NUCLEAR
INSTRUMENTS
3
(1958)
57-68;
NORTH-HOLLAND
PUBLISHING
CO. -
AMSTERDAM
A NEW METHOD IN GAMMA-RAY SPECTROSCOPY: A TWO CRYSTAL
SCINTILLATION SPECTROMETER WITH IMPROVED RESOLUTION
A. M. H O O G E N B O O M
Fysisch Laboratorium der Rijksuniversiteit te Utrecht
Received 11 M a r c h 1958
T h e m o s t i m p o r t a n t features of t h e t e c h n i q u e are:
A n e w m e t h o d h a s been d e v e l o p e d to m e a s u r e t h e s p e c t r a
of g a m m a r a d i a t i o n e m i t t e d in cascade d i s i n t e g r a t i o n s . Use
is m a d e of a t w o - c r y s t a l scintillation s p e c t r o m e t e r a n d a
g a t e d m u l t i - c h a n n e l a n a l y s i n g device. T h e p u l s e s p r o d u c e d
b y s u m m i n g t h e o u t p u t s of t h e t w o c r y s t a l - p h o t o m u l t i p l i e r
c o m b i n a t i o n s are selected b y a s i n g l e - c h a n n e l differential
d i s c r i m i n a t o r . T h e o u t p u t of t h i s differential d i s c r i m i n a t o r
gates the multi-channel analyser whenever the sum pulse
c o r r e s p o n d s to t h e release in t h e c r y s t a l s of t h e full e n e r g y
a v a i l a b l e in t h e cascade. T h e s p e c t r u m d i s p l a y e d is t h a t of
e i t h e r of t h e two detectors.
(a) o n l y " f u l l - e n e r g y " p e a k s are d e t e c t e d ;
(b) i m p r o v e d resolution is o b t a i n e d especially a t h i g h e r
g a m m a - r a y energies;
(c) one ),-~ or p ~ - ~ a n g u l a r correlation e x p e r i m e n t
d e t e r m i n e s t h e a n g u l a r correlation of t h e g a m m a r a y s of all
double cascades d e e x c i t i n g a g i v e n level.
D e t a i l s of o p e r a t i o n a n d t y p i c a l s p e c t r a are presented.
I t is s u g g e s t e d t h a t t h e t e c h n i q u e be called t h e " s u m coincidence" m e t h o d .
1. Introduction
In a normal single-crystal gamma-ray scintillation spectrometer the pulse-height distribution produced b y monoenergetic gamma radiation is rather complicated because of the different
processes which arise in the conversion of the
gamma-ray energy into an electric pulse.
Therefore, since the beginning of gamma-ray
scintillation spectroscopy there has been a
tendency to simplify the observed spectra b y
using more than one crystal. In the two-crystal
coincidence spectrometer developed b y Hofstadter and Mclntyre 1) Compton-scattering
processes are selected by a coincidence arrangement between the incident radiation and the
radiation scattered at a certain angle. In the
two-crystal anticoincidence spectrometer introduced b y Albert 2) only those pulses from one
crystal are accepted which are not in coincidence
with a pulse in a large crystal surrounding the
first one. In the three-crystal triple-coincidence
spectrometer constructed b y Johansson3), and
independently b y Maienschein and Bair4), only
those pair processes are accepted which are in
coincidence with the detection of both annihiAUGUST 1958
lation quanta in lateral crystals. All these
solutions suffer from the disadvantage that if
the resolution is good the efficiency becomes
very small and vice versa. This is especially
serious if the gamma-ray spectrum is complicated and contains a number of coincident lines.
It is almost impossible to use one of these
spectrometers to measure 7-Y coincidence
spectra or 7-7 angular correlations.
In the present paper a new type of scintillation
spectrometer is described especially suited to
measure 7-9' coincidence spectra and 7-7
angular correlations. The new spectrometer
combines good resolution with a relatively high
efficiency for both low and medium gamma-ray
energies. The main features are:
(a) The pulse distribution shows only one
peak, the "full energy" peak, for one specific
gamma transition. There is no contribution to
the spectrum from processes in which only part
1) R. H o f s t a d t e r a n d J. A. M c l n t y r e , P h y s . Rev. 78
(1950) 619.
3) R. D. Albert, Rev. Sci. I n s t r . 24 (1953) 1096.
3) S. A. E. J o h a n s s o n , N a t u r e 166 (1950) 794.
4) F. C. M a i e n s e h e i n a n d J. K. Bair, P h y s . Rev. 82
(1951) 317 (A).
57
58
A.M. H O O G E N B 0 0 M
of the available gamma-ray energy is absorbed.
(b) The absolute half-widths of the peaks due
to coincident gamma rays are, to first approximation, equal.
(c) The detection efficiences of coincident
gamma rays are equal.
2. Principle of operation
In many cases (e.g. in all (p,y) reactions) a
complicated nuclear decay scheme can be
subdivided into a number of cascades starting
all at one single level and ending at the ground
tillation counters. If both scintillation counters
have the same energy calibration the sum of
their output pulses is proportional to the sum
of the energies absorbed in the two crystals.
Therefore, if both gamma quanta of a cascade
are fully absorbed, this sum pulse as obtained
from a linear adding network corresponds to the
release of the total energy involved in the
cascade. Pulses from one of the scintillation
counters which are in coincidence with these
special sum pulses all belong to processes of
full-energy absorption of one or both gamma
Co60
x Single s p e c t r u m
800
700
600-
2.50 MeV
o Sum coi'neidence spectrum
--
C
D
0
o
1.17MeV 1.33MeV
Co6o 2 . ~ O -
o
~'~
s°°-. //°"2°~'*
j~
123
II
Y ~, I
"~.x
i/I
T~,
Ey in MeV
~x
0
oft~, 6oo,~c
I
/
xX~X
,9~
P
,4
"0
I
/
~ \
|
X~x.X
o
0
0.5
1.0
1.5
2D
2.5
Fig. 1. Single and sum-coincidence spectrum of Co6° using 2" crystals. The single spectrum indicated b y crosses is or~
a n a r b i t r a r y scale. T h e s u m - c h a n n e l s e t t i n g is a t 2.50 MeV. I n t h i s m e a s u r e m e n t s no lead s h i e l d i n g w a s applied b e t w e e n
crystals. T h e s m a l l p e a k s a t 0.25, 1.0, 1.6, a n d 2.30 MeV are d u e to b a c k - s c a t t e r i n g .
state of a nucleus. The principle of operation is
based on the fact that the total energy involved
in different cascades is the same. For simplicity
the discussion will be limited to cascades of two
gamma rays only.
The two gamma rays of one of these cascades
can be detected in coincidence with two scin-
quanta in this crystal. Thus this coincidence
spectrum shows only the full-energy peaks of
the gamma rays of the cascade, accompanied
by a peak due to the absorption of both gamma
quanta in one crystal. In practice this "sumcoincidence" spectrum is obtained by gating a
multi-channel pulse-height analyser. The gate
A NEW METHOD
IN GAMMA-RAY
pulse is selected from the spectrum of sum
pulses by a differential discriminator.
The sum-coincidence method will be elucidated b y a simple example of a single cascade.
The nuclide Co e° decays b y / ~ - emission to the
2.50 MeV level in Ni 6°. The 2.50 MeV level is
deexcited by a cascade of 1.17 and 1.33 MeV
gamma rays to the ground state. No cross-over
is observed. In fig. 1 the pulse spectrum is
shown obtained b y applying the sum-coincidence
method. In this case the channel of the differential discriminator of 2% width was set at 2.50
Me¥. A further explanation of fig. 1 is given in
section 5.
In the next section a description will be given
of the necessary apparatus.
SPECTROSCOPY
59
second coincidence circuit between the output
pulse from "D.D. sum" and the output pulse
from the first coincidence circuit.
The output of amplifier 2 can be used as a
monitor in angular correlation experiments.
Source z-Lead shield.
I '
3. Apparatus
In this section a description is given of a sumcoincidence scintillation spectrometer. A schematic diagram is shown in fig. 2. The crystals
CR1 and CR2 are shielded from each other b y
lead cones. About 7 cm of lead is put around
the crystals to reduce background. The pulses
from the cathode followers CFla and CF2a are
fed to the amplifiers 1 and 2, and to the linear
adding network. The linear adding network
comprises the cathode followers C F l b and
CF2b, the resistors R1 and R2, and a potentiometer RV1. The values of R~ and R~ are about
l0 times the output impedance of the cathode
followers. As mentioned in the preceding section
the energy calibration of both detectors has to
be the same. This is done b y adjusting the high
voltage of one of the multiplier tubes. The
potentiometer RV1 serves as a fine adjustment.
After amplification the sum pulses are fed into
a differential discriminator to select the sum
channel. The multi-channel analyser is gated
with these selected pulses.
In fig. 2 no special coincidence arrangement is
included. Actually the adding network acts as
a slow coincidence circuit with a time resolution
of about 3 #sec. However, at high counting
rates a coincidence circuit between CFla and
CF2a will be necessary. The extension to a
system for high counting rates comprises also a
to monitor
MutU-
I Sum l
channel
Analyzer
I roate/
IFig. 2. E x p e r i m e n t a l a r r a n g e m e n t of t h e s u m - c o i n c i d e n c e
m e t h o d . CR1 a n d CR2 are t h e two crystals, P M I a n d PM2
i n d i c a t e p h o t o m u l t i p l i e r s . T h e four c a t h o d e followers a r e
labelled C F l a a n d b a n d C F 2 a a n d b. T h e p u l s e s s u m m e d
i n t h e a d d i n g n e t w o r k are amplified b y t h e amplifier " S u m " .
T h e s u m - c h a n n e l is c h o s e n w i t h t h e differential d i s c r i m inator "D.D.sum".
The bias and channel width of the differential
discriminator "D.D. sum" influence the shape
of individual gamma-ray peaks. This is discussed
in the next section.
4. Resolution and Efficiency
It is assumed that the gamma rays Yl and ~
with energies E01 and E0~ respectively, are in
cascade, and that the pulse distributions
f l(E1 - - Eol ) and f2(E2 - - Eo2) corresponding to
the "full-energy" peaks are gaussian with halfwidths (full width at half maximum) of Fx and
F~, respectively. For mathematical simplicity
the sum channel will also be assumed to have
a gaussian transmission fs(E1 + E 2 - E)os
60
A. M. H O O G E N B O O M
with a half-width/'s. The bias of the sum channel
is set such that E0s = E01 + Eo2. The functions
f l and f2 are normalized such that the total
numbers of pulses in the corresponding fullenergy peaks equal el and e~, where el and e2
are the full-energy efficiencies (including solid
angle) for detection of ~l and Y2, respectively.
The area under f~ amounts to/'~.
B y multiplyingfl, f2, andre, and by integrating
over E~ one obtains the pulse distribution in the
sum-coincidence spectrum of the peak corresponding to 71. The half-width /'sl of this peak
is given by:
/~$1 = /~1 V
~
/ V ~12 + -F22 + ]iS2 "
(1)
This proves that a peak in the sum-coincidence
spectrum is always narrower than the corresponding peak in the single spectrum.
The best energy resolution is obtained, of
course, if the sum channel is made vanishingly
narrow (Ys ~ I'1 a n d / ' s ~/'2). Then:
Fs~ = F ~ = F1F2 / v
'
~
•
(2)
In this case the peaks in the sum-coincidence
spectrum corresponding to Yl a n d Y2 have the
same width. Both peaks are narrower than the
narrowest of the two peaks in the single spectrum.
This especially serves to improve the resolution
in the high-energy region. If a 1 MeV and a
6 MeV gamma ray are in cascade, both having
full-energy peaks in the single spectrum of 6~/o
width, the width of the high-energy gamma ray
in the sum-coincidence spectrum will only be
1%. If ~1 and ~ have about equal energies and
widths (which applies to the Co 6° case) the
improvement in resolution will still be a factor
%/2. The improvement obtained is especially
welcome when the single-spectrum resolution is
low, which is the case e.g. for large crystals. In
practice there is no advantage in making Fs
smaller than the smallest o f / ' l and/'~.
If the bias of the sum channel is not set
correctly (E0~ :# E01 + Eo2) the peaks in the
sum spectrum corresponding to ~1 and Y2 are
still gaussian but they are shifted. This shift is
not a constant percentage of the setting error
E0s - - (E01 -k E0~) and thus the spectrum is distorted. Careful bias setting is thus necessary.
The efficiency esl for detection of V1 with the
sum-coincidence method is easily found by
integrating the corresponding pulse distribution
over E v This yields:
~1 = 2Vl-fi27Y ~le~r~ / V r ?
+ r~2 + r ~ 2 .
(3)
As this is symmetric in the indices 1 and 2 the
areas of the peaks corresponding to 7l and Y2
have to be equal. Any deviation from equality,
outside statistics, can only be caused b y a wrong
setting of the potentiometer RV1 in the adding
circuit. The fact that (3) contains the product
of the full-energy efficiencies means that the
detection efficiency in the sum-coincidence
spectrum does not depend strongly on gammaray energy.
In every sum-coincidence spectrum a "sum
peak" appears corresponding to the energy E0s
chosen by the sum channel. The intensity of this
peak contains contributions from:
(a) the full-energy peak of the cross-over
transition;
(b) events in which the two gamma rays of
one cascade both dissipate their total energy in
crystal 1 ;
(c) background.
If the experimental arrangement is symmetric
(crystals of equal size at equal distance from the
source) contribution (b) exactly amounts to one
half the sum of the intensities of all other peaks
in the sum-coincidence spectrum. Contribution
(c) can easily be measured. In a symmetric
arrangement the sum peak can thus be used as a
sensitive measure to obtain the intensity of the
cross-over transition relative to that of the
cascades. With the analysis given above it is not
difficult to deduce an expression relating this
intensity ratio to the areas of the relevant peaks.
5. Measurements o f spectra
To demonstrate the possibilities of the sumcoincidence method a number of gamma-ray
spectra were measured. In the following discussion Yl, E~1, a n d / ' l will be used for the lowerenergy gamma ray of a cascade.
A NEW METHOD
IN GAMMA-RAY SPECTROSCOPY
61
5.1. SPECTRA MEASURED WITH TWO 2" CRYSTALS somewhat smaller than that to crystal 2.
The two 2" crystals used to measure the Therefore the number of counts in the sum peak
following spectra were both of medium quality is higher than the number of counts in the 1.17
giving about I0% half-width at E~, = 1 MeV and 1.33 MeV peaks. The latter numbers are
equal as they should be.
and about 7% at 8 MeV.
The small peaks at about 0.25, 1.0, 1.6, and
5.1.1. Coe°
2.3 MeV originate from back-scattering of one
The spectrum already mentioned in section 2 detector to the other. In fig. 1 these peaks are
consists only of one cascade. As shown in fig. 1 relatively high because the lead shielding
this cascade gives rise to two well resolved peaks between the detectors was removed in order to
at 1.17 and 1.33 MeV. Because the energies of show this effect clearly. Back-scattering can be
7~ and 73 are nearly the same while the sum avoided easily by only one centimeter of lead
between the crystals in the way shown in fig. 2.
channel is relatively narrow (2%) one has
5.1.2. N a 2=
Fig. 1 also shows the single spectrum giving
9% half-width for the 1.33 MeV peak. Substitution of this value predicts a 6% half-width for
this peak in the sum spectrum. This is in good
agreement with the measured value of 5.5%.
The decay of Na ~ by fl+ emission gives rise
to two 0.51 MeV annihilation quanta emitted
from the source in opposite directions and
coincident with the gamma ray of 1.28 MeV
from the first level in Ne ~2 to the ground state.
Na 22
Counters at 180 ° w i t h
respect to source
x Single spectrum
o Sum co'incidence spectrum
(Sum channel a t 2.30 MeV)
3001.28MeV
ix/
0"51xMeV
II
l/
/ ~
/I
//
--
X
]/~I
k
III/
200 "(5
llxx,
.~x
IF41~=11°/o
h
'x,
"XX
Ill}"
ll/
Xx
af+-er 500 sec
X
/
I
/
(15
~ /
o I
ilc~
Ne22
.~
V N/_,E_,°,,
I i
\
~
0
1.0
1.2B
\ 41ec =lO.,o
X
0
2
~'
x
~x / I~ \
x
x-
~rnc
1.79MeV
~x
~
i
\x7
I/
0
~.~
r~lO *I* ~
x
No 22
X
/ /
/ |
Z X (:Ifter
5seclII ~x xXxX~<X"~x
~
lOO-
X
x /
0
~Bockground
x x
/
r
1.5
~
"
230MeV
E,,nMeV
X
2.0
2.5
Fig. 3. Single a n d s u m - c o i n c i d e n c e s p e c t r u m of 2qa22 u s i n g 2" c r y s t a l s . The c o u n t e r s are p l a c e d a t 180 ° w i t h r e s p e c t to
t h e source. The s u m c h a n n e l is set a t 2.30 MeV. T h e s i n g l e s p e c t r u m is g i v e n on a n a r b i t r a r y scale. N o t e t h e b a c k g r o u n d m e a s u r e d n e a r 2.30 MeV.
Because Co6o is known to emit no 2.50 MeV
gamma ray the sum peak in this case is only
due to events in which both gamma rays are
absorbed in one crystal. In this measurement
the distance from the source to crystal 1 was
Therefore, depending on the position of the
counters and the setting of the sum channel, two
different spectra can be obtained:
(a) Putting the counters at 180 ° with respect
to the source gives the possibility of absorption
62
A. M. H O O G E N B O O M
/"s ~/"2, and also /"1 ~
~/"2. Using eq. (2) one
finds for this case /"s2 ~/"1. Because also
/"81 m F1 the absolute half-width of the peaks
at 0.51 MeV and 1.79 MeV should be the same.
The measurement gives /'st = 55 keV and
/"s~ = 54 keV. This means a relative half-width
for 72 of only 3% compared with a 10% halfwidth in the single spectrum in fig. 3.
of one 0.51 MeV quantum in one crystal in
coincidence with the absorption of the other
0.51 MeV quantum plus the 1.28 MeV quantum
in the second crystal. In this case the sum of the
energies involved amounts to 2.30 MeV. Fig. 3
represents a measurement with the sum channel
set at 2.30 MeV. It clearly shows the impossibility of absorption of the two annihilation quanta
Na 22
1.79 MeV
X
150 -
at 90 ° with
respectto source
x Singlespectrum
o SumcoYncidencespectrum
(Sumchannelat 1.79MeV)
0.51MeV
el
Counters
1.27 MeV
!!
.=
100
I li
50
after 5 sec
II
x
x
xx
o
0
xxxxx,X :
/-I
\
iJ
00o0o OOnno~
0
ufter45sec x~I
x
I
0.5
1.0
1.5
2.0
Fig. 4. Single and sum-coincidence s p e c t r u m of N a 2z using 2 u crystals. The counters are placed a t 90 ° w i t h respect to
the source. The s u m channel is set at 1.79 MeV. The single s p e c t r u m is given on an a r b i t r a r y scale.
in one crystal by the complete absence of the
1.28 MeV line. For the same reason the height
of the sum peak reduces to zero after subtraction
of background. The width of the sum peak as
determined by the channel width of the differential discriminator amounts to 1.5%. Therefore
Because in this measurement the source was
nearer to crystal 2 than to crystal 1 the intensity
of the 0.51 MeV peak is somewhat higher than
the intensity of the 1.79 MeV peak.
(b) Putting the counters a~ 90 ° with respect
to the source limits the sum of the energies of
A NEW METHOD
IN GAMMA-RAY SPECTROSCOPY
the gamma rays absorbed in coincidence to
1.79 MeV. Therefore, setting the sum channel at
1.79 MeV one gets the spectrum of fig. 4 showing
the 0.51 MeV and the 1.28 MeV gamma ray.
Here the sum peak arises from the absorption
of both gamma rays in one crystal. Substituting
the values 125 keV for/'2, 50 keV for /,1, and
36 keV for/,s, as taken from the single spectrum
and from the sum peak in fig. 4, into eq. (1),
gives P s i = 58 keV. The measured value
amounts to 53 keV or about 4%.
63
spectrum of Co n° (taken to be equal to that of
the 1.28 MeV line in Na ~2) amounts to 1'i ~ / , ~
145 keV. From fig. 5 one finds/,s = 100 keV.
Using eq. (1) one g e t s / , s l m/,,2 ~ 110 keV or
about 8.5%. The measured value is 90/0.
In this experiment the shielding between the
crystals was rather good. Comparison of fig. 1
with fig. 5 indeed shows the suppression of the
scattering peaks in the latter.
5.2.2. Mg24(p,7)A125 r e s o n a n c e a t EIp = 222 k e Y
5.2. SPECTRA MEASURED WITH TWO 4" CRYSTALS
In this case the counters consisted of two 4"
Harshaw crystals and two 5" Dumont 6394
photomultiplier tubes. These counters gave a relative half-width in the single spectrum of about
15% at 0.51 MeV and about 10% at 8 MeV.
The decay scheme of the resonance at
Ep = 222 keV in the reaction Mg24(p,7)AP is
shown in fig. 6. The relative intensities indicated
are taken from the review article b y Endt and
BraamsS). The spectrum comprises the two
cascades 2.06, 0.45 MeV and 1.56, 0.95 MeV.
The relative half-width of 5% found for the
Co 60
x Single spectrum (arbitrary scale)
o Sum coYncidence spectrum
1.33 MeV
_2.50 MeV
1.17MeV
300
X1/2
(,
C
D
0u
200
E
D
z
,
!
-~=g%
~×1
100
-~=4%
X~x x 4 0
\
x
x
X X x ~ x XXXx
\x~X~X~
\ x x x j~x.--x x Xx x -xx xX~jX/
x
x
j
x/,
i•
/
0
on
0
~
9
~
0.5
-
~
' ~ ~.
IJ
1.0
Eyin MeV
1.5
2.0
2.5
I
3.0
Fig. 5. S u m - c o i n c i d e n c e a n d single s p e c t r u m of Co e° t a k e n w i t h 4" c r y s t a l s . T h e s u m c h a n n e l is placed a t 2.50 MeV.
5.2.1. Co 6°
The peaks in the spectrum of fig. 5 are
somewhat broader than the peaks in the Co8°
spectrum of fig. 1 because of the lower quality
of the large crystals. The half-width in the single
2.06 MeV line is in agreement with the calculated
value from eq. (1) assuming a 10% relative
half-width for the single spectrum and using the
5) p. M. E n d t a n d C. M. B r a a m s , R e v s . Mod. P h y s . 29
(1957) 683.
64
A.M. HOOGENBOOM
ground-state transition of about 6%. The
spectrum of the 5.27, 0.69 MeV cascade represented in fig. 7 clearly shows the good resolution
for two high-energy gamma rays having an
measured value of 100 keV for Fs. The widths of
the lines corresponding to the 0.95 and 1.56 MeV
gamma rays are also reduced. Because in this
experiment the lead shielding between the
24
25
Mg ( p , y ) A I
- 0 . 4 5 MeV
800
C a s c a d e s in t h e r e s o n a n c e
at
Ep=222keV
2.51MeV
- - - f24. . . . . - J - - I Mg + p
700
88
12
2.51 MeV
600
0.95 --
-- --
2 D 6 M eV
0.4 5 --
500
A125
400
O.95MeV
I
1.56MeV
300
JAE-4o/,
--_
- ~ =5°/o
¢
200 -~=9%
(1.83 MeVZ
1 0 0 .-
I
0
0.5
1.0
1.5
2.0
2.5
E y in MeV
Fig. 6. Sum-coincidence m e a s u r e m e n t w i t h 4" crystals showing cascades of 1.56, 0.95 MeV a n d 2.06, 0.45 MeV in the
reaction Mg2a(p,7)A125 a t Ep = 222 keV. The peaks a t 0.68 and 1.83 MeV are explained in the text. The s u m channel
is p u t at 2.51 MeV.
crystals was partly removed the strong cascade
2.06, 0.45 MeV is accompanied by scattering
peaks. The most evident scattering peak is
observed at 0.68 MeV, whereas its complement
is present as a small shoulder near 1.83 MeV. The
low peaks in the 1.1 and 1.35 MeV region are not
due to scattering because they appear with
equal intensity in measurements with good lead
shielding. They are unexplained at the present
time.
5.2.3, S P ( p , y ) P a° resonance at Ep = 414 keV
This resonance decays primarily by a cascade
of 5.27 and 0.69 MeV gamma rays. There is a
energy difference about equal to their singlespectrum half-width. The dotted line shows the
single spectrum measured with the same 4"
crystal. Even with the rather broad sum channel
of 4%,/'s~ is about 0.5 F~.
5.2.4. Si3°(p,v)Pal" resonance a t Ep = 622 keV
This resonance shows a very strong groundstate transition as can be seen clearly from the
single spectrum given in fig. 8. The low-energy
part (below 3 MeV) of this spectrum suggests
the existence of two cascades by the appearance
of the rather clear 1.27 MeV peak and the
low peaks at 2.4 and 2.9 MeV. However, the
A NEW METHOD
IN GAMMA-RAY SPECTROSCOPY
high-energy complements of these gamma rays
are not resolved in the single spectrum. The sumcoincidence spectrum clearly shows 2.88, 5.01
MeV and 6.62, 1.27 MeV cascades. The intensities
of these cascades relative to the ground-state
transition amount to about 3% for each. The
large intensity of the ground-state transition is
0 . 6 9 MeV
200
-
65
The complement of this peak appears as a small
shoulder near 7.4 MeV.
At this strong resonance a background is
visible resulting from random coincidences. A
reduction b y a factor of about 100 would be
possible by the use of the fast-slow coincidence
technique as indicated in section 3.
2D
p30
Si (p,y)
,
Cascade in the resonance a t E p : 4 1 4 keY
o Sum co'incidence s p e c t r u m
. . . . Single s p e c t r u m o f 5 . 2 7 M e V g a m m a r a y
(arbitrary scale)
)
15o
-
~=
5 . 9 6 MeV
3
0.414
8
.....
f .......
g
Si2+p
'~
I
I
6
94
5.96MeV
5.27 MeV
100 - ~
p30
- ~ = 4°/o
0
1.0
2.0
3.0
4.0
5.0
6.0
Fig. 7. S u m - c o i n c i d e n c e m e a s u r e m e n t w i t h 4" c r y s t a l s s h o w i n g a cascade of 5.27, 0.69 MeV in t h e r e a c t i o n Si~(p,~)P ~° a t
Ep = 414 keV. T h e s u m c h a n n e l is set a t 5.96 MeV. T h e d o t t e d line r e p r e s e n t s t h e single s p e c t r u m :
apparent from the reduction factor of 1080 used 5.2.5. Si3°(p,y)P al r e s o n a n c e a t Ep = 675 keV
in drawing the 7.89 MeV sum peak in fig. 8.
The resonance at Ep = 675 keV in the reaction
The decay scheme shown in fig. 8 was derived Si3°(p,~)P 31 presents a rather complicated decay
from the observed cascades using the known scheme. The sum-coincidence spectrum showing
level scheme 5) of p~l Because it is known that
the cascades in this decay is given in fig. 9.
there is no level at 2.88 MeV, it is concluded that There are three strong cascades namely the 6.67,
the 2.88, 5.01 MeV cascade decays through a 1.27 MeV, the 4.81, 3.13 MeV, and the 4.43,
level at 5.01 MeV.
3.51 MeV cascade. Three known levels 5) through
The peak at 0.51 MeV arises from pair forma- which these three cascades can proceed are the
tion b y 7.89 MeV quanta in crystal 2 and detec- levels at 1.27, 3.13, and 3.51 MeV. The relative
tion of one of the annihilation quanta in crystal 1. :~ intensities are given in the decay scheme
66
A.M. HOOGENBOOM
inserted in fig. 9. In this decay scheme three
weak cascades are indicated as derived from
this experiment. The corresponding relative
intensities have not been corrected for possible
strong triple cascades with two gamma rays of
the three absorbed in one crystal. Therefore,
triple coincidence measurements are necessary
to confirm the results given.
30
relative intensities as derived from the sumcoincidence spectra have not been corrected for
triple angular correlation effects. In the case of
the 622 keV resonance no such effect could
occur because the spin of the resonance level is
½5). However, the spin of the 675 keV resonance
is known to be {. For this resonance a correction
would have been necessary.
31
Si ( p H ) P
Cascades in the
x Single s p e c t r u m
250
at Ep=622keV
resonance
0 Sum coincidence
spectrum
01
200
3
u0
7.SgMeV
-l-I
s~ +op - - rg.4
3 a-
.o
1.27 MeV-¢
z
n
150
tx
oo, l/t
/
(0.51MeV)
100
, ,
x
~x
x
~" \
'"
2.88MeVX-
l
,o, X
5.ol MeV
x
x
=
l
6.62 M e \
,~'~
x
/~
T "~
II
/
50
\
x
0000
d
I
1
I
2
0
I
3
0
I
4
0
0000 0 .
I
5
.
.
.
I
6
t
7
E•in
8
9
MeV
Fig. 8. S u m - c o i n c i d e n c e m e a s u r e m e n t w i t h 4 t' c r y s t a l s s h o w i n g t h e cascades 6.62, 1.27 MeV a n d 2.88, 5.01 MeV
in t h e reaction Si~0(p,7)P31 a t Ep = 622 keV. T h e s u m c h a n n e l is s e t a t 7.89 MeV. C o m p a r i s o n w i t h t h e single
s p e c t r u m s h o w s t h e g a i n in resolution o b t a i n e d w i t h t h e s u m - c o i n c i d e n c e m e t h o d . N o t e t h e s t r o n g g r o u n d - s t a t e t r a n s i t i o n
(the s u m p e a k h a s a r e d u c t i o n factor of 1080).
6. Angular correlation measurements
The measurement of triple angular correlaIn the SP°(p,7)P 31 experiments described tions serves as a tool to determine, in many
above the detectors were placed at + 90 ° and cases uniquely, spins and parities of the lev- - 9 0 ° with respect to the proton beam. The "els involved. Therefore a description of the
A N E W M E T H O D IN GAMMA-RAY S P E C T R O S C O P Y
application of the sum-coincidence method to a
triple angular correlation measurement is included here.
The example chosen is the resonance at
Ep = 760 keV in the reaction Si3°(p,7)p31. In
this experiment the detectors are placed at a
1.27 and 6.76 MeV gamma rays. The other gamma
rays all are slightly anisotropic. The sum peak
itself gives (after correction for back-ground
and summing effects in crystal 1) the angular
distribution for the ground-state transition. In
the measurement the ground-state transition
3Q
31
Si ( p , y ) P
1.27MeV
L13 MeV
3.51 MeV
i
~-
Si + p
[ 26j 24113~
(6)' 5 . 9 8 - 4 4 +-I- -I-"-$ (5) 5 3 6 - J r + T + + ~ t + -
4.81 MeV
(r--3)
(3) 3.13
(2) 2.23
E
'3
0
o
"6(o.51)
300
o
I
Ili[IJi
(,-0
6.67 MeV
t
(r-6)
V84
' '
llilli;
p31
L!
]
200
7.94 MeV
l! H'
~,)127 I ~ i l l ! i
xY4
:1.7
Cascades in resonance at
Ep: 675 keY
• ~ 7.94MeV
4.43 MeV(r.4 )
400
67
-=3.5°/-
II
(r~5)
1.94 2.52 MeV
tl
t
(r--2)
100
iI
0
0
I
/\\
1
2
/ \~
\\
I
II
3
'~ //\
\ \I
/ \
I\ \ / /
4
V
k\I/ 1~\
iN\
\
,i \
5
6
\\
I
I
7
8
E y i n MeV
-
Fig. 9. Sum-coincidence measurement with 4" crystals showing cascades in the reaction SiS°(p,7)P 81 at Ep -- 675 keV.
The sum channel is set at 7.94 MeV. The decay scheme given in the insert can be derived from this measurement. An
indication (r --~i) above a peak points to the position of the corresponding transition in the decay scheme. The peak at
1.78 MeV is of analogous origin as the peak at 0.51 MeV (see § 5.2.4).
distance of 10 cm from the target. Crystal 1
can rotate in the plane determined b y the proton
beam and by crystal 2 as elucidated in the lower
insert in fig. 10. The resonance level decays
through a weak ground-state transition and
through three cascades via the levels at 1.27,
2.23, and 3.51 MeV. The spectra given in fig. 10
are taken at angles of 90 °, 45 °, and 0 °, respectively. They show a strong anisotropy of the
appears almost isotropic. The implications of
these measurements will not be discussed here.
7. Conclusions
In sections 4 and 5 theoretical and experimental results are given for the application of
the sum-coincidence method to the measurement of cascades of two gamma rays. An
extension of this method to cases where three
A.M. HOOGENBOOM
68
transitions determine a sequence is easily
possible. It will not always be necessary to sum
the signals from all three detectors involved.
For example triple cascades having one transition 7~ in common (where Ev~ is smaller than
the energy of all other gamma rays) can be
observed by detecting 7~ with a third crystal
and requiring a coincidence between the signal
from crystal 3 and the sum signal from crystals
1 and 2. The sum channel in this case has to be
set at the total available energy minus E~.
Si3~p.y3t} p31 t r i p l e a n g u l a r
Ep = 760 keY
correlation
My
f ( )B.O3MeV
--.7~-" ~-G-;~-V
200
52 30
Si +p
150
(3)3..51- - ~
(2 )2.23 - f - - ~ L ~
( I ) 1.27 - - ~
(o) 0 .J.J--LL
p31
100
2
3
4
5
8. Acknowledgements
This investigation is part of the research
program of the "Stichting voor Fundamenteel
Onderzoek der Materie", and was made possible
by financial support from the "Nederlandse
Organisatie voor Zuiver Wetenschappelijk Onderzoek".
x~2
50
0
1
the requirement that beta particles in a certain
energy range be in coincidence with a sum pulse
from the gamma detectors can select this
special sequence. Thus all gamma cascades are
observed deexciting the level fed by the selected
beta transition.
6
~.=go°
8
E¥ in MeV
200
cr,2
1.50
pPotonbeQm
100
~o
O
2
3
4
.5
6
7
E~in MeV
N~
8
100
.50
(r~2)
5.80
O
O
1
2
3
4
5
t5
7
8
Fig. 10. Sia°(p,yT)P 31 triple angular correlation at E p
760 keV. The arrangement of the crystals with respect to
the proton beam is given in the lower insert. The first and
the second gamma ray of a cascade are denoted by y~ and 7z
respectively. Tile spectra taken at angles of 90 °, 45 °, and
0 ° show the angular correlations of six gamma rays with
respect to the proton beam. The energies of the gamma rays
are given in the spectrum at ~ = 0 °. The decay scheme is
presented in the upper insert. Note the strong anisotropies
of the gamma rays at 1.27 and 6.76 MeV. The sum peak
represents (after subtraction of background and correction
for summing effects in one crystal) the angular distribution
of the ground-state transition with repseet to the proton
beam.
Eyim MeV
Another example is a radioactive isotope
emitting beta and gamma radiation. Here a
special sequence of one beta transition and two
gamma transitions can be selected by using a
beta detector insensitive to gamma rays. Then
The author wishes to express his gratitude to
Prof, P. M. Endt and Dr. P. B. Smith for their
participation in the experiments and for kindly
reading the manuscript and suggesting valuable
improvements.