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Inelastic scattering of 14 MeV neutrons on light nuclei
Journalof NuclearEnergyPartsA/B, 1964, Vol. 18. pp. 596 to 598. PergamonPressLtd. Printedin Northern
Ireland
LETTERS TO THE EDITORS
Inelastic scattering of 14 MeV neutrons on light nuclei* (Received 25 March 1963) to the lack of data on the spectra of fast neutrons inelastically scattered by light nuclei with atomic weights in the range 6-16, it is difficult to make calculations on the passage of neutrons through thick layers of various materials. Some information on the spectra of neutrons scattered by beryllium and carbon has been published. (1--8) GRAVES and ROSEN’*’ have measured the temperatures of scattered neutrons having energies 0.5-4-O MeV, but these are not much use in such calculations since, when neutrons with energies exceeding 10 MeV are scattered, a substantial role is played by direct interaction processes between the neutrons and the individual nucleons of the nucleus. This leads to an appreciable increase in the average energy of the inelastically scattered neutrons. In the work reported here the spectra of neutrons inelastically scattered from lithium, beryllium boron, carbon, nitrogen and oxygen were studied at an incident neutron energy of 14 MeV. A time-of-flight method similar to that described by STRIZHAK et al. w was used in these measurements. The geometry of the experiment is illustrated in Fig. 1. OWING
600x600~600
FIG.
l-lead shield; 2-neutron mator; 7-water shield;
l.-Experimental geometry. detector; 3-sample; 4-lead; 8-tritium target; 9-cast-iron
%-monitor; 6-collicube; lo-a-counter.
The neutron detector was a plastic scintillator with a diameter and height of 100 mm viewed by a FEU-36 photomultiplier. The resolving time of the equipment (27), according to measurements an the y-peak, was equal to 3.5 x 10-O sec. For experiments in which neutrons are counted, this time is increased to 5.4 x 10-O set due to the finite time of flight of the neutrons through the detector and because of the small size and spread in amplitude of the pulses in the scintillator. The samples had dimensions 60 x 100 x 100 mm and consisted of: lithium hydride (LiH), beryllium, carbon (graphite), boron carbide (B,C), melamine (C,H,N,) and water. Since the measurements were made at an angle of 90” to the primary neutron beam, the presence of hydrogen in these compounds had no effect on the results of the measurements to within the limits of the experimental errors. With the * Translated
by D. L.
ALLAN
from Atomnuya Energiya 15,411 (1963).
597
Letters to the editors
help of shielding it was possible to obtain an effect to background ratio in the region of the elastic peak of about 3-4 at a counting rate of 20-25 pulses per minute. Figure 2 shows the instrumental spectra dN/dt of scattered 14 MeV neutrons. Since the resolving power of the equipment was not good enough to make a clean separation of the elastic peak from the spectrum of inelastically scattered neutrons, this separation was effected by making use of the
7
:;:
I 0
10
20
30
50
40
Flight
60
70
80
90
n set
time,
6 5 4 3 82 I 0
10
20
30
40
Flight
50
time,
60
m
0
80
10
20
nsec
30
Flight
-
40
50
time,
60
m
80
“SW
2
:;I 0
IO
20
30
Flight
40
time,
50
60
70
80
0
IO
20
nsec
30
Flight
40
time,
50
60
m
60
n set’
FIG. 2.-Time
spectra of neutrons scattered by (a) lithium, (b) beryllium, (c) boron, (d) carbon, (e) nitrogen, (f) oxygen. The dash-dot lines in (c) and (d) are the separated spectra for boron and nitrogen; the broken lines appearing in all the spectra represent the lines of division between elastic and inelastic scattering. published datacB’ on the energies of the first few levels of IlB, ‘“C, ‘*N and 160. For each nucleus, the number of neutrons scattered with the excitation of a particular level in the nucleus was assumed to be proportional to exp (-I&/@, where Ei is the energy of the level and 0 is an empirical parameter chosen so that the neutron energy, averaged over all the states of the nucleus which it is possible to excite, is equal to the average energy of the neutrons E,, found from the experimental spectrum
C Ei’exp
(-E&I)
Eav = ‘2exp (-E&l)
’
598
Letters to the editors
where Ei’ is the energy of the scattered neutrons corresponding to the excitation of the given level. To determine the experimental quantity EBV,an approximate separation of the elastic and inelastic parts of the spectrum was first made on the assumption that the first part of the spectrum, corre sponding to inelastic scattering, had a Gaussian shape peaked in the region of the first few levels. After choosing 6, a neutron time spectrum was plotted allowing for the resoiution of the equipment. In the final plot of the inelastically scattered neutron spectrum only the first part of the computed spectrum was used.
TABLE i.-SPECTRA
OF INELASTICALLY SCATTERED NEUTRONS NUCLEI
FOR VARIOUS
Relative numbers of scattered neutrons (%) Energy interval (MeV)
Li
Be
<8.5 8.5-60 60-45 45-3.0 3.0-20 2.0-1.5
18 24 22 21 16
Error
jz3.0
C B
1
2
3
17 23 19 16 14 11
19 21 17 16 16 11
15 19 12 19 19 16
-
-
*20
28 21 16 13 11 10 13.5
1
4
34 16 23 16 11
39 23 20 20 9
*3*0
-
N
0
18 24 19 15 16 7
27 20 21 19 13
*4.5
k3.0
Note: Columns headed 1, 2, 3, 4, give data from REMY and WINTER'~), ROSEN and STEWART(~), and SLINGLATARY and WOOD(~) respectively.
The situation was more complicated for beryllium because of the (n, 2n) reaction. In separating the elastic from the inelastic scattering components the broken line shown in Fig. 2 was drawn in such a way that the ratio of the areas under the curves corresponded to the known elastic and inelastic scattering cross sections for beryllium, it being assumed that the angular distribution of the Since the lowest level of lithium neutrons from the (n, 2n) reaction was spherically symmetrical. has a very low excitation energy (470 keV), its contribution was included in with the elastic scattering. This is completely acceptable for the purpose of calculations on the passage of neutrons through matter. In Figs. 2(a, b), in addition to the experimental curves, there are also continuous lines (without points) representing the inelastically scattered neutron spectra calculated assuming a Maxwellian spectrum with a temperature T = 2E,,. It can be seen that these temperature curves, which correspond to the statistical model, differ substantially from the experimental curves. The final results of the measurements are presented in Table 1 which compares the relative numbers of neutrons in various energy ranges with the results obtained by other workers.‘7-s’ It is evident that the results of the various measurements are in satisfactory agreement. E. M. OPAI~N A. I. SALJKOV R.S.SHWALOV
REFERENCES 1. ANDERSON. J. Whys. Rev. 111, 572 (1958). 2. HUGHES D. J. and SCHWARTZ R. B. Neutron Cross Sections, Suppl. I (1957). 3. GOIWEEV I. V. et al. Handbook of Nuclear Physics Constants for Reactor Calculations (1960). 4. GRAVES E. and ROSEN L. Phys. Rev. 89,343 (1953). 5. STRIZHAK V. I., BOBIR' V. V. and GRONA L. YA. Zh. eksp. teor.Jiz. 40,725 (1961). 6. Nucl. Phys. 5, 11 (1959). 7. REMY E. and WINTER K. Nuova Cimento 11,664 (1958). 8. SINGLATARY J. and WOOD D. Phys. Rev. 114, 1595 (1959). 9. ROSEN L. and STEWART L. Phys. Rev. 107,824 (1957).
Ireland
LETTERS TO THE EDITORS
Inelastic scattering of 14 MeV neutrons on light nuclei* (Received 25 March 1963) to the lack of data on the spectra of fast neutrons inelastically scattered by light nuclei with atomic weights in the range 6-16, it is difficult to make calculations on the passage of neutrons through thick layers of various materials. Some information on the spectra of neutrons scattered by beryllium and carbon has been published. (1--8) GRAVES and ROSEN’*’ have measured the temperatures of scattered neutrons having energies 0.5-4-O MeV, but these are not much use in such calculations since, when neutrons with energies exceeding 10 MeV are scattered, a substantial role is played by direct interaction processes between the neutrons and the individual nucleons of the nucleus. This leads to an appreciable increase in the average energy of the inelastically scattered neutrons. In the work reported here the spectra of neutrons inelastically scattered from lithium, beryllium boron, carbon, nitrogen and oxygen were studied at an incident neutron energy of 14 MeV. A time-of-flight method similar to that described by STRIZHAK et al. w was used in these measurements. The geometry of the experiment is illustrated in Fig. 1. OWING
600x600~600
FIG.
l-lead shield; 2-neutron mator; 7-water shield;
l.-Experimental geometry. detector; 3-sample; 4-lead; 8-tritium target; 9-cast-iron
%-monitor; 6-collicube; lo-a-counter.
The neutron detector was a plastic scintillator with a diameter and height of 100 mm viewed by a FEU-36 photomultiplier. The resolving time of the equipment (27), according to measurements an the y-peak, was equal to 3.5 x 10-O sec. For experiments in which neutrons are counted, this time is increased to 5.4 x 10-O set due to the finite time of flight of the neutrons through the detector and because of the small size and spread in amplitude of the pulses in the scintillator. The samples had dimensions 60 x 100 x 100 mm and consisted of: lithium hydride (LiH), beryllium, carbon (graphite), boron carbide (B,C), melamine (C,H,N,) and water. Since the measurements were made at an angle of 90” to the primary neutron beam, the presence of hydrogen in these compounds had no effect on the results of the measurements to within the limits of the experimental errors. With the * Translated
by D. L.
ALLAN
from Atomnuya Energiya 15,411 (1963).
597
Letters to the editors
help of shielding it was possible to obtain an effect to background ratio in the region of the elastic peak of about 3-4 at a counting rate of 20-25 pulses per minute. Figure 2 shows the instrumental spectra dN/dt of scattered 14 MeV neutrons. Since the resolving power of the equipment was not good enough to make a clean separation of the elastic peak from the spectrum of inelastically scattered neutrons, this separation was effected by making use of the
7
:;:
I 0
10
20
30
50
40
Flight
60
70
80
90
n set
time,
6 5 4 3 82 I 0
10
20
30
40
Flight
50
time,
60
m
0
80
10
20
nsec
30
Flight
-
40
50
time,
60
m
80
“SW
2
:;I 0
IO
20
30
Flight
40
time,
50
60
70
80
0
IO
20
nsec
30
Flight
40
time,
50
60
m
60
n set’
FIG. 2.-Time
spectra of neutrons scattered by (a) lithium, (b) beryllium, (c) boron, (d) carbon, (e) nitrogen, (f) oxygen. The dash-dot lines in (c) and (d) are the separated spectra for boron and nitrogen; the broken lines appearing in all the spectra represent the lines of division between elastic and inelastic scattering. published datacB’ on the energies of the first few levels of IlB, ‘“C, ‘*N and 160. For each nucleus, the number of neutrons scattered with the excitation of a particular level in the nucleus was assumed to be proportional to exp (-I&/@, where Ei is the energy of the level and 0 is an empirical parameter chosen so that the neutron energy, averaged over all the states of the nucleus which it is possible to excite, is equal to the average energy of the neutrons E,, found from the experimental spectrum
C Ei’exp
(-E&I)
Eav = ‘2exp (-E&l)
’
598
Letters to the editors
where Ei’ is the energy of the scattered neutrons corresponding to the excitation of the given level. To determine the experimental quantity EBV,an approximate separation of the elastic and inelastic parts of the spectrum was first made on the assumption that the first part of the spectrum, corre sponding to inelastic scattering, had a Gaussian shape peaked in the region of the first few levels. After choosing 6, a neutron time spectrum was plotted allowing for the resoiution of the equipment. In the final plot of the inelastically scattered neutron spectrum only the first part of the computed spectrum was used.
TABLE i.-SPECTRA
OF INELASTICALLY SCATTERED NEUTRONS NUCLEI
FOR VARIOUS
Relative numbers of scattered neutrons (%) Energy interval (MeV)
Li
Be
<8.5 8.5-60 60-45 45-3.0 3.0-20 2.0-1.5
18 24 22 21 16
Error
jz3.0
C B
1
2
3
17 23 19 16 14 11
19 21 17 16 16 11
15 19 12 19 19 16
-
-
*20
28 21 16 13 11 10 13.5
1
4
34 16 23 16 11
39 23 20 20 9
*3*0
-
N
0
18 24 19 15 16 7
27 20 21 19 13
*4.5
k3.0
Note: Columns headed 1, 2, 3, 4, give data from REMY and WINTER'~), ROSEN and STEWART(~), and SLINGLATARY and WOOD(~) respectively.
The situation was more complicated for beryllium because of the (n, 2n) reaction. In separating the elastic from the inelastic scattering components the broken line shown in Fig. 2 was drawn in such a way that the ratio of the areas under the curves corresponded to the known elastic and inelastic scattering cross sections for beryllium, it being assumed that the angular distribution of the Since the lowest level of lithium neutrons from the (n, 2n) reaction was spherically symmetrical. has a very low excitation energy (470 keV), its contribution was included in with the elastic scattering. This is completely acceptable for the purpose of calculations on the passage of neutrons through matter. In Figs. 2(a, b), in addition to the experimental curves, there are also continuous lines (without points) representing the inelastically scattered neutron spectra calculated assuming a Maxwellian spectrum with a temperature T = 2E,,. It can be seen that these temperature curves, which correspond to the statistical model, differ substantially from the experimental curves. The final results of the measurements are presented in Table 1 which compares the relative numbers of neutrons in various energy ranges with the results obtained by other workers.‘7-s’ It is evident that the results of the various measurements are in satisfactory agreement. E. M. OPAI~N A. I. SALJKOV R.S.SHWALOV
REFERENCES 1. ANDERSON. J. Whys. Rev. 111, 572 (1958). 2. HUGHES D. J. and SCHWARTZ R. B. Neutron Cross Sections, Suppl. I (1957). 3. GOIWEEV I. V. et al. Handbook of Nuclear Physics Constants for Reactor Calculations (1960). 4. GRAVES E. and ROSEN L. Phys. Rev. 89,343 (1953). 5. STRIZHAK V. I., BOBIR' V. V. and GRONA L. YA. Zh. eksp. teor.Jiz. 40,725 (1961). 6. Nucl. Phys. 5, 11 (1959). 7. REMY E. and WINTER K. Nuova Cimento 11,664 (1958). 8. SINGLATARY J. and WOOD D. Phys. Rev. 114, 1595 (1959). 9. ROSEN L. and STEWART L. Phys. Rev. 107,824 (1957).