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Energy characteristics of planar-channeling radiation for high-energy electrons in diamond
Volume 83A, number 7
PHYSICS LETTERS
15 June 1981
ENERGY CHARACTERISTICS OF PLANAR-CHANNELING RADIATION FOR HIGH-ENERGY ELECTRONS IN DIAMOND Yu.N. ADISHCHEV, A.N. DIDENKO, V.V. KAPLIN, A.P. POTYLITSIN and S.A. VOROBIEV Nuclear Physics Institute, 634050 Tomsk, USSR Received 5 February 1981
7-ray spectra have been measured for (110) and (111) planar channeling of 600—900 MeV electrons in a diamond crystal. It is shown that in the case of (111) crystallographic planes the influence of molecular-type motion on the formation of the spectra is predominant.
In a number of recent papers the characteristics and properties of channeling radiation have been investigated. The spectra of y-radiation for electrons moving through single crystals under planar channeling conditions, were measured forE 0 ~ 50 MeV [1,21 and E0 ~ 1.0 GeV [3,4]. For electrons with lower energy narrow peaks in the radiation spectrum were observed, which could be associated with the radiative transitions between a few bound states in the transverse motion. The calculated system of levels for this motion gives a satisfactory explanation for these peak positions in the experimental spectra. In the energy range of ultrarelativistic electrons there is no good agreement between the experimental data and the theoretical results in the framework of the existing simple model [3]. Here the common spectral peak is formed by means of addition of many radiative transitions between the different bound states in the average potential with a form, which depends on the crystallographic direction, In the present work we present an investigation of the 7-ray spectra for (110) and (111) planar channeling of electrons in the energy range E0 = 600—900 MeV for a diamond crystal of 0.35 mm thickness. The experimental setup is analogous to that previously described [5,6]. The beam of photons produced2 incollithe diamond crystal was formed with a 2 X 2 mm mator and viewed with a ~ 200 X 200 mm2 NaI(Tl)
crystal. The energy resolution of the NaI(T1) spectrometer was measured, with a radioactive 60Co source, to be about 9% full width at half maximum. The energy threshold of the spectrometer was about 1.5 MeV.
The internal electron beam of the Tomsk synchrotron has an angular divergence of less than iO—~rad and a monochromaticity of~0.5%.The electron beam was monitored by the synchroton radiation intensity during the experimental runs. The diamond crystal was oriented relative to the electron beam by the thin-wall ionization chamber [7] with an uncertainty of 0.05 mrad. Fig. la (curve 1) shows the measured ‘y-radiation spectrum N7(w) of 900 MeV electrons for a = 0, I~Iy = 6 mrad diamond orientation, i.e., the electron momentum coincided with the (110) atomic plane and made an angle of 6 mrad with the (110) crystallographic axis. Fig. lb (curve 1) shows the corresponding intensity spectrum 1(w) = w N7(w) with the maximum positioned at the photon energy w0 8.5 MeV. This peak position is in satisfactory agreement with the theoretical value of o~ 7.5 MeV [8,9]. When channeling conditions are violated the low-energy part w < 30 MeV of the 7-ray spectra decreased and the general shape of the spectral distribution transformed to the known bremsstrahlung spectrum from an amorphous target. Figs. la,b also show the 7-radiation spectraN 7(w) and the corresponding intensity spectra~H 11y = 6 mrad, spectrometer placed ~5000 mm downstream of the 1(w) for the diamond orientations ~ 0 031—9163/81/0000—0000/s 02.50 © North-Holland Publishing Company 337
Volume 83A, number 7
PHYSICS LETTERS
20
15 June 1981
.
-
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18 16
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= 11 1(w) mrad. The intensity spectrum of diachanFig. 1. (a) The measured -y-radiation spectra N7(w) and (b) the intensity 1H spectra for(c) 900 MeV electrons and the1(w) (110) mond radiation neling orientation ofI’V 900= MeV 6 mmd electrons and (1)in4H (111) = IJ,(2) diamond. 4’H = 0.45 mrad,(3) \
338
Volume 83A, number 7
PHYSICS LETTERS
0.45 mrad 2i,lJ~(curve 2), and ~‘V= 6 mrad, ~‘H 1.1 mrad (curve 3). Here ~1c 0.25 mrad is the critical angle for (110) planar channeling. In the latter case the intensity spectrum practically coincided with the intensity spectrum measured for an amorphous target (0.4 mm Ta). As can be seen in figs. la,b (curve 2) for the ~v 2~orientation the radiation spectra
15 June 1981
demonstrated an increase of 7-ray yield in the energy range w ~ 30MeV without any observable peak due, probably, to the upper-barrier particle radiation. Fig. ic shows the intensity spectrum 1(w) measured under the conditions of electron channeling along the (111) atomic planes. The potential well for the (111) double plane is the superposition of two
= =
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A
A
A
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F, 750 M~V
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E
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0 A500MeV 13
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LQ~, MeV. Fig. 2. (a) The measured 7-radiation spectra N7(w) and (b) the intensity spectra 1(w) in (110) diamond for electrons with energyE0 600 and 750 MeV.
339
:
Volume 83A, number 7
PHYSICS LETTERS
single potential wells, and two seperate maxima are clearly the 7-radiation spectrum, positions ofobserved which areindetermined by this specificthe type of planar potential. Under electron channeling within such a molecular-type potential three different forms of stable trajectories are realized [10]: (a) within the potential wells of separate atomic planes, (b) within the effective potential of two neighbour planes, and (c) the upper-barrier quasibound motion in the set of planar potentials. Then, the first peak in the intensity spectrum 1(w) at the energy w~ 3.5 MeV corresponds to the channeling 2~radiation 10 MeVoftotype type (b), (a). and Type the trajectories second peakshould at wSgive radiation intensity approx(c) imately in the energy region 10 < w <30 MeV, as in the case of (110) planar channeling, when ~V > 0. In the case of the (ill) atomic plane the effective width of the potential well d, which is formed due to the superposition of two potential wells for single planes, is about twice as large as the respective value for a
15 June 1981
that the variation of the peak energy w0 with energy 2[8,9]. E0 is close thethat theoretical E~’ Finally, we to note in spite relation of strongw0dechanneling (the crystal thickness is greater than the dechanneling length) the channeling radiation dominates in the measured spectral distributions, the contribution of coherent and bremsstrahlung radiation being not greater than 10% at photon energies w w 0. In conclusion we would like to remark, that in the special case of a diatomic crystal, for example GaSb ‘—
or MgO, in (110) and (111) channeling we should have the axissecond and planes, consist eitherhave the first or the type ofwhich atoms. Theseofatoms dif-
ferent Z numbers; therefore we get two systems of bound states in the average electric fields of the planes or atomic strings. Due to radiative transitions between the levels in each system we get two spectral peaks of 7-radiation and an extra peak arising from
particle tunneling through the potential barrier between the potential wells of different depths.
(110) plane. Moreover, the depth U 0 of this potential well is 1.23 times less. Therefore, from the quasiclassical estimate for the number of energy levels N -‘ 2d X.~/~U0/~hc in a potential well, we can show that the energy difference z5~E U0/N between neighbouring levels and, as a consequence, the 7-quanta energy for . molecular-type motion should be approximately in the ratio: irr
tUO(1l 1)! U0(110)
1
j
1/2 (1(110)/0(111).
These estimates are close to the experimental ratio of peak positions. Fig. 2 shows (a) the 7-radiation and (b) the intensity spectra for the (110) atomic plane and the channeled electrons with energiesE0 = 750 and 600 MeV. The peak positions in the intensity spectra are displaced to the low-energy region, w0 6.5 MeV and w0 4.5 MeV, respectively. The data obtained show
340
References [1] R.L. Swent et al., Phys. Rev. Lett. 43 (1979) 1723. [2] J.U. Andersen and E. Laegsgaard, Phys. Rev. Lett. 44
(1980) 1079. [3] A.O. Aganyants et al., Pis’ma Zh. Eksp. Teor. Fiz. 29 (1979) 554. 14] VI. Vitko et al., Pis’ma Zh. Tekh. Fiz. 5 (1979) 1291. [5] Yu.N. Adishchev et al., Pis’ma Zh. Tekh. Fir. 5 (1979) 1300. [6] Yu.N. Adishchev et al., Phys. Lett. 75A (1980) 316. [7] D. Luckey and R.F. Schwitters, Nucl. Instrum. Methods 81(1970)164 [8] MA. Kumakhov, Zh. Eksp. Teor. Fir. 72 (1977) 1485. [9] V.N. Baier, V.M. Katkov and V.M. Strakhovenko, Dokl. Akad. Nauk SSSR 246 (1979) 1347.
[10] V.V. Kaplin and S.A. Vorobiev, Fiz. Tverd. Tela 20 (1978) 31.
PHYSICS LETTERS
15 June 1981
ENERGY CHARACTERISTICS OF PLANAR-CHANNELING RADIATION FOR HIGH-ENERGY ELECTRONS IN DIAMOND Yu.N. ADISHCHEV, A.N. DIDENKO, V.V. KAPLIN, A.P. POTYLITSIN and S.A. VOROBIEV Nuclear Physics Institute, 634050 Tomsk, USSR Received 5 February 1981
7-ray spectra have been measured for (110) and (111) planar channeling of 600—900 MeV electrons in a diamond crystal. It is shown that in the case of (111) crystallographic planes the influence of molecular-type motion on the formation of the spectra is predominant.
In a number of recent papers the characteristics and properties of channeling radiation have been investigated. The spectra of y-radiation for electrons moving through single crystals under planar channeling conditions, were measured forE 0 ~ 50 MeV [1,21 and E0 ~ 1.0 GeV [3,4]. For electrons with lower energy narrow peaks in the radiation spectrum were observed, which could be associated with the radiative transitions between a few bound states in the transverse motion. The calculated system of levels for this motion gives a satisfactory explanation for these peak positions in the experimental spectra. In the energy range of ultrarelativistic electrons there is no good agreement between the experimental data and the theoretical results in the framework of the existing simple model [3]. Here the common spectral peak is formed by means of addition of many radiative transitions between the different bound states in the average potential with a form, which depends on the crystallographic direction, In the present work we present an investigation of the 7-ray spectra for (110) and (111) planar channeling of electrons in the energy range E0 = 600—900 MeV for a diamond crystal of 0.35 mm thickness. The experimental setup is analogous to that previously described [5,6]. The beam of photons produced2 incollithe diamond crystal was formed with a 2 X 2 mm mator and viewed with a ~ 200 X 200 mm2 NaI(Tl)
crystal. The energy resolution of the NaI(T1) spectrometer was measured, with a radioactive 60Co source, to be about 9% full width at half maximum. The energy threshold of the spectrometer was about 1.5 MeV.
The internal electron beam of the Tomsk synchrotron has an angular divergence of less than iO—~rad and a monochromaticity of~0.5%.The electron beam was monitored by the synchroton radiation intensity during the experimental runs. The diamond crystal was oriented relative to the electron beam by the thin-wall ionization chamber [7] with an uncertainty of 0.05 mrad. Fig. la (curve 1) shows the measured ‘y-radiation spectrum N7(w) of 900 MeV electrons for a = 0, I~Iy = 6 mrad diamond orientation, i.e., the electron momentum coincided with the (110) atomic plane and made an angle of 6 mrad with the (110) crystallographic axis. Fig. lb (curve 1) shows the corresponding intensity spectrum 1(w) = w N7(w) with the maximum positioned at the photon energy w0 8.5 MeV. This peak position is in satisfactory agreement with the theoretical value of o~ 7.5 MeV [8,9]. When channeling conditions are violated the low-energy part w < 30 MeV of the 7-ray spectra decreased and the general shape of the spectral distribution transformed to the known bremsstrahlung spectrum from an amorphous target. Figs. la,b also show the 7-radiation spectraN 7(w) and the corresponding intensity spectra~H 11y = 6 mrad, spectrometer placed ~5000 mm downstream of the 1(w) for the diamond orientations ~ 0 031—9163/81/0000—0000/s 02.50 © North-Holland Publishing Company 337
Volume 83A, number 7
PHYSICS LETTERS
20
15 June 1981
.
-
a)
18 16
E0
•
/
1412
900
MeV
(-lie)
• A •
0
A
0 A
A —
~
0
AA
z
/
/
AAA
0
4—
20
00
0
.
AAA
A
2
000
~
/000 0
I
1
2
I
4
5
a 6 7 8
5
11 — 40-
+4
I
7 7 77
10
41+4+444
20
~
30
40 50 60 7080
6)
+
+ 4
0
E0~900 MeV
-~
(-iio) +
4
44 4 o
444 44444444+
+
-
4444
+
44
2-
4 + ~+4+~ ~
1— 0 1 5-
a 2
t
3
a
3
4
5
II
444+
~
~ III
6 7 89
11111
10
30
20
tIll
Ill
40 50 607080
~
-
C)
E0~9ooMeV
+
4
+
++
-
(411)
+ +
4
02.
4
+444
~
4 +
-
a
I
I
4
2
3
4
11111
5 6 ‘1
8 9
11111
40
11111
20
30
II
~o50 60 7080 (ii, Me V.
= 11 1(w) mrad. The intensity spectrum of diachanFig. 1. (a) The measured -y-radiation spectra N7(w) and (b) the intensity 1H spectra for(c) 900 MeV electrons and the1(w) (110) mond radiation neling orientation ofI’V 900= MeV 6 mmd electrons and (1)in4H (111) = IJ,(2) diamond. 4’H = 0.45 mrad,(3) \
338
Volume 83A, number 7
PHYSICS LETTERS
0.45 mrad 2i,lJ~(curve 2), and ~‘V= 6 mrad, ~‘H 1.1 mrad (curve 3). Here ~1c 0.25 mrad is the critical angle for (110) planar channeling. In the latter case the intensity spectrum practically coincided with the intensity spectrum measured for an amorphous target (0.4 mm Ta). As can be seen in figs. la,b (curve 2) for the ~v 2~orientation the radiation spectra
15 June 1981
demonstrated an increase of 7-ray yield in the energy range w ~ 30MeV without any observable peak due, probably, to the upper-barrier particle radiation. Fig. ic shows the intensity spectrum 1(w) measured under the conditions of electron channeling along the (111) atomic planes. The potential well for the (111) double plane is the superposition of two
= =
18 17
16
a)
A
A
A
-
F, 750 M~V
•
-
E
A
0 A500MeV 13
•
A
12
A
•
A
A
A
a
10
Q
A
A
A ‘~ cj
•
‘~
-6
a
S
•
A
a
••
a
3
A
2
S~
A
I
s
1
2
5
4
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5 7 6110
5
1
S.
LII,,
AA
23
t
3D
•
•
#.A
W 50 6D 7081
10
+
1 ~‘
-
~
-
Eo~750~18V
E3: 60001eV
+ 4
~0-’
4 4444 4
+4 +
1+
+4 +++
+
4
4+44
+
~
+ 2
1
4
5 6 7 6010
20
33
~O 50507080
LQ~, MeV. Fig. 2. (a) The measured 7-radiation spectra N7(w) and (b) the intensity spectra 1(w) in (110) diamond for electrons with energyE0 600 and 750 MeV.
339
:
Volume 83A, number 7
PHYSICS LETTERS
single potential wells, and two seperate maxima are clearly the 7-radiation spectrum, positions ofobserved which areindetermined by this specificthe type of planar potential. Under electron channeling within such a molecular-type potential three different forms of stable trajectories are realized [10]: (a) within the potential wells of separate atomic planes, (b) within the effective potential of two neighbour planes, and (c) the upper-barrier quasibound motion in the set of planar potentials. Then, the first peak in the intensity spectrum 1(w) at the energy w~ 3.5 MeV corresponds to the channeling 2~radiation 10 MeVoftotype type (b), (a). and Type the trajectories second peakshould at wSgive radiation intensity approx(c) imately in the energy region 10 < w <30 MeV, as in the case of (110) planar channeling, when ~V > 0. In the case of the (ill) atomic plane the effective width of the potential well d, which is formed due to the superposition of two potential wells for single planes, is about twice as large as the respective value for a
15 June 1981
that the variation of the peak energy w0 with energy 2[8,9]. E0 is close thethat theoretical E~’ Finally, we to note in spite relation of strongw0dechanneling (the crystal thickness is greater than the dechanneling length) the channeling radiation dominates in the measured spectral distributions, the contribution of coherent and bremsstrahlung radiation being not greater than 10% at photon energies w w 0. In conclusion we would like to remark, that in the special case of a diatomic crystal, for example GaSb ‘—
or MgO, in (110) and (111) channeling we should have the axissecond and planes, consist eitherhave the first or the type ofwhich atoms. Theseofatoms dif-
ferent Z numbers; therefore we get two systems of bound states in the average electric fields of the planes or atomic strings. Due to radiative transitions between the levels in each system we get two spectral peaks of 7-radiation and an extra peak arising from
particle tunneling through the potential barrier between the potential wells of different depths.
(110) plane. Moreover, the depth U 0 of this potential well is 1.23 times less. Therefore, from the quasiclassical estimate for the number of energy levels N -‘ 2d X.~/~U0/~hc in a potential well, we can show that the energy difference z5~E U0/N between neighbouring levels and, as a consequence, the 7-quanta energy for . molecular-type motion should be approximately in the ratio: irr
tUO(1l 1)! U0(110)
1
j
1/2 (1(110)/0(111).
These estimates are close to the experimental ratio of peak positions. Fig. 2 shows (a) the 7-radiation and (b) the intensity spectra for the (110) atomic plane and the channeled electrons with energiesE0 = 750 and 600 MeV. The peak positions in the intensity spectra are displaced to the low-energy region, w0 6.5 MeV and w0 4.5 MeV, respectively. The data obtained show
340
References [1] R.L. Swent et al., Phys. Rev. Lett. 43 (1979) 1723. [2] J.U. Andersen and E. Laegsgaard, Phys. Rev. Lett. 44
(1980) 1079. [3] A.O. Aganyants et al., Pis’ma Zh. Eksp. Teor. Fiz. 29 (1979) 554. 14] VI. Vitko et al., Pis’ma Zh. Tekh. Fiz. 5 (1979) 1291. [5] Yu.N. Adishchev et al., Pis’ma Zh. Tekh. Fir. 5 (1979) 1300. [6] Yu.N. Adishchev et al., Phys. Lett. 75A (1980) 316. [7] D. Luckey and R.F. Schwitters, Nucl. Instrum. Methods 81(1970)164 [8] MA. Kumakhov, Zh. Eksp. Teor. Fir. 72 (1977) 1485. [9] V.N. Baier, V.M. Katkov and V.M. Strakhovenko, Dokl. Akad. Nauk SSSR 246 (1979) 1347.
[10] V.V. Kaplin and S.A. Vorobiev, Fiz. Tverd. Tela 20 (1978) 31.