- Email: [email protected]
Two-fold focussing 2 × π2-angle beta-spectrometer
NUCLEAR
INSTRUMENTS
AND
METHODS
17
(1962)
94-96; N O R T H - H O L L A N D
PUBLISHING
CO.
TW0-FOLD FOCUSSING 2 × n%/2-ANGLE BETA-SPECTROMETER S. A. S H E S T O P A L O V A
Mendelejev's Institute o/Meteorology, Leningrad, U.S.S.R. R e c e i v e d 10 April 1962
T h e following p a p e r is a d e s c r i p t i o n of a n e w two-fold f o c u s s i n g 2 × 7~%/~[angle f l - s p e c t r o m e t e r w h i c h h a s t w o a d v a n t a g e s o v e r
u s u a l i n s t r u m e n t s of t h i s t y p e : s m a l l s c a t t e r i n g a n d small b a c k g r o u n d - - l e s s t h a n one coincidence p e r 40 hours.
High resolution and high transmission are the main requirements for a modern fl-spectrometer. The best instruments from this point of view are the double focussing~ %/2--angle spectrometers 1 - 3). For a number of physical problems, however, some other characteristics of the spectrometer are important in addition to these two e.g., absence of scattering in the instrument and absence of the background in the detector. The scattering is removed or eliminated b y the use of many-fold focussing as in the case of the three-fold focussing spectrometers 4' 5) and in the case of the instrument with two-fold focussing in the sector field and in the lens. The arrangement of thin-wall Geiger-Miiller counters behind the focuses and the use of the coincidence method in these spectrometers is a good solution to the background problem at the same time. Since the ~ %/2 type instruments have the best electro-optical properties, it is desirable if manyfold focussing is to be used, to maintain the focussing at the angle n ~v/2, if possible. This appears to be practical in a magnetic field with axial symmetry
and decreasing along the radius in which the electrons undergo oscillations with p and with Z. If the source is placed above the symmetry plane of the magnetic field, the focuses appear to be located below and beyond the symmetry plane of the field successively. Figs. 1 and 2 represent photographs of a model electron beam in the new spectrometer, side view and top view respectively. As it is shown in fig. 1, the first focus is placed A
A
Fig. 1. P h o t o g r a p h of t h e m o d e l e l e c t r o n b e a m in t h e spectrom e t e r ; side view. S, source; F1F 2, focuses; AA, t h e s y m m e t r y p l a n e of t h e m a g n e t i c field.
1) K. Siegbahn, E d i t o r , B e t a - a n d g a m m a - r a y s p e c t r o s c o p y , ( N o r t h - H o l l a n d P u b l i s h i n g Co., A m s t e r d a m , 1955), Ch. 3, p. 74. 2) A. V. Z o l o t a v i n , Bull. Acad. Sci. U S S R p h y s . ser. 18 (1954) 127. 3) S. A. 13aranov, A. F. M a l o v a n d K. N, Shlagin, P r i b o r i i t e h n i k a e k s p e r i m e n t a , N. 1 (1956) 3, 4) B. S. D~.elepow, N. M. A n t o n j e v a a n d S. A. S h e s t o p a l o v a , R e p . Acad. Sci. U S S R 64 (1949) 309. ]3. S. D~elepow, I. F. U c h e v a t k i n a n d S. A. S h e s t o p a l o v a , J o u r . E x p e r . Theor. P h y s . U S S R 37 (1959) 858. 5) O. E. K r a f t a n d 13. S. D2elepow, 13ull. Acad. Sci. U S S R p h y s . sci. 20 (1956) 318.
Fig. 2. P h o t o g r a p h of t h e m o d e l electron b e a m in t h e spectrom e t e r , t o p view. 94
TWO-FOLD
FOCUSSING
below the s y m m e t r y plane of the magnetic field. To determine the shape of the focus one can use all the analytical and numerical calculations referring to the field with focussing at the angle ~ %,/}-. Since it is known2), that this focus is curved, the first slit ought to be curved too. The shape of the outer edge of the slit and three diaphragms have been calculated by M. A. Listengarten from the equations of motion for electrons with accuracy in the terms of the third order. The other diaphragms have been calculated by the author from the first approximamation formulas given in referencea). After passing the first slit and the Geiger-Miiller counter with thin film windows, the electron beam starts rising, then goes under the source and is focussed for the second time at 254.5 ° after the first focus. The second focus is located above the s y m m e t r y plane of the magnetic field at the same height as the source. Two Geiger-Miiller counters are placed behind the second focus. The triple coincidences of the discharges are counted. As the calculations by M. A. Listengarten have shown, the second focus of the instrument appears to be narrower than the first one and is linear. However, the second focussing can be regarded merely as means to eliminate the background and the probability of counting electrons scattered in the first part of the spectrometer. Then the slit at the second focus can be widened in order to capture
BETA-SPECTROMETER
95
the electrons scattered in the first counter. The resolving power is determined by the first slit, the dimensions of the source and the geometry of the beam during the first focussing. Nj
K-585
5
N~ omuea
/(- 26/z~
2"
!
t
/ A
B
Fig. 3. C o n v e r s i o n line of t h e a c t i v e d e p o s i t of r a d i o t h o r i u m : A, f r o m t h e )~-transition 583 keV; B, f r o m t h e T - t r a n s i t i o n 2614 keV, = 0.21%.
zJH~/H~
The radius of the equilibrium orbit in the instrument is 140 mm. Over the whole working area we have succeeded in fitting the actual distribution of the field in the gap with the theoretical one within 0.2 % (the accuracy of the measurements ot the field topography).
N
cov.~, 750o
/(
/i
5000
i
/
25001
0
L
°,t_--.-.--/ 550O
• • m a
3350
A
\
12.
-
545O
Fig. 4. C o n v e r s i o n electron s p e c t r u m of Cs za7 y-662 keV.
JS~ @
AHo/He = 0.32 %.
96
S. A. S H E S T O P A L O V A
The source is 15 mm high; the centre of the source is located 24 mm above the s y m m e t r y plane of the magnetic field. The slit width at the first focus is 1 mm, at the second focus 14 ram. Under these conditions the resolving power of the spectrometer is 0.2% (fig. 3). (The source is an active deposit of radiothorium 0.5 mm wide.) Some properties of the instrument were also investigated with Cs 137 as the source. At first the instrument was adjusted manually; then the position of optimum focussing was found by moving the source along the optical axis. The results are shown in fig, 5. Unfortunately, because of the poor quality of the source, the conversion lines of Cs 137 measured under the same conditions as the radiothorium lines had half-width (0.32 + 0.02) % (fig. 4). With Cs 137 as the source, the background arising from accidental and cosmic coincidences at zero current in the magnet is somewhat less than one event per 40 hours; beyond the hard spectrum, the background is less than one coincidence per 10 hours. The author expresses her profound gratitude to Prof. B. S. D~elepow for formulating the problem, for a n u m b e r of essential remarks and for his constant interest to this work; to A. F. Malov for valuable discussion; to M. A. Listengarten for
valuable advice and for calculation of the images of some diaphragms; to I. F. Utchevatkin and A. I. Medvedev for participation in setting up and testing the instrument; to A. V. Zolotavin and J. P. Grigorjev for useful practical advice on the construction of the required configuration of the magnetic field. fbc5
~H2 0.6, -5000
-~500 O.2
0 Fig. 5. Results of the e x p e r i m e n t to find t h e o p t i m u m focussing conditions. The crosses refer to t h e resolving power, dots to t h e c o u n t s a t t h e m a x i m u m of t h e K-line of Cs 187 662 keV. The d o t t e d line refers to t h e a c t u a l working conditions.
INSTRUMENTS
AND
METHODS
17
(1962)
94-96; N O R T H - H O L L A N D
PUBLISHING
CO.
TW0-FOLD FOCUSSING 2 × n%/2-ANGLE BETA-SPECTROMETER S. A. S H E S T O P A L O V A
Mendelejev's Institute o/Meteorology, Leningrad, U.S.S.R. R e c e i v e d 10 April 1962
T h e following p a p e r is a d e s c r i p t i o n of a n e w two-fold f o c u s s i n g 2 × 7~%/~[angle f l - s p e c t r o m e t e r w h i c h h a s t w o a d v a n t a g e s o v e r
u s u a l i n s t r u m e n t s of t h i s t y p e : s m a l l s c a t t e r i n g a n d small b a c k g r o u n d - - l e s s t h a n one coincidence p e r 40 hours.
High resolution and high transmission are the main requirements for a modern fl-spectrometer. The best instruments from this point of view are the double focussing~ %/2--angle spectrometers 1 - 3). For a number of physical problems, however, some other characteristics of the spectrometer are important in addition to these two e.g., absence of scattering in the instrument and absence of the background in the detector. The scattering is removed or eliminated b y the use of many-fold focussing as in the case of the three-fold focussing spectrometers 4' 5) and in the case of the instrument with two-fold focussing in the sector field and in the lens. The arrangement of thin-wall Geiger-Miiller counters behind the focuses and the use of the coincidence method in these spectrometers is a good solution to the background problem at the same time. Since the ~ %/2 type instruments have the best electro-optical properties, it is desirable if manyfold focussing is to be used, to maintain the focussing at the angle n ~v/2, if possible. This appears to be practical in a magnetic field with axial symmetry
and decreasing along the radius in which the electrons undergo oscillations with p and with Z. If the source is placed above the symmetry plane of the magnetic field, the focuses appear to be located below and beyond the symmetry plane of the field successively. Figs. 1 and 2 represent photographs of a model electron beam in the new spectrometer, side view and top view respectively. As it is shown in fig. 1, the first focus is placed A
A
Fig. 1. P h o t o g r a p h of t h e m o d e l e l e c t r o n b e a m in t h e spectrom e t e r ; side view. S, source; F1F 2, focuses; AA, t h e s y m m e t r y p l a n e of t h e m a g n e t i c field.
1) K. Siegbahn, E d i t o r , B e t a - a n d g a m m a - r a y s p e c t r o s c o p y , ( N o r t h - H o l l a n d P u b l i s h i n g Co., A m s t e r d a m , 1955), Ch. 3, p. 74. 2) A. V. Z o l o t a v i n , Bull. Acad. Sci. U S S R p h y s . ser. 18 (1954) 127. 3) S. A. 13aranov, A. F. M a l o v a n d K. N, Shlagin, P r i b o r i i t e h n i k a e k s p e r i m e n t a , N. 1 (1956) 3, 4) B. S. D~.elepow, N. M. A n t o n j e v a a n d S. A. S h e s t o p a l o v a , R e p . Acad. Sci. U S S R 64 (1949) 309. ]3. S. D~elepow, I. F. U c h e v a t k i n a n d S. A. S h e s t o p a l o v a , J o u r . E x p e r . Theor. P h y s . U S S R 37 (1959) 858. 5) O. E. K r a f t a n d 13. S. D2elepow, 13ull. Acad. Sci. U S S R p h y s . sci. 20 (1956) 318.
Fig. 2. P h o t o g r a p h of t h e m o d e l electron b e a m in t h e spectrom e t e r , t o p view. 94
TWO-FOLD
FOCUSSING
below the s y m m e t r y plane of the magnetic field. To determine the shape of the focus one can use all the analytical and numerical calculations referring to the field with focussing at the angle ~ %,/}-. Since it is known2), that this focus is curved, the first slit ought to be curved too. The shape of the outer edge of the slit and three diaphragms have been calculated by M. A. Listengarten from the equations of motion for electrons with accuracy in the terms of the third order. The other diaphragms have been calculated by the author from the first approximamation formulas given in referencea). After passing the first slit and the Geiger-Miiller counter with thin film windows, the electron beam starts rising, then goes under the source and is focussed for the second time at 254.5 ° after the first focus. The second focus is located above the s y m m e t r y plane of the magnetic field at the same height as the source. Two Geiger-Miiller counters are placed behind the second focus. The triple coincidences of the discharges are counted. As the calculations by M. A. Listengarten have shown, the second focus of the instrument appears to be narrower than the first one and is linear. However, the second focussing can be regarded merely as means to eliminate the background and the probability of counting electrons scattered in the first part of the spectrometer. Then the slit at the second focus can be widened in order to capture
BETA-SPECTROMETER
95
the electrons scattered in the first counter. The resolving power is determined by the first slit, the dimensions of the source and the geometry of the beam during the first focussing. Nj
K-585
5
N~ omuea
/(- 26/z~
2"
!
t
/ A
B
Fig. 3. C o n v e r s i o n line of t h e a c t i v e d e p o s i t of r a d i o t h o r i u m : A, f r o m t h e )~-transition 583 keV; B, f r o m t h e T - t r a n s i t i o n 2614 keV, = 0.21%.
zJH~/H~
The radius of the equilibrium orbit in the instrument is 140 mm. Over the whole working area we have succeeded in fitting the actual distribution of the field in the gap with the theoretical one within 0.2 % (the accuracy of the measurements ot the field topography).
N
cov.~, 750o
/(
/i
5000
i
/
25001
0
L
°,t_--.-.--/ 550O
• • m a
3350
A
\
12.
-
545O
Fig. 4. C o n v e r s i o n electron s p e c t r u m of Cs za7 y-662 keV.
JS~ @
AHo/He = 0.32 %.
96
S. A. S H E S T O P A L O V A
The source is 15 mm high; the centre of the source is located 24 mm above the s y m m e t r y plane of the magnetic field. The slit width at the first focus is 1 mm, at the second focus 14 ram. Under these conditions the resolving power of the spectrometer is 0.2% (fig. 3). (The source is an active deposit of radiothorium 0.5 mm wide.) Some properties of the instrument were also investigated with Cs 137 as the source. At first the instrument was adjusted manually; then the position of optimum focussing was found by moving the source along the optical axis. The results are shown in fig, 5. Unfortunately, because of the poor quality of the source, the conversion lines of Cs 137 measured under the same conditions as the radiothorium lines had half-width (0.32 + 0.02) % (fig. 4). With Cs 137 as the source, the background arising from accidental and cosmic coincidences at zero current in the magnet is somewhat less than one event per 40 hours; beyond the hard spectrum, the background is less than one coincidence per 10 hours. The author expresses her profound gratitude to Prof. B. S. D~elepow for formulating the problem, for a n u m b e r of essential remarks and for his constant interest to this work; to A. F. Malov for valuable discussion; to M. A. Listengarten for
valuable advice and for calculation of the images of some diaphragms; to I. F. Utchevatkin and A. I. Medvedev for participation in setting up and testing the instrument; to A. V. Zolotavin and J. P. Grigorjev for useful practical advice on the construction of the required configuration of the magnetic field. fbc5
~H2 0.6, -5000
-~500 O.2
0 Fig. 5. Results of the e x p e r i m e n t to find t h e o p t i m u m focussing conditions. The crosses refer to t h e resolving power, dots to t h e c o u n t s a t t h e m a x i m u m of t h e K-line of Cs 187 662 keV. The d o t t e d line refers to t h e a c t u a l working conditions.