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Three photon annihilations of positrons and positronium in solids with two detectors in coincidence
Radiation Physics and Chemistry 58 (2000) 749±753
www.elsevier.com/locate/radphyschem
Three photon annihilations of positrons and positronium in solids with two detectors in coincidence M.H. Weber*, K.G. Lynn Department of Physics, PO Box 642814, Washington State University, Pullman, WA 99164-2814, USA
Abstract The two-detector coincidence positron annihilation system at Washington State University was used to observe three-photon annihilation events of positrons. The decay of ortho-positronium (o-Ps) can be distinguished for paraPs decay and positron two photon annihilations by the unique dierence energy distribution. The apparatus was used to detect rare three-photon annihilations of positrons in metals. 7 2000 Elsevier Science Ltd. All rights reserved.
Doppler broadening spectroscopy of positron annihilation g quanta is a well-established technique in solid state studies of defects (Schultz and Lynn, 1988). It is based on the observation that almost all positrons will thermalize in a target material within several picoseconds long before a signi®cant fraction annihilates. A typical lifetime of positrons in solids is 200 ps. In an improvement of the Doppler broadening techniques, both annihilation quanta are detected in coincidence by detectors with good energy resolution (1.6 keV full width at half maximum at 511 keV each) placed on opposite sides of the sample (Asoka-Kumar et al., 1996; MacDonald et al., 1978). The advantages are an improvement in signal-to-noise by three to four orders of magnitude and the detection of the full Doppler shift due to the momentum of the electron±positron pair parallel to the direction of the emitted photons. This permits the identi®cation of the chemical type of an atomic neighbor of a defect.
* Corresponding author. Tel.: +1-509-335-4020; fax: +1509-335-7816. E-mail address: [email protected] (M.H. Weber).
A small fraction of the positrons in solids will annihilate via the emission of three photons. If the two detectors are placed close enough together, it is possible to detect two of the three quanta with one detector in coincidence with the remaining photon in the second detector. The third photon tends to carry much larger energies than the typical pc associated with Doppler broadening. Thus three photon events will appear as a very broad ``Doppler distribution'' under the standard two-photon distribution. ére and Powell (1949) calculated the spin-averaged three to two photon annihilation ratio in the zero velocity approximation to be 1/370. Drisko (1956) calculated the spin dependent angular distribution. They also give the energy and angular distribution of the three photons. The energy distribution was veri®ed by Tianbao et al. (1985). In the experiments discussed here we detected such a broad ``Doppler distribution'' and veri®ed that it is indeed due to three photon annihilation events. In the following the used technique is described in more detail. First results are presented and discussed. Here only two and three photon annihilation events will be discussed. Higher numbers of photons are allowed but
0969-806X/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 6 X ( 0 0 ) 0 0 2 5 2 - 8
750
M.H. Weber, K.G. Lynn / Radiation Physics and Chemistry 58 (2000) 749±753
Fig. 1. Two detector coincidence spectrum for 70 keV positrons impinging on gold coated carbon foil. Scale from white (<2) to black to white in the thermal annihilation peak (DE = 0 and SE = 1022 keV).
Fig. 2. Relative probability of observing the third photon together with one of the other two as a function of the eective dierence energy expressed in atomic units.
M.H. Weber, K.G. Lynn / Radiation Physics and Chemistry 58 (2000) 749±753
751
Fig. 3. Doppler broadening two-dimensional histogram of Xerogel. Shown is an energy window of 250 keV in dierence energy (total of 100 keV) and 220 keV in sum energy direction. The top data set was taken with unshielded detectors and the bottom one with 1/4 in. lead in front of detector number 1. Counts in each bin are color-coded on a log10 scale with white corresponding to less than two counts and gradually changing to black. The thermal annihilation peak again is in white. The background and ridges have been subtracted.
will occur with a probability far below the current detection limit of the apparatus. When a positron annihilates with an electron into two or three photons the combined energy and momentum has to be conserved. In the case of two photons the momentum component of the annihilating pair parallel to the emerging photons will cause slight blue and red shifts of the energies of the photons. The total energy of the photons will increase by the amount of the kinetic energy of the positron and decrease by the binding energy of the electron. The momentum component perpendicular to the photon direction causes small angular deviations, which are detected in two-dimensional angular correlation measurements. A detection system that can observe the sum and the dierence of the energies of the photons can be used to reconstruct the total energy of the electron±positron pair and their relative momentum component parallel to the direction of the photons. Two detectors with high energy resolution and operating in coincidence can accomplish this. The dierence in the detected
energies of a coincidence event corresponds to the Doppler shift and the sum of the energies equals the total energy of the electron±positron pair. SE 2m0 c 2 T ÿ Eb
1
DE pp c:
2
T and Eb are the kinetic energy of the positron and the binding energy of the electron. The momentum of the pair parallel to the emitted photons is pp. The result of such a coincidence measurement is shown in Fig. 1. The horizontal axis corresponds to the dierence energy and the vertical axis to the sum energy (both in keV). The intensity of events at each intersection of SE and DE are coded from white being low to dark and white (for the thermal positron peak) again meaning large. In this case 70 keV positrons impinged onto a thin foil of carbon coated with gold. Most positrons will annihilate after thermalization but on occasion annihilation will occur ®rst. The wide line
752
M.H. Weber, K.G. Lynn / Radiation Physics and Chemistry 58 (2000) 749±753
Fig. 4. Intensity as a function of eective ``Doppler shift'' as observed by the two detectors. The solid angle was changed by separating the detectors further apart. Distances given are from the sample center to the detector front face each. One curve was measured with 1/8 in. lead and 1/16 in. cadmium placed in front of each detector to absorb the low energy third photon. The 120 mm distance data overlap the dataset where lead and cadmium are used.
at SE = 1092 keV is caused by the latter. Intermediate events, where partial thermalization occurs prior to annihilation, cause the bowl-shaped feature between 1022 and 1092 keV.
In three-photon annihilations, momentum and energy have to be conserved as well. The additional degrees of freedom result in a very broad energy and angular distribution of the emerging photons. By pla-
Fig. 5. Three-photon decay in metals as a function of the eective ``Doppler shift'' momentum. All metal data fall between the data from the porous material and the data with lead inserted. Above 8 a.u. the metal data overlap within statistical variations.
M.H. Weber, K.G. Lynn / Radiation Physics and Chemistry 58 (2000) 749±753
cing the two detectors close enough to the sample there is a ®nite probability that the third photon will be registered by one of them. In Fig. 2 a Monte Carlo simulation of this process is shown for a number of acceptance angles for the detectors. The case of 458 is close to the geometry used here. To observe this a sample of a highly porous silicon Xerogel was placed in the beam. Positrons were implanted into the layer at 1 keV and formed Ps. In one run a 1/8 in. thick lead plate was placed in front of one detector to preferentially absorb low energy photons. The resulting two dimensional spectra are shown in Fig. 3. The total two and three photon events can be evaluated by integrating across SE. The result for several detector geometries is shown in Fig. 4. The data are folded about the zero ``Doppler shift'' line of symmetry. The solid angle was changed by moving both detectors further away from the target. In this case the material was a porous coating on silicon. The results are very similar in shape to the Monte Carlo simulations. The data show a larger narrow central peak because it also includes two-photon annihilation events. The observed signal-to-noise ratio of better than 105 permits a search for rare three-photon annihilations in metals. A foil of beryllium and single crystal aluminum, iron and nickel were investigated. The results are shown in Fig. 5. A component with large ``Doppler shifts'' can be observed. Its shape is similar to that in the porous material with Ps formation and vanishes when the lead absorber is inserted. In order to compare these results to the predictions of the three to two photon ratio by ére and Powell (1949) the cross section for detecting three photons in two detectors has to be included. Also, thick targets were used. They can absorb some of the low energy
753
photons. These issues will be addressed in the near future. More interesting, however, are some intriguing possibilities. In fully magnetized samples the ratio of three to two photon events should depend on the relative alignment of the positron and electron spins. With a polarized positron beam it should be possible to investigate the spin structure of defects in magnetic bulk materials and thin layers.
Acknowledgements This work was funded, in part, by the US Department of Energy.
References Asoka-Kumar, P., Alatalo, M., Ghosh, V.J., Kruseman, A.C., Nielsen, B., Lynn, K.G., 1996. Increased elemental speci®city of positron annihilation spectra. Phys. Rev. Lett. 77, 2097. Drisko, R.M., 1956. Spin and polarization eects in the annihilation of triplet positronium. Phys. Rev. 102, 1542. MacDonald, J., Lynn, K.G., Boie, R.A., Robbins, M.F., 1978. A two-dimensional Doppler broadened technique in positron annihilation. Nucl. Instrum. Meth. 153, 189. ére, A., Powell, J., 1949. Three-photon annihilation of an electron±positron pair. Phys. Rev. 75, 1696. Schultz, P.J., Lynn, K.G., 1988. Interaction of positron beams with surfaces, thin ®lms, and interfaces. Rev. Mod. Phys., 60, 3, p. 701. Tianbao, C., Hsiaowei, T., Yaoqing, L., 1985. The gamma ray energy spectrum in orthopositronium 3 gamma decay. In: Jain, P.C., Singru, R.M., Gopinathan, K.P. (Eds.), Positron Annihilation. World Scienti®c, Singapore, p. 212.
www.elsevier.com/locate/radphyschem
Three photon annihilations of positrons and positronium in solids with two detectors in coincidence M.H. Weber*, K.G. Lynn Department of Physics, PO Box 642814, Washington State University, Pullman, WA 99164-2814, USA
Abstract The two-detector coincidence positron annihilation system at Washington State University was used to observe three-photon annihilation events of positrons. The decay of ortho-positronium (o-Ps) can be distinguished for paraPs decay and positron two photon annihilations by the unique dierence energy distribution. The apparatus was used to detect rare three-photon annihilations of positrons in metals. 7 2000 Elsevier Science Ltd. All rights reserved.
Doppler broadening spectroscopy of positron annihilation g quanta is a well-established technique in solid state studies of defects (Schultz and Lynn, 1988). It is based on the observation that almost all positrons will thermalize in a target material within several picoseconds long before a signi®cant fraction annihilates. A typical lifetime of positrons in solids is 200 ps. In an improvement of the Doppler broadening techniques, both annihilation quanta are detected in coincidence by detectors with good energy resolution (1.6 keV full width at half maximum at 511 keV each) placed on opposite sides of the sample (Asoka-Kumar et al., 1996; MacDonald et al., 1978). The advantages are an improvement in signal-to-noise by three to four orders of magnitude and the detection of the full Doppler shift due to the momentum of the electron±positron pair parallel to the direction of the emitted photons. This permits the identi®cation of the chemical type of an atomic neighbor of a defect.
* Corresponding author. Tel.: +1-509-335-4020; fax: +1509-335-7816. E-mail address: [email protected] (M.H. Weber).
A small fraction of the positrons in solids will annihilate via the emission of three photons. If the two detectors are placed close enough together, it is possible to detect two of the three quanta with one detector in coincidence with the remaining photon in the second detector. The third photon tends to carry much larger energies than the typical pc associated with Doppler broadening. Thus three photon events will appear as a very broad ``Doppler distribution'' under the standard two-photon distribution. ére and Powell (1949) calculated the spin-averaged three to two photon annihilation ratio in the zero velocity approximation to be 1/370. Drisko (1956) calculated the spin dependent angular distribution. They also give the energy and angular distribution of the three photons. The energy distribution was veri®ed by Tianbao et al. (1985). In the experiments discussed here we detected such a broad ``Doppler distribution'' and veri®ed that it is indeed due to three photon annihilation events. In the following the used technique is described in more detail. First results are presented and discussed. Here only two and three photon annihilation events will be discussed. Higher numbers of photons are allowed but
0969-806X/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 6 X ( 0 0 ) 0 0 2 5 2 - 8
750
M.H. Weber, K.G. Lynn / Radiation Physics and Chemistry 58 (2000) 749±753
Fig. 1. Two detector coincidence spectrum for 70 keV positrons impinging on gold coated carbon foil. Scale from white (<2) to black to white in the thermal annihilation peak (DE = 0 and SE = 1022 keV).
Fig. 2. Relative probability of observing the third photon together with one of the other two as a function of the eective dierence energy expressed in atomic units.
M.H. Weber, K.G. Lynn / Radiation Physics and Chemistry 58 (2000) 749±753
751
Fig. 3. Doppler broadening two-dimensional histogram of Xerogel. Shown is an energy window of 250 keV in dierence energy (total of 100 keV) and 220 keV in sum energy direction. The top data set was taken with unshielded detectors and the bottom one with 1/4 in. lead in front of detector number 1. Counts in each bin are color-coded on a log10 scale with white corresponding to less than two counts and gradually changing to black. The thermal annihilation peak again is in white. The background and ridges have been subtracted.
will occur with a probability far below the current detection limit of the apparatus. When a positron annihilates with an electron into two or three photons the combined energy and momentum has to be conserved. In the case of two photons the momentum component of the annihilating pair parallel to the emerging photons will cause slight blue and red shifts of the energies of the photons. The total energy of the photons will increase by the amount of the kinetic energy of the positron and decrease by the binding energy of the electron. The momentum component perpendicular to the photon direction causes small angular deviations, which are detected in two-dimensional angular correlation measurements. A detection system that can observe the sum and the dierence of the energies of the photons can be used to reconstruct the total energy of the electron±positron pair and their relative momentum component parallel to the direction of the photons. Two detectors with high energy resolution and operating in coincidence can accomplish this. The dierence in the detected
energies of a coincidence event corresponds to the Doppler shift and the sum of the energies equals the total energy of the electron±positron pair. SE 2m0 c 2 T ÿ Eb
1
DE pp c:
2
T and Eb are the kinetic energy of the positron and the binding energy of the electron. The momentum of the pair parallel to the emitted photons is pp. The result of such a coincidence measurement is shown in Fig. 1. The horizontal axis corresponds to the dierence energy and the vertical axis to the sum energy (both in keV). The intensity of events at each intersection of SE and DE are coded from white being low to dark and white (for the thermal positron peak) again meaning large. In this case 70 keV positrons impinged onto a thin foil of carbon coated with gold. Most positrons will annihilate after thermalization but on occasion annihilation will occur ®rst. The wide line
752
M.H. Weber, K.G. Lynn / Radiation Physics and Chemistry 58 (2000) 749±753
Fig. 4. Intensity as a function of eective ``Doppler shift'' as observed by the two detectors. The solid angle was changed by separating the detectors further apart. Distances given are from the sample center to the detector front face each. One curve was measured with 1/8 in. lead and 1/16 in. cadmium placed in front of each detector to absorb the low energy third photon. The 120 mm distance data overlap the dataset where lead and cadmium are used.
at SE = 1092 keV is caused by the latter. Intermediate events, where partial thermalization occurs prior to annihilation, cause the bowl-shaped feature between 1022 and 1092 keV.
In three-photon annihilations, momentum and energy have to be conserved as well. The additional degrees of freedom result in a very broad energy and angular distribution of the emerging photons. By pla-
Fig. 5. Three-photon decay in metals as a function of the eective ``Doppler shift'' momentum. All metal data fall between the data from the porous material and the data with lead inserted. Above 8 a.u. the metal data overlap within statistical variations.
M.H. Weber, K.G. Lynn / Radiation Physics and Chemistry 58 (2000) 749±753
cing the two detectors close enough to the sample there is a ®nite probability that the third photon will be registered by one of them. In Fig. 2 a Monte Carlo simulation of this process is shown for a number of acceptance angles for the detectors. The case of 458 is close to the geometry used here. To observe this a sample of a highly porous silicon Xerogel was placed in the beam. Positrons were implanted into the layer at 1 keV and formed Ps. In one run a 1/8 in. thick lead plate was placed in front of one detector to preferentially absorb low energy photons. The resulting two dimensional spectra are shown in Fig. 3. The total two and three photon events can be evaluated by integrating across SE. The result for several detector geometries is shown in Fig. 4. The data are folded about the zero ``Doppler shift'' line of symmetry. The solid angle was changed by moving both detectors further away from the target. In this case the material was a porous coating on silicon. The results are very similar in shape to the Monte Carlo simulations. The data show a larger narrow central peak because it also includes two-photon annihilation events. The observed signal-to-noise ratio of better than 105 permits a search for rare three-photon annihilations in metals. A foil of beryllium and single crystal aluminum, iron and nickel were investigated. The results are shown in Fig. 5. A component with large ``Doppler shifts'' can be observed. Its shape is similar to that in the porous material with Ps formation and vanishes when the lead absorber is inserted. In order to compare these results to the predictions of the three to two photon ratio by ére and Powell (1949) the cross section for detecting three photons in two detectors has to be included. Also, thick targets were used. They can absorb some of the low energy
753
photons. These issues will be addressed in the near future. More interesting, however, are some intriguing possibilities. In fully magnetized samples the ratio of three to two photon events should depend on the relative alignment of the positron and electron spins. With a polarized positron beam it should be possible to investigate the spin structure of defects in magnetic bulk materials and thin layers.
Acknowledgements This work was funded, in part, by the US Department of Energy.
References Asoka-Kumar, P., Alatalo, M., Ghosh, V.J., Kruseman, A.C., Nielsen, B., Lynn, K.G., 1996. Increased elemental speci®city of positron annihilation spectra. Phys. Rev. Lett. 77, 2097. Drisko, R.M., 1956. Spin and polarization eects in the annihilation of triplet positronium. Phys. Rev. 102, 1542. MacDonald, J., Lynn, K.G., Boie, R.A., Robbins, M.F., 1978. A two-dimensional Doppler broadened technique in positron annihilation. Nucl. Instrum. Meth. 153, 189. ére, A., Powell, J., 1949. Three-photon annihilation of an electron±positron pair. Phys. Rev. 75, 1696. Schultz, P.J., Lynn, K.G., 1988. Interaction of positron beams with surfaces, thin ®lms, and interfaces. Rev. Mod. Phys., 60, 3, p. 701. Tianbao, C., Hsiaowei, T., Yaoqing, L., 1985. The gamma ray energy spectrum in orthopositronium 3 gamma decay. In: Jain, P.C., Singru, R.M., Gopinathan, K.P. (Eds.), Positron Annihilation. World Scienti®c, Singapore, p. 212.