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The (n, 2n) cross section of 2H in the energy region 4.0–6.5 MeV
[
2.F
[
Nuclear Physics A129 (1969) 327--330; ( ~ North-Holland Publishing Co., Amsterdam Not
to be reproduced by photoprint or microfilm without written permission from the publisher
T H E (n, 2n) C R O S S S E C T I O N OF 2H IN T H E ENERGY R E G I O N 4.0-6.5 MeV M. HOLMBERG Research Institute o f National Defence, Stockholm 80, Sweden t Received 23 December 1968 The (n, 2n) cross section of ~H was measured in the energy region 4.0-6.5 MeV. The observed cross sections agree with earlier calculations by Frank and Gammel.
Abstract:
E I
N U C L E A R REACTIONS ~H(n' 2n)' E : 4"0"6"5 MeV; measured or(E)" D~O target"
]
1. Introduction This paper gives data on the (n, 2n) cross section of deuterium in the energy region 4.0-6.5 MeV. The threshold for the 2H(n, np)n reaction is at 3.34 MeV. The calculations by Frank and Gammel 1) give an almost linear energy dependence of the (n, 2n) cross section up to 8 MeV of incident neutron energy. There is good agreement between the calculated values and the (n, 2n) cross sections at 6.1 and 6.5 MeV measured by Catron et al. a). However, above 7 MeV incident neutron energy there is a discrepancy between the calculated and measured cross sections. Therefore it was thought that measurements below 6 MeV could be of value, since no earlier measurement exists below that energy. In the present experiment the neutrons from the (n, 2n) reactions were detected by a large liquid scintillator and the incident neutron flux was measured by the use of a plastic scintillator. 2. Experimental method The incident neutrons were produced at the 5.5 MeV Van de Graaff accelerator at Studsvik using the 2H(d, n)3He reaction. The special technique used in the (n, 2n) detection required a rather low flux of the incident neutrons, and a sufficient neutron flux was produced by using an adsorbed target. The collimator system consisted of an 1.5 m iron collimator, 20 cm square and with a conical hole 10 m m in diameter at the entrance and 40 m m at the end. The iron collimator was surrounded by a lead and paraffin shield, about 1 m square and 1.5 m in length. The large liquid scintillator was surrounded by 20 cm of lead and 20 cm of paraffin. * Preliminary results were reported at the Paris Conference on Nuclear Data for Reactors in Oct. 1966. 327
328
M. HOLMBERG
The liquid scintillator has earlier been used in ~-measurements and is described in detail by Asplund-Nilsson et al. 3). It has also been used in (n, 2n) measurements of Be. A detailed account of the experimental technique for the (n, 2n) measurement is given by Holmberg and Hans6n 4). The D 2 0 sample was located at the centre of the axial tube of the large liquid scintillator. An elastically scattered neutron entering the Gd-loaded scintillator gives rise to a prompt pulse due to the proton recoils produced in the slowing-down of the neutron. This prompt pulse was removed by the use of an anticoincidence arrangement. The second pulse due to the capture of the thermalized neutron in a Gd nucleus occurs about 20 #s later. For the capture pulses the time distribution between two successive pulses is random, if only one neutron is emitted in each reaction which occurs in the sample. However, for an (n, 2n) event there exists a time correlation between the two capture pulses. Consequently the number of (n, 2n) events could be separated from the randomly distributed background. The time correlation was measured by the use of a time-to-pulse-height converter. The randomly distributed background was measured by using scatterers with the (n, 2n) thresholds above the actual energy region. Carbon and H 2 0 samples were used. The experimental procedure and the (n, 2n) cross section evaluation are described elsewhere 4). 3. Corrections
The corrections dependent on the special technique involved in the (n, 2n) detection are described elsewhere 4). The following corrections were applied to the measured (n, 2n) cross sections: (i) Multiple scattering correction. The elastic cross sections and the angular distributions of 2H and O were used to calculate the fraction of the (n, 2n) events induced by neutrons which have first undergone elastic scattering. The correction was calculated using the Monte-Carlo program written by Zetterstr~Sm s). The correction was 9 ~ at 6 MeV with an estimated error of 2 9/0. (ii) Neutron escape along the axial channel of the large scintillator tank. This correction depends on the angular distribution of the emitted neutrons and to a lesser extent on the energies of the two neutrons. There are no measurements in the actual energy region but recommendations and cross sections are given in the compilation prepared by Horsley and Stewart 6). These energy and angular distributions (given in the lab system) were calculated from a phase-space model. It should be noted that isotropy in the c.m. system is implicit in the phase-space model and the particles are emitted in a direct break-up reaction. This is, of course, only an approximation since final-state interactions are neglected. There are, however, indications that the predictions from the phase-space model agree reasonably well with experimental results 7) for nucleons with incident energies less than 6 MeV. We have used the angular distributions given by Horsley and Stewart 6) and neglected any correlations in the angular distributions of the emitted neutrons. The effective cone angle of the axial channel
~n(n, 2n) CROSSSECTION
329
was estimated f r o m a Monte-Carlo calculation 5). The correction to the (n, 2n) cross section was 10 70 at 6.0 MeV and a rather arbitrary error o f 50 ~ was estimated for the correction. (iii) Variation o f neutron detector efficiency with neutron energy. This correction was calculated on the basis of the energy distributions of the emitted neutrons. These distributions were taken from the compilation of Horsley and Stewart 6). The correction was then calculated using the detector efficiency measured by AsplundNilsson et al. s). The correction was 3 ~o at 6 MeV o f incident neutron energy. TABLE 1 ZH(n, 2n) cross sections in m b '~.. 2. (mb)
Incident energy (MeV) 4.10 4.40 4.60 4.90 5.20 5.85 6.30 6.55
13±8 17±7 25±6 34±6 45~6 61 ± 7 60±7 64±7
a n,2n mb 70-
60-
50-
40-
30-
20-
10-
0
...... oLo
~ INCIDENT
~ NEUTRON
ENERGY, MeV
Fig. I. T h e (n, 2n) cross section for 2H as a f u n c t i o n o f n e u t r o n energy. T h e solid circles represent the present data. T h e open triangles are f r o m C a t r o n et al. ~) a n d the solid curve is the (n, 2n) cross section calculated by F r a n k a n d G a m m e l 1).
330
M. HOLMBERG
4. Results and discussion
The corrected values o f trn, 2n a r e given in table 1 and are shown in fig. 1. The (n, 2n) cross sections measured by Catron et al. 2) are also shown in fig. 1. There is reasonably good agreement between the present results and those of Catron et al. and also with the cross sections calculated by Frank and Gammel 1). The calculations by Frank and Gammel were based on the impulse method with a zero-range approximation and a final-state n-p interaction. The authors pointed out that this approximation gave a surprisingly good fit to experimental energy and angular distributions at 10 MeV and 14 MeV. Now there are available more accurate experimental results, which are not reproduced by these calculations 9). At 14 MeV incident neutron energy the measurements of the energy distribution of the protons emitted at small forward angles show structure. The observed peak at the high-energy end is ascribed to n-n final-state interactions and the broader peak at intermediate energies is interpreted as an effect of the n-p interaction. Theoretical calculations by Aaron and Amado 10) reproduce the major features of these experimental distributions. However, for the integral (n, 2n) cross section in the actual energy region there seems to be agreement between the calculations by Aaron et al. ~ ) and Frank and Gammel 1). This may indicate that rather approximative calculations give the correct magnitude and energy dependence of the integral (n, 2n) cross section but the accuracy of the present results permits only a rough comparison with the theoretical calculations. The author wishes to thank H.-O. Zetterstr6m for performing the Monte-Carlo calculations and for many fruitful discussions. References 1) R. M. Frank and J. L. Gammel, Phys. Rev. 93 (1954) 463 2) H. C. Catron, M. D. Goldberg, R. W. Hill, J. M. LeBlanc, J. P. Stoering, C. J. Taylor and M. A. Williamson, Phys. Rev. 123 (1961) 218 3) I. Asplund-Nilsson, H. Cond6 and N. Starfelt, Nucl. Sci. and Eng. 20 (1964) 527 4) M. Holmberg and J. Hans6n, Nucl. Phys. A129 (1969) 305 5) H.-O. Zetterstr6m, unpublished 6) A. Horsley and L. Stewart, LASL-Report 3271 (1968); A. Horsley, Nucl. Data A4 (1968) 321 7) L. M. Delves, Nucl. Phys. 26 (1961) 136 8) I. Asplund-Nilsson, H. Cond6 and N. Starfelt, Nucl. Sci. and Eng. 16 (1963) 124 9) I. ~laus, Rev. Mod. Phys. 39 (1967) 575 10) R. Aaron and R. D. Amado, Phys. Rev. 150 (1966) 857 11) R. Aaron, R. D. Amado and Y. Y. Yam, Phys. Rev. 140 (1965) B1291
2.F
[
Nuclear Physics A129 (1969) 327--330; ( ~ North-Holland Publishing Co., Amsterdam Not
to be reproduced by photoprint or microfilm without written permission from the publisher
T H E (n, 2n) C R O S S S E C T I O N OF 2H IN T H E ENERGY R E G I O N 4.0-6.5 MeV M. HOLMBERG Research Institute o f National Defence, Stockholm 80, Sweden t Received 23 December 1968 The (n, 2n) cross section of ~H was measured in the energy region 4.0-6.5 MeV. The observed cross sections agree with earlier calculations by Frank and Gammel.
Abstract:
E I
N U C L E A R REACTIONS ~H(n' 2n)' E : 4"0"6"5 MeV; measured or(E)" D~O target"
]
1. Introduction This paper gives data on the (n, 2n) cross section of deuterium in the energy region 4.0-6.5 MeV. The threshold for the 2H(n, np)n reaction is at 3.34 MeV. The calculations by Frank and Gammel 1) give an almost linear energy dependence of the (n, 2n) cross section up to 8 MeV of incident neutron energy. There is good agreement between the calculated values and the (n, 2n) cross sections at 6.1 and 6.5 MeV measured by Catron et al. a). However, above 7 MeV incident neutron energy there is a discrepancy between the calculated and measured cross sections. Therefore it was thought that measurements below 6 MeV could be of value, since no earlier measurement exists below that energy. In the present experiment the neutrons from the (n, 2n) reactions were detected by a large liquid scintillator and the incident neutron flux was measured by the use of a plastic scintillator. 2. Experimental method The incident neutrons were produced at the 5.5 MeV Van de Graaff accelerator at Studsvik using the 2H(d, n)3He reaction. The special technique used in the (n, 2n) detection required a rather low flux of the incident neutrons, and a sufficient neutron flux was produced by using an adsorbed target. The collimator system consisted of an 1.5 m iron collimator, 20 cm square and with a conical hole 10 m m in diameter at the entrance and 40 m m at the end. The iron collimator was surrounded by a lead and paraffin shield, about 1 m square and 1.5 m in length. The large liquid scintillator was surrounded by 20 cm of lead and 20 cm of paraffin. * Preliminary results were reported at the Paris Conference on Nuclear Data for Reactors in Oct. 1966. 327
328
M. HOLMBERG
The liquid scintillator has earlier been used in ~-measurements and is described in detail by Asplund-Nilsson et al. 3). It has also been used in (n, 2n) measurements of Be. A detailed account of the experimental technique for the (n, 2n) measurement is given by Holmberg and Hans6n 4). The D 2 0 sample was located at the centre of the axial tube of the large liquid scintillator. An elastically scattered neutron entering the Gd-loaded scintillator gives rise to a prompt pulse due to the proton recoils produced in the slowing-down of the neutron. This prompt pulse was removed by the use of an anticoincidence arrangement. The second pulse due to the capture of the thermalized neutron in a Gd nucleus occurs about 20 #s later. For the capture pulses the time distribution between two successive pulses is random, if only one neutron is emitted in each reaction which occurs in the sample. However, for an (n, 2n) event there exists a time correlation between the two capture pulses. Consequently the number of (n, 2n) events could be separated from the randomly distributed background. The time correlation was measured by the use of a time-to-pulse-height converter. The randomly distributed background was measured by using scatterers with the (n, 2n) thresholds above the actual energy region. Carbon and H 2 0 samples were used. The experimental procedure and the (n, 2n) cross section evaluation are described elsewhere 4). 3. Corrections
The corrections dependent on the special technique involved in the (n, 2n) detection are described elsewhere 4). The following corrections were applied to the measured (n, 2n) cross sections: (i) Multiple scattering correction. The elastic cross sections and the angular distributions of 2H and O were used to calculate the fraction of the (n, 2n) events induced by neutrons which have first undergone elastic scattering. The correction was calculated using the Monte-Carlo program written by Zetterstr~Sm s). The correction was 9 ~ at 6 MeV with an estimated error of 2 9/0. (ii) Neutron escape along the axial channel of the large scintillator tank. This correction depends on the angular distribution of the emitted neutrons and to a lesser extent on the energies of the two neutrons. There are no measurements in the actual energy region but recommendations and cross sections are given in the compilation prepared by Horsley and Stewart 6). These energy and angular distributions (given in the lab system) were calculated from a phase-space model. It should be noted that isotropy in the c.m. system is implicit in the phase-space model and the particles are emitted in a direct break-up reaction. This is, of course, only an approximation since final-state interactions are neglected. There are, however, indications that the predictions from the phase-space model agree reasonably well with experimental results 7) for nucleons with incident energies less than 6 MeV. We have used the angular distributions given by Horsley and Stewart 6) and neglected any correlations in the angular distributions of the emitted neutrons. The effective cone angle of the axial channel
~n(n, 2n) CROSSSECTION
329
was estimated f r o m a Monte-Carlo calculation 5). The correction to the (n, 2n) cross section was 10 70 at 6.0 MeV and a rather arbitrary error o f 50 ~ was estimated for the correction. (iii) Variation o f neutron detector efficiency with neutron energy. This correction was calculated on the basis of the energy distributions of the emitted neutrons. These distributions were taken from the compilation of Horsley and Stewart 6). The correction was then calculated using the detector efficiency measured by AsplundNilsson et al. s). The correction was 3 ~o at 6 MeV o f incident neutron energy. TABLE 1 ZH(n, 2n) cross sections in m b '~.. 2. (mb)
Incident energy (MeV) 4.10 4.40 4.60 4.90 5.20 5.85 6.30 6.55
13±8 17±7 25±6 34±6 45~6 61 ± 7 60±7 64±7
a n,2n mb 70-
60-
50-
40-
30-
20-
10-
0
...... oLo
~ INCIDENT
~ NEUTRON
ENERGY, MeV
Fig. I. T h e (n, 2n) cross section for 2H as a f u n c t i o n o f n e u t r o n energy. T h e solid circles represent the present data. T h e open triangles are f r o m C a t r o n et al. ~) a n d the solid curve is the (n, 2n) cross section calculated by F r a n k a n d G a m m e l 1).
330
M. HOLMBERG
4. Results and discussion
The corrected values o f trn, 2n a r e given in table 1 and are shown in fig. 1. The (n, 2n) cross sections measured by Catron et al. 2) are also shown in fig. 1. There is reasonably good agreement between the present results and those of Catron et al. and also with the cross sections calculated by Frank and Gammel 1). The calculations by Frank and Gammel were based on the impulse method with a zero-range approximation and a final-state n-p interaction. The authors pointed out that this approximation gave a surprisingly good fit to experimental energy and angular distributions at 10 MeV and 14 MeV. Now there are available more accurate experimental results, which are not reproduced by these calculations 9). At 14 MeV incident neutron energy the measurements of the energy distribution of the protons emitted at small forward angles show structure. The observed peak at the high-energy end is ascribed to n-n final-state interactions and the broader peak at intermediate energies is interpreted as an effect of the n-p interaction. Theoretical calculations by Aaron and Amado 10) reproduce the major features of these experimental distributions. However, for the integral (n, 2n) cross section in the actual energy region there seems to be agreement between the calculations by Aaron et al. ~ ) and Frank and Gammel 1). This may indicate that rather approximative calculations give the correct magnitude and energy dependence of the integral (n, 2n) cross section but the accuracy of the present results permits only a rough comparison with the theoretical calculations. The author wishes to thank H.-O. Zetterstr6m for performing the Monte-Carlo calculations and for many fruitful discussions. References 1) R. M. Frank and J. L. Gammel, Phys. Rev. 93 (1954) 463 2) H. C. Catron, M. D. Goldberg, R. W. Hill, J. M. LeBlanc, J. P. Stoering, C. J. Taylor and M. A. Williamson, Phys. Rev. 123 (1961) 218 3) I. Asplund-Nilsson, H. Cond6 and N. Starfelt, Nucl. Sci. and Eng. 20 (1964) 527 4) M. Holmberg and J. Hans6n, Nucl. Phys. A129 (1969) 305 5) H.-O. Zetterstr6m, unpublished 6) A. Horsley and L. Stewart, LASL-Report 3271 (1968); A. Horsley, Nucl. Data A4 (1968) 321 7) L. M. Delves, Nucl. Phys. 26 (1961) 136 8) I. Asplund-Nilsson, H. Cond6 and N. Starfelt, Nucl. Sci. and Eng. 16 (1963) 124 9) I. ~laus, Rev. Mod. Phys. 39 (1967) 575 10) R. Aaron and R. D. Amado, Phys. Rev. 150 (1966) 857 11) R. Aaron, R. D. Amado and Y. Y. Yam, Phys. Rev. 140 (1965) B1291