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Total neutron cross sections of Zr isotopes in the energy range up to 20 keV
Nuclear Physics 53 (1964) 667--672; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced b y photoprint or microfilm without written permission from the publisher
T O T A L N E U T R O N CROSS SECTIONS OF Z r I S O T O P E S IN T H E ENERGY RANGE U P T O 20 keY S. S. MOSKALEV, H. V. M U R A D I A N and Yu. V. A D A M C H U K
L V. Kurchatov Atomic Energy Institute, Academy of Sciences, Moscow, USSR Received 1 August 1963 Abstract: The total neutron cross sections for separated Zr isotopes are measured by a time-of-flight
technique at the linear electron accelerator of the Kurchatov Atomic Energy Institute. The best resolution in these measurements was 0.006 psec/m. The parameters of the discovered levels are determined and isotopic identification is made. The values of the strength functions for Zr isotopes are in agreement with the predictions of the optical model.
1. Introduction The zirconium isotopes lie in a mass region where the S-wave strength function has a minimum and where the largest discrepancy is observed between the values of
F°/Dpredicted by the optical model and most experimental data available to date
x).
2. Equipment and Samples Time-of-flight techniques were used for the measurement of the neutron cross sections. The flight path was 108 m, the neutron burst width 0.6 #see, the channel width o f a 2048-channel time analyser 0.4 #see and the pulse-repetition rate I00 pulses per second. The samples were placed between the neutron source and detector at a distanee ~ 40 m from the source. The counting rate per channel was ,~ 60 counts/h. The background in the measurements did not exceed 6 ~o of the effect. The instrumentation is described in refs. 2, 3). The dioxide or metal powder Zr material was enriched for the measured isotopes to no less than 60~o. The number o f Zr atoms per cm 2 was between 6.102x and 20 • 102x and the amount of contamination was less than 0.2 ~o. The Hfcontamination in the samples o f separated isotopes was < 10-3~..
3. Results and Discussion The total neutron cross sections of Zr isotopes were determined from the neutron transmission data. The resonance parameters were determined by the area method taking into account the Doppler broadening o f levels and potential and resonance scattering interference 4, 5). 667
s. s. MOSKALEVet aL
668
TABLE 1 Parameters values Isotopes Spin Zr 8°
0
Zr o~
f]
Eo (eV)
Z r o,
Zr"
0
0
0
/'n (eV)
Fn ° (eV)
39124-25 46904-30 136704-160
13.6 4-0.5 8.0 4-3.0 65 4-15
178504-250 182.5+0.3
200 4-70 0.0134-0.002
2404-1 a) 293.35:0.5
ZrO~
/'3" (MeV)
0.006+0.003 0.57 -4-0.10
Method of determining parameter
0.22 4-0.08 0.1204-0.044 0.56 4-0.13
/'n >>/'3' /'n > > / ' y /'n > > / ' y /'n > > / ' 7
1.50 -4-0.52 (9.6 4-1.5). I0-' /'3"= 2504-60 M e V
41504-4-30
3.5
4-0.5
4660:1:30 68804-60 22735:10
10 80 0.8
4-4 4-10 4-0.1
(3.9 4-1.9). 10-~ I'3' -----2504- 60 MeV 0.0335:0.006 Method of two samples 0.028-4-0.005 /'7 = 250-t-60 MeV 0.26 -4-0.03 /'n>>/'3' 0.011±0.007 /'3' -----250260 MeV 0.05 5:0.02 /'n >> -F7 0.13 +0.03 /'n>>/'3' 0.35 -4-0.13 /'n > > / ' / 0.0465:0.014 /'n >>/'3' 0.034+0.013 /'n >>/'3" 0.008-4-0.002 /'3" = 2504-60 MeV 0.28 5:0.04 /'a>>/" r 0.0554-0.008 /'a >> F 7 0.15 -I-0.06 /'n >>/" 0.96 4-0.11 /'n > > / ' ~ 0.0174-0.002 /'7 = 2504-60MeV
58705:60
27
d:7
0.35 4-0.09
/'n >~/'~,
4-8 -1-7 d:40 5:0.02 4-0.3 4-1.0 5:2.0 4-8.0
0.85 4-0.10 0.1754-0.060 0.9 4-0.3 0.0104-0.001 0.031 4-0.006 0.0735:0.016 0.1954-0.032 0.2154-0.110
/'n > > / ' y /'n > > / ' y /'n >>/'3' /'~, -----2504-60 MeV /'n >>/'3' /'n > > / ' 7 /'n > > / ' 7 /'a >>/'3'
1804-140
687-t-2 1538+6 1950-4-20 2020-4-20 2490+12 2720-t-15 3175+30 5600-4-50 18605:8 2720-I-15
0.73 10.0 0.5 2.3 6.5 18 2.6 2.5 0.35 14.4
72204-60 128004-160 198604-270 302.7±0.5 23804-15 38404-40 4150:~30 55104-50
72 20 125 0.17 1.5 4.5 12.5 16.0
-4-0.12 -4-1.0 5:0.3 4-0.7 ±1.5 -4-7 -4-0.8 5:1.0 +0.10 4-4-2.0
a) The level apparently corresponds to the interaction with neutron p-wave. TABLE 2 Average level spacings and strength functions Isotope
90
91
92
D(eV) D* (eV)
45005:1600 7160
7004-160 14000
1200-t-400 1080
0 . 85 :~o.e5 ~°'z~
I "~:~o.s n*o.2
/'n°/D( × 104)
1• 2 ±0.4 e~o.s
94 2400-4-900 1550 *o.s 1.1 ± o.s
96 1000-4-300 393 0 . 9 ±±o o ~ s85
T h e v a l u e s o f the p a r a m e t e r s are listed i n table 1. Besides the levels g i v e n i n the table s o m e Z r levels were detected for 880 a n d 1110 eV w h i c h were a s c r i b e d to Z r 9t in ref. 6).
TOTAl,,N E U T R O N
CROSS SECTIONS
~
Fig. I represents the transmission of the natural Zr in the energy range from 1.5 to 20 keV. Average level spacings of natural Zr and separated isotopes were obtained from T
Zr
i£
0.~
O.E
i~.~ 1
90+96 0.:
Ol+g2 100(30
5000
2oo
'
3,0pO
s~
2000 ~
'
EB,~
s;
Fig. 1. Transmission o f natural Zr in the energy range from 1.5 to 20 keV.
tot
\~ :~
i0 ~'
/ ',. /
\
\
\
# 56
57 $8
59
N Fig. 2. Average level spacings of Zr and Mo isotopes D*, reduced to the same excitation energy versus the number of neutrons in the compound nucleus. Dashed line connects the values of D* for Zr isotopes and solid line those for M o isotopes.
the experimental data (see table 2). For the natural sample D = 230 _ 40 eV. The average level spacing for Zr 9x per one spin state is given in table 2. Since the neutron binding energies for Zr isotope differ by ~ 3 MeV the average level spacings D* reduced to the same excitations energy 7, s) U = 6.5 MeV were calculated for different isotopes (dashed line in fig. 2). Clearly, D* has the largest value for Zr 9° which has a closed neutron shell. As the atomic weight increases the
s.s. M O S K A L E V et al.
670
D* of even isotopes decreases. For an odd-neutron isotope (Zr 9~) D* has a higher value due to a larger temperature° of the corresponding compound nucleus. The reduced level density decreases for the Zr 94 nucleus, for which the number of neutrons in the compound nucleus is equal to 55. A similar phenomenon was observed earlier in the measurement of the cross sections for isotopes of molybdenum s). The D*
0
zo
40
oo
~0
too
tP.0
i40
160 t80 200 220 TARGET ATOMIC WEIGHT
240
Fig. 3. Comparison of experimental values of strength function with optical model predictions. Black squares indicate the values obtained in this investigation, black triangles the results of ref. s) and white circles the data of other authors. The solid curve corresponds to the calculation of Fn°/D on the assumption of surface absorption and the dashed curve corresponds to the same on the assumption of volume absorption.
for Mo isotopes is given in the same figure (solid lines). The increase of D* is visible for the M o 96 isotope which also has 55 neutrons in the compound nucleus. Fig. 3 gives the experimental values of the strength function F°[D versus atomic weight. Squares indicate the quantities obtained in this study (see table 2), triangles the results of ref. 5) and circles the data of other authors x). It is clear from fig. 3 that our values of the strength function in the region A ~ 100 lie above the experimental points of other authors. Two theoretical curves for the strength functions in the optical model are given in fig. 3. The real part of the optical potential V(r)is chosen in the generally used Saxon
TOTAL NEUTRON CROSS SECTIONS
671
form 9) with a nuclear radius equal to 1.245 A÷ fm, diffuse boundary parameter 0.65 fm and the potential wen depth Vo = 50 MeV. The solid curve in fig. 3 is calculated under the assumption of the surface absorption with the imaginary part of the optical potential in the form W(r) = - Wo exp -
(~-b~) 2 .
The value of the parameter b characterizing the size of the absorption region is assumed to be 1 fm and Wo = 0.15, Vo = 7.5 MeV. The dashed curve is calculated under the assumption of the volume absorption with the imaginary part in the form W(r) = ~ V(r), where the volume absorption coefficients ~ = 0.075. Our experimental values F°/D of Zr and Mo isotopes are in good agreement with both thcoretical curves lo, 11). In several recent papers 12-14), attempts have been made to modify the optical potential so as to obtain in this region a deeper minimum of the strength function So ~ (0.1 to 0.2)× 10 -4. It is assumcd that the absorption takes place outside the nucleus where the real part of the potential is negligibly small. The results of our experiments indicate that there is no nced for such modifications of the optical potential. Table 2 indicates two kinds of errors for strength function values. The upper values are the usual experimental errors connected with the determination of F°/D by the formula Fn
D
~
Er°, "
AE
where AE is the energy range within which the summation of F°~ is made and F°~ is the reduced neutron width of the i-th resonance. The lower values are the ones connected with the fluctuations of the averages of F ° and D in the region AE under consideration. These quantities can be determined by the conventional statistical formula 15). For comparison the conventional experimental errors in the determination of F°/D are given in fig. 3, though the table of strength function values of ref. 5) indicates only the largest errors connected with the fluctuations. The authors express gratitude to P. E. Nemirovsky, Yu. P. Yelagin and M. I. Pevsner for the discussion of the results and stimulating suggestions and to E. M. Strelnikov and V. E. Charnko for participation in the measurements and processing of the data.
672
s.s. MOSKAXJ~et aL
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15)
B. Buck and F. Perey, Phys. Rev. Lett. 8 (1962) 444 Yu. V. Adamchuk, S. S. Moskalev and M. I. Pevsner, preprint JINR 956, Dubna (1962) S. S. Moskalev, Yu. V. Adamchuk and S. K. Sotnikov, Prib. Tekh. Eksp. 3 (1963) 58 V. N. Yefimov and I. I. Shelontsev, preprint JINR P-641, Dubna (1961) M. I. Pevsner, Yu. V. Adarnchuk, L. S. Danelian, B. V. Yefimov, S. S. Moskalev and H. V. Muradian, JETP 44 (1963) 1187 J. Julien, Ch. Corge, V. D. Huynh, J. Morgenstern, preprint Saclay (1962) H. Bethe, Revs. Mod. Phys. 9 (1937) 69 Yu. V. Adamchuk and V. M. Strutinsky, preprint of the Kurchatov Atomic Energy Institute No. 94 (1960) R. D. Woods and D. S. Saxon, Phys. Rev. 95 (1954) 577 Yu. P. Yelagin, V. A. Lyulka and P. E. Nemirovsky, JETP 41 (1961) 959 Yu. P. Yelagin, JETP 44 (1963) 371 T. K. Krueger and B. Margolis, Nuclear Physics 28 (1961) 578 P. A. Moldauer, Phys. Rev. Lett. 9 (1962) 17 H. Fiedelday and W. E. Frahn, Ann. Phys. 16 (1961) 387 E. G. Bulpuch, K. K. Seth, C. D. Bowman, R. H. Tabony, R. C. Smith and H. W. Newson, Ann. Phys. 14 (1961) 387
T O T A L N E U T R O N CROSS SECTIONS OF Z r I S O T O P E S IN T H E ENERGY RANGE U P T O 20 keY S. S. MOSKALEV, H. V. M U R A D I A N and Yu. V. A D A M C H U K
L V. Kurchatov Atomic Energy Institute, Academy of Sciences, Moscow, USSR Received 1 August 1963 Abstract: The total neutron cross sections for separated Zr isotopes are measured by a time-of-flight
technique at the linear electron accelerator of the Kurchatov Atomic Energy Institute. The best resolution in these measurements was 0.006 psec/m. The parameters of the discovered levels are determined and isotopic identification is made. The values of the strength functions for Zr isotopes are in agreement with the predictions of the optical model.
1. Introduction The zirconium isotopes lie in a mass region where the S-wave strength function has a minimum and where the largest discrepancy is observed between the values of
F°/Dpredicted by the optical model and most experimental data available to date
x).
2. Equipment and Samples Time-of-flight techniques were used for the measurement of the neutron cross sections. The flight path was 108 m, the neutron burst width 0.6 #see, the channel width o f a 2048-channel time analyser 0.4 #see and the pulse-repetition rate I00 pulses per second. The samples were placed between the neutron source and detector at a distanee ~ 40 m from the source. The counting rate per channel was ,~ 60 counts/h. The background in the measurements did not exceed 6 ~o of the effect. The instrumentation is described in refs. 2, 3). The dioxide or metal powder Zr material was enriched for the measured isotopes to no less than 60~o. The number o f Zr atoms per cm 2 was between 6.102x and 20 • 102x and the amount of contamination was less than 0.2 ~o. The Hfcontamination in the samples o f separated isotopes was < 10-3~..
3. Results and Discussion The total neutron cross sections of Zr isotopes were determined from the neutron transmission data. The resonance parameters were determined by the area method taking into account the Doppler broadening o f levels and potential and resonance scattering interference 4, 5). 667
s. s. MOSKALEVet aL
668
TABLE 1 Parameters values Isotopes Spin Zr 8°
0
Zr o~
f]
Eo (eV)
Z r o,
Zr"
0
0
0
/'n (eV)
Fn ° (eV)
39124-25 46904-30 136704-160
13.6 4-0.5 8.0 4-3.0 65 4-15
178504-250 182.5+0.3
200 4-70 0.0134-0.002
2404-1 a) 293.35:0.5
ZrO~
/'3" (MeV)
0.006+0.003 0.57 -4-0.10
Method of determining parameter
0.22 4-0.08 0.1204-0.044 0.56 4-0.13
/'n >>/'3' /'n > > / ' y /'n > > / ' y /'n > > / ' 7
1.50 -4-0.52 (9.6 4-1.5). I0-' /'3"= 2504-60 M e V
41504-4-30
3.5
4-0.5
4660:1:30 68804-60 22735:10
10 80 0.8
4-4 4-10 4-0.1
(3.9 4-1.9). 10-~ I'3' -----2504- 60 MeV 0.0335:0.006 Method of two samples 0.028-4-0.005 /'7 = 250-t-60 MeV 0.26 -4-0.03 /'n>>/'3' 0.011±0.007 /'3' -----250260 MeV 0.05 5:0.02 /'n >> -F7 0.13 +0.03 /'n>>/'3' 0.35 -4-0.13 /'n > > / ' / 0.0465:0.014 /'n >>/'3' 0.034+0.013 /'n >>/'3" 0.008-4-0.002 /'3" = 2504-60 MeV 0.28 5:0.04 /'a>>/" r 0.0554-0.008 /'a >> F 7 0.15 -I-0.06 /'n >>/" 0.96 4-0.11 /'n > > / ' ~ 0.0174-0.002 /'7 = 2504-60MeV
58705:60
27
d:7
0.35 4-0.09
/'n >~/'~,
4-8 -1-7 d:40 5:0.02 4-0.3 4-1.0 5:2.0 4-8.0
0.85 4-0.10 0.1754-0.060 0.9 4-0.3 0.0104-0.001 0.031 4-0.006 0.0735:0.016 0.1954-0.032 0.2154-0.110
/'n > > / ' y /'n > > / ' y /'n >>/'3' /'~, -----2504-60 MeV /'n >>/'3' /'n > > / ' 7 /'n > > / ' 7 /'a >>/'3'
1804-140
687-t-2 1538+6 1950-4-20 2020-4-20 2490+12 2720-t-15 3175+30 5600-4-50 18605:8 2720-I-15
0.73 10.0 0.5 2.3 6.5 18 2.6 2.5 0.35 14.4
72204-60 128004-160 198604-270 302.7±0.5 23804-15 38404-40 4150:~30 55104-50
72 20 125 0.17 1.5 4.5 12.5 16.0
-4-0.12 -4-1.0 5:0.3 4-0.7 ±1.5 -4-7 -4-0.8 5:1.0 +0.10 4-4-2.0
a) The level apparently corresponds to the interaction with neutron p-wave. TABLE 2 Average level spacings and strength functions Isotope
90
91
92
D(eV) D* (eV)
45005:1600 7160
7004-160 14000
1200-t-400 1080
0 . 85 :~o.e5 ~°'z~
I "~:~o.s n*o.2
/'n°/D( × 104)
1• 2 ±0.4 e~o.s
94 2400-4-900 1550 *o.s 1.1 ± o.s
96 1000-4-300 393 0 . 9 ±±o o ~ s85
T h e v a l u e s o f the p a r a m e t e r s are listed i n table 1. Besides the levels g i v e n i n the table s o m e Z r levels were detected for 880 a n d 1110 eV w h i c h were a s c r i b e d to Z r 9t in ref. 6).
TOTAl,,N E U T R O N
CROSS SECTIONS
~
Fig. I represents the transmission of the natural Zr in the energy range from 1.5 to 20 keV. Average level spacings of natural Zr and separated isotopes were obtained from T
Zr
i£
0.~
O.E
i~.~ 1
90+96 0.:
Ol+g2 100(30
5000
2oo
'
3,0pO
s~
2000 ~
'
EB,~
s;
Fig. 1. Transmission o f natural Zr in the energy range from 1.5 to 20 keV.
tot
\~ :~
i0 ~'
/ ',. /
\
\
\
# 56
57 $8
59
N Fig. 2. Average level spacings of Zr and Mo isotopes D*, reduced to the same excitation energy versus the number of neutrons in the compound nucleus. Dashed line connects the values of D* for Zr isotopes and solid line those for M o isotopes.
the experimental data (see table 2). For the natural sample D = 230 _ 40 eV. The average level spacing for Zr 9x per one spin state is given in table 2. Since the neutron binding energies for Zr isotope differ by ~ 3 MeV the average level spacings D* reduced to the same excitations energy 7, s) U = 6.5 MeV were calculated for different isotopes (dashed line in fig. 2). Clearly, D* has the largest value for Zr 9° which has a closed neutron shell. As the atomic weight increases the
s.s. M O S K A L E V et al.
670
D* of even isotopes decreases. For an odd-neutron isotope (Zr 9~) D* has a higher value due to a larger temperature° of the corresponding compound nucleus. The reduced level density decreases for the Zr 94 nucleus, for which the number of neutrons in the compound nucleus is equal to 55. A similar phenomenon was observed earlier in the measurement of the cross sections for isotopes of molybdenum s). The D*
0
zo
40
oo
~0
too
tP.0
i40
160 t80 200 220 TARGET ATOMIC WEIGHT
240
Fig. 3. Comparison of experimental values of strength function with optical model predictions. Black squares indicate the values obtained in this investigation, black triangles the results of ref. s) and white circles the data of other authors. The solid curve corresponds to the calculation of Fn°/D on the assumption of surface absorption and the dashed curve corresponds to the same on the assumption of volume absorption.
for Mo isotopes is given in the same figure (solid lines). The increase of D* is visible for the M o 96 isotope which also has 55 neutrons in the compound nucleus. Fig. 3 gives the experimental values of the strength function F°[D versus atomic weight. Squares indicate the quantities obtained in this study (see table 2), triangles the results of ref. 5) and circles the data of other authors x). It is clear from fig. 3 that our values of the strength function in the region A ~ 100 lie above the experimental points of other authors. Two theoretical curves for the strength functions in the optical model are given in fig. 3. The real part of the optical potential V(r)is chosen in the generally used Saxon
TOTAL NEUTRON CROSS SECTIONS
671
form 9) with a nuclear radius equal to 1.245 A÷ fm, diffuse boundary parameter 0.65 fm and the potential wen depth Vo = 50 MeV. The solid curve in fig. 3 is calculated under the assumption of the surface absorption with the imaginary part of the optical potential in the form W(r) = - Wo exp -
(~-b~) 2 .
The value of the parameter b characterizing the size of the absorption region is assumed to be 1 fm and Wo = 0.15, Vo = 7.5 MeV. The dashed curve is calculated under the assumption of the volume absorption with the imaginary part in the form W(r) = ~ V(r), where the volume absorption coefficients ~ = 0.075. Our experimental values F°/D of Zr and Mo isotopes are in good agreement with both thcoretical curves lo, 11). In several recent papers 12-14), attempts have been made to modify the optical potential so as to obtain in this region a deeper minimum of the strength function So ~ (0.1 to 0.2)× 10 -4. It is assumcd that the absorption takes place outside the nucleus where the real part of the potential is negligibly small. The results of our experiments indicate that there is no nced for such modifications of the optical potential. Table 2 indicates two kinds of errors for strength function values. The upper values are the usual experimental errors connected with the determination of F°/D by the formula Fn
D
~
Er°, "
AE
where AE is the energy range within which the summation of F°~ is made and F°~ is the reduced neutron width of the i-th resonance. The lower values are the ones connected with the fluctuations of the averages of F ° and D in the region AE under consideration. These quantities can be determined by the conventional statistical formula 15). For comparison the conventional experimental errors in the determination of F°/D are given in fig. 3, though the table of strength function values of ref. 5) indicates only the largest errors connected with the fluctuations. The authors express gratitude to P. E. Nemirovsky, Yu. P. Yelagin and M. I. Pevsner for the discussion of the results and stimulating suggestions and to E. M. Strelnikov and V. E. Charnko for participation in the measurements and processing of the data.
672
s.s. MOSKAXJ~et aL
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15)
B. Buck and F. Perey, Phys. Rev. Lett. 8 (1962) 444 Yu. V. Adamchuk, S. S. Moskalev and M. I. Pevsner, preprint JINR 956, Dubna (1962) S. S. Moskalev, Yu. V. Adamchuk and S. K. Sotnikov, Prib. Tekh. Eksp. 3 (1963) 58 V. N. Yefimov and I. I. Shelontsev, preprint JINR P-641, Dubna (1961) M. I. Pevsner, Yu. V. Adarnchuk, L. S. Danelian, B. V. Yefimov, S. S. Moskalev and H. V. Muradian, JETP 44 (1963) 1187 J. Julien, Ch. Corge, V. D. Huynh, J. Morgenstern, preprint Saclay (1962) H. Bethe, Revs. Mod. Phys. 9 (1937) 69 Yu. V. Adamchuk and V. M. Strutinsky, preprint of the Kurchatov Atomic Energy Institute No. 94 (1960) R. D. Woods and D. S. Saxon, Phys. Rev. 95 (1954) 577 Yu. P. Yelagin, V. A. Lyulka and P. E. Nemirovsky, JETP 41 (1961) 959 Yu. P. Yelagin, JETP 44 (1963) 371 T. K. Krueger and B. Margolis, Nuclear Physics 28 (1961) 578 P. A. Moldauer, Phys. Rev. Lett. 9 (1962) 17 H. Fiedelday and W. E. Frahn, Ann. Phys. 16 (1961) 387 E. G. Bulpuch, K. K. Seth, C. D. Bowman, R. H. Tabony, R. C. Smith and H. W. Newson, Ann. Phys. 14 (1961) 387