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MEASUREMENT OF CROSS SECTIONS OF PHOTONEUTRON REACTIONS
The dependence of the cross section of photonuclear reactions on the excitation energy is highly important for understanding the mechanism of the interaction of γ-quanta with nuclei. The usual method of measuring excitation curves by means of induced activity proves inapplicable if the final reaction product is stable or has a very long lifetime. In such cases one must resort to recording the emitted particles themselves.
In the work reviewed below¹, the yield of photoneutrons from 22 elements irradiated with the γ-spectrum from a betatron with maximum energy \((E)\) of 23 MeV is investigated. At the same time, the sum of the \((\gamma n)\)-, \((\gamma 2n)\)-, and \((\gamma np)\)-reactions is studied. The neutrons are detected by means of a \(BF_3\) counter,
Basic data of photonuclear reactions
| Element | Half-width (MeV), γn | Half-width (MeV), total | \(E_m\) (MeV) | \(\sigma_m\) \((10^{-24}\ \mathrm{cm}^2)\) | Integral cross section \((\mathrm{MeV}\times10^{-24}\ \mathrm{cm}^2)\), γn | Integral cross section \((\mathrm{MeV}\times10^{-24}\ \mathrm{cm}^2)\), γp | Integral cross section \((\mathrm{MeV}\times10^{-24}\ \mathrm{cm}^2)\), γ2n | Integral cross section \((\mathrm{MeV}\times10^{-24}\ \mathrm{cm}^2)\), γn + γnp + \(2(\gamma 2n)\) | Literature |
|---|---|---|---|---|---|---|---|---|---|
| Be\(^9\) | 4.7 | 22.2 | 0.0027 | 0.011 | 2 | ||||
| C | 2.0 | 21.4 | 0.014 | 0.029 | 1 | ||||
| C\(^ {12}\) | 2.8 | 22.9 | 0.013 | 0.046 | 3 | ||||
| C | 1.7 (γp) | 21.5 | 0.034 | 0.063 | 4 | ||||
| N\(^ {14}\) | 24.2 | 0.0028 | 0.015*) | 5 | |||||
| O | 21.9 | 0.0089 | 0.019*) | 1 | |||||
| O\(^ {16}\) | 24.2 | 0.011 | 0.031*) | 5 | |||||
| F\(^ {19}\) | ∼13 | ∼20 | 0.0035 | 0.076 | 0.005 | 6 | |||
| Na | 6.0 (γp) | 18.3 | 0.013 | 0.081 | 1 | ||||
| Mg | 3.9 (γp) | 18.8 | 0.011 | 0.048 | 1 | ||||
| Mg\(^ {24}\) | 5.8 | 19.4 | 0.0098 | 0.057 | |||||
| Mg\(^ {25+26}\) | ∼4.2 | 17.8 | ∼0.016 | ∼0.065 | 1 | ||||
| Mg\(^ {25}\) | 6.0 (γp) | 21.7 | 0.015 | 0.10 | 7 | ||||
| Mg\(^ {26}\) | 3.3 (γp) | 22.6 | 0.019 | 0.085 | 7 | ||||
| Al | 4.0 | 19.7 | 0.023 | 1 | |||||
| Al\(^ {27}\) | 4.7 | 19.2 | 0.008 | 0.045 | 7 | ||||
| Al | 5.4 (γp) | 21.2 | 0.022 | 0.12 | 4 | ||||
| Si\(^ {28}\) | 3.5 | 20.9 | 0.021 | 0.070 | 8 | ||||
| P | 5.7 | 20.5 | 0.029 | 0.14 | 0.034 (γnp) | 0.17 | 1 | ||
| P\(^ {31}\) | 6.5 | 19.5 | 0.017 | 0.13 | 9 | ||||
| P\(^ {31}\) | 20 | 0.017 | 0.099 | 0.047 (γnp) | 0.15 | 10 | |||
| S | 5.2 | 19.8 | 0.013 | 0.075 | 1 |
*) Integral cross section up to the maximum of the curve.
Continuation
| Element | Half-width (MeV), γn | Half-width (MeV), total | $E_m$ (MeV) | $\sigma_m$ ($10^{-24}\ \mathrm{cm}^2$) | Integral cross section ($\mathrm{MeV}\times 10^{-24}\ \mathrm{cm}^2$), γn | Integral cross section, γp | Integral cross section, γ2n | Integral cross section, γn + γnp + 2(γ2n) | Literature |
|---|---|---|---|---|---|---|---|---|---|
| S$^{32}$ | 4,5 | 20,1 | 0,015 | 0,069 | 8 | ||||
| S$^{32}$ | 1,0 (γd) | 25,6 | 0,006 | 0,016 (γd) | 9, 11 | ||||
| S$^{34}$ | 4 | ∼17 | ∼0,066 | ∼0,20 | 1 | ||||
| Ca$^{40}$ | 4,2 | 19,3 | 0,015 | 0,065 | 8 | ||||
| Mn | >8 | ∼19 | 0,10 | ∼0,46 *) | 1 | ||||
| Fe | 6,1 | 18,0 | 0,075 | 0,47 | 1 | ||||
| Fe$^{54}$ | 6,3 | 18,7 | 0,067 | 0,48 | 3 | ||||
| Ni$^{58}$ | 5,6 | 18,5 | 0,054 | 0,34 | 3 | ||||
| Ni | 5,4 (γp) | 18,7 | 0,058 | 0,32 | 4 | ||||
| Co | 5,4 | 16,9 | 0,13 | 0,75 | 1 | ||||
| Co | 5,7 (γp) | 21,5 | 0,024 | 0,14 | 4 | ||||
| Cu | 7,1 | 19,5 | 0,12 | 0,87 | 1 | ||||
| Cu$^{63}$ | 6,1 | 18,1 | 0,10 | 0,66 | 3 | ||||
| Cu$^{65}$ | 7,0 | 18,6 | 0,15 | 1,11 | 3 | ||||
| Zn$^{64}$ | 7,9 | 18,7 | 0,12 | 0,99 | 3 | ||||
| As | ∼6,2 | 9,4 | 17 | 0,093 | 0,76 | 0,11 | 0,98 | 1 | |
| Br$^{80}$ | 8,0 | 18,0 | 0,13 | 1,08 | 12 | ||||
| Rb$^{87}$ | 6,0 | 17,5 | 0,23 | 1,68 | 13 | ||||
| Zr$^{90}$ | 5,7 | 18,0 | 0,27 | 1,67 | 13 | ||||
| Mo | 6,1 | 15,7 | 1,62 | 1 | |||||
| Mo$^{92}$ | 6,0 | 18,7 | 0,14 | 0,85 | 13 | ||||
| Nb | 6,1 | 17,3 | 0,26 | 1,71 | 1 |
*) Integral cross section up to the maximum of the curve.
Continuation
| Element | Half-width (MeV), γn | Half-width (MeV), total | \(E_m\) (MeV) | \(\sigma_m\) (\(10^{-24}\ \mathrm{cm}^2\)) | Integral cross section (\(\mathrm{MeV}\times 10^{-24}\ \mathrm{cm}^2\)), γn | Integral cross section (\(\mathrm{MeV}\times 10^{-24}\ \mathrm{cm}^2\)), γp | Integral cross section (\(\mathrm{MeV}\times 10^{-24}\ \mathrm{cm}^2\)), γ2n | Integral cross section (\(\mathrm{MeV}\times 10^{-24}\ \mathrm{cm}^2\)), γn + γnp + 2(γ2n) | Literature |
|---|---|---|---|---|---|---|---|---|---|
| Nb | 6,6 (γp) | 21,3 | 0,018 | 0,12 | 4 | ||||
| Ag | 9,2 | 16,3 | 0,20 | 2,1 | 0,22 | 2,5 | 1 | ||
| Ag\(^{109}\) | 4,6 | 16,5 | 0,32 | 1,65 | 14 | ||||
| In | ∼5,8 | 8,0 | 15,2 | 0,25 | ∼1,6 | ∼0,20 | ∼2,0 | 1 | |
| In\(^{115}\) | 5,5 | 15,0 | 0,42 | 2,7 | 15 | ||||
| In\(^{115}\) | ∼8 (γγ′) | ∼15 | 0,05 | ∼0,4 (γγ) | 15 | ||||
| Sb | 7,2 | 15,2 | 0,44 | 3,1 | 1 | ||||
| Sb\(^{121}\) | 4,8 | 14,8 | 0,68 | 3,5 | 3 | ||||
| Sb\(^{123}\) | 4,8 | 14,8 | 0,36 | 1,9 | 3 | ||||
| I | ∼5,0 | 6,6 | 15,2 | 0,45 | 3,1 | 1 | |||
| Ta\(^{181}\) | 4,6 | 13,9 | >0,47 | 3 | |||||
| Au | ∼5,6 | 6,3 | 14,2 | 0,70 | 4,6 | 1 | |||
| Au\(^{197}\) | ∼10 (γγ′) | 15 | >0,025 | >0,25 (γγ′) | 16 | ||||
| Pb | 5,3 | 13,7 | 0,81 | 4,8 | 1 | ||||
| Pb\(^{207+208}\) | ∼6,5 (γp) | 22,0 | 0,028 | ∼0,17 | 17 | ||||
| Bi | ∼5,2 | 5,4 | 14,2 | 0,92 | 4,1 | 1 |
surrounded by paraffin (see figure). By selecting the position of the counter, the authors succeeded in obtaining the same probability of recording neutrons of different energies. As evidence of this, the paper gives yield curves for the \((\gamma n)\) reaction measured on carbon \([at \(E=23\) MeV the reaction \((\gamma 2n)\) and \((\gamma np)\) on \(C^{12}\) is energetically impossible]) by the activation method and by the counter method. The greatest discrepancy (4%) is observed 6 MeV above threshold. To reduce the background from neutrons, the counting device is placed behind a 2-meter concrete wall and is located 9 meters from the betatron target. The electronic circuit records neutrons in the interval 20–800 μsec after the end of the pulse. The neutron yield for each element was compared with the yield on copper at \(E=18\) MeV. A correction for absorption of \(\gamma\)-radiation in the samples was introduced into the results.
In the table the following data are presented for photoneutron reactions (obtained in the present work, as well as in previously published experiments): 1) name of the element or isotope, 2) half-width of the cross-section curve of the \((\gamma n)\) reaction, or 3) total curve, 4) position of the resonance maximum \((E_m)\), 5) value of the maximum cross section (in \(10^{-24}\ \text{cm}^2\)), 6) integral cross section of the reactions \((\gamma n)\); \((\gamma p)\); \((\gamma 2n)\); \((\gamma n)+(\gamma np)+2(\gamma 2n)\), and in the last column, references to the literature.
Analysis of the results leads the authors to the following conclusions: the value \((\sigma_{\max})_{\gamma n}\) is proportional to \(A^{5/3}\), where \(A\) is the atomic number of the element. The half-width of the resonance curves, with increasing \(A\), first increases (up to \(A \sim 60\)), and then slowly decreases. For \(E_m\) and the threshold energy \(E_0\), the expressions \(E_m=37A^{-0.186}\) and \(E_0=32A^{-0.270}\) were obtained. For the elements As and In at \(E_\gamma=17, 18,\) and \(19\) MeV, the ratio of the cross sections of the \((\gamma 2n)\) and \((\gamma n)\) reactions was compared with the ratio calculated according to statistical theory, and satisfactory agreement was obtained.
B. R.
CITED LITERATURE
- Montalbetty, Katz and Goldenberg, Phys. Rev. 91, 659 (1953).
- Haslam et al., Can. J. Phys. 31, 210 (1953).
- L. Katz and A. G. W. Cameron, Can. J. Phys. 29, 518 (1951).
- J. Halpern and A. K. Mann, Phys. Rev. 83, 370 (1951).
- Johns et al., Phys. Rev. 84, 856 (1951).
- Horsley et al., Phys. Rev. 87, 756 (1952).
- L. Katz and A. G. W. Cameron, Phys. Rev. 84, 1115 (1951).
- Summers-Gill et al., Can. J. Phys. 31, 70 (1953).
- K. Katz and A. S. Penfold, Phys. Rev. 81, 815 (1951).
- Halpern et al., Phys. Rev. 88, 958 (1952).
- L. Katz and A. S. Penfold, Phys. Rev. 83, 169 (1951).
- L. Katz et al., Can. J. Phys. 30, 476 (1952).
- L. Katz et al., Can. J. Phys. 31, 250 (1953).
- B. C. Diven and G. M. Almy, Phys. Rev. 80, 407 (1950).
- J. Goldenberg and L. Katz, Phys. Rev. 90, 308 (1953).
- A. G. W. Cameron and L. Katz, Phys. Rev. 84, 608 (1951).
- A. G. W. Cameron and L. Katz, Phys. Rev. 83, 1264 (1951).