ^
5
=
i n
a
shows
agreement
from
(1983)
t h e o r e t i c a l S
with
MHz
energy
measured
o b t a i n
the
e x p e r i m e n t a l
t r a n s i t i o n
to
the
1057.845(9)
technique
s t a t e
2
are
a l r e a d y
on
2.2
c u r r e n t
P a l ' c h i k o v
r e l y i n g
the
F=1
2
f i e l d
s p l i t t i n g s .
t e c h n i q u e ,
The
o b t a i n s
2 p ^
from
Table
hydrogen
(1981)
S
c o n t r i b u t i n g
v a l u e s .
s h i f t
of
CALCULATIONS
muonium.
o s c i l l a t o r y
h y p e r f i n e
d i f f e r e n t
for
terms
and
Lundeen
separated
deduced
the
SHIFT
v a r i o u s
hydrogen
for
proton
i n c r e a s e
LAMB
shows
r e s u l t i n g
each
to
the
B o r i e .
OF
2.1
s h i f t s
i s
of
by
using
which
he
v a l u e s
of
used
a
much
c a l c u l a t i o n =
of
1057.8514(19)
MHz. Mohr's v a l u e
of
(1976)
the
r . m . s .
h i s
r e s u l t
one
o b t a i n s
the
e x p e r i m e n t a l
i n c l u d e MHz,
even
S
=
B o r i e ' s
which
o b t a i n s
for
S
=
more
c o r r e c t i o n
i s
r e s u l t charge
the
c u r r e n t l y
r e s u l t s
c o r r e c t i o n ,
1057.93(1) than here
MHz,
Mohr's
g i v e s
S
=
a
of
the
a c c e p t e d
MHz,
by
agreement
hydrogen
r a d i u s
1057.88(1)
i n
for
which few
which
value
i s
d i s a g r e e s
MHz,
0.862(9) w i t h
both
d e v i a t i o n s .
experiment.
c a l c u l a t i o n .
i n c o r r e c t C o r r e c t i n g
of
d i s a g r e e s
r e s u l t
1057.89(1)
an
p r o t o n .
standard
M o h r ' s w i t h
used
S
*
we
(1977)
experiment
I n c l u d i n g which
of
1057.84(1)
E r i c k s o n w i t h
If
fm
B o r i e ' s i s
s t i l l
33
EFFECT
HYDROGEN
MUONIUM
(MHz) SELF
ENERGY
Second
order
(2.23)
F o u r t h
o r d e r
(2.24)
g
e
- 2
(MHz)
( 2 . 8 )
AND
997.611
1009.924 0.444
0.444
(2.25)
Second
order
67.720
66.928
F o u r t h
order
- 0 . 1 0 3
- 0 . 1 0 3
VACUUM
POLARIZATION - 2 7 . 0 8 4
- 2 6 . 7 3 9
Second
order
F o u r t h
order
RELATIVISTIC
(2.26) ( 2 . 2 7 )
i I
- 0 . 2 3 9
EFFECTS
(2.28)
- 0 . 2 3 9
7.140
7.140
j
I
i
NUCLEUS
DIRAC
MOMENT
(2.10)
-0.171
- 0 . 0 0 2
j i
HIGHER
ORDER
EFFECTS
(
(2.29)
!
E r i c k s o n
- 0 . 3 7 2
- 0 . 3 7 2
Mohr
- 0 . 4 2 4
-0.424
RECOIL Owen
(Coulomb
FINITE B o r i e
(2.18)
0.359 r e c o i l )
SIZE ( f i n i t e
s i z e
Table 2 . 1 : V a r i o u s and Muonium.
C o n t r i b u t i o n s
3 . 188
- 0 . 0 7 4
- 0 . 6 5 6
0.145
0.000
0.000
- 0 . 0 4 2
c o r r e c t i o n )
t o
t h e
Lamb
S h i f t
1
i n
Hydrogen
34
higher
than
Owen f i r s t
experiment
h a s c a l c u l a t e d
p r i n c i p l e s ,
c a l c u l a t i o n , h y p e r f i n e
r e s u l t .
of
however,
(Owen, Owen's
f o r
t h e
(which the
he
hydrogen
r e s u l t
by
method The
appears
t o
t h e
Lamb
c o r r e c t i o n
Table
2 . 9 )
2 . 2 :
LAMB
i s
Lamb
SHIFT
r e c o i l " ) .
t o
s h i f t
MHz
f o r
t h e
seen
t o
s h i f t
muonium
he
t o
t h i s
moment
the l a t e r s h i f t
value
one
method
- 0 . 6 5 MHz term
i n
reduces
the
g i v i n g
A p p l y i n g •
h i s
good Mohr's
1047.64
MHz.
of
muon
the
n e g l i g i b l e .
c a l c u l a t i o n
(MHz)
t h e
thus
S
f o r
Lamb
E r i c k s o n
g i v e s
from In
E r i c k s o n
experiment.
anomalous be
t h e
I n c l u d i n g
1057.86(1)
i n
t h e
amounting
of
a n d
which
from
u s i n g
c a l c u l a t i o n
t h e o r y
1973).
v a l u e s
atom
d i f f e r
term
muonium
(Owen,
a f f e c t i n g t o
d e v i a t i o n s .
i n
i n c o r r e c t
s h i f t
s i n g l e
s h i f t
MHz
between
(equation
TOTAL
r e s u l t
Lamb
0.074
agreement
without
"Coulomb
MHz
muonium
1984)
a
standard
s h i f t
1047.03
t h e
Lamb
of
Lamb
o b t a i n e d
of
by
c a l l s
c o u p l e
t h e
he
muonium
c a l c u l a t i o n
a
o b t a i n i n g
s t r u c t u r e
c o r r e c t e d
o b t a i n s
by
r e s u l t s
from
HYDROGEN
Table
2.1
MUONIUM
E r i c k s o n
1057.93
1047.69
Mohr
1057.88
1047.64
E r i c k s o n
and
B o r i e
1057.89
1047.69
E r i c k s o n
a n d
Owen
1057.66
1047.03
1057.84
1047.64
Mohr
and
B o r i e
3.
3.1 A
GENERAL
Lamb
measurement
( r e c a l l
l i f e t i m e ,
1.6
the n s ,
width
of
i t
t h e r e f o r e
i s
times
about
of
100
must
2p In
n e c e s s a r y
order t o
longer
remain
i n
l e a s t
order
of
10
such
that
over
t h e
f l i g h t
T h i s
i s
a l s o
samples t h e r m a l ,
t h e
mean
We
now
s o u r c e s beam
t h e a s
METHODS
t h e
r a p i d l y
(such
3.2
to
i s
OF
case S i 0
2
i n )
l i n e s
muons of
second
c a n
l i n e s .
W i t h i n
t h e be t h e
t h e
a l t h o u g h
time
be
free
of
f o r
times
at
must
be
p r o b a b l i t y
of
atom
i s
10*
T o r r ;
5
l o w .
c o l l i s i o n a l
p r o d u c t i o n
methods
of
t h e
This
o t h e r w i s e p r o c e s s e s .
muonium
i n
powder
e n e r g i e s
i s
very
s h o r t .
t o
form
muonium
d i s c u s s e d
a v a i l a b l e meson
than
f o r n=2
experiment
t h e
by
l e v e l s
a r e
MUONIUM
v a r i o u s
above.
today
a r e
f a c t o r i e s .
d e l i v e r e d time
b e t t e r
where,
c o l l i s i o n
c o n s i d e r a t i o n s of
of
n=2
The
g a s m o l e c u l e s
d e - e x c i t e d
FORMING
examine
of
path
l e v e l
muonium
and
t h e
mean
a
l i f e t i m e .
a p p a r a t u s
t h e
t h e
e x c i t e d The
t o
n=2
l e v e l
Hence
i n t e r a c t i o n
muonium
t h e
n s .
vacuum
vacuums
t h e
n=2
1.1).
d e - e x c i t e
and
a
t h e
c o r r e s p o n d s t o
than
i n
F i g u r e
w a l l s
i n
means
of
observe
t h e
performed
the
MUONIUM
muonium
l e v e l
t h e
t h e
r e q u i r e s
t h e
w i t h
g e n e r a l l y
2S
diagram
i n t e r a c t i o n of
OF
l e v e l
MHz.
s i g n i f i c a n t l y
muonium
FORMATION
CONSIDERATIONS
s h i f t
s t a t e
THE
t o
s t r u c t u r e
35
an of
The
those
w i t h
most
of
t h e
T y p i c a l l y
10
experiment t h e
proton
by
a
view
c o p i o u s secondary
s
v*
these beam
per beam which
36 produces
the
The
muons,
p o s i t i v e l y
converted
to
c o n v e r s i o n
work
e f f i c i e n c y
i s
the
v e l o c i t y
the
a
w e l l
of
the
u+
f l u x v
methods
used
i n
v a p o u r ) ,
higher to have a l s o
a
e x c i t e d
Hence,
( e . g . ,
p r o c e e d i n g i n t e n s e
v e l o c i t i e s ,
but
i n
r e a s o n a b l e
improve momentum
slowed
s i z e , down.
proposed
the
c r i t i c a l s t a t e .
must
be
methods
of
if
and
They
t h e i r r e q u i r e
to
optimize
one
wishes
U n f o r t u n a t e l y ,
beam
l i n e s
f i n d s
i s
of
that
charged
beams,
charge
exchange
to the
rather
the
more
as
those
such
b r i g h t n e s s
beams.
the
beam
be
order
i n
Caesium
suggested.
r e c o m b i n a t i o n
has
been
r e l a t i v e l y keep
the
muonium
thus
produced
(Taqqu,
space 1984)
d e c r e a s e
would methods
p o t e n t i a l l y
momentum
the
even
apparatus
c o m p r e s s i o n which
of
i n v e s t i g a t e d
e f f i c i e n t
to
Phase
and
been
Coulomb
e l e c t r o n c o u l d
been
g r e a t e r .
c/100)
"tuned"
have by
and
be
>
b
we
have A p
0
the / A p
law *
( p / p
0
)
5
/
2
. . . ( 3 . 8 )
which P
i n
x
per
d e t e r m i n e s the
u n i t
the
degrader
i n c i d e n t
number as
a
of
f u n c t i o n
momentum, P
x
p a r t i c l e s
p
( p ) d p
0
.
=
of
One
the
=
p
0
( v
0
u n i t
number
momentum,
of
p a r t i c l e s
has
Po(Po)rfPo
(v/b) Pv(v)
per
5 / 2
) ( v
X
0
/ b )
5
+1 trn— /
2
+ 1 . . . ( 3 . 9 )
E q u a t i o n momentum for
f a l l s
u n i f o r m
momentum degrader
1
3 . 9 shows
One
l i n e a r
p
t h a t
r a p i d l y
p r o d u c t i o n ,
the
w i l l
have
0
n o t e s depth
t h a t of
the
i n
as
of
the
of
of
f o l l o w i n g
g e n e r a l
p e n e t r a t i o n
p a t h
p a r t i c l e s
v e l o c i t y
p a r t i c l e s
number the
number
i s
reduced
throughout
p a r t i c l e s
per
a
and
degrader
emerging
from
u n i t t h a t of the
shape:
l e n g t h
because
of
i s
g r e a t e r
m u l t i p l e
than
the
s c a t t e r i n g .
45
F i g u r e 3 . 3 : Muon v e l o c i t y as a f u n c t i o n of p a t h l e n g t h i n an aluminum d e g r a d e r .
46
PROTON
F i g u r e
3.4:
aluminum
VELOCITY
Proton
d e g r a d e r .
v e l o c i t y
IN
a s
a
RLUMINUM
f u n c t i o n
of
DLGRRDER
p a t h
l e n g t h
i n
an
47
P K
(v/b)5/2+1
"*
x
0
;
;
p < p
}
o t h e r w i s e
. . . T h i s
i s
j u s t
t h e
s i t u a t i o n
Numerous
e x p e r i m e n t s
3 . 5
t h e
shows
have
r e s u l t s
f o r
i n
the
c o n f i r m e d
t h e
M13
(3.10)
p r o d u c t i o n equation
beamline
a t
t a r g e t .
3.10.
Figure
TRIUMF
(Oram,
p r o d u c t i o n
target
1981b). The s e l e c t s the
secondary a
c h a n n e l
range
channel
of
v i e w i n g
momenta
momentum.
the
s p e c i f i e d
C l e a r l y ,
by
f o r
Ap
/ p
f i x e d
where Ap
/ p c
e q u a t i o n
( 3 . 8 ) )
the
number
of
muons
p
i s (see
c
t r a n s p o r t e d
w i l l
7/2 decrease
a s
p „ c
.
P a r t i c l e s
of
i n c i d e n t
on
f a l l
a
i s
p
i n ).
degrade i n t o
a
t o
x
,
a a
we
can
p
x
t o
p
n o n - z e r o
t h i c k n e s s
p
-
y
A p
v a l u e
however,
remove
a
beam A p
l o n g
c o n t r i b u t e
secondary
x.
(the
x
of
a s
and
from
c
of
m o n o - e n e r g e t i c
account?
s t r a g g l i n g A p
degrader
range
Even
momentum
The
when
x
output
maximum ( i . e .
a s
Ap
=
0)
s t r a g g l i n g
output would
i s
taken
e f f e c t s
amounts
t o
a r e
momenta
momentum
random
e q u a l
channel
l i k e
the
range
w r i t e * P
A
X
Px
7/2
P r
Pc ...(3.11)
Now,
s i n c e
p r e d i c t s t o p ,
Ap
/ p
the
r a t i o
g i v e n
t h e
i s p _ / p
value
v
by
d e f i n t i o n
f o r of
which
Ap
/ p C
. C
l e s s
than
p a r t i c l e s Attempts
u n i t y ,
w i l l t o
we c a n
begin
i n c r e a s e
t o
p_/p C
v
A
48
i—i—i—i—j—i—i
i i—|—r
f> MeV/c F i g u r e 3 . 5 : Number of p a r t i c l e s a v a i l a b l e f r o m t h e M13 a t T R I U M F a s a f u n c t i o n o f m o m e n t u m p e r *iA o f p r i m a r y c u r r e n t at 500 MeV.
beam l i n e p r o t o n
49
w i l l
r e s u l t
p a r t i c l e s of
i n
more
emerging
p a r t i c l e s ) ,
c o n d i t i o n s t r i k i n g
that t h e
from,
I, A p
x
p a r t i c l e s the
d e g r a d e r .
emerging
/ p
=
x
degrader
1
s t o p p i n g
i s
from
"
Av
(v C
S i n c e
t h e
i n t e n s i t y
I
and
i n t e n s i t y
degrader
t o
fewer
t h e
(number
under
the
i n t e n s i t y ,
I
by
( 2 / 7 ) v ( v / b ) 1
The
a
r e l a t e d
i n ,
/ b )
5
/
2
I
c
. . . ( 3 . 1 2 )
C
s t r i k i n g
c
+ v
5 / 2
the
degrader
i s
p r o p o r t i o n a l
7/2 to
v
c
A p
c
/ p
c
A p
c
/ p
c
A v .
c
For =
7%
emerging
/ v
momentum.
c / 5 0
The
Given
that
>
maximize
t h e
h a l f
i s
of
t h e
v a l u e s
experiment
one
c a l c u l a t e s
MeV/c
that
0.012
I
of
t h e
" e f f i c i e n c y " and
the
c / 5 0
t h e
which
3t
*
" _
...(4.7) where
V
r a d i u s
= -eE0/2K o f t h e i s
Let
u s d e f i n e
and
| < p | x | s > |
2
=
3 a
2
s t a t e ) . a
u n i t a r y
t r a n s f o r m a t i o n
A ,
( a i s t h e Bohr
62
A
e
«
+
i
"
t
n
/
,
2
0
-i«t/2
...(4.8) we
a l s o
d e f i n e
H
«= A / / A 1 "
k
iK3A/3t
+
A1"
... (4.9) so #
A
t h a t .
The
A14/>
s a t i s f i e s
t r a n s f o r m e d
e q u a t i o n
H a m i l t o n i a n
when
4.1 i s
a
L> -cV2-i7 /2, V e i8 1 s
V e
i
0
s
6
y /2-i
,
u
7 p
sum
/2
Ve
- i
i s
H of
,Ve
r e p l a c e d
two
+ i
by
t e r m s :
fit
6t , 0
... ( 4 . 10) The
f i r s t
s m a l l ,
term
i . e .
u
i f
of
#
=*
A
s d i a g o n a l f i r s t
term
term
v a r y i n g
and
second
approximat The
Ve
1
*
w i l l
n e g l e c t term.
i s
time ,
independent.
then
the
If
e f f e c t
i t s
t r a c e
of
the
i s off
p be f o r T h i s
l a r g e . the i s
We
d e f i n e
time
known
as
#'
b e i n g the
e q u a l the
to
the
r a p i d l y
" r o t a t i n g
f i e l d
i o n " . s o l u t i o n
f o r
the
time
U(t)
«- e x p {
e v o l u t i o n
o p e r a t o r
i s
now
s i m p l y :
-iff't/X)
...(4.11) C l e a r l y ,
a
t r a n s f o r m a t i o n
which
d i a g o n a l i z e s
h"
w i l l
a l s o
63
d i a g o n a l i z e
U.
The
e i g e n v a l u e s
Kx + (u
-u 9
P
-u-i
{«
=
s
B
of
+V
are
H
%
i (
V
1
7_/2+ i 7 / 2 ) • 1 + ( 4 V < / ( «
P
3
KX - (o>s-ajp-o)- i
/
2
+
i 7-/2 + 1 7 _ / 2 ) } / 2
P
P
9
{us+cop-i 5
-
p
p
r
p
(Ug-u
p
7 / 2 + i 7 / 2 ) } /2
- u - i
2
s
p
... where and
X
c o r r e s p o n d s
g
to
Xp
The mean the
that
which
imaginary
l i f e t i m e , square
1
-
the
i s
mostly
p a r t of
1/T
root
to
one
s t a t e
of
a
i s
mostly
an
s - s t a t e
the
i n v e r s e
p - s t a t e .
i s
X
the
which
(4.12)
p r o p o r t i o n a l
s - s t a t e
i n
the
RF
to
f i e l d .
Expanding
o b t a i n s
V (7 -7_) 2
n
=
-2ImX
*
e
+
7, s
E——
(a> s
W p
-u)
(7 -7 )V4
2 +
s
P
. . . ( 4 . 1 3 ) We
note
that
that
there
the
e x p r e s s i o n
i s
no
o b s e r v a b l e
resonance
i s
symmetric
u
about
u n l e s s
-
w
s
~ " p
d i f f e r s
7
and from
9
7 7
P
.
The
decay
r a t e
i s
s m a l l
for
s
about power
1/7
s e c o n d .
f l u x
n e g l e c t i n g
g
we
a
the
maximum 2s
s t a t e
W r i t i n g
=
o 7
i s
for
which
(4.13)
cE|/16ir
i n
T
a
of
the
Of
u>^. p mean
| |
2
S
i d e n t i c a l Work
-
s
has
of
(u-u
K c
P
o r i g i n a l
u>
terms
i n s t e a d
4ire2o
- = 7 T
i s
=
course
l i f e t i m e the
of
average
e l e c t r i c
f i e l d ,
have
1
T h i s
w
(Lamb,
to
the
1952).
-o)) + 7 2
P
e x p r e s s i o n
2 D
2
/4
P
a p p e a r i n g
. . . ( 4 . 1 4 ) i n
Lamb's
64 4 . 2 . 1
DC
STARK
EFFECT
E q u a t i o n s for
t h e
the
case
" 2 s "
i n c r e a s e are
and t h e i r
a l s o
"2p"
a l s o
a
e l e c t r i c
DC
"2p"
s t a t e s
and
i s
d e c r e a s e d .
give
s e p a r a t i o n .
equal
s t a t e
e q u a t i o n
of
4.12
The
(4.12)
i n
the A
f o r
c
_ A
such
7 -
small
V) -7
v a l u e s
not
i n v o l v e
neglect
4 . 2 . 2
AC The
t h i s over
a l l
Stark
by
the
e q u a t i o n
" r o t a t i n g
the presence
STARK second
term
c o n s i d e r AC
given
i s
v a l u e s i t
as
s h i f t
r a t e s
l i f e t i m e
Stark
t o
of
the
" 2 s "
s t a t e
e f f e c t
(from
g i v e n
below:
)
p 2
p S
The
as
decay
the
a r e S
so
of
^
V
S
t h e
V » < 7 *
= -AE
i n
of
S
AE
o p p o s i t e
the
l i f e t i m e
s h i f t s
and
q u a d r a t i c
of
and
energy
t h a t
that
the
l i m i t
7_
e q u a l
and
s h i f t
The
changes
o p p o s i t e
r e s u l t s
energy
f i e l d . a r e
i n c r e a s e d
The
the
4.12
f i e l d
of
t h e P^/2
of
#
. . . ( 4 . 1 5 )
P
f o r
the
DC
Stark
a p p r o x i m a t i o n " s
2
t
a
t
e
s
but
e f f e c t
do
s t i l l
do
«
SHIFT term
s i m i l a r of a
A
t o
v a r i e s the
DC
r a p i d l y . Stark
e f f e c t
r e d u c i n g
the
DC
p e r t u r b a t i o n
and
o b t a i n
6,
(from
e q u a t i o n
AE
- -AE
4 . 1 0 ) .
=*
The
r e s u l t an
e f f e c t
when by
of
averaged h a l f .
e s t i m a t e
of
We the
65 4 . 2 . 3
EFFECT The
and
2
RF
P3/2
2 5 ^ 2 one
THE
f i e l d
2?^
a l s o
s t a t e s
C o n s i d e r i n g v a r i o u s
OF
l e v e l
h a s m a t r i x
which
these
m a t r i x
STATE
/2
a s
we
have
(one t o
now
and
h y p e r f i n e
t h e
summing
of
t h e
2 s
1 / / 2
n e g l e c t e d . over
the
of
t h e
component
two components
2 p
3
^
2
l e v e l )
o b t a i n s ( e E AE
=
0
)
2
- 2
2K2
s
| < p ^
v a l u e
of
| < p
3
y
2
| x | s > |
2
i s 3 a
3 / 2
« 2
| x | s > |
, P
s
The
between
u n t i l
p e r t u r b a t i o n s
elements connects
elements
.
3
/
9
/
2
2
. . . ( 4 . 1 7 )
5.
DESCRIPTION
5.1
VACUUM
The
a p p a r a t u s
beam
l i n e
OF
THE
APPARATUSAND
shown a
a p p r o x i m a t e l y
50 10~
i n
F i g u r e
mm m y l a r T o r r
5
o p e r a t i n g
through
v a l v e
a s s e m b l y .
The
t h e on
c o n t r o l l e d by
only
p o s s i b l e
i m p o r t a n t l y , apparatus an
10"
free
pumping t h e
o p e r a t i n g
i t
would
would the
4
The i f
be
of
t r a p
o i l
to
vacuum t o
a v a i l a b l e
would
have
was
were
much
more
i n t o
u p .
t o not
but
the
Had
there
a
turbo
( e . g . ,
been
o i l
prevent
pump
warm
gate
valve
p a r t i c l e s
begin
and
d e l e t e r i o u s
gate
c l o s e d
of
d i f f u s i o n
minimize
had
t h e
the
p r e s s u r e
t r a p
t o
have
from
i n c h
c o l d
d i f f u s i o n
system
system
a
necessary
that
flow
c o l d
by
p l a t e s .
t o
t h e
pump)
The
was
so
Torr
s h o u l d
s i m p l e r
and
r e l i a b l e .
SCINTILLATION
The
i n c i d e n t
were
RF
s i d e s 1.3
on
s l i d i n g
r e g i o n s .
of
of t h e
cm
r e m a i n i n g
COUNTERS
s c i n t i l l a t o r
mounted
c o n s i s t e d
x
5
s e p a r a t e d
n i t r o g e n
which
p o s s i b l e
5.2
and
t r a p
damage
t h e
o i l
m o l e c u l a r more
c o l d
l i q u i d
m i c r o c h a n n e l
about
was
window.
a u t o m a t i c a l l y
change
been
a
apparatus
t h e
5.1
was m a i n t a i n e d
pump
e f f e c t s
PROCEDURE
SYSTEM
by
e n t e r i n g
EXPERIMENTAL
The two
f i v e
and
f l a n g e s
f r o n t
of
t o t h e
c o l l i m a t i n g permit box
s c i n t i l l a t o r s which
apparatus s l i t
(X)
a t
and meshed the
entrance
s c i n t i l l a t o r s which
66
a c c e s s
t o
the
s c i n t i l l a t o r e n t e r e d
together t o
s c i n t i l l a t o r
the
formed
t o
from form
quench t h e
(BOX)
opposite a
3 . 8
r e g i o n .
t o p ,
f o i l
cm The
bottom,
67
F i g u r e
5.1:
A
schematic
diagram
of
the
a p p a r a t u s .
68
s i d e s
and
rear
l i g h t
guides of
so
l e v e l
low
t h e
e n t e r i n g
wrapping a
of
t h e
box from
" c r o s s
s c i n t i l l a t o r s
of
t h e
diameter
63
Mm t h i c k .
o p p o s i t e
l i g h t
aluminum each
wrapping.
v a l v e
would
( i n
be
to
t h e
the
a p p a r a t u s .
s e c t i o n
was
of
n o t
was
The
c o m p l e t e l y
observed
i n c i d e n t
L i g h t
and
c o l l e c t i o n
on
t h e
i n t e r l o c k e d
5.1)
o f f
s o
and
t h e
t h e
v a r i o u s 2 . 5
from
t h i n
i n
the
same
t h e
cm two
0 . 7 5 urn
way
f o r
a s
the
p h o t o m u l t i p l i e r s
apparatus
( p o s s i b l y )
t i g h t
was a
a
The
l i g h t
was
by
f i v e
p h o t o m u l t i p l i e r s
t h a t
s h o u l d
i n
counter
f a c i l i t a t e d
v o l t a g e s
were
p r e s s u r e
box
p o s i t r o n s
e x i t e d
s c i n t i l l a t o r (see
a p p a r a t u s ,
(7.5
t h e
rear
on
opened,
be
l e t
up
a d m i t t i n g
to
l i g h t
s c i n t i l l a t o r s .
The
The
b o x .
The
turned
atmospheric
mounted
t a l k "
guides
s c i n t i l l a t o r
gate
were
s c i n t i l l a t o r s of
d i s k ,
s c i n t i l l a t o r
box
i n c i d e n t /xm)
F i g u r e
and decay
t h e
was
used
3 . 5 ) ,
p o s i t r o n s
t r i g g e r i n g
counter
c o u l d
s c i n t i l l a t o r
which
which (one
one
a l s o
t o
t h e
+
a
s i m u l a t i o n
p l a t e s .
v e r y of
the which
M !)
m i c r o c h a n n e l by
beam
through
every
r e p l a c e d
p e r m i t t e d
c o p i o u s
passed
f o r
of be
veto
t h e
t h i n muon
241
beam
u s i n g
an
5.3
NEUTRAL
The
0 . 7 5
the
RF
5.1
summarizes
Am a l p h a
PRODUCTION
Mm A l
s o u r c e .
FOIL
f o i l
used
t o
t r a n s m i s s i o n
l i n e
assembly
t h e
v a r i o u s
produce
masses
n e u t r a l s
shown i n
t h e
i n
was mounted
F i g u r e
beam.
5 . 2 .
on Table
69
Table Masses Ma t e r i a
1
t(«xm)
i n
5.1 the
Beam
p(g/cm2)
Mass
E q u i v a l e n t
(mg/cm2)
Mass
A l
(mg/cm2) M y l a r
Beam
Window,
P i p e
( C
5
H , 0
S c i n t i l l a t o r (CH)
2
)
T o t a l
(Al)
(Al)
7.65
63
1.03
6.54
7.32
1 .50
2.70
0.40
0.40
0.75
2.70
0.20
0.20
E q u i v a l e n t
Mass
(Al)
Table
5 . 1 :
beam.
7.06
i l l a t o r
Wrapping F o i l
1.39
(X)
k
Sc i n t
51
16.6
Summary
of
m a t e r i a l s
p r e s e n t
i n
the
p a t h
of
the
muon
70 5.4 RF REGION The
RF r e g i o n was a r a d i o f r e q u e n c y
shown i n F i g u r e (Pipkin, given
5.2. I t was b a s e d on a d e s i g n
1982). A simple
in
Figure
of t h e l i n e
calculation
using
by F.M. the
calculation.
of
the
RF t r a n s m i s s i o n
I f P i s t h e power
(rms)
line Pipkin
dimensions
5.2 shows t h a t t h e i m p e d a n c e a t t h e c e n t r e
i s a b o u t 50 ohms. M e a s u r e m e n t o f
characteristics
average
transmission
voltage
difference
rms
r m c
impedance
l i n e confirmed the
transmitted
c o n d u c t o r and t h e grounded o u t e r V
the
in
between
watts, the
the
central
conductor i s :
= /50~P [ v o l t ] ...(5.1)
The
power d e n s i t y
i n t h e upper p a r t of the t r a n s m i s s i o n
line
is: 0.04 P [ w / c m ] 2
...(5.2) The and 5.3. data
power
continuously
regulated using
The f r e q u e n c y
frequency
every
few
minutes.
t r a n s m i t t e d was r e a d
switched In
by a
for a
addition
of
t h e power
level.
subsequent
computer c o n t r o l l e d
shown i n F i g u r e
was r e m o t e l y to
addition, frequency
b a c k t o t h e c o m p u t e r t o be r e c o r d e d
improvement
l i n e was m o n i t o r e d
the c i r c u i t
o f t h e RF s o u r c e
a c q u i s i t i o n computer, which
frequency
sent
through the t r a n s m i s s i o n
s e t by t h e
a
different the
counter
with other
experiment
actual
would
s w i t c h i n g and read
and
d a t a . An be
the
back o f
F i g u r e 5.2: The R F t r a n s m i s s i o n l i n e arrangement
72
COMPUTER SET
POWER
LEVEL
SELECTED from
VARIABLE
FREQUENCY
CAMAC
FREQUENCY SOURCE
25
WATT
POWER AMPLIFIER
I RF
TRANSMISSION
ATTENUATOR
RF POWER
METER
I
-30
dB
SPLITTER -10
dB
I
FREQUENCY METER
F i g u r e 5.3: The RF system.
READ
LINE
73
5 . 5
THE
QUENCH
F i g u r e
5 . 4
shows
the
quench
the
a p p a r a t u s
equal
a t
beam and
r e g i o n
t h e t h e
l a b e l l e d
s e r v e d
t o
prevent
quench (MCP1
photons
(122
(92 the
75
muonium
atoms,
counter
(X)
from
f o i l
11.4
of
.
s t a r k
over
a
1
The
a
photons
three
manufactured
The
l a y e r a
of
the
above
used
A
the
V/cm),
f i e l d
a l s o
f o i l
from
and
below
t o
t h e
m i c r o c h a n n e l
d e t e c t
of
was
time
of
Lyman-a
any
l a r g e r
(MCPB)
minimum
e x c i t e d
r e c t a n g u l a r
used
t o
f l i g h t
e f f e c t i v e
G a l i l e o
p l a t e s
area
t o
front C s l
f a c t o r
m i c r o c h a n n e l by
to
stop
from
path
the
l e n g t h
c m .
t y p e s .
by
were
r e g i o n .
d e t e r m i n i n g
s e n s i t i v e
Lyman
the
500
e l e c t r i c
from
and
microchannel
mm d i a m e t e r
p l a t e
t h e i r
a
p l a t e s
t h e
(30
m a i n t a i n e d
(about
quenching
quench
i n c r e a s e
w i t h
40
These
m i c r o c h a n n e l
f a c t o r y )
of
p a r a l l e l
s c i n t i l l a t o r
three
unfunneled
midplane
f i e l d
200 V/cm at
two
t h e t h e
i n
e q u i p o t e n t i a l s
e n t r a n c e
r e g i o n
f i e l d
p l a t e s . box
1
t h e
channel
e j e c t e d
A l l
f o r
t h e
quench
m i c r o c h a n n e l
i n c i d e n t t h e
t h e
from
a t
The
t h r e e
about
were
e n t e r e d mm)
at
The
and M C P 2 ) nm)
which
mm x
i n s i d e
s i d e
e l e c t r i c
e l e c t r i c
t h e
e l e c t r o n s
r e g i o n
p l a t e s
s t a t e s
t o
m i c r o c h a n n e l
S i t u a t e d
t h e
was a p p r o x i m a t e l y
s t r o n g e s t
MCPB.
t h e
t h e
of
s l i t
l i n e a r l y
p l a t e
from
that
PLATES
map of
n u m e r i c a l l y ) .
f a c e s
entrance
t h e
viewed
show
front
d e c r e a s e d
the
a s
MICROCHANNEL
p o t e n t i a l
(computed
d i r e c t i o n ,
r e a c h i n g
AND
t h e
increments)
between g r i d
REGION
of
p l a t e s
68% from
f a c e s
t o
were
were
enhance
t e n used
C o r p o r a t i o n ,
(see i n
" f u n n e l e d " the
value
coated
t h e i r
t h i s
of
55%
(at
the
e f f i c i e n c y
F i g u r e
M a s s . ,
t o
5 . 5 ) .
experiment USA.
t o The
were
F i g u r e 5 . 4 : The e l e c t r i c the s i d e a t the v e r t i c a l
f i e l d i n t h e quench r e g i o n . View i s from midplane.
75
F i g u r e 5.5: E f f i c i e n c y of c h a n n e l e l e c t r o n m u l t i p l i e r s as a f u n c t i o n of wave l e n g t h .
76 enhancement
i s ,
however,
i s
h y d r o s c o p i c .
was
observed
to
t o
r e j u v e n a t e
b u l b s
were
1
of
t h e
the
front
Even
t h e
c a u s i n g
c o a t i n g .
I t
some
m i c r o c h a n n e l
m a i n t a i n e d
m a i n t a i n i n g
t h e
-2000
quench
q u a r t z of
t h e
p o s s i b l e
of
longer
c i r c u i t r y t h e
V ,
r e g i o n
which
was
f i e l d
A
D i g i t a l
the
program
(CAMAC,
1
Chosen
50% would
t o
t h e i r
used
a c q u i r e
s m a l l
the
there
i s
a n d
s i z e .
to
The
independent
t h e
system
i t
t o
shut
o f f .
HV that
v o l t a g e s .
an
As
i n c r e a s e
a i n
TRIGGER
1983)
t o
three
that
cause
EVENT
by
each
above.
so
M i l e s ,
was
of
f o r
s e t
MULTI
and
f o r
was
C o r p o r a t i o n
(T.
C s l
run
of
d e s c r i b e d
MCP's
Equipment
1982)
parameters
supply
AND
the
r e s p o n s i b l e
a n d p h o t o m u l t i p l i e r
ACQUISITION
the
MCP
v a l v e
DATA
i n
each
gate
5 . 6
t h e
t o
s u r f a c e
i n t e r l o c k e d
about
t o
f r o n t
used
each
by
heat
wavelengths
were
c u r r e n t
r a p i d l y
response
s u p p l i e s
each
s l i t
from
power
measure,
order
entrance
water
s u p p l i e d
s a f e t y
a i r
55 W
b u l b s
v o l t a g e s
t h e
In
these
h i g h
c o n t r o l l e d
room
halogen
t o
t h e
C s l
d e t e c t i o n .
T y p i c a l l y
a t
t h e
of
two
observe
even
t o
e f f i c i e n c y .
u s i n g
t o
because
exposure
r i g h t
then
MCP's
at
shows
p l a t e .
a n d
p o s s i b l e
s i n c e
of
c o a t i n g ,
was
m a i n t i a n
t h e i r
d e s o r p t i o n
p r o b a b i l i t y 5 . 6
It
t o
minutes
l e f t
t h e
t h e
was a l s o
F i g u r e
was
t o
of
photons
s m a l l
C s l
r e g i o n .
s u r f a c e s
few
decrease
MCP's
i n s t a l l e d
quench
t o
a
g r e a t l y
vacuum,
MCP's
d i f f i c u l t
PDP-11/34 a n d
c o n t r o l r e c o r d
computer
u s i n g
standard
v a r i o u s d a t a .
running CAMAC
e x p e r i m e n t a l A
s i m p l i f i e d
77
CHEVRON MICRO-CHANNEL PLATE
CONFIGURATION
CHARGE COLLECTION PLATE
rh
JT m
m
0 fl COAXIAL CABLE
INSIDE VACUUM TANK OUTSIDE VACUUM TANK
r
!
1
FERRITE BEADS
MV - 2 0 0 0 V MONITOR OUTPUT
(mutt b « vtry
high
imp«donc«)
SIGNAL
F i g u r e 5 . 6 : T y p i c a l c i r c u i t used t o r u n a m i c r o - c h a n n e l p l a t e . S p e c i f i c v a l u e s of t h e r e s i s t a n c e s and c a p a c i t a n c e s depend on t h e s i z e and k i n d o f m i c r o - c h a n n e l p l a t e s .
78
l o g i c
s c h e m a t i c The
5.7).
event
A
muon
s t a r t e d
the
d u r i n g or
i s
CAMAC a
muonium
q u e n c h i n g
However,
i t
o f f - l i n e
by
from
have
a c c e p t e d
was
many
as
the
r e q u i r e m e n t s
i n c i d e n t
w e l l
MCPB
and
as
ns
gate
from
one
or
other
to
u n l i k e l y
s e l e c t
t i m e s
T h i s
l i k e l y
of
to
the
a l l
F i g u r e
s c i n t i l l a t o r
500
events
those
(see
a
d e t e c t e d .
more
than
5.7.
three
the
been
p o s s i b l e
s i n c e
F i g u r e
had
TDC's
p u l s e
must
o b v i o u s l y
i n
t r i g g e r
d e t e c t e d
w h i c h
MCP2
shown
(WIDE of
event to
on
to
due
the
MCP1
due
to
i n t e r e s t i n g
p u l s e s
X)
t r i g g e r
be
be
(X)
2s i t .
events
MCP's
were
r e c o r d e d . Each a d d i t i o n a l p u l s e
r e c o r d e d
p i e c e s
of
h e i g h t s
MCP's
were
r e c o r d e d on
event
the
of
were
i n c i d e n t
the
as
times
as
i n c i d e n t
5.7
PARAMETERS
experiment
focus
of
F i g u r e
the
BOX
of
the
was
to
the
time
p u l s e s
on
the
c o l l i m a t i n g next
The
and
three
monitored
of
and
s e v e r a l
above.
s c i n t i l l a t o r s
( r e l a t i v e
p r e v i o u s
had
mentioned
frequency
and
tape)
of
each
a
and p u l s e
of
the
s c i n t i l l a t o r , p u l s e s
i n
the
s c i n t i l l a t o r .
BEAM
The
the
RF
times
not
i n c i d e n t
s c i n t i l l a t o r ) of
w e l l
four
The
the
s c i n t i l l a t o r s
magnetic
i n f o r m a t i o n
r e c o r d e d . as
(on
the 5.8
beam
l i n e
Ap/p
of
was
AND
performed
secondary i s
a
i n
was
at
c h a n n e l
diagram
momentum 0.5%
EXPERIMENTAL
of
the
a d j u s t e d
order
to
the
M13
RATES f i r s t
at
beam
TRIUMF l i n e
u s i n g f i n d
doubly
the
a
achromatic
(Oram,
198lb).
c o n f i g u r a t i o n . r e l a t i v e l y p o i n t
of
The small
maximum
79
F i g u r e 5.7: S i m p l i f i e d acquisition.
d i a g r a m of
the
electronic
logic for
data
horizontal B vertical jaws
rvocuum valve beom blocker
beamline IA
X F 3 final focus
4
target ^ IATI
diagnostics^/ vertical tlit horizontal tlit•colt
0
I
2
3fttt
CD
O
81 p r o d u c t i o n
of
c/100
F i g u r e
(see
Once
the
p a r t i c l e s
optimum
channel
a v a i l a b l e
in
F i g u r e
d e t e c t e d proton
32,000
Hz
muon
( i . e .
t h e r e
much
raw
80
WIDE
numerous
found,
the
Ap/p
7%.
and
the
low
p u l s e
i s
shown
s c i n t i l l a t o r for
Beam
than
s c i n t i l l a t o r s ,
of
a
primary a
a c c e p t e d
X).
10
the
mm
about
p o s i t r o n s muons
the
height
and
n e u t r a l .
s t r i k i n g
5.7
box
KHz
4.2
at
KHz,
on
on
and a
requirement
or
w i t h i n
d e t e c t i o n
15 of
the
to
Lyman-a
beam
j u s t
at but
c o l l i m a t i n g
p u l s e s
from
c o n d i t i o n s
p o s i t r o n s
120 8 . 9
KHz.
KHz.
the
the
c o r r e s p o n d e d
to
a 500
L a t e r events
ns
13.1%
MCPB.
The
be
p r e s e n t
from
gate
reduced
the
a n a l y s i s
showed
p u l s e ns
was
by
The
500
about
8
that per
averaged
which
About
( w i t h i n
d e t e c t e d
that same
these
about
c o r r e l a t e d
Hz.
c o n d i t i o n s .
of
r a t e
b e i n g
t r i g g e r
about
r a t e
under
l a r g e l y
T h i s
u*. (X)
MCPB was
t h i s was
i n c i d e n t
these
more
MeV
F i g u r e KHz
a
second
the
reduced
i n c i d e n t
to
32
be
i n c i d e n t
per
500
to
c/50
momentum
by
r a t e
a p p a r a t u s
MCP2
at of
were
the
muons
*iA
of
to
was
i n c r e a s e d
f u n c t i o n
36,000
l i k e l y
MeV/c
MeV/c
l o g i c
were
was
between
s c i n t i l l a t o r .
The
system
15.4
a
15.4
The
s c i n t i l l a t o r ,
an
At
as
t a r g e t .
vetoed
about
f l u x
100
were
i n c i d e n t
of
of
momentum
p a r t i c l e s
a c c e p t a n c e
3 . 5 .
t h i s
r a t e ,
momentum
c u r r e n t
v e l o c i t i e s
i . e .
a p p r o x i m a t e l y
g r a p h i t e
the
3 . 8 ) ;
momentum
The
w i t h
e n t e r e d
BOX
h a l f
of
veto t h i s
gate) of
the
w i t h muons
a d d i t i o n a l e i t h e r
MCP1
t r i g g e r
r a t e
the hour,
r a t e
of
under
6.
6.1
tape and
r e d u c t i o n
s c i n t i l l a t o r .
a l l
t h e
t i m i n g
for
d e t e c t o r s c o u l d
be
AND
shows
the
time
photon
a
ANALYSIS
from
t h e
6 . 2
random
i n
t h e
a r e
c o n s i s t e n t
t y p i c a l
backgrounds.
(b)
c o i n c i d e n c e
near
O c c a s i o n a l l y p e n e t r a t i n g
t h e
t h e
w i l l
t h e
i n c i d e n t
d e t e c t o r s , t h e
w i t h
t h e
r a t e s
d i a g o n a l
=
f l
random
and
a
t h e
p u l s e s
Lyman-a
beam
which manage
s c i n t i l l a t o r
82
t o b o x .
t i m i n g
a l l
t
h i s t o g r a m
of
t h e
t o
events f o r
and
i n
three (a)
one
of
enhancement a n d a
d e t e c t o r . a n d a r e
MCPB,
l a b e l l e d
MCPB
t r i g g e r
t o
p u t a t i v e
p l a t e
MCPB
MCPB
F i g u r e
t i m e - o f - f l i g h t
s m a l l e r
T h i s
c a s e s ,
( r e l a t i v e
of
on
of
( r e l a t i v e
muon)
p o s i t r o n s
s t r i k e
a
expected
on
The
p r o v i d e d
and MCPB.
enhancement
t ) .
MCP
(t)
channel
events
on
r e s o l u t i o n .
o v e r a l l
m a j o r i t y
(t
ns
data each
In
time
The
X
one
2
r u n ) .
between
p o s i t r o n s
than
counter
of
of
r e l a t i v e
back
from
t h e
p l o t
s i m u l t a n e o u s
a l l of
t h e
t h e
r e s u l t e d
on
beam
t o
The
d e t e c t o r s
t r i g g e r
a l l of
i n c i d e n t
X
t i m i n g
e l e c t r o n i c s .
a g a i n s t
counter
a l l t h e
t i m e - o f - f l i g h t
Lyman-a
c o u n t e r ) ,
of
t h e
t h e
b e t t e r
of
a
Lyman-a
d o e s n ' t
t h e
d e t e c t i o n
t o
t o
t y p i c a l
f o r
c o r r e s p o n d s
l a b e l l e d
a
of
i n
and a s s o c i a t e d
i n c i d e n t
(again
s c a n n i n g
determined
d i m e n s i o n a l
d e t e c t i o n
i n c i d e n t
which
between
of
the
F i g u r e
P o s i t r o n s
shows
two
w i t h
h i s t o g r a m s
determined
6.1
p a r t i c l e s
6.2
of
s i g n a t u r e
Figure
not
s t a r t e d
and g e n e r a t i o n
d e f i n i t i v e
the
REDUCTION
TIMING Data
t
DATA
That
i s ,
X
t h e r e f o r e
vetoed
MCPB
happens
r e a l
by
X.
without a t
random
83 times
relative
to
muons
enhancement l a b e l l e d
X.
stopped
the
in
It
i n coincidence resulted
Lyman-a
from
decay
detectors
t
was
used
to
geometry) t h e f r a c t i o n of time traversal of
region.
This
s p e n t by t h e
before
the
permitted particle
positrons
and
(t ^
=
r
which
MCPB.
The
total
0.289
particle
the
t)
spent
in
l i n e a s w e l l a s t h e amount entered
the
quench
o f t h e amount o f t i m e
quench
d e - e x c i t a t i o n p h o t o n was d e t e c t e d ,
region
tg = t
f l
before
its
- 0.404 t .
On t h e b a s i s o f t i m i n g , t h e e v e n t s c o u l d be and
coincidence
randomly i n c o i n c i d e n c e
calculation in
on
c a l c u l a t e (on t h e b a s i s o f
o f t h e RF t r a n s m i s s i o n
time e l a p s e d
the t h i r d pulses
with a real
w i t h t h e p a s s a g e o f a muon b e t w e e n X time-of-flight
X. F i n a l l y
( c ) i s t h e r e s u l t o f random
t h e Lyman-a d e t e c t o r s o f MCPB a n d
triggering
classified
t h e number o f e v e n t s w o r t h y o f f u r t h e r c o n s i d e r a t i o n a s
p o s s s i b l e 2s muonium g r e a t l y r e d u c e d . The criteria
are i l l u s t r a t e d
by F i g u r e s
( i ) The t i m e - o f - f l i g h t required
to
correspond
t
following
timing
6.2 a n d 6.3:
between
X
and
MCPB
to a p a r t i c l e with
was
velocity
b e t w e e n c / 5 5 a n d c / 2 0 0 ; i . e . , 21 ns < t < 76 ns [ s e e Figure (ii)
6.3, l a b e l ( i ) ] .
The i n t e r v a l
region
and
t ^ between e n t r y
detection
of
a
into
Lyman-a
the
quench
photon
r e q u i r e d t o be s u c h t h a t t h e
particle
the
l e s s t h a n 20 n s i n i t ;
i.e.,
region
but
0 ns < L
[see F i g u r e
Q
had
spent
< 20 n s o r t
6.3, l a b e l
a
(ii)].
had
was
entered
- 20 ns < 0.404 t < t
a
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A t y p i c a l t i m e - o f - f l i g h t h i s t o g r a m for p a r t i c l e s between the i n c i d e n t s c i n t i l l a t o r a n d MCP B.
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