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Total photoabsorption cross sections for high-Z ELEMENTS in the energy range 7–20 MeV
Nuclear Physic A3~ (198(1) 97-104 ; ©1Varth-HoJlaedPrWWtinp Co., Mutsrdatx
Not to be reproduced by photoprFut ar mian®lm without written pamieeim >tom the publisher
TOTAL PHOTOABSORPTION CROSSSECTIONS FOR HIGH-Z ELEMENTS IN THE ENERGY RANGE 7-20 MeV G . M . GUREVICH, L. E . LAZAREVA, V . M . MAZUR, S . Yu. MERKULOV and G . V. SOLODUKHOV
Institutejor Nuclear Research, Academy of Sciences, Mosrnw, USSR Received 24 October 1979
A6e
E
NUCLEAR REACTIONS '~Sm, '' 6 Gd, ' bs13o, ' 6 BEr, "`Yb, lea . iao~ ~e~ Ta~ ~e~, iaa, is6W, i9~Au. ~o9B i(y ~~ E = 7-20 MeV ; measured total o(E~ ; deduced electromagnetic o. Enriched, natural targets.
1. Introtlncdion
Täe use of the electromagnetic probes, i.e. photons and electrons for the investigation of nuclear structure has certain advantages in comparison with the use, for example, of hadron probes. The form of the Hamiltonian of the electromagnetic field nucleon system interaction is well known, and therefore the use oftheelectromagnetic probes provides us with matrix elements giving direct information on nuclear wave functions. T1iis information has been essential for the development ofnuclear models, and good knowledge ofthe quantum numbers associated with specific multipoles has notably simplified the analysis of the fundamental modes of nuclear motion . All this explains the fact that experiments with electron and real photon beams are currently being carried out in a large number of laboratories throughout the world Although the primary purpose in each of these experiments is to obtain nuclear information, that is not always the sole information obtained. A characteristic example is the investigation of the total photoabsorption cross sections. The narrow beam attenuation method used in these experiments is based on the measurements of the y-beam attenuation coefficients for an absorber of precisely known thickness. In this case the e~cperimental cross section tr is a sum of the nuclear absorption cross section tro ~t and the cross sections of pure electromagnetic processes iphotaelectric effect aph, Compton effect try, pair production in the Coulomb field of the nucleus 97
98
G . M . GUREVICH et al.
Qp and pair production in the electron field tri): tr = Qnoo~+Qu = (1/A)lII(1Vo(~/N(~), tr = Qph+QC+Up+tT where No(~ and N(E~ are the numbers of photons in a given energy bin with and without the absorber in the y-beam respectively, and A is a coefficient indicating the number of the absorber atoms per cm2. Unfortunately, the photonuclear cross section does not exceed approximately 5 ~ of tr even in the giant resonance maximum and its contribution decreases with increasing Z. Thus in these experiments the electromagnetic cross section is considered as an unwanted background, which increases considerably the requirements on the experimental accuracy . In fact the accuracy obtained in recent total photoabsorption measurements is not worse than a few tenths of a percent 1 Z). Therefore, independently of the experimenter's interest these measurements give directly very accurate information on tr in the energy region where the nuclear cross section could be neglected. Furthermore, one should keep in mind that for heavy nuclei tro,~, can be determined with good accuracy from photoneutron experiments using quasimonochromatic photons from positron annihilation in flight 3). Thus, subtracting the photoneutron cross section from tr one can determine the non-nuclear cross section with good accuracy even in the giant resonance energy range. Precise measurements of the total photoabsorption cross sections stimulated more accurate theoretical calculations for the accompanying electromagnetic processes a) since previous theoretical expressions s) were not adequate for an extraction of the nuclear cross sections giving tr in the E1 giant resonance energy range for high-Z elements at an average within 2 ~ too small. In this work the results of the total photoabsorption cross-section measurements for several heavy elementsarepresented. Since theprimaryobjectiveof thesemeasure~
Fig . 1 . The experimental set-up : 1 - synchroton target ; 2 - aluminium beam hardener ; 3 - abetirber ; 4 - cleaning magnet ; 5 - txdmium shield ; 6 - scintillator.
TOTAL PHOTOABSORPTION
99
menu was to obtain the nuclear cross sections in the El giant resonance energy range, the measurements were carried out at energies 7-20 MeV. 2. Experimental procedure The experimental layout is presented in fig. 1 . The measurements were carried out using a 30 MeV synchrotron. The bremsstrahlung beam passed through the aluminium beam hardener and hit the scintillation spectrometer . The beam solid angle was approximately 10 e sr. To compensate the effect of beam parameter variation the measurements were carried out with the absorber alternately inside and outside the beam . The characteristics of the absorbers are given in table 1 . T~et~ 1 The characteristics of the absorbers used in the measurements Isotope
Natural abundance
Average enrichment
Thickness z (8/an )
Form
i sasm iss~ ~ssHo ~seEr ~7a~rb i,eL.If ~eo~ ~e~Ta ie~ W i e~~, ~ es~, "'Au zo9Bi
22.71 20.47 100 27.07 31 .84 27.14 35 .24 99 .99 26.41 30 .64 28 .41 100 100
98 .3 94.5
34.744 33 .402 32.950 36.176 36.878 31 .404 31 .471 31 .952 32.737 29 .765 29 .765 18 .868 37 .230
Sm~O j Gd~0 3 metal Er2 0, Ybz 03 HNO= HtO~ metal metal powder metal powder metal powder metal metal
98 .0 98 .0 91 .6 93 .8 90 .8 95 .6 99 .8
When the absorber was in an oxide form, the water sample containing an equivalent number of oxygen atoms per ctn 2 was put into the beam during the measurement with the absorber outside the beam . The corrections for hydrogen el%cts were introduced during the processing of the experimental data . The experimental procedure is described in more detail elsewhere 2 ) . For most of the absorbers investigated the accuracy of measurements was better than 0.3 %. 3. Resalts and discoeeion The experimental total photoabsorption cross sections are presented in fig. 2 and table 2. The root-mean-square errors are given in table 2. The errors of the experimental points are smaller than the plotted circles in fig. 2.
G. M. GUREVICH et a1.
100 6 (b) 22
21
0 0
00 00
00
0
00
0
0
0
00
20
191
18
17 "~- "°°' ~f'. 1a
o~
~
1a
141
13
12
cp~d~°o°°~~ eP- o
d~~o°up
cP " °°
ee
o
" ehPee " o ô"" ~ e d~ e e e 00°PaP 0~0~ es "" s° O ooo~ar aP o°°o "'" r~ fpeeas d " ~~N oe~ee ô~ePo o " e oo"~e "°g " ee~"e~ "p "° "" e N"d" o O o° "~r0"~ d~ 00 ~JOe°"-" O "e"' Ô " ~ "O o "~
cô
- gr
- m -sm
11
10 10
1a
20
E( MeV)
Fig. 2. Total photoabsorption croaa sedions for Sm, Gd, Ho, Er, Yb, Hf, Te, W, Au, Bi .
It should be pointed out that the existing data on the total photoabsorption cross sections for heavy elements are very scanty . Those are mainly the results obtained with the monoenergetic photons from the (n, y) reaction using nuclear reactor neutrons 6 ''). The energies of these photons are in the range X11 MeV. A oom-
TOTAL PHOTOABSORPTION
101
T~e~ 2
Measured total photoabsorption cross sections at 8, 12, 16 and 20 MeV Total photoabsorption soss section (b)
lsotope ----~e m '°°Gd '°'Ho '°sEr "`Yb ""Hf ~soHf 's'Ta 's=W 's4W isbW
' 9'Au 2°'Bi
8 MeV 12 MeV 16 MeV 20 MeV ----------------------------------10.1 910.027 11 .42010 .032 12 .45010.036 13 .19010.057 10.85210 .026 12 .15110 .033 13 .28110.042 I4.07910.066 11 .55610 .020 13 .19910.027 14.31510.031 15 .37210 .050 12.19510 .026 13 .74310.032 14.99910.039 15 .82210 .052 12.49610.022 14 .19810 .026 16.38410.051 15 .43710 .034 13 .24910.029 15 .00610 .034 16.32010 .043 17.41910.051 13 .26810.030 15 .01710 .033 16.31910 .041 13 .43210.032 I5 .29310 .040 16.55310.046 17.68110 .061 13 .71410.037 15 .68710 .045 16.99310.050 18.13310 .065 13 .58610 .028 16.87210 .048 15 .51910 .034 13 .68010.030 15.59110 .035 16.99110 .040 15 .35410.031 17.31610 .034 19 .04210 .044 20 .31910.068 16.53110.030 18.81710 .035 20 .50810 .051 22 .11810.060
6 (b) 1z
16
1a
14
13
B
10
12
14
la
E(M~V)
Fig. 3. Acomparison between the results of this work for Ta (opencircles) and the data ofthe experiments with monoenergetic photons s) (crosses). Upper curve : calculations 4) ; lower corn : calculations ~.
10 2
G . M . GUREVICH et al.
6 . (b)
1z
16
1a
13
Fig. 4. A comparison between the results of this word for W (open circles) and the data of the experiments with monoenergetîc photons : + ref. 6), x ref. '). Upper curve : calculations') ; lower curve : calculations') .
parison is given in figs . 3 and 4 between the results of this work for Ta and Wand the photoabsorption cross sections from refs. 6''). Open çircles represent the results of this work and crosses the data obtained with the moncenergetic photons. These results are in fairly good agreement with each other. The calculated atomic cross sections from the work of Gimm and Hubbell ¢) are shown (upper solid line) as well as older results of Storm and Israel s) (lower solid line). The direct comparison of the experimental results of this work with the latest atomic cross-section calculations a) is impossible due to the relatively large contribution of the photonuclear processes in the energy region under consideration. What could be used, however, is the fact that for heavy non-fissionable nuclei the photonuclear cross section is nearly totally exhausted by the sum of photoneutron cross sections which can be obtained with good accuracy from experiments with quasimonochromatic photons 3). For the 7-20 MeV energy range ~n~~i
x ~Y, n) + Q(Y, Pn) + a{Y, ~)~
Therefore, the narrow beam attenuation method gives the possibility of obtaining electromagnetic cross sections even in the giant resonance region .
103
TOTAL PHOTOAHSORP'l'ION
10
1b
20
E(M~V)
Fig. 5 . The dilFerences between the total photoabsorption aoss sections of thin work and the photoneutron cross sedions 3) (open circles) . Solid lines : cakvlated atomic cross sections 4 ) .
The differences between the total photoabsorption cross sections of this work and the photoneutron cross sections of ref. s) for Hf, Ta, W, Au and Bi are presented in fig. 5. The calculated atomic cross sections a) are shown by the solid lines . The deviations of the experimental values from the calculations do not generally exceed
10 4
G. M. GUREVICH ct al.
0.4 ~. The agreement of the calculated atomic cross sections with the experimental results indicates that it is preferable to use relativistic form factors to compute the screening correction term in the pair production cross section as was done in ref. 4). Refereaces t) J. Ahrens, H. Horchart, K. H. Czeclc, H. B . Eppkr, D. Gimm, H. Gendrum, M. Krônig, P. Riehe, G. Sits Ram, A Ziegler and B . Ziegler, Nucl . Phys . A2S1 (1975) 479 2) G. M. Gurevich, L. E. Lazareva, V. M. Mazur, G. V. Solodukhov and B. A Tulupov, Nucl . Phys. A273 (1976) 326 3) B. L. Herman, Atomic Data and Nucl . Data Tabks IS (1975) 319 4) H. A Gimm and J. H. Hubbell, NBS Tech . Note 968 (1978) ; and private communication 5) E. Storm and H. I. Israel, Nucl. Data A7 (1970) 365 6) R. Moreh, D. Salzuren and Y. Wand, Phys. Lett. 30B (1969) 336; R. Moroh and Y. Wand, Nucl . Phys. A252 (1973) 423 7) L. C. Henry and T. J. Kauraft, Can. J. Phys. ~9 (1971) 1167
Not to be reproduced by photoprFut ar mian®lm without written pamieeim >tom the publisher
TOTAL PHOTOABSORPTION CROSSSECTIONS FOR HIGH-Z ELEMENTS IN THE ENERGY RANGE 7-20 MeV G . M . GUREVICH, L. E . LAZAREVA, V . M . MAZUR, S . Yu. MERKULOV and G . V. SOLODUKHOV
Institutejor Nuclear Research, Academy of Sciences, Mosrnw, USSR Received 24 October 1979
A6e
E
NUCLEAR REACTIONS '~Sm, '' 6 Gd, ' bs13o, ' 6 BEr, "`Yb, lea . iao~ ~e~ Ta~ ~e~, iaa, is6W, i9~Au. ~o9B i(y ~~ E = 7-20 MeV ; measured total o(E~ ; deduced electromagnetic o. Enriched, natural targets.
1. Introtlncdion
Täe use of the electromagnetic probes, i.e. photons and electrons for the investigation of nuclear structure has certain advantages in comparison with the use, for example, of hadron probes. The form of the Hamiltonian of the electromagnetic field nucleon system interaction is well known, and therefore the use oftheelectromagnetic probes provides us with matrix elements giving direct information on nuclear wave functions. T1iis information has been essential for the development ofnuclear models, and good knowledge ofthe quantum numbers associated with specific multipoles has notably simplified the analysis of the fundamental modes of nuclear motion . All this explains the fact that experiments with electron and real photon beams are currently being carried out in a large number of laboratories throughout the world Although the primary purpose in each of these experiments is to obtain nuclear information, that is not always the sole information obtained. A characteristic example is the investigation of the total photoabsorption cross sections. The narrow beam attenuation method used in these experiments is based on the measurements of the y-beam attenuation coefficients for an absorber of precisely known thickness. In this case the e~cperimental cross section tr is a sum of the nuclear absorption cross section tro ~t and the cross sections of pure electromagnetic processes iphotaelectric effect aph, Compton effect try, pair production in the Coulomb field of the nucleus 97
98
G . M . GUREVICH et al.
Qp and pair production in the electron field tri): tr = Qnoo~+Qu = (1/A)lII(1Vo(~/N(~), tr = Qph+QC+Up+tT where No(~ and N(E~ are the numbers of photons in a given energy bin with and without the absorber in the y-beam respectively, and A is a coefficient indicating the number of the absorber atoms per cm2. Unfortunately, the photonuclear cross section does not exceed approximately 5 ~ of tr even in the giant resonance maximum and its contribution decreases with increasing Z. Thus in these experiments the electromagnetic cross section is considered as an unwanted background, which increases considerably the requirements on the experimental accuracy . In fact the accuracy obtained in recent total photoabsorption measurements is not worse than a few tenths of a percent 1 Z). Therefore, independently of the experimenter's interest these measurements give directly very accurate information on tr in the energy region where the nuclear cross section could be neglected. Furthermore, one should keep in mind that for heavy nuclei tro,~, can be determined with good accuracy from photoneutron experiments using quasimonochromatic photons from positron annihilation in flight 3). Thus, subtracting the photoneutron cross section from tr one can determine the non-nuclear cross section with good accuracy even in the giant resonance energy range. Precise measurements of the total photoabsorption cross sections stimulated more accurate theoretical calculations for the accompanying electromagnetic processes a) since previous theoretical expressions s) were not adequate for an extraction of the nuclear cross sections giving tr in the E1 giant resonance energy range for high-Z elements at an average within 2 ~ too small. In this work the results of the total photoabsorption cross-section measurements for several heavy elementsarepresented. Since theprimaryobjectiveof thesemeasure~
Fig . 1 . The experimental set-up : 1 - synchroton target ; 2 - aluminium beam hardener ; 3 - abetirber ; 4 - cleaning magnet ; 5 - txdmium shield ; 6 - scintillator.
TOTAL PHOTOABSORPTION
99
menu was to obtain the nuclear cross sections in the El giant resonance energy range, the measurements were carried out at energies 7-20 MeV. 2. Experimental procedure The experimental layout is presented in fig. 1 . The measurements were carried out using a 30 MeV synchrotron. The bremsstrahlung beam passed through the aluminium beam hardener and hit the scintillation spectrometer . The beam solid angle was approximately 10 e sr. To compensate the effect of beam parameter variation the measurements were carried out with the absorber alternately inside and outside the beam . The characteristics of the absorbers are given in table 1 . T~et~ 1 The characteristics of the absorbers used in the measurements Isotope
Natural abundance
Average enrichment
Thickness z (8/an )
Form
i sasm iss~ ~ssHo ~seEr ~7a~rb i,eL.If ~eo~ ~e~Ta ie~ W i e~~, ~ es~, "'Au zo9Bi
22.71 20.47 100 27.07 31 .84 27.14 35 .24 99 .99 26.41 30 .64 28 .41 100 100
98 .3 94.5
34.744 33 .402 32.950 36.176 36.878 31 .404 31 .471 31 .952 32.737 29 .765 29 .765 18 .868 37 .230
Sm~O j Gd~0 3 metal Er2 0, Ybz 03 HNO= HtO~ metal metal powder metal powder metal powder metal metal
98 .0 98 .0 91 .6 93 .8 90 .8 95 .6 99 .8
When the absorber was in an oxide form, the water sample containing an equivalent number of oxygen atoms per ctn 2 was put into the beam during the measurement with the absorber outside the beam . The corrections for hydrogen el%cts were introduced during the processing of the experimental data . The experimental procedure is described in more detail elsewhere 2 ) . For most of the absorbers investigated the accuracy of measurements was better than 0.3 %. 3. Resalts and discoeeion The experimental total photoabsorption cross sections are presented in fig. 2 and table 2. The root-mean-square errors are given in table 2. The errors of the experimental points are smaller than the plotted circles in fig. 2.
G. M. GUREVICH et a1.
100 6 (b) 22
21
0 0
00 00
00
0
00
0
0
0
00
20
191
18
17 "~- "°°' ~f'. 1a
o~
~
1a
141
13
12
cp~d~°o°°~~ eP- o
d~~o°up
cP " °°
ee
o
" ehPee " o ô"" ~ e d~ e e e 00°PaP 0~0~ es "" s° O ooo~ar aP o°°o "'" r~ fpeeas d " ~~N oe~ee ô~ePo o " e oo"~e "°g " ee~"e~ "p "° "" e N"d" o O o° "~r0"~ d~ 00 ~JOe°"-" O "e"' Ô " ~ "O o "~
cô
- gr
- m -sm
11
10 10
1a
20
E( MeV)
Fig. 2. Total photoabsorption croaa sedions for Sm, Gd, Ho, Er, Yb, Hf, Te, W, Au, Bi .
It should be pointed out that the existing data on the total photoabsorption cross sections for heavy elements are very scanty . Those are mainly the results obtained with the monoenergetic photons from the (n, y) reaction using nuclear reactor neutrons 6 ''). The energies of these photons are in the range X11 MeV. A oom-
TOTAL PHOTOABSORPTION
101
T~e~ 2
Measured total photoabsorption cross sections at 8, 12, 16 and 20 MeV Total photoabsorption soss section (b)
lsotope ----~e m '°°Gd '°'Ho '°sEr "`Yb ""Hf ~soHf 's'Ta 's=W 's4W isbW
' 9'Au 2°'Bi
8 MeV 12 MeV 16 MeV 20 MeV ----------------------------------10.1 910.027 11 .42010 .032 12 .45010.036 13 .19010.057 10.85210 .026 12 .15110 .033 13 .28110.042 I4.07910.066 11 .55610 .020 13 .19910.027 14.31510.031 15 .37210 .050 12.19510 .026 13 .74310.032 14.99910.039 15 .82210 .052 12.49610.022 14 .19810 .026 16.38410.051 15 .43710 .034 13 .24910.029 15 .00610 .034 16.32010 .043 17.41910.051 13 .26810.030 15 .01710 .033 16.31910 .041 13 .43210.032 I5 .29310 .040 16.55310.046 17.68110 .061 13 .71410.037 15 .68710 .045 16.99310.050 18.13310 .065 13 .58610 .028 16.87210 .048 15 .51910 .034 13 .68010.030 15.59110 .035 16.99110 .040 15 .35410.031 17.31610 .034 19 .04210 .044 20 .31910.068 16.53110.030 18.81710 .035 20 .50810 .051 22 .11810.060
6 (b) 1z
16
1a
14
13
B
10
12
14
la
E(M~V)
Fig. 3. Acomparison between the results of this work for Ta (opencircles) and the data ofthe experiments with monoenergetic photons s) (crosses). Upper curve : calculations 4) ; lower corn : calculations ~.
10 2
G . M . GUREVICH et al.
6 . (b)
1z
16
1a
13
Fig. 4. A comparison between the results of this word for W (open circles) and the data of the experiments with monoenergetîc photons : + ref. 6), x ref. '). Upper curve : calculations') ; lower curve : calculations') .
parison is given in figs . 3 and 4 between the results of this work for Ta and Wand the photoabsorption cross sections from refs. 6''). Open çircles represent the results of this work and crosses the data obtained with the moncenergetic photons. These results are in fairly good agreement with each other. The calculated atomic cross sections from the work of Gimm and Hubbell ¢) are shown (upper solid line) as well as older results of Storm and Israel s) (lower solid line). The direct comparison of the experimental results of this work with the latest atomic cross-section calculations a) is impossible due to the relatively large contribution of the photonuclear processes in the energy region under consideration. What could be used, however, is the fact that for heavy non-fissionable nuclei the photonuclear cross section is nearly totally exhausted by the sum of photoneutron cross sections which can be obtained with good accuracy from experiments with quasimonochromatic photons 3). For the 7-20 MeV energy range ~n~~i
x ~Y, n) + Q(Y, Pn) + a{Y, ~)~
Therefore, the narrow beam attenuation method gives the possibility of obtaining electromagnetic cross sections even in the giant resonance region .
103
TOTAL PHOTOAHSORP'l'ION
10
1b
20
E(M~V)
Fig. 5 . The dilFerences between the total photoabsorption aoss sections of thin work and the photoneutron cross sedions 3) (open circles) . Solid lines : cakvlated atomic cross sections 4 ) .
The differences between the total photoabsorption cross sections of this work and the photoneutron cross sections of ref. s) for Hf, Ta, W, Au and Bi are presented in fig. 5. The calculated atomic cross sections a) are shown by the solid lines . The deviations of the experimental values from the calculations do not generally exceed
10 4
G. M. GUREVICH ct al.
0.4 ~. The agreement of the calculated atomic cross sections with the experimental results indicates that it is preferable to use relativistic form factors to compute the screening correction term in the pair production cross section as was done in ref. 4). Refereaces t) J. Ahrens, H. Horchart, K. H. Czeclc, H. B . Eppkr, D. Gimm, H. Gendrum, M. Krônig, P. Riehe, G. Sits Ram, A Ziegler and B . Ziegler, Nucl . Phys . A2S1 (1975) 479 2) G. M. Gurevich, L. E. Lazareva, V. M. Mazur, G. V. Solodukhov and B. A Tulupov, Nucl . Phys. A273 (1976) 326 3) B. L. Herman, Atomic Data and Nucl . Data Tabks IS (1975) 319 4) H. A Gimm and J. H. Hubbell, NBS Tech . Note 968 (1978) ; and private communication 5) E. Storm and H. I. Israel, Nucl. Data A7 (1970) 365 6) R. Moreh, D. Salzuren and Y. Wand, Phys. Lett. 30B (1969) 336; R. Moroh and Y. Wand, Nucl . Phys. A252 (1973) 423 7) L. C. Henry and T. J. Kauraft, Can. J. Phys. ~9 (1971) 1167