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Spectra of secondary neutrons produced in the passage of 14 MeV neutrons through layers of fissile material
J. Nucl. Energy II, 1959. Vol. 9, pp. 194 to 199. Per&mm Press Ltd.. London. Printed in Northern Ireland
SPECTRA OF SECONDARY NEUTRONS PRODUCED IN THE PASSAGE OF 14 MeV NEUTRONS THROUGH LAYERS OF FISSILE MATERIAL* Yu. S. ZAMYATNIN, I. N. SAFINA,E. K. GUTNIKOVAand N. I. IVANOVA (Received 7 September 1957)
Abstract-Measurements are presented of the energy spectra of secondary neutrons formed in layers of *Y”h, **%J,*YJ, ssaU and *9u under bombardment by 14 MeV neutrons. It is shown that all the spectra contain two components, characteristic respectively of fission and evaporation proceases. The coefficients involved in resolving the spectra into their components have been expressed as a function of the nuclear constants.
WHEN 14 MeV neutrons are incident upon heavy fissile nuclei, the following processes may occur: (a) absorption of the neutron, followed by the emission of charged particles or gamma radiation; (b) elastic scattering, in which the energy of the primary neutron is not materially changed; (c) the evaporation of neutrons from an excited intermediate nucleus, giving rise to inelastic scattering (n,n’y), (n,2n) processes, and so on; and (d) fission. Thus if fast neutrons are transmitted through a layer of fissile material, the emergent spectrum will contain not only groups corresponding to unscattered and elastically scattered neutrons, but also a contribution from (c) and (d). A number of studies(1-4) have shown that the energy distribution of secondary neutrons produced by the 14 MeV neutron bombardment of non-fissile elements is that appropriate to their evaporation from an excited compound nucleus according to statistical theory: F(E) = C,E exp (-E/T).
(1)
The parameter T defines the temperature of the residual nucleust, while C, is a normalizing factor. On the other hand, neutrons from the thermal-neutron-induced fission of heavy elements have a spectrum(5~s) F(E) = C, sinh [2(wE)*/TJ . exp (-E/T,).
(2)
Tf here is the temperature of a fission fragment after emission of the neutron, w is the mean kinetic energy of a nucleon within the fragment, and C, is another normalizing factor. If 14 MeV neutrons are passed through fissile material, a secondary spectrum containing contributions of both types, (1) and (2), may be expected. We now present some measurements, made during the years 1950-1956, which confirm this supposition. * Translated from Atomnayu Energiyu 4, 337 (1958). t Strictly speaking, a more complex distribution applies to the (n,Zn) process due to the different temperatures at which the first and second neutrons are evaporated. However, T depends only weakly on the excitation energy of the intermediate nucleus, so that (1) adequately describes what is observed. 194
Spectra of secondary neutrons produced in the passage of 14 MeV neutrons
195
METHOD
The 14 MeV neutrons were obtained by bombarding a tritium-zirconium target with 150 keV deuterons. Layers of the various fissile materials were placed round the source in turn, their thicknesses being chosen such that the primary flux was not attenuated more than 30 per cent. As shown in Table 1, this led to transverse dimensions ranging from 0.15 to O-4 times the mean free path I for inelastic collisions; the contribution of multiple inelastic scattering to the readings was therefore not large. 232Th, 233U, 23W, 238U, 23gPu and mixtures containing different proportions of 23W and 238U were used. I Isotope
‘232Th
TABLE 1.
I
! Thickness of Essile layer in terms of the mean free path 1
Nlltllber of tracks measured
/
3f
I
.__
---I 0.4
Apparent fraction of the , ne”haIs arising from fission
2000
*
True fraction of the Ix”trots arising from fission “f
_---
_~ 0.20
Correction to col. 4 due to inelastic collisions of secondary neutrons
wo5
0.03
zsq_J
0.15
4400
0.75 & 0.1
0.01
0.36
6700
0.65 z 0.05
0.03
I
0.05 0.08 mean . . . 002
in extrapolating
nucleus T, (Mew
the fission neutron
j
i
Temperature of the fragment Tf (MeV)
I
__
23qJ
* This value was assumed
,,~t~~e~~~$
@23 f
0%
0.76 i
@l
0.54 f
0.05
0.55 + 0.1
0.68 z!: 0.06
0.4 *
. . :‘:g&*O:: 0.49 f 0.05
zzz$E
0.72 + 0.1
053
@OS
f
0.06
__-
1 / !
1.2*
i
&O&s
1
1.25 I
1.2
??0.08
1.05 f
0.06
0.08
spectrum.
The emergent neutrons were detected in Ilford C-2 and NIKFI K plates with 100 p emulsions. Energy measurements were made by selecting those proton recoils which gave tracks within &15” of the forward direction. A further irradiation was performed with no fissile sample in place, to determine the background intensity; a correction for this was subsequently made on the assumption that the number of background tracks was proportional to the flux of primary neutrons. In searching for neutrons in the energy range above 2.5 MeV, an additional area of emulsion was examined to increase the statistical accuracy. The total number of recoil tracks measured for each substance studied is given in an accompanying table. RESULTS
Neutron spectra R’(E) were derived from the observed proton energy distributions after introducing a correction for the finite emulsion thickness; they appear in Fig. 1. Allowance was made for the energy variation of the neutron scattering crosssection of hydrogen. The ratio F(;(E)/E has been plotted on a semi-logarithmic scale, so that the spectrum (1) must appear as a straight line. As T, > T, the harder part of the neutron spectrum-in practice above about 3 MeV-is due almost entirely to fission neutrons; by extrapolation of the appropriate fit to low energies the evaporation spectrum could be separated off. The distribution of neutrons found in excess of the fission spectrum was, as a rule, in good agreement with (I), and the T values deduced are given in Table 1. Extrapolation of the fission spectrum normally was carried out with the aid of expression (2). w was taken in all cases to be 0.5 MeV, and values for T, were deduced from the hard end of the spectrum. It is of some interest to notice that the slopes of the graphs above 3 MeV for 233U, 23W and 23gPu gave Tf values essentially
Yu. S. ZAMYATNIN, I. N. SAHNA, E. K. GUTNJKOVA
196
FIG. l(a) * c ii
and N. 1.~VANOVA
5
2 0.0: 7 5 3 2
yqgyq I I 1 2
O*OOl
0
L
3 4 E, MeV
FIG.
(-).oo,l I I I I I ! I’ I I I I I I 0
1
2
3
4
E,
5
6
5
6
7
6
7
l(b)
7
MeV
O*OOl 0
1
2
4
5
Spectra of secondary neutrons produced in the passage of 14 MeV neutrons
197
K 0.01 9 7 5 3 2
OQOl
/
!
’ I 1 I I I I I I I 1 ’N 0 1 2 3 4 5 6
I 7
FIG. l(e)
E,
MeV
FIG. l(f) FIG. I.-The spectra of secondary neutrons produced in the passage of 14 MeV neutrons through a thickness (a) 0.4 I of 232Th; (b) 0.15’3, of za3U; (c) 0.36 j? of *=U (d) 0.24 3, of zs*U; (e) 0.34 1 of zssU; (f) @29 I of narPu. i --0
1
2
3 E,
4 MeV
5
6
7
& I
experimental
results.
extrapolation of the fission neutron spectrum. spectrum neutrons.
of
evaporation
198
Yu. S. ZAMYATNIN,I. N. SAFINA, E. K. GUTNIKOVAand N. I. IVANOVA
the same as those which apply for thermal-neutron-induced fission. One may conclude that the fission spectrum depends only weakly on the incident neutron energy and this fact allowed the known spectra from thermal fission to be used in making the extrapolation. The two coefficients a,and a, presented in the figures indicate the apparent fractions. of the total number of neutrons arising respectively from fission and from evaporation. A correction has to be applied to these results to take proper account of the inelastic collisions of the secondary neutrons themselves in the specimen. As the fission cross-. sections diminish with increase of neutron energy towards 14 MeV, the probability of an inelastic event is higher for secondary neutrons than for primary ones, and this effect somewhat reduces the number of fission neutrons in the final spectrum. Estimates showed that the correction is significant even for quite thin specimens. It was determined by taking the difference between the number of fission neutrons lost through inelastic scattering and the number gained due to the fission capture of evaporation neutrons; the appropriate mean path lengths described by secondary neutrons in the specimens were employed. The magnitudes of these corrections and the corrected a’s appear in the Table. DISCUSSION
It is apparent from the table of results that the spectra from the three comparatively easily fissioned nuclei mu, YJ and 23QPucontain a preponderant fraction of fission neutrons, whereas less fission neutrons are observed with the more stable nuclei s?Ih and a3eU. This qualitative agreement with expectation may be rendered more exact by relating the a’s to the nuclear constants of the isotopes. Consider the total cross-sectionfor the formation of secondary neutrons, i.e. the sum:* YoG=
YCf +
UT&y +
%,w
(3)
The second and third terms in (3) relate to evaporation processes, the first to fission. It must be realized, however, that the fission term does in fact account for a certain number of ‘evaporation’ neutrons, because at an incident energy of 14 MeV the excited intermediate nucleus could evaporate off a neutron in an (n,n’f> process before dividing. (For simplicity we ignore the n,2n’fprocess, on account of its low probability). of, therefore, should be regarded as the sum of two cross-sections; of0 for direct fission, and a,, which applies when the fission is preceded by an evaporation event.“) Thus yof in (3) should be replaced by r+,of, + (vl + l)cfm. or, and a, accordingly become af
VOGfc
+
a, =
VlOf93
=
Of,
+
fJTa,ny +
%,zn~
vc
WC
In practice it is more convenient to have the formulae in terms of the directly measured quantities v, af and afO, rather than vo, v1 and ufn:af =
a = R
YUf
-s(of
(Of -
-
Of,)
,
T;+~*,ny+ %h2n
. . .
?PJc
1
(4)
* Where an (n,3n) reaction is energetically possible, an extra term would need to be added to (3). The cross-section for radiative capture may be ignored at 14 MeV.
Spectra of secondary neutrons produced in the passage of 14 MeV neutrons
199
X~may also be written CQ= v&l;loC, in which v, is the true number of neutrons from fission processes, estimated with no allowance for preliminary evaporation. Then v,of = voj - (~7~- g&, i.e. V~= v - (oJof),. In the case of the specimens containing two different isotopes, an effective af and a, can be found in terms of the individual coefficients for the two constituents; an, af 2, a,1 and an2. Writing & and B2for the proportional concentrations of the isotopes, the total cross-section for the formation of secondary neutrons is the sum y1 + y2 of two contributions, with y1 = @l~Ylla,, and y2 = B292uC2.Then *Jlafl + 72af2
af =
YlfY2
a, =
w,l
(5) *-*'
+ haa2 ./1+y2
@aI -
af and a, have been computed from (4) and (5) for the various specimens examined. The values obtained were in general within experimental error the same as the experimental values given herein. The only discrepancies were encountered with 233Uand 230Pu, for which the experimental af was somewhat below the calculated quantity. Acknowledgements-We are indebted to V. A. DAVIDENKOfor his interest in the work and for a discussion of the results. Thanks are ‘also due to A. G. SHLYGINA,who took part in the early stages of the investigation, and to Yu. A. VASILEV,G. S. MALKIEL and E. I. SIROTININfor exposing the photographic plates at the accelerator. L. S. ANDREEVA,L. V. EVSEEVA,N. F. NIKOLAEVAand V. A. CHERNYSHOVA assisted with the microscopic examination of the emulsions. REFERENCES ZAMYATNIN Yu. S., GUTNIKOVAE. K.,I VANOVAN. I. and SAF~A I. N., J. Nucl. Energy 9,41 (1959). STELSONP. H. and GOODMANC., Phys. Reu. 82, 69 (1951). GRAVENE. R. and ROSENL., Phys. Reo. 89, 343 (1953). NEILE G. K. O., Phys. Rev. 95, 1235 (1955). GIJREVICHI. I. and MUKHIN K. N. Unpublished work, (1951). EROZOLIM~KY B. G., Atomnuyu Energiya, Suppl. No. 2, p. 74 (1957). 6. W~rr B. E., Whys. Rev. 87, 1037 (1952). Yu. S. Atomnaya Energiya, Suppl. No. 1, p. 27 (1957). 7. ZAMYA1. 2. 3. 4. 5.
SPECTRA OF SECONDARY NEUTRONS PRODUCED IN THE PASSAGE OF 14 MeV NEUTRONS THROUGH LAYERS OF FISSILE MATERIAL* Yu. S. ZAMYATNIN, I. N. SAFINA,E. K. GUTNIKOVAand N. I. IVANOVA (Received 7 September 1957)
Abstract-Measurements are presented of the energy spectra of secondary neutrons formed in layers of *Y”h, **%J,*YJ, ssaU and *9u under bombardment by 14 MeV neutrons. It is shown that all the spectra contain two components, characteristic respectively of fission and evaporation proceases. The coefficients involved in resolving the spectra into their components have been expressed as a function of the nuclear constants.
WHEN 14 MeV neutrons are incident upon heavy fissile nuclei, the following processes may occur: (a) absorption of the neutron, followed by the emission of charged particles or gamma radiation; (b) elastic scattering, in which the energy of the primary neutron is not materially changed; (c) the evaporation of neutrons from an excited intermediate nucleus, giving rise to inelastic scattering (n,n’y), (n,2n) processes, and so on; and (d) fission. Thus if fast neutrons are transmitted through a layer of fissile material, the emergent spectrum will contain not only groups corresponding to unscattered and elastically scattered neutrons, but also a contribution from (c) and (d). A number of studies(1-4) have shown that the energy distribution of secondary neutrons produced by the 14 MeV neutron bombardment of non-fissile elements is that appropriate to their evaporation from an excited compound nucleus according to statistical theory: F(E) = C,E exp (-E/T).
(1)
The parameter T defines the temperature of the residual nucleust, while C, is a normalizing factor. On the other hand, neutrons from the thermal-neutron-induced fission of heavy elements have a spectrum(5~s) F(E) = C, sinh [2(wE)*/TJ . exp (-E/T,).
(2)
Tf here is the temperature of a fission fragment after emission of the neutron, w is the mean kinetic energy of a nucleon within the fragment, and C, is another normalizing factor. If 14 MeV neutrons are passed through fissile material, a secondary spectrum containing contributions of both types, (1) and (2), may be expected. We now present some measurements, made during the years 1950-1956, which confirm this supposition. * Translated from Atomnayu Energiyu 4, 337 (1958). t Strictly speaking, a more complex distribution applies to the (n,Zn) process due to the different temperatures at which the first and second neutrons are evaporated. However, T depends only weakly on the excitation energy of the intermediate nucleus, so that (1) adequately describes what is observed. 194
Spectra of secondary neutrons produced in the passage of 14 MeV neutrons
195
METHOD
The 14 MeV neutrons were obtained by bombarding a tritium-zirconium target with 150 keV deuterons. Layers of the various fissile materials were placed round the source in turn, their thicknesses being chosen such that the primary flux was not attenuated more than 30 per cent. As shown in Table 1, this led to transverse dimensions ranging from 0.15 to O-4 times the mean free path I for inelastic collisions; the contribution of multiple inelastic scattering to the readings was therefore not large. 232Th, 233U, 23W, 238U, 23gPu and mixtures containing different proportions of 23W and 238U were used. I Isotope
‘232Th
TABLE 1.
I
! Thickness of Essile layer in terms of the mean free path 1
Nlltllber of tracks measured
/
3f
I
.__
---I 0.4
Apparent fraction of the , ne”haIs arising from fission
2000
*
True fraction of the Ix”trots arising from fission “f
_---
_~ 0.20
Correction to col. 4 due to inelastic collisions of secondary neutrons
wo5
0.03
zsq_J
0.15
4400
0.75 & 0.1
0.01
0.36
6700
0.65 z 0.05
0.03
I
0.05 0.08 mean . . . 002
in extrapolating
nucleus T, (Mew
the fission neutron
j
i
Temperature of the fragment Tf (MeV)
I
__
23qJ
* This value was assumed
,,~t~~e~~~$
@23 f
0%
0.76 i
@l
0.54 f
0.05
0.55 + 0.1
0.68 z!: 0.06
0.4 *
. . :‘:g&*O:: 0.49 f 0.05
zzz$E
0.72 + 0.1
053
@OS
f
0.06
__-
1 / !
1.2*
i
&O&s
1
1.25 I
1.2
??0.08
1.05 f
0.06
0.08
spectrum.
The emergent neutrons were detected in Ilford C-2 and NIKFI K plates with 100 p emulsions. Energy measurements were made by selecting those proton recoils which gave tracks within &15” of the forward direction. A further irradiation was performed with no fissile sample in place, to determine the background intensity; a correction for this was subsequently made on the assumption that the number of background tracks was proportional to the flux of primary neutrons. In searching for neutrons in the energy range above 2.5 MeV, an additional area of emulsion was examined to increase the statistical accuracy. The total number of recoil tracks measured for each substance studied is given in an accompanying table. RESULTS
Neutron spectra R’(E) were derived from the observed proton energy distributions after introducing a correction for the finite emulsion thickness; they appear in Fig. 1. Allowance was made for the energy variation of the neutron scattering crosssection of hydrogen. The ratio F(;(E)/E has been plotted on a semi-logarithmic scale, so that the spectrum (1) must appear as a straight line. As T, > T, the harder part of the neutron spectrum-in practice above about 3 MeV-is due almost entirely to fission neutrons; by extrapolation of the appropriate fit to low energies the evaporation spectrum could be separated off. The distribution of neutrons found in excess of the fission spectrum was, as a rule, in good agreement with (I), and the T values deduced are given in Table 1. Extrapolation of the fission spectrum normally was carried out with the aid of expression (2). w was taken in all cases to be 0.5 MeV, and values for T, were deduced from the hard end of the spectrum. It is of some interest to notice that the slopes of the graphs above 3 MeV for 233U, 23W and 23gPu gave Tf values essentially
Yu. S. ZAMYATNIN, I. N. SAHNA, E. K. GUTNJKOVA
196
FIG. l(a) * c ii
and N. 1.~VANOVA
5
2 0.0: 7 5 3 2
yqgyq I I 1 2
O*OOl
0
L
3 4 E, MeV
FIG.
(-).oo,l I I I I I ! I’ I I I I I I 0
1
2
3
4
E,
5
6
5
6
7
6
7
l(b)
7
MeV
O*OOl 0
1
2
4
5
Spectra of secondary neutrons produced in the passage of 14 MeV neutrons
197
K 0.01 9 7 5 3 2
OQOl
/
!
’ I 1 I I I I I I I 1 ’N 0 1 2 3 4 5 6
I 7
FIG. l(e)
E,
MeV
FIG. l(f) FIG. I.-The spectra of secondary neutrons produced in the passage of 14 MeV neutrons through a thickness (a) 0.4 I of 232Th; (b) 0.15’3, of za3U; (c) 0.36 j? of *=U (d) 0.24 3, of zs*U; (e) 0.34 1 of zssU; (f) @29 I of narPu. i --0
1
2
3 E,
4 MeV
5
6
7
& I
experimental
results.
extrapolation of the fission neutron spectrum. spectrum neutrons.
of
evaporation
198
Yu. S. ZAMYATNIN,I. N. SAFINA, E. K. GUTNIKOVAand N. I. IVANOVA
the same as those which apply for thermal-neutron-induced fission. One may conclude that the fission spectrum depends only weakly on the incident neutron energy and this fact allowed the known spectra from thermal fission to be used in making the extrapolation. The two coefficients a,and a, presented in the figures indicate the apparent fractions. of the total number of neutrons arising respectively from fission and from evaporation. A correction has to be applied to these results to take proper account of the inelastic collisions of the secondary neutrons themselves in the specimen. As the fission cross-. sections diminish with increase of neutron energy towards 14 MeV, the probability of an inelastic event is higher for secondary neutrons than for primary ones, and this effect somewhat reduces the number of fission neutrons in the final spectrum. Estimates showed that the correction is significant even for quite thin specimens. It was determined by taking the difference between the number of fission neutrons lost through inelastic scattering and the number gained due to the fission capture of evaporation neutrons; the appropriate mean path lengths described by secondary neutrons in the specimens were employed. The magnitudes of these corrections and the corrected a’s appear in the Table. DISCUSSION
It is apparent from the table of results that the spectra from the three comparatively easily fissioned nuclei mu, YJ and 23QPucontain a preponderant fraction of fission neutrons, whereas less fission neutrons are observed with the more stable nuclei s?Ih and a3eU. This qualitative agreement with expectation may be rendered more exact by relating the a’s to the nuclear constants of the isotopes. Consider the total cross-sectionfor the formation of secondary neutrons, i.e. the sum:* YoG=
YCf +
UT&y +
%,w
(3)
The second and third terms in (3) relate to evaporation processes, the first to fission. It must be realized, however, that the fission term does in fact account for a certain number of ‘evaporation’ neutrons, because at an incident energy of 14 MeV the excited intermediate nucleus could evaporate off a neutron in an (n,n’f> process before dividing. (For simplicity we ignore the n,2n’fprocess, on account of its low probability). of, therefore, should be regarded as the sum of two cross-sections; of0 for direct fission, and a,, which applies when the fission is preceded by an evaporation event.“) Thus yof in (3) should be replaced by r+,of, + (vl + l)cfm. or, and a, accordingly become af
VOGfc
+
a, =
VlOf93
=
Of,
+
fJTa,ny +
%,zn~
vc
WC
In practice it is more convenient to have the formulae in terms of the directly measured quantities v, af and afO, rather than vo, v1 and ufn:af =
a = R
YUf
-s(of
(Of -
-
Of,)
,
T;+~*,ny+ %h2n
. . .
?PJc
1
(4)
* Where an (n,3n) reaction is energetically possible, an extra term would need to be added to (3). The cross-section for radiative capture may be ignored at 14 MeV.
Spectra of secondary neutrons produced in the passage of 14 MeV neutrons
199
X~may also be written CQ= v&l;loC, in which v, is the true number of neutrons from fission processes, estimated with no allowance for preliminary evaporation. Then v,of = voj - (~7~- g&, i.e. V~= v - (oJof),. In the case of the specimens containing two different isotopes, an effective af and a, can be found in terms of the individual coefficients for the two constituents; an, af 2, a,1 and an2. Writing & and B2for the proportional concentrations of the isotopes, the total cross-section for the formation of secondary neutrons is the sum y1 + y2 of two contributions, with y1 = @l~Ylla,, and y2 = B292uC2.Then *Jlafl + 72af2
af =
YlfY2
a, =
w,l
(5) *-*'
+ haa2 ./1+y2
@aI -
af and a, have been computed from (4) and (5) for the various specimens examined. The values obtained were in general within experimental error the same as the experimental values given herein. The only discrepancies were encountered with 233Uand 230Pu, for which the experimental af was somewhat below the calculated quantity. Acknowledgements-We are indebted to V. A. DAVIDENKOfor his interest in the work and for a discussion of the results. Thanks are ‘also due to A. G. SHLYGINA,who took part in the early stages of the investigation, and to Yu. A. VASILEV,G. S. MALKIEL and E. I. SIROTININfor exposing the photographic plates at the accelerator. L. S. ANDREEVA,L. V. EVSEEVA,N. F. NIKOLAEVAand V. A. CHERNYSHOVA assisted with the microscopic examination of the emulsions. REFERENCES ZAMYATNIN Yu. S., GUTNIKOVAE. K.,I VANOVAN. I. and SAF~A I. N., J. Nucl. Energy 9,41 (1959). STELSONP. H. and GOODMANC., Phys. Reu. 82, 69 (1951). GRAVENE. R. and ROSENL., Phys. Reo. 89, 343 (1953). NEILE G. K. O., Phys. Rev. 95, 1235 (1955). GIJREVICHI. I. and MUKHIN K. N. Unpublished work, (1951). EROZOLIM~KY B. G., Atomnuyu Energiya, Suppl. No. 2, p. 74 (1957). 6. W~rr B. E., Whys. Rev. 87, 1037 (1952). Yu. S. Atomnaya Energiya, Suppl. No. 1, p. 27 (1957). 7. ZAMYA1. 2. 3. 4. 5.