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A note on pair production in the giant resonance region
Volume
24B, number
8
PHYSICS
2. C. D. Kavaloski, J.S. Lilley, P.Richard and N.Stein, Phys. Rev. Letters 21 (1966) 677. 3. L.J.Parish, S.A,A.Zaidi, P.v.Brentan0andC.F. Moore, Technical Report No. 1, University of Texas, 1966 (unpublished); C.F.Moore, L.J.Parish, P.v.Brentan0andS.A.A. Zaidi, Phys. Letters 22 (1966) 616. 4. S.Fiarman, L.Michelman and A.B.Robins, Proc. Intern. Conf. on Nuclear physics, Gatlinburg, Tennessee (1966); Bull. Am. Phys. Sot. 12 (1967), Washington Meeting. 5. P.Mukherjee and B. L. Cohen, Phys. Rev. 127 (1962) 1284; J.C.Hafele and A.G.Blair, Bull. Am. Phys. Sot. 11 (1966) 12; J.C.Hafele and R.Woods, Phys. Letters 23 (1966) 579.
A NOTE
ON PAIR
PRODUCTION
17 April
LETTERS
1967
6. J.H.Bjerregaard, O.Hansen, 0. Nathan and S.Hinds, Nucl. Phys. A94 (1967) 457. 7. B. L. Anderson, J. P. Bondorf and B.S. Madsen, Phys. Letters 22 (1966) 651. 8. W. J.Thompson and E.Gille, Technical Report No. 9, Florida State University, September 1966 (unpublished). We are indebted to J. L.Adams for furnishing a copy of this program. 9. D. J. Bredin, 0. Hansen, G.H. Lenz and G. M.Temmer Phys. Letters 21 (1966) 677. 10. G.Vallois, J.Saudinos, O.Beer, M.Gendrot and P.Lopato, Phys. Letters 22 (1966) 659. 11. O.Nathan, Nucl. Phys. 30 (1962) 332, 12. L. C.Biedenharn, private communication. 13. G.M.Temmer, Proc. Intern. Conf. on Nuclear physics, Gatlinburg, Tennessee (1966).
IN THE
GIANT
RESONANCE
REGION*
A. RON** and M. E. ROSE Department
of Physics,
University Received
The process of pair production by a between this and the process of pair sidered. It is found that the nuclear sections there are quite small. For
of Virginia, 20 March
Virginia
1967
decaying nucleus, excited by the incident photon, and the interference production by the incident photon in the field of the nucleus are concontributions are pronounced for large scattering angles but the cross forward scattering the Bethe-Heitler cross section is dominant.
In a recent paper Hubbard and Rose [l] showed the existence of interference phenomena between the processes of bremsstrahlung and nuclear gamma rays arising from the decay of a nucleus which was excited by the incident electron. Such effects are expected to be pronounced in the region of the giant resonances where the excitation of nuclei is favourable. Acker [2] considered a simplified case of the general formulas given by Hubbard and Rose [l]. He came to the conclusion that besides some modifications in the formulas for bremsstrahlung and inelastic electron scattering cross sections, his results may be used in certain experiments which determine spins and parities of nuclear levels. One would expect similar results for the process of pair production which is closely related to bremsstrahlung. As Hubbard and Rose pointed out, by application of the substitution law to their formulas one can obtain cross sections for the case of pair production. The cross section then arises from three contributions: 1) The creation of an electron-positron pair by a photon interacting with the 3’72
Charlottesville,
nuclear field. 2) The creation of a pair by a decaying nucleus which was excited by the incident photon. 3) The interference between processes 1 and 2. The original calculation of Hubbard and Rose [l] was done in the Born approximation which is expected to be valid for light nuclei. Therefore we have calculated the cross sections for 150. For El transitions we had to consider the five electric dipole states Jr = l-, T = 1. We used the experimental level energies and widths as measured by Tanner et al. [3]. The nuclear wave functions used were those of Gillet and Vinh Mau [4] and Green [5] ***. The use of either set of wave functions produces results which differ by some few percent. This difference does not exceed the inherent inaccuracy of the calculation caused by the use of the Born approximation and * Work supported by the U.S. Atomic Energy Comis-
sion. Document ORO-2915-74. ** On leave of absence from the Hebrew University of Jerusalem, Israel. *** We thank Professor A.M.Green for sending us the wave functions he calculated.
Volume 24B, number 8
PHYSICS
LETTERS
17 April 1967
.f and b_, and 4” is the angle between the planes k -& and k-p+. The solid line in fig. 1 is the sum of the cross sections for each of the three parts mentioned above. The dashed line describes the well-known Bethe-Heitler [6] formula, which corresponds to process 1. We find that in this case the nuclear effects (contributions 2 and 3) are pronounced for backward scattering at which the cross sections are quite small. The nuclear effects are hardly seen for the case of forward scattering. This behaviour of the cross section may be understood as follows: The Bethe-Heitler cross section is large for small angles and decreases rapidly. The nuclear cross section (corresponding to part 2) is very small for small angles, then increases till it reaches a maximum value and decreases again. Only when it is comparable with or bigger than the Bethe-Heitler cross section are nuclear effects important. Fig. 1. The cross section for pair production in 160 as function of the angle 0_ between the photon and the electron. the long wavelength limit and by the neglect of screening effects. In the case of bremsstrahlung the incident electron could have any energy exceeding the excitation energy of a nuclear level so that nuclear effects will be pronounced in the resonance case. In our case the energy of incident photons is limited to the range of the nuclear excitation energies for nuclear effects to be important. A typical angular distribution in the giant resonance range of 160 is presented in fig. 1. The photon energy is w and R is the ratio of the energy of the positron to that of the electron. Let fi,., fi_, & be unit vectors in the directions of the positron, electTon and photon. Then 8, is the angle between k and @+, O_ is the angle between
One of us (A.R.) would like to thank Professor J. M. Eisenberg for clarifying discussions. Thanks are also due to Dr. V. Devanathan and Dr. M. Rho for helpful comments.
References 1.
2. 3. 4. 5. 6.
D. F. Hubbard and M. E. Rose, Nuclear Physics 84 (1966) 337. H. L,Acker, A study of nuclear effects in bremsstrahlung, preprint University of Virginia, to be published, N. W.Tanner, G. C,Thomas and E.D. Earle, Nucl. Phys. 52 (1964) 45, V.Gillet and N.Vinh Mau, Nucl. Phys. 54 (1964) 321. A.M,Green, private communication. H.A.Bethe and W.Heitler, Proc. Roy. Sot. 146 (1934) 83.
373
24B, number
8
PHYSICS
2. C. D. Kavaloski, J.S. Lilley, P.Richard and N.Stein, Phys. Rev. Letters 21 (1966) 677. 3. L.J.Parish, S.A,A.Zaidi, P.v.Brentan0andC.F. Moore, Technical Report No. 1, University of Texas, 1966 (unpublished); C.F.Moore, L.J.Parish, P.v.Brentan0andS.A.A. Zaidi, Phys. Letters 22 (1966) 616. 4. S.Fiarman, L.Michelman and A.B.Robins, Proc. Intern. Conf. on Nuclear physics, Gatlinburg, Tennessee (1966); Bull. Am. Phys. Sot. 12 (1967), Washington Meeting. 5. P.Mukherjee and B. L. Cohen, Phys. Rev. 127 (1962) 1284; J.C.Hafele and A.G.Blair, Bull. Am. Phys. Sot. 11 (1966) 12; J.C.Hafele and R.Woods, Phys. Letters 23 (1966) 579.
A NOTE
ON PAIR
PRODUCTION
17 April
LETTERS
1967
6. J.H.Bjerregaard, O.Hansen, 0. Nathan and S.Hinds, Nucl. Phys. A94 (1967) 457. 7. B. L. Anderson, J. P. Bondorf and B.S. Madsen, Phys. Letters 22 (1966) 651. 8. W. J.Thompson and E.Gille, Technical Report No. 9, Florida State University, September 1966 (unpublished). We are indebted to J. L.Adams for furnishing a copy of this program. 9. D. J. Bredin, 0. Hansen, G.H. Lenz and G. M.Temmer Phys. Letters 21 (1966) 677. 10. G.Vallois, J.Saudinos, O.Beer, M.Gendrot and P.Lopato, Phys. Letters 22 (1966) 659. 11. O.Nathan, Nucl. Phys. 30 (1962) 332, 12. L. C.Biedenharn, private communication. 13. G.M.Temmer, Proc. Intern. Conf. on Nuclear physics, Gatlinburg, Tennessee (1966).
IN THE
GIANT
RESONANCE
REGION*
A. RON** and M. E. ROSE Department
of Physics,
University Received
The process of pair production by a between this and the process of pair sidered. It is found that the nuclear sections there are quite small. For
of Virginia, 20 March
Virginia
1967
decaying nucleus, excited by the incident photon, and the interference production by the incident photon in the field of the nucleus are concontributions are pronounced for large scattering angles but the cross forward scattering the Bethe-Heitler cross section is dominant.
In a recent paper Hubbard and Rose [l] showed the existence of interference phenomena between the processes of bremsstrahlung and nuclear gamma rays arising from the decay of a nucleus which was excited by the incident electron. Such effects are expected to be pronounced in the region of the giant resonances where the excitation of nuclei is favourable. Acker [2] considered a simplified case of the general formulas given by Hubbard and Rose [l]. He came to the conclusion that besides some modifications in the formulas for bremsstrahlung and inelastic electron scattering cross sections, his results may be used in certain experiments which determine spins and parities of nuclear levels. One would expect similar results for the process of pair production which is closely related to bremsstrahlung. As Hubbard and Rose pointed out, by application of the substitution law to their formulas one can obtain cross sections for the case of pair production. The cross section then arises from three contributions: 1) The creation of an electron-positron pair by a photon interacting with the 3’72
Charlottesville,
nuclear field. 2) The creation of a pair by a decaying nucleus which was excited by the incident photon. 3) The interference between processes 1 and 2. The original calculation of Hubbard and Rose [l] was done in the Born approximation which is expected to be valid for light nuclei. Therefore we have calculated the cross sections for 150. For El transitions we had to consider the five electric dipole states Jr = l-, T = 1. We used the experimental level energies and widths as measured by Tanner et al. [3]. The nuclear wave functions used were those of Gillet and Vinh Mau [4] and Green [5] ***. The use of either set of wave functions produces results which differ by some few percent. This difference does not exceed the inherent inaccuracy of the calculation caused by the use of the Born approximation and * Work supported by the U.S. Atomic Energy Comis-
sion. Document ORO-2915-74. ** On leave of absence from the Hebrew University of Jerusalem, Israel. *** We thank Professor A.M.Green for sending us the wave functions he calculated.
Volume 24B, number 8
PHYSICS
LETTERS
17 April 1967
.f and b_, and 4” is the angle between the planes k -& and k-p+. The solid line in fig. 1 is the sum of the cross sections for each of the three parts mentioned above. The dashed line describes the well-known Bethe-Heitler [6] formula, which corresponds to process 1. We find that in this case the nuclear effects (contributions 2 and 3) are pronounced for backward scattering at which the cross sections are quite small. The nuclear effects are hardly seen for the case of forward scattering. This behaviour of the cross section may be understood as follows: The Bethe-Heitler cross section is large for small angles and decreases rapidly. The nuclear cross section (corresponding to part 2) is very small for small angles, then increases till it reaches a maximum value and decreases again. Only when it is comparable with or bigger than the Bethe-Heitler cross section are nuclear effects important. Fig. 1. The cross section for pair production in 160 as function of the angle 0_ between the photon and the electron. the long wavelength limit and by the neglect of screening effects. In the case of bremsstrahlung the incident electron could have any energy exceeding the excitation energy of a nuclear level so that nuclear effects will be pronounced in the resonance case. In our case the energy of incident photons is limited to the range of the nuclear excitation energies for nuclear effects to be important. A typical angular distribution in the giant resonance range of 160 is presented in fig. 1. The photon energy is w and R is the ratio of the energy of the positron to that of the electron. Let fi,., fi_, & be unit vectors in the directions of the positron, electTon and photon. Then 8, is the angle between k and @+, O_ is the angle between
One of us (A.R.) would like to thank Professor J. M. Eisenberg for clarifying discussions. Thanks are also due to Dr. V. Devanathan and Dr. M. Rho for helpful comments.
References 1.
2. 3. 4. 5. 6.
D. F. Hubbard and M. E. Rose, Nuclear Physics 84 (1966) 337. H. L,Acker, A study of nuclear effects in bremsstrahlung, preprint University of Virginia, to be published, N. W.Tanner, G. C,Thomas and E.D. Earle, Nucl. Phys. 52 (1964) 45, V.Gillet and N.Vinh Mau, Nucl. Phys. 54 (1964) 321. A.M,Green, private communication. H.A.Bethe and W.Heitler, Proc. Roy. Sot. 146 (1934) 83.
373