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Anomalous transmission of gamma-rays of 0.662 MeV energy through single crystals of gallium garnets
Nuclear Instruments and Methods in Physics Research B 174 (2001) 392±396
www.elsevier.nl/locate/nimb
Letter to the Editor
Anomalous transmission of gamma-rays of 0.662 MeV energy through single crystals of gallium garnets R.A. Khairulin *, A.V. Baginskii, S.V. Stankus Institute of Thermophysics, Siberian Branch of the Russian, Academy of Sciences, St. Kutateladze 2, 630090 Novosibirsk, Russia Received 15 August 2000; received in revised form 7 November 2000
Abstract It has been found experimentally that gamma-ray absorption Ec 0:662 MeV in single crystals of Gd3 Ga5 O12 and Ca3 Nb; Ga2 Ga3 O12 decreases at small angles between major crystallographic directions and beam direction. A magnitude of the eect is enhanced markedly as a temperature gradient perpendicular to the beam direction is created in the sample. The angular dependences of absorption coecient look like orientation dependences observed at channeling of charged particles. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 78.70. g Keywords: Gamma-ray; Garnet; Channeling
In the foregoing years, a number of theoretical papers had been published wherein a possibility of the channeling of gamma±quanta through crystals was predicted, see for example [1±3]. It had been shown that this possibility could be realized in the crystals with layer structure and with large spacing, where the layers with high and low electron density alternate. The gallium garnets are composed of light oxygen ions and heavy cations. In addition, they have crystal lattice with relatively large spacing. In particular, the gadolinium±gallium garnet,
* Corresponding author. Tel.: +7-3832-391541; fax: +73832-343480. E-mail addresses: [email protected] (R.A. Khairulin), [email protected] (S.V. Stankus).
Gd3 Ga5 O12 GGG, and the calcium±niobium± gallium one, Ca3 Nb; Ga2 Ga3 O12 (CNGG), have and a cubical lattice with spacing equal to 12.37 A respectively. Hence, these compounds are 12.50 A, attractive objects to check the theoretical predictions. Besides, in studies of thermal properties of these garnets [4] we observed special features in behavior of their absorption coecients. This was a further reason for choosing these objects for experimentation. The measurements of gamma-ray absorption in the garnets were performed with a gamma-densitometer which has been described in detail elsewhere [5]. A basic schematic of the experimental arrangement is shown in Fig. 1. Diameter of the ®rst collimator was equal to 6 mm. Diameter of the second collimator was varied (6, 4 and 3 mm).
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 0 ) 0 0 5 8 4 - X
R.A. Khairulin et al. / Nucl. Instr. and Meth. in Phys. Res. B 174 (2001) 392±396
393
Fig. 1. Collimated geometry arrangement for gamma-ray absorption measurements.
The intensity of gamma radiation was measured with scintillation counter. Dead time of the counting channel was considered in computation. The samples for studying were cut from single crystals grown by the Czochralski method, so that the faces of the samples were oriented normally to the major crystallographic axes. Mass absorption coecient (l) was found from the equation l h LnJ0 =J h ql
1
cos h;
which follows from the well-known absorption law. Here, J h and J0 are the radiation intensities after passage through the apparatus with and without the sample, respectively; q is the density of the sample (7.096 and 4:694 g=cm3 , respectively, for GGG and CNGG); lcos h 1 is absorption distance. The initial intensity, J0 , fell in the range 10,000±46,000 s 1 in accordance with the diameter of the second collimator. The value of J comprised 7±35% of J0 , depending on the density and on the thickness of the samples. The intensity measurements at any point were performed during a period of 300±400 s, to minimize statistical errors, the measurement uncertainty of the absorption coef®cient did not exceed 0.25±0.35%. Typical orientation dependences of the absorption coecient measured in the experiments with the GGG are shown in Fig. 2 (the dependences are symmetric about h 0). When h P 50 mrad, the measured values of l for all diameters of the second collimator agree with calculated value [6], to within experimental error. That is, the quantity of photons scattered by the sample
Fig. 2. Orientation dependence of l for the ®rst GGG sample (l 30 mm). h is the angle between h1 0 0i direction and the beam axis. The axis of rotation is parallel to another (perpendicular) h1 0 0i direction. 1, 2, 3 are the data for the collimators of 6, 4, 3 mm diameters, respectively. Dashed±dot line is the value of l calculated from the data of [6].
(Compton and Rayleigh scattering) through a small angle into the detector is slight in comparison to the quantity of transmitted quanta (the condition of ``good geometry'' is ful®lled). As the angle is decreased, l rises to a maximum value at h 15 mrad. On further angular decrease the absorption coecient falls sharply and approaches a minimum at h 0. The depth of the minimum increases as the diameter of the collimator is reduced. But when the diameter falls from 4 mm to 3 mm, the change of l does not already exceed the measurement error. It is likely that the eect observed with the collimators of 4 and 3 mm diameters is not too dierent from the eect for ideally collimated beam. In order to establish the manner in which deformations of the crystals in¯uence on the magnitude of the eect, temperature gradients were created in the samples. In the case that the gradient is parallel to the crystallographic axis oriented along the beam, it has not been found changes in the observed dependences, to within experimental error. But in the case that the gradient is normal to this axis (the orientation of the gradient with re-
394
R.A. Khairulin et al. / Nucl. Instr. and Meth. in Phys. Res. B 174 (2001) 392±396
spect to the axis of rotation is of little importance), the contrast of the observed pattern grows materially. As is seen from Fig. 3, the intensity of transmitted radiation at h 0 increases (l decreases) with increasing temperature gradient. This dependence is practically symmetric about zero point, that is, the magnitude of the eect is dependent on the absolute value of the gradient only, but not on its direction. The side peaks in the dependences l h (the side dips in the dependences J h also grow. Steep rise of the extremums occurs at the gradients up to 1 K/mm. Further increasing of the temperature dierence does not produce marked changes in the angular dependences. As is seen from Fig. 4, magnitudes of the extremums at the gradient of 1 K/mm are 5.5 times greater than those for isothermal sample. Amplitude spectra of the signals from a photomultiplier of the scintillation counter obtained at dierent orientations of the crystals about the beam axis are similar in form and dier only by magnitude (Fig. 5). Because at large angles the condition of good geometry is ful®lled, that is to say, that the dips in measured dependences l h at small angles are connected with rise of the
Fig. 3. The temperature gradient dependence of the radiation intensity transmitted through the ®rst GGG sample at h 0. The gradient is parallel to the axis of rotation. Diameter of the second collimator equals 3 mm. J0 10 050 s 1 .
Fig. 4. h-Dependence of l for the ®rst GGG sample at zero temperature gradient, curve 1 (the same as curve 3 in Fig. 2), and at gradient equal to 1 K/mm, curve 2. The gradient is normal both to h1 0 0i axis oriented along the beam and to the axis of rotation. Diameter of the second collimator equals 3 mm. Dashed±dot line is the calculated l.
Fig. 5. Amplitude spectra of the signals from the photomultiplier obtained at h 50 mrad (normal transmission), curve 1, and at h 0 (anomalous transmission), curve 2. Diameter of the second collimator equals 6 mm. The gradient is equal to 1 K/mm. The data have been obtained with the spectrum analyzer Robotron 20050.
R.A. Khairulin et al. / Nucl. Instr. and Meth. in Phys. Res. B 174 (2001) 392±396
quantity of transmitted quanta that are very slightly or not at all modi®ed in energy and direction. Further investigations have shown that analogous orientation dependences are also observed at small angles between the beam axis and the other major (h1 1 0i and h1 1 1i) crystal axes. The dip and the side peaks in the h-dependences of l decrease with increase in thickness of the samples. However the decrease is not very signi®cant, so the relative magnitudes of the extremums in the dependences J h do rise with distance of absorption. When the temperature gradient is created, a dierence between the intensities of the transmitted radiation measured at h 0 and at h 15 mrad is as much as 40% (Fig. 6). Orientation dependences of l and J for the CNGG crystal (Fig. 7) are analogous to those for GGG. But creation of temperature gradients in the CNGG crystal does not signi®cantly aect the magnitude of dips and peaks. At the gradient equal to 1 K/mm the extremums increase only by a factor of 1.3.
Fig. 6. Orientation dependence of the radiation intensity transmitted through the second GGG sample (l 48 mm) at the gradient equal to 1 K/mm. h is the angle between h1 0 0i direction and the beam axis. The axis of rotation and the gradient are parallel to h1 1 0i direction. Diameter of the second collimator equals 4 mm. J0 18 700 s 1 .
395
Fig. 7. h-Dependence of l for the CNGG sample (l 30 mm). h is the angle between h1 1 1i direction and the beam axis. The axis of rotation is parallel to h1 1 0i direction. Diameter of the second collimator equals 3 mm.
The eect of anomalous transmission of lowenergy X-rays through thick crystals at h equal to Bragg angle (the Borrmann eect) has been much studied [7]. But for Ec 0:662 MeV the Bragg angle is of about 0.7 mrad only (it is less than the angular aperture), while the side extremums are observed at h 15 mrad. Notice that their position is not dependent on the collimator diameter (on the angular aperture). This suggests that in our case the anomalous transmission is not the usual diraction phenomenon. Alternatively, the obtained angular dependences are truly similar to those that observed at the channeling of charged particles [8,9]. In particular, the side peaks in the h-dependences of l (anomalous scattering) appear to be analogues of the so-called ``compensation shoulders'' in the angular dependences for charged particles. Creation of the temperature gradient in the sample produces two types of the deformation: (1) bending of the crystal; (2) monotone variation of the lattice spacing in the direction normal to the beam axis. Some facts suggest that the second reason is responsible for the increase of the eect, but this question calls for further investigation.
396
R.A. Khairulin et al. / Nucl. Instr. and Meth. in Phys. Res. B 174 (2001) 392±396
References [1] N.N. Nasonov, Pis'ma v Zhurnal Tekhnicheskoi Fiziki (Tech. Phys. Lett.) 5 (1979) 982. [2] N.K. Zhevago, Doklady Akademii Nayk SSSR (Dokl. Phys.) 281 (1985) 67. [3] V.I. Vysotskii, R.N. Kuz'min, Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki (J. Exp. Theor. Phys.) 94 (1988) 351. [4] S.V. Stankus, Phys.-Math. Doct. Thesis, Institute of Thermophysics, Novosibirsk, Russia, 1991 (in Russian).
[5] S.V. Stankus, R.A. Khairulin, Teplo®zika Vysokikh Temperatur (High Temp.) 30 (1992) 487. [6] O.F. Nemets, Yu.V. Gofman, Handbook on Nuclear Physics, Naukova Dumka, Kiev, 1975 (in Russian). [7] B.W. Batterman, H. Cole, Rev. Mod. Phys. 36 (1964) 681. [8] D.S. Gemmell, Rev. Mod. Phys. 46 (1974) 129. [9] A.H. Sùrensen, Nucl. Instr. and Meth. B 119 (1996) 1.
www.elsevier.nl/locate/nimb
Letter to the Editor
Anomalous transmission of gamma-rays of 0.662 MeV energy through single crystals of gallium garnets R.A. Khairulin *, A.V. Baginskii, S.V. Stankus Institute of Thermophysics, Siberian Branch of the Russian, Academy of Sciences, St. Kutateladze 2, 630090 Novosibirsk, Russia Received 15 August 2000; received in revised form 7 November 2000
Abstract It has been found experimentally that gamma-ray absorption Ec 0:662 MeV in single crystals of Gd3 Ga5 O12 and Ca3 Nb; Ga2 Ga3 O12 decreases at small angles between major crystallographic directions and beam direction. A magnitude of the eect is enhanced markedly as a temperature gradient perpendicular to the beam direction is created in the sample. The angular dependences of absorption coecient look like orientation dependences observed at channeling of charged particles. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 78.70. g Keywords: Gamma-ray; Garnet; Channeling
In the foregoing years, a number of theoretical papers had been published wherein a possibility of the channeling of gamma±quanta through crystals was predicted, see for example [1±3]. It had been shown that this possibility could be realized in the crystals with layer structure and with large spacing, where the layers with high and low electron density alternate. The gallium garnets are composed of light oxygen ions and heavy cations. In addition, they have crystal lattice with relatively large spacing. In particular, the gadolinium±gallium garnet,
* Corresponding author. Tel.: +7-3832-391541; fax: +73832-343480. E-mail addresses: [email protected] (R.A. Khairulin), [email protected] (S.V. Stankus).
Gd3 Ga5 O12 GGG, and the calcium±niobium± gallium one, Ca3 Nb; Ga2 Ga3 O12 (CNGG), have and a cubical lattice with spacing equal to 12.37 A respectively. Hence, these compounds are 12.50 A, attractive objects to check the theoretical predictions. Besides, in studies of thermal properties of these garnets [4] we observed special features in behavior of their absorption coecients. This was a further reason for choosing these objects for experimentation. The measurements of gamma-ray absorption in the garnets were performed with a gamma-densitometer which has been described in detail elsewhere [5]. A basic schematic of the experimental arrangement is shown in Fig. 1. Diameter of the ®rst collimator was equal to 6 mm. Diameter of the second collimator was varied (6, 4 and 3 mm).
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 0 ) 0 0 5 8 4 - X
R.A. Khairulin et al. / Nucl. Instr. and Meth. in Phys. Res. B 174 (2001) 392±396
393
Fig. 1. Collimated geometry arrangement for gamma-ray absorption measurements.
The intensity of gamma radiation was measured with scintillation counter. Dead time of the counting channel was considered in computation. The samples for studying were cut from single crystals grown by the Czochralski method, so that the faces of the samples were oriented normally to the major crystallographic axes. Mass absorption coecient (l) was found from the equation l h LnJ0 =J h ql
1
cos h;
which follows from the well-known absorption law. Here, J h and J0 are the radiation intensities after passage through the apparatus with and without the sample, respectively; q is the density of the sample (7.096 and 4:694 g=cm3 , respectively, for GGG and CNGG); lcos h 1 is absorption distance. The initial intensity, J0 , fell in the range 10,000±46,000 s 1 in accordance with the diameter of the second collimator. The value of J comprised 7±35% of J0 , depending on the density and on the thickness of the samples. The intensity measurements at any point were performed during a period of 300±400 s, to minimize statistical errors, the measurement uncertainty of the absorption coef®cient did not exceed 0.25±0.35%. Typical orientation dependences of the absorption coecient measured in the experiments with the GGG are shown in Fig. 2 (the dependences are symmetric about h 0). When h P 50 mrad, the measured values of l for all diameters of the second collimator agree with calculated value [6], to within experimental error. That is, the quantity of photons scattered by the sample
Fig. 2. Orientation dependence of l for the ®rst GGG sample (l 30 mm). h is the angle between h1 0 0i direction and the beam axis. The axis of rotation is parallel to another (perpendicular) h1 0 0i direction. 1, 2, 3 are the data for the collimators of 6, 4, 3 mm diameters, respectively. Dashed±dot line is the value of l calculated from the data of [6].
(Compton and Rayleigh scattering) through a small angle into the detector is slight in comparison to the quantity of transmitted quanta (the condition of ``good geometry'' is ful®lled). As the angle is decreased, l rises to a maximum value at h 15 mrad. On further angular decrease the absorption coecient falls sharply and approaches a minimum at h 0. The depth of the minimum increases as the diameter of the collimator is reduced. But when the diameter falls from 4 mm to 3 mm, the change of l does not already exceed the measurement error. It is likely that the eect observed with the collimators of 4 and 3 mm diameters is not too dierent from the eect for ideally collimated beam. In order to establish the manner in which deformations of the crystals in¯uence on the magnitude of the eect, temperature gradients were created in the samples. In the case that the gradient is parallel to the crystallographic axis oriented along the beam, it has not been found changes in the observed dependences, to within experimental error. But in the case that the gradient is normal to this axis (the orientation of the gradient with re-
394
R.A. Khairulin et al. / Nucl. Instr. and Meth. in Phys. Res. B 174 (2001) 392±396
spect to the axis of rotation is of little importance), the contrast of the observed pattern grows materially. As is seen from Fig. 3, the intensity of transmitted radiation at h 0 increases (l decreases) with increasing temperature gradient. This dependence is practically symmetric about zero point, that is, the magnitude of the eect is dependent on the absolute value of the gradient only, but not on its direction. The side peaks in the dependences l h (the side dips in the dependences J h also grow. Steep rise of the extremums occurs at the gradients up to 1 K/mm. Further increasing of the temperature dierence does not produce marked changes in the angular dependences. As is seen from Fig. 4, magnitudes of the extremums at the gradient of 1 K/mm are 5.5 times greater than those for isothermal sample. Amplitude spectra of the signals from a photomultiplier of the scintillation counter obtained at dierent orientations of the crystals about the beam axis are similar in form and dier only by magnitude (Fig. 5). Because at large angles the condition of good geometry is ful®lled, that is to say, that the dips in measured dependences l h at small angles are connected with rise of the
Fig. 3. The temperature gradient dependence of the radiation intensity transmitted through the ®rst GGG sample at h 0. The gradient is parallel to the axis of rotation. Diameter of the second collimator equals 3 mm. J0 10 050 s 1 .
Fig. 4. h-Dependence of l for the ®rst GGG sample at zero temperature gradient, curve 1 (the same as curve 3 in Fig. 2), and at gradient equal to 1 K/mm, curve 2. The gradient is normal both to h1 0 0i axis oriented along the beam and to the axis of rotation. Diameter of the second collimator equals 3 mm. Dashed±dot line is the calculated l.
Fig. 5. Amplitude spectra of the signals from the photomultiplier obtained at h 50 mrad (normal transmission), curve 1, and at h 0 (anomalous transmission), curve 2. Diameter of the second collimator equals 6 mm. The gradient is equal to 1 K/mm. The data have been obtained with the spectrum analyzer Robotron 20050.
R.A. Khairulin et al. / Nucl. Instr. and Meth. in Phys. Res. B 174 (2001) 392±396
quantity of transmitted quanta that are very slightly or not at all modi®ed in energy and direction. Further investigations have shown that analogous orientation dependences are also observed at small angles between the beam axis and the other major (h1 1 0i and h1 1 1i) crystal axes. The dip and the side peaks in the h-dependences of l decrease with increase in thickness of the samples. However the decrease is not very signi®cant, so the relative magnitudes of the extremums in the dependences J h do rise with distance of absorption. When the temperature gradient is created, a dierence between the intensities of the transmitted radiation measured at h 0 and at h 15 mrad is as much as 40% (Fig. 6). Orientation dependences of l and J for the CNGG crystal (Fig. 7) are analogous to those for GGG. But creation of temperature gradients in the CNGG crystal does not signi®cantly aect the magnitude of dips and peaks. At the gradient equal to 1 K/mm the extremums increase only by a factor of 1.3.
Fig. 6. Orientation dependence of the radiation intensity transmitted through the second GGG sample (l 48 mm) at the gradient equal to 1 K/mm. h is the angle between h1 0 0i direction and the beam axis. The axis of rotation and the gradient are parallel to h1 1 0i direction. Diameter of the second collimator equals 4 mm. J0 18 700 s 1 .
395
Fig. 7. h-Dependence of l for the CNGG sample (l 30 mm). h is the angle between h1 1 1i direction and the beam axis. The axis of rotation is parallel to h1 1 0i direction. Diameter of the second collimator equals 3 mm.
The eect of anomalous transmission of lowenergy X-rays through thick crystals at h equal to Bragg angle (the Borrmann eect) has been much studied [7]. But for Ec 0:662 MeV the Bragg angle is of about 0.7 mrad only (it is less than the angular aperture), while the side extremums are observed at h 15 mrad. Notice that their position is not dependent on the collimator diameter (on the angular aperture). This suggests that in our case the anomalous transmission is not the usual diraction phenomenon. Alternatively, the obtained angular dependences are truly similar to those that observed at the channeling of charged particles [8,9]. In particular, the side peaks in the h-dependences of l (anomalous scattering) appear to be analogues of the so-called ``compensation shoulders'' in the angular dependences for charged particles. Creation of the temperature gradient in the sample produces two types of the deformation: (1) bending of the crystal; (2) monotone variation of the lattice spacing in the direction normal to the beam axis. Some facts suggest that the second reason is responsible for the increase of the eect, but this question calls for further investigation.
396
R.A. Khairulin et al. / Nucl. Instr. and Meth. in Phys. Res. B 174 (2001) 392±396
References [1] N.N. Nasonov, Pis'ma v Zhurnal Tekhnicheskoi Fiziki (Tech. Phys. Lett.) 5 (1979) 982. [2] N.K. Zhevago, Doklady Akademii Nayk SSSR (Dokl. Phys.) 281 (1985) 67. [3] V.I. Vysotskii, R.N. Kuz'min, Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki (J. Exp. Theor. Phys.) 94 (1988) 351. [4] S.V. Stankus, Phys.-Math. Doct. Thesis, Institute of Thermophysics, Novosibirsk, Russia, 1991 (in Russian).
[5] S.V. Stankus, R.A. Khairulin, Teplo®zika Vysokikh Temperatur (High Temp.) 30 (1992) 487. [6] O.F. Nemets, Yu.V. Gofman, Handbook on Nuclear Physics, Naukova Dumka, Kiev, 1975 (in Russian). [7] B.W. Batterman, H. Cole, Rev. Mod. Phys. 36 (1964) 681. [8] D.S. Gemmell, Rev. Mod. Phys. 46 (1974) 129. [9] A.H. Sùrensen, Nucl. Instr. and Meth. B 119 (1996) 1.