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Total nuclear photoabsorption cross sections in the region 150 < A < 190
Nuclear Physics A351 (1981)257 - 268; @ North-Holland Publishing Co,, Amsferdam Not to be reproduced
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or microfilm without written permission
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TOTAL NUCLEAR PHOTOABSORPTION CROSS SECTIONS IN THE REGION 150 < A < 190 G. M. GUREVICH, L. E. LAZAREVA, V. M. MAZUR, S. YU. MERKULOV, G. V. SOLODUKHOV and V. A. TYUTIN Institute .fbr Nuclrur Research, Academy of’ Sciences of’ the USSR Received 28 January 1980 (Revised 4 July 1980) Abstract: The curves of the total gamma-absorption cross sections (a,,,) in the El giant resonance energy range for the nuclei ‘%m, ‘lhGd, “‘Ho, lbsEr, ‘74Yb, ‘78Hf, ‘*‘Hf, “ITa, “‘W, ls4W, “‘W and lg7Au have been measured using the absorption method. Parameters of the Lorentz curves fitting the measured cross sections ctn, aregiven. Quadrupole moments (Qo) and nuclear deformation parameters (/I) were obtained. For deformed nuclei in the - 155 < A < - 180 region a violation of the correlation between giant resonance widths (F) and nuclear deformation parameters was found. I’, and fz, the widths of the resonances corresponding to vibrations of nucleons along and across the nuclear deformation axis, were observed to decrease with the increase of A which could be accounted for by the presence of an N = 108 subshell.
NUCLEAR REACTIONS ‘?jrn, “‘Gd, lh5Ho, lh8Er, ‘74Yb, “‘*+‘*“Hf, “‘Ta. 182.184. rsbW ‘“‘AU (7. X). E = 7-20 MeV; measured total ~(0; deduced integrated 0, Lorentzlincpkameters. ‘?Sm, ls6Gd, ‘65Ho. “‘Er, ‘74Yb, ‘78,180Hf, ‘**Ta, 182.184.i86W, lQ7Au deduced /?, QO. r, giant resonance evolution. Enriched, natural targets.
E L
1. Introduction A fair amount of information is at present available on the cross sections for total nuclear absorption of y-quanta ((TV,,)in the region of the El giant resonance obtained by summing up the partial reactions accompanied by the emission of neutrons “). The total cross sections c,, = o(y, n)+a(y, np)+a(y, 2n)+. . . were measured using both bremsstrahlung and “monochromatic” photons obtained by positron annihilation in-flight in high-current linear electron accelerators. Intermediate nuclei with A - 150 [ref. “)I and A - 190 [ref. 3)] have been thoroughly investigated in recent years, whereas the region between A - 150 and A - 190 has been explored much less comprehensively. Therefore it seemed interesting to perform a systematic investigation of this A region. This paper presents the results of measuring the total nuclear absorption cross sections for 150 < A c 190 nuclei in the El giant resonance energy range carried out using the absorption method. The chosen method of direct measurement of 257
258
G. M. Gurevich et al. / Total nuclear photoabsorption
0 ml
is very laborious but it takes into account all the possible partial reaction contributions including (7, y) and (y, r’), which are known only scarcely for heavy nuclei.
2. Experimental pracedure The 35 MeV synchrotron of the Institute for Nuclear Research was used in the experiment. The experimental layout is shown in fig. 1. The absorption coefficients for thick specimens, tl = N,,/N(t) = exp (C&t), (Q is the total y-absorption cross section, n is the number of atoms per 1 g and t is the specimen thickness in g/cm2) were measured using a bremsstrahlung beam with a maximum energy Eymax - 27 MeV (500 ~LSy-flash length and 150 Hz repetition rate). The y-quanta were detected by a NaI(T1) scintillation spectrometer 150 mm in diameter and 100 mm thick. Narrow aperture collimators combined with a large absorber-detector separation made it possible to detect y’s only at angles very close to zero, excluding practically all scattered photons. The energy resolution of the spectrometer in this geometry (the beam diameter on the front wall of the crystal was h 10 mm and the linear angle of beam divergence was f 3 x 10e4 rad) in the 10 to 20 MeV range was about 10 %. The maximum counting rate in the NaI spectrometer was of the order of 500 pps (without a specimen in the beam). The total running time per measured photo-absorption curve was approximately 200 h. The photomultiplier pulses were fed to a pulse analyzer, after the amplifier and discriminator, whence the amplitude spectra were transmitted in small portions to the computer and were corrected using reference y-lines. The positions of these lines were established by means of a thermostable divider at the amplifier input. In order to decrease systematic errors due to the beam parameter variation, measurements were made alternately with and without a specimen in the beam (N and N, respectively) in short series (approximately 2 min per spectrum). A detailed description of the process of measurement is given in refs. 4, ‘). A correction was introduced in the data obtained directly from experiment, which took into account the curve distortion due to the shape of the spectrometer response function. The
Fig. 1. The experimental set-up.
G. M. Gureuich
et al. i Total nuclear
photoabsorption
259
response functions for photons of different energies were determined using the method suggested in ref. 6, from the bremsstrahlung spectra, which were measured for various maximum energies E,,,, in the same geometry. Corrections for response function distortions of the measured cross sections were calculated separately for each absorber. This procedure is described in detail in ref. ‘). The additional cross section uncertainty resulting from such a correction was within 0.05 %. Table 1 lists the basic characteristics of the specimens used. Nearly all specimens were in powder form, packed in thin-walled aluminium containers. When measuring the intensity N, (without a specimen), a similar empty container was placed into the y-beam instead of the specimen. With specimens in oxide form, to measure the intensity N,, a layer of H,O equivalent in the number of oxygen nuclei was put in place of a specimen in addition to the empty container. The isotopically enriched specimens were relatively small in diameter (20 to 25 mm) and the uncertainty of determination of the container internal diameter, within + 0.1 mm, could give an error in the total absorption cross section Q of up to one per cent. TABLE
Main characteristics
Isotope
‘%m “‘Gd 16sHo lhsEr ‘?b “sHf lsoHf ‘sITa 182W
184W lSbW ‘y7AU
Average richment 98.3 94.5 100 98.0 98.0 91.6 93.8 100 90.8 95.6 99.8 100
en-
Form
(%) oxide oxide metal oxide oxide oxide oxide metal metal metal metal metal
powder powder disk powder powder powder powder disk powder powder powder disk
1
of the absorbing
specimens
Weight
Diameter
Thickness
(8)
(mm)
(s/cm’)
170.55 163.96 414.06 177.58 115.86 154.15 154.48 225.86 231.40 210.40 210.40 237.10
25 25 40 25 20 25 25 30 30 30 30 40
Normalisation factor
34.74 33.40 32.95 36.18 36.88 31.40 31.47 31.95 32.74 29.76 29.76 18.87
1.006 1.014 1.013 1.032 1.016 1.028 1.029 1.021 1.020 1.014 1.020 I .030
The nuclear absorption cross section (T,~,is the difference between the total absorption cross section Q, calculated from the directly measured attenuation coefficients, and the sum of electromagnetic cross sections: Compton, pair production and photoelectric (G,,). The calculated values of oat were taken from the tables of Storm and Israel ’ ) +. The total uncertainty of the calculated cross sections in the energy range from 5 to 25 MeV is comparable to the nuclear cross section to be determined. Thus, regardless of the accuracy with which the specimen thickness is determined, + When handling the bulk of the experimental material, atomic cross sections published in ref. 9, were still absent.
the latest more accurate
calculations
of the
260
G. M. Gurevich et al. / Total nuclear photoabsorption
an additional normalization of the atomic cross-section curves is required. The chosen normalization procedure was carried out as follows. For heavy and medium nuclei the most accurate experimental data are available for the photoneutron cross sections in the range from the threshold of the (y, n) reaction (E,) up to the threshold of the (y, 2n) reaction (&J. At 2 or 3 MeV above En and up to E,, the cross section o(y, n) is equal to otO,within several per cent [the (y, y) and (y, y’) reactions], i.e. one might normalize the atomic cross sections using the cross sections o(y, n) known for a given nucleus or a nucleus adjacent to it in this energy range. Such a tentative normalization is common practice. However, the real spread of experimental data obtained by various authors is fairly great and the error in this case can be up to 5&60 mb. In order to reduce errors, the normalization was carried out in the region where otO,decreases drastically, i.e. in the energy range 2 or 3 MeV below or near the threshold E,(a,,,, = a(y, y)+o(y, y’)). The cross sections gtot in this case were determined from the Lorentz curves fitting the photoneutron cross sections. (An analysis of the limited number of data on the cross sections for the (y, y) and (y, y’) reactions shows that the total cross sections for these reactions are well described by Lorentz curves extrapolated to this energy region.) With the same relative spread of experimental data obtained for a(y, n) in l&14 MeV energy range the absolute normalization errors considerably diminish with the decrease of otot. In the 8 to 9 MeV range the normalization accuracy is approximately f 10 mb, being k3 mb at 6 MeV. The normalization errors for the investigated nuclei listed in table 1 were, on average, 3 to 5 mb. The correction factors for the calculated atomic cross sections are given in table 1.
3. Results Fig. 2 presents the total nuclear absorption cross sections gtot obtained using the above procedure for the following twelve isotopes: ’ 54Sm, 156Gd, “j5Ho, 168Er, 174Yb, 178Hf, “‘Hf, ‘*lTa, “‘W, 184W, 186W and lg7Au. The errors shown are the rms values. The solid lines correspond to the best fits of the respective cross sections with two Lorentz curves (one Lorentz curve in the case of lg7Au):
The obtained values of the fit parameters are listed in table 2. For all the nuclei from ‘54Sm to 186W the shape of the cross-section curves is typical for strongly deformed rigid nuclei. The ratios of the areas under the Lorentz curves a2~2/ol~l are given in the eighth column of table 2. According to the OkamotoDanos model 11,12) in the cas e of axially symmetric prolate nuclei the area under the high-energy Lorentz curve should be twice as large as that for the low-energy
261
G. M. Gurecich et al. / Total nuclear photoabsorption
300
200 loo 0 !200
IO
I5
t,naJ
__
2oE,nev
Fig. 2. Total nuclear y-absorption cross sections (CT,,,)measured by the absorption method for “%m, IsbGd, lh5Ho ‘68Er, 1’4Yb I’sHf, lsoHf, “‘Ta, lszW, la4W, ‘86W and “‘AU. Rms error bars are shown.
curve. The average of the a,T,/a,T, values in table 2 is 1.90&0.07. Table 3 gives the ratios of the nuclear ellipsoid axes (k), the deformation parameters (/I) and the intrinsic quadrupole moments (QJ calculated using Danos’ formula 12) + from the ratios of the resonance energies E2 and El given in table 2. Lorentz
+ E,/E, = 0.91 lkf0.089; p z $Jz/S(k’I)//c”~; Q0 = fZriA2’3(k2charge and mass number of the nucleus and r0 = 1.2fm.)
I)//c~‘~. (2 and A are the
G. M.
262
Gurerich
et al. 1 Total
nuclear photoabsorption
TABLE 2
Parameters of Lorentz curves fitting the experimental data on (I,,, Nucleus ’ %rn ’ 56Gd IasH rb8Er r7’Yb ‘=Hf ‘*‘Hf ‘arTa tszw
184W ISbW 19’Au Average error
E, (McV)
(rnij
12.2 12.3 12.3 11.9 12.3 12.2 12.2 12.1 11.9 11.9 12.0 13.7
188 206 202 222 297 291 286 272 267 315 246 535
1.4%
Il.Z”i,
Ez (MeV)
(I&
(M6;)
3.4 3.2 2.3 3.2 2.9 3.1 3.2 3.0 3.2 2.9 3.3 5.2
15.7 15.7 15.2 15.5 15.5 15.5 15.3 15.0 14.8 14.8 14.5
207 220 239 275 320 334 324 316 303 321 332
5.7 5.5 4.8 4.5 4.9 4.9 5.1 5.i 5.6 4.7 5.1
9.3 %
1.50/o
1.85 1.81 2.47 1.73 1.80 1.80 1.81 1.97 2.01 1.65 2.07
8.1 7.7 7.0 7.4 7.1 7.2 7.1 6.8 6.8 6.8 6.4
0.22
0.2 MeV
-9.7 yd
4.6 %
The integral characteristics of the El giant resonance (cl0 = ~~~~~(~)d~, CJ~= &r,,,W)tlIE)d& c-2 = fo,,,(E)( 1/E2)dE) obtained in the energy range 8 to 20 MeV from the experimental values for gtOtare given in table 4. This table also gives the integral characteristics calculated from the Lore&z line parameters of table 2: (zoL= f: o,(E)dE, C_ rL = j: o,(E)(l/E)dE and o_~,_ = f; oL(E)(1/E2)dE (or = oL1 + crL2) +. As can be seen from table 4, the integral cross sections crOexpin the range from 8 to 20 MeV for nuclei with A - 150-170 and A - 170-200 constitute respectively about 90 y0 and 110 y0 of the value given by the classical dipole sum rule [ref. 14)]. The ratios 0,,/0.06 NZ/A constitute, in the same (TOtheor = 0.06 NZ/A nuclear mass ranges, - 1.3 and - 1.5, respectively, which supports the assumption that the fraction of two-particle exchange forces K must be about 0.5 (crO= 0.06 (NZ,/A)( 1 -i- 0.8 K)). The energy-weighted integral cross sections CT_,L calculated from the Lorentz line parameters (column 7) lie slightly lower than the theoretical values (~_r obtained by Levinger Is) within the framework of the shell model with a harmonic oscillator potential (ET_, = 0.36 A4j3 mb) and on the basis of the independent-particle model with a square well of finite depth (G- 1 = 0.30 A4’3 mb). Taking into account the roughness of the model assumptions this discrepancy must not be considered essential. Changes in the proportionality factors in the expressions for G_ lr (column 8) and c._~~ (column 11) for nuclei around A - 170 seem to be more interesting. The values LT._ 2L obtained for A - 170-200 nuclei agree quite well with the Levinger empirical value (T_~ = 3.5 A513 pb/MeV [ref. “)I. The width of the giant resonance. Table 2 (column 9) gives the FWHM values r t For nuclei with A > 150 the cross section a,(El) [ref. r3)].
(T+
I)
giant resonance contribution
is less than * 2 % of the integral
19’Au
I84W ISbW
1s%m l%d ‘65H~ “*Er 174Yb ‘78Hf ‘*‘Hf ‘*‘Ta lSZW
1.302
156(-&j
6.2 +0.3
5.8 +0.8
0.87 0.91 0.78 0.92 1.07 I.11 1.05 1.09 1.09 I.05 1.08 1.10
_. .~~. 2.86 2.95 2.53 3.07 3.82 3.99 4.03 3.81 4.01 3.80 3.95 4.37
7.0 kO.6
0.296 iO.024
1.289
‘14Yb
7.5 +0.8
0.303 + 0.032
I .296
“sHf
1.2 +0.9
0.288 + 0.036
1.281
‘s”Hf
1.29 1.30 1.06 1.26 1.52 1.55 1.56 1.46 1.52 I .43 I .48 1.54
eot.; 0.06h’Z A
l43k4.6 155+4.4 I61 54.3 195h3.4 208k4.9 20054.4 21Ok5.3 2111_5.3 207) 5.3 214k5.3 229k4.2
117+3.5
0-1 (mbf 156 163 I60 197 240 247 250 245 256 251 256 276
C-tL tmb)
0.189 0.194 0. I77 0.212 0.247 0.247 0.246 0.239 0.248 0.240 0.241 0.241
(mb)
K,,,A-43
Integral characteristics of El giant resonance
7.5 kO.7
0.334 + 0.032
1.327
lhsEr
*oL (MeV b)
0.266 iO.036
1.259
lh5Ho
00 exp! 0.06NZ A
0.309 iO.016
1.94kO.06 2.07+0.07 1.86*0.06 2.24kO.06 2.69kO.05 2.85 + 0.07 2.72iO.06 2.84kO.07 2.865 0.07 2.78+0.07 2.90+ 0.07 3.12+0.06
.-
(M~~b)
k3
PO
Nucleus
0.326 kO.017
B
+0.3
1.320
1 “4Sm
k
Nucleus
TABLE3
9. I & 0.3 10.5+0.4 10.1+0.3 12.0+0.3 14.540.3 15.3Ito.4 15.1+0.3 16.0+0.4 16.2kO.4 15.9iro.4 16.2kO.4 18.6+0.4
(mb.?$V-‘)
6.9 +0.7
0.270 i 0.026
I .263
‘sITa
14.9 12.6 16.0 19.2 20.2 20.7 20.0 21.6 20.9 21.6 23.3
14.3
I .268
IWj&l
7.1 kO.8
D_.2L‘4-5’3
6.2 +0.9
0.235 + 0.033
I .229
l8hW
3.30 2.54 3.13 3.54 3.59 3.61 3.45 3.70 3.51 3.56 3.49
3.23
(pb.MeV-‘)
0.214 k 0.032
(rnb~~~-~)
7.2 kO.8
0.278 + 0.030
I.271
lSlW
Ratios of nuclear ellipsoid axes (k), deformation parameters (s) and intrinsic quadrupole moments (QJ, calculated from El/E,
!z
3
+, F i? *o 2 8
s
B
r” cr
c, g CI
264
G. M. Gurevich et al. / Total nuclear photoabsorption
Fig. 3. El giant resonance widths f for oLOtof this work and ref. “) (0) and for o, measured with “monochromatic” Is-beams (Saclay 0. Livermore A). Crosses are the deformation parameters [I (scale on the right).
of the cto, curves for the investigated deformed nuclei with E,,, = $(E, +2E,). Fig. 3 contains the r-values for A > - 140 obtained for crtotin this work and in ref. 16) by the absorption method as well as the widths r obtained in the same A-region for the total photoneutron cross sections (cr, = ~$7, n) +a(?, pn) + a(~, 2n)+. .) measured with “monochromatic” y-beams by the Saclay and Livermore groups +. As is well known, for deformed axially symmetric rigid nuclei (e.g., for 150 < A < 190) the El giant resonance width r should be determined from the widths I-r and r2 of the resonances corresponding to vibrations of nucleons along and across the deformation axis and from the energy separation between these resonances (E, -E,). This separation is a function of deformation and generally determines the resonance broadening with increase of the deformation parameter fi: E,/E,
&-El
= I +0.91 l(k-
1) z
z 80A +p( 1 -$+$‘)
1+0.91 I,$ - const A -+/?.
+ The results of measurements of the total neutron cross sections 4, made with the bremsstrahlung spectrum in the energy region above E,,,,,, have a much lower accuracy. Therefore they are not used in the discussion of the resonance widths I’.
265
G. M. Gureckh et al. / Total nuclear photoahsorption
In fig. 3 the crosses represent p-values (scale on the right) taken from ref. I’). The zero position for p corresponds to r = 4 MeV (spherical nuclei with fi = 0), p z 0.3 being correlated with the curve r = j(f(A) in the vicinity of A = 155. Fig. 3 shows that for nuclei with N 155 < A < - 180, the expected correlation between the deformation parameter fi and the resonance width is violated. While fi remains approximately constant, the widths r decrease rather drastically by a value of about 1 MeV. In the case of strongly deformed nuclei the full resonance width r can be qualitatively represented as a sum r z (+r, ++r,)+(E, -E,). Therefore, to explain the absence of a correlation between r and /I in this atomic mass region the changes in the first and second terms of this sum must be considered separately as a function of A. Fig. 4 gives the differences of the positions of the Lorentz maxima (E, -E,) obtained for 159 < A < 190 nuclei from the data of this work and from the photoneutron cross sections measured with quasimonochromatic y-beams. The crosses represent the deformation parameters B (scale on the right); /I z 0.3 corresponds to the (E2-Ei) values at A - 155. As fig. 4 implies, the experimental values (E, -E,) are in good correlation with the behaviour of fi. Thus, the discrepancy found must be associated with the behaviour of the widths ri and r2. Figs. 5 and 6 give the values dT = r-(E, -E,) and the widths of the Lorentz curves r1 and r2 obtained from cto, and cn of the works used in figs. 3 and 4. Fig. 5 I
1
AL=
EL-E,,
P
MeV
- 0.3 3-
2-
- 42
+
++
+* ++ + +
t
i 1.
3.
150
I.
4.1.
a.
1.
200
II
A
Fig. 4. Differences of the resonance energies (E, - E,) for deformed nuclei for 150 < A K 190. 0, from the otO, curves of this work; l and A, from photoneutron cross section curves measured respectively in Saclay and Livermore; +, deformation parameters /?.
G. M. Gurevich et al. 1 Total nuclear photoabsorption
266
I
I
Cl0
I
160
I
170
I
(80
'!m
A
Fig. 5. Experimental AT = T-(E, -E,) values for deformed A = 1533186 nuclei: 0, this work, Saclay group; A, Livermore group. Ordinates are shifted by 0.15 MeV up and down respectively the Saclay and Livermore data due to the small systematic difference in the absolute values.
0, for
co-
so-
40-
90-
20-
150
I60
170
180
A
Fig. 6. rr and r2 widths of the Lorentz curves fitting clot for deformed 153 5 A s 186 nuclei: q , Saclay group, A, Livermore group, 0, this work. rI values obtained from 6, are superposed on r, values from o,,, of this work for A = 1533154.
G. M. Gurrcich et al. )/_Totul nuclear photoabsorption
267
shows that AT z +r, +$Tz really decreases by about 1 MeV with A increasing from 153 to _ 175. This is confirmed by the behaviour of the experimental values rI and TZ given in fig. 6. The relative changes in the widths U/T, and N,/T, are approximately equal and constitute about 20 %. For nuclei with A > 175 the deformation parameters /3 tend to decrease and, consequently, the Lorentz curves come closer and overlap more strongly. As a result AT becomes somewhat smaller than f(r, + r,). This fact as well as the behaviour of experimental points for AT (plateau in the interval A - 175-186) and for rI and TZ allows one to assume that the resonance widths rI and r2 have a minimum at A - 175 and then slightly increase. As was mentioned earlier ‘*), this observed effect has not been discussed in the literature until recently and no explanation has been suggested. One of the possible causes of such behaviour of the widths r, and r2 may be the presence of a subshell with neutron number N = 108 in this A-range 19,20) (the “‘Hf, 181Ta, lE2W and 1840s nuclei). The decrease of the widths rI and r2 in this case would mean a decrease in the number of possible dipole transitions or a larger concentration of transitions in the resonance energy region due to the filling of the deformed N = 108 subshell. It is interesting to note that it is precisely in the same region of A where the correlation between the El resonance width and the deformation parameter /I is violated the experiments on inelastic electron scattering have revealed specific features in the behaviour of the charge density inside nuclei 21) (166Er and 176Yb). A comparison between the data for the widths rl and r2 presented by different authors (fig. 6) shows that the absolute values of r2 obtained from the absorption cross sections and the photoneutron cross sections on are in good agreement whereas the absolute values of rl obtained from the photoneutron data are 15 to 20 % smaller. This could be explained by the fact that near the (y, n) threshold (down from energies 2-3 MeV above E,) (T, falls off much more steeply than ctot giving a systematic error in the rI values obtained from the photoneutron cross sections c,,.
References I j B. Btilow and B. Forkman, Technical reports series No. 156, Handbook on nuclear activation cross sections, IAEA, Vienna (1974) p. 475; B. L. Berman, Atomic Data and Nuclear Data Tables 15 (1975) 319 2) 0. V. Vasihjev, G. N. Zalesny, S. F. Semenko and V. A. Semenov, Phys. Lett. 30B (I 969) 97; S. F. Semenko, 0. V. Vasilijev and V. A. Semenov, Phys. Lett. 31B (1970) 429; 0. V. Vasilijev, V. A. Semenov and S. F. Semenko, Yad. Fiz. 13 (1971) 463; P. Carlos, H. Beil, R. Bergere, A. Lepretre and A. Veyssiere, Nucl. Phys. Al72 (1971) 437; P. Carlos, H. Beil, R. Bergere, A. Lepretre, A. de Miniac and A. Veyssiere, Nucl. Phys. A225 (I 974) I71 3) A. M. Gorjachev, G. N. Zalesny, S. F. Semenko and B. A. Tulupov, Yad. Fiz. 17 (1973) 463; A. M. Gorjachev and G. N. Zalesny, JETP Lett. 26 (1977) 107 4) G. M. Gurevich, V. A. Zapevalov, M. N. Kostin, L. E. Lazareva and G. V. Solodukhov, INR preprint, Moscow (1971) 5) G. M. Gurevich, V. A. Zapevalov, L. E. Lazareva, G. V. Solodukhov and V. I. Yavorovsky, PTE N4 (1973) 35 6) J. M. Wyckoff and H. W. Koch, Phys. Rev. 117 (1960) 1261
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G. M. Gurerich et al.
)I Total nuclear photoahsorption
7) G. M. Gurevich, V. M. Mazur and G. V. Solodukhov, PTE N2 (1975) 59 8) E. Storm and H. 1. Israel. Nucl. Data Tables 7 (1970) 565 9) L. C. Maximon, NBS Technical Note 955 (1977): H. A. Gimm and J. H. Hubbell, NBS Technical Note 968 (1978) IO) G. M. Gurevich. L. E. Lazareva. V. M. Mazur and G. V. Solodukhov. Proc. 111 Seminar on electromagnetic interactions of nuclei at low and medium energies. Moscow, 1975 (Nauka, Moscow. 1976) p. 60 II) K. Okamoto, Progr. Theor. Phys. 15 (1956) 75; K. Okamoto. Phys. Rev. 110 (1958) 143 12) M. Danos, Nucl. Phys. 5 (1958) 23 13) E. Hayward, B. F. Gibson and J. S. O’Connell, Phys. Rev. CS (1972) 846 14) J. S. Levinger and H. A. Bethe, Phys. Rev. 78 (1950) I15 15) J. S. Levinger, Nuclear photo-disintegration (Oxford University Press, 1960) p. 54 16) G. M. Gurevich. L. E. Lazareva. V. M. Mazur, G. V. Solodukhov and B. A. Tulupov, Nucl. Phys. A273 ( 1976) 326 17) K. E. G. Liibner. M. Vetter and V. Honig, Nuclear Data Tables A7 (1970) 495 18) G. M. Gurevich. L. E. Lazareva, V. M. Mazur and G. V. Solodukhov, JETP Lett. 23 (1976) 411 19) S. G. Nilsson. C. Fu Tsang, A. Sobiczewski, Z. Szymanski, S. Wycech, C. Gustafson, 1. L. Lamm, P. Moller and B. Nilsson. Nucl. Phys. A131 (1969) I 20) J. Jastrzebski, Acta Phys. Pol. B3 (1972) 397 21) W. Bertozzi, Proc. 111 Seminar on electromagnetic interactions of nuclei at low and medium energies, Moscow, I975 (Nauka, Moscow, 1976) p. 213
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TOTAL NUCLEAR PHOTOABSORPTION CROSS SECTIONS IN THE REGION 150 < A < 190 G. M. GUREVICH, L. E. LAZAREVA, V. M. MAZUR, S. YU. MERKULOV, G. V. SOLODUKHOV and V. A. TYUTIN Institute .fbr Nuclrur Research, Academy of’ Sciences of’ the USSR Received 28 January 1980 (Revised 4 July 1980) Abstract: The curves of the total gamma-absorption cross sections (a,,,) in the El giant resonance energy range for the nuclei ‘%m, ‘lhGd, “‘Ho, lbsEr, ‘74Yb, ‘78Hf, ‘*‘Hf, “ITa, “‘W, ls4W, “‘W and lg7Au have been measured using the absorption method. Parameters of the Lorentz curves fitting the measured cross sections ctn, aregiven. Quadrupole moments (Qo) and nuclear deformation parameters (/I) were obtained. For deformed nuclei in the - 155 < A < - 180 region a violation of the correlation between giant resonance widths (F) and nuclear deformation parameters was found. I’, and fz, the widths of the resonances corresponding to vibrations of nucleons along and across the nuclear deformation axis, were observed to decrease with the increase of A which could be accounted for by the presence of an N = 108 subshell.
NUCLEAR REACTIONS ‘?jrn, “‘Gd, lh5Ho, lh8Er, ‘74Yb, “‘*+‘*“Hf, “‘Ta. 182.184. rsbW ‘“‘AU (7. X). E = 7-20 MeV; measured total ~(0; deduced integrated 0, Lorentzlincpkameters. ‘?Sm, ls6Gd, ‘65Ho. “‘Er, ‘74Yb, ‘78,180Hf, ‘**Ta, 182.184.i86W, lQ7Au deduced /?, QO. r, giant resonance evolution. Enriched, natural targets.
E L
1. Introduction A fair amount of information is at present available on the cross sections for total nuclear absorption of y-quanta ((TV,,)in the region of the El giant resonance obtained by summing up the partial reactions accompanied by the emission of neutrons “). The total cross sections c,, = o(y, n)+a(y, np)+a(y, 2n)+. . . were measured using both bremsstrahlung and “monochromatic” photons obtained by positron annihilation in-flight in high-current linear electron accelerators. Intermediate nuclei with A - 150 [ref. “)I and A - 190 [ref. 3)] have been thoroughly investigated in recent years, whereas the region between A - 150 and A - 190 has been explored much less comprehensively. Therefore it seemed interesting to perform a systematic investigation of this A region. This paper presents the results of measuring the total nuclear absorption cross sections for 150 < A c 190 nuclei in the El giant resonance energy range carried out using the absorption method. The chosen method of direct measurement of 257
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G. M. Gurevich et al. / Total nuclear photoabsorption
0 ml
is very laborious but it takes into account all the possible partial reaction contributions including (7, y) and (y, r’), which are known only scarcely for heavy nuclei.
2. Experimental pracedure The 35 MeV synchrotron of the Institute for Nuclear Research was used in the experiment. The experimental layout is shown in fig. 1. The absorption coefficients for thick specimens, tl = N,,/N(t) = exp (C&t), (Q is the total y-absorption cross section, n is the number of atoms per 1 g and t is the specimen thickness in g/cm2) were measured using a bremsstrahlung beam with a maximum energy Eymax - 27 MeV (500 ~LSy-flash length and 150 Hz repetition rate). The y-quanta were detected by a NaI(T1) scintillation spectrometer 150 mm in diameter and 100 mm thick. Narrow aperture collimators combined with a large absorber-detector separation made it possible to detect y’s only at angles very close to zero, excluding practically all scattered photons. The energy resolution of the spectrometer in this geometry (the beam diameter on the front wall of the crystal was h 10 mm and the linear angle of beam divergence was f 3 x 10e4 rad) in the 10 to 20 MeV range was about 10 %. The maximum counting rate in the NaI spectrometer was of the order of 500 pps (without a specimen in the beam). The total running time per measured photo-absorption curve was approximately 200 h. The photomultiplier pulses were fed to a pulse analyzer, after the amplifier and discriminator, whence the amplitude spectra were transmitted in small portions to the computer and were corrected using reference y-lines. The positions of these lines were established by means of a thermostable divider at the amplifier input. In order to decrease systematic errors due to the beam parameter variation, measurements were made alternately with and without a specimen in the beam (N and N, respectively) in short series (approximately 2 min per spectrum). A detailed description of the process of measurement is given in refs. 4, ‘). A correction was introduced in the data obtained directly from experiment, which took into account the curve distortion due to the shape of the spectrometer response function. The
Fig. 1. The experimental set-up.
G. M. Gureuich
et al. i Total nuclear
photoabsorption
259
response functions for photons of different energies were determined using the method suggested in ref. 6, from the bremsstrahlung spectra, which were measured for various maximum energies E,,,, in the same geometry. Corrections for response function distortions of the measured cross sections were calculated separately for each absorber. This procedure is described in detail in ref. ‘). The additional cross section uncertainty resulting from such a correction was within 0.05 %. Table 1 lists the basic characteristics of the specimens used. Nearly all specimens were in powder form, packed in thin-walled aluminium containers. When measuring the intensity N, (without a specimen), a similar empty container was placed into the y-beam instead of the specimen. With specimens in oxide form, to measure the intensity N,, a layer of H,O equivalent in the number of oxygen nuclei was put in place of a specimen in addition to the empty container. The isotopically enriched specimens were relatively small in diameter (20 to 25 mm) and the uncertainty of determination of the container internal diameter, within + 0.1 mm, could give an error in the total absorption cross section Q of up to one per cent. TABLE
Main characteristics
Isotope
‘%m “‘Gd 16sHo lhsEr ‘?b “sHf lsoHf ‘sITa 182W
184W lSbW ‘y7AU
Average richment 98.3 94.5 100 98.0 98.0 91.6 93.8 100 90.8 95.6 99.8 100
en-
Form
(%) oxide oxide metal oxide oxide oxide oxide metal metal metal metal metal
powder powder disk powder powder powder powder disk powder powder powder disk
1
of the absorbing
specimens
Weight
Diameter
Thickness
(8)
(mm)
(s/cm’)
170.55 163.96 414.06 177.58 115.86 154.15 154.48 225.86 231.40 210.40 210.40 237.10
25 25 40 25 20 25 25 30 30 30 30 40
Normalisation factor
34.74 33.40 32.95 36.18 36.88 31.40 31.47 31.95 32.74 29.76 29.76 18.87
1.006 1.014 1.013 1.032 1.016 1.028 1.029 1.021 1.020 1.014 1.020 I .030
The nuclear absorption cross section (T,~,is the difference between the total absorption cross section Q, calculated from the directly measured attenuation coefficients, and the sum of electromagnetic cross sections: Compton, pair production and photoelectric (G,,). The calculated values of oat were taken from the tables of Storm and Israel ’ ) +. The total uncertainty of the calculated cross sections in the energy range from 5 to 25 MeV is comparable to the nuclear cross section to be determined. Thus, regardless of the accuracy with which the specimen thickness is determined, + When handling the bulk of the experimental material, atomic cross sections published in ref. 9, were still absent.
the latest more accurate
calculations
of the
260
G. M. Gurevich et al. / Total nuclear photoabsorption
an additional normalization of the atomic cross-section curves is required. The chosen normalization procedure was carried out as follows. For heavy and medium nuclei the most accurate experimental data are available for the photoneutron cross sections in the range from the threshold of the (y, n) reaction (E,) up to the threshold of the (y, 2n) reaction (&J. At 2 or 3 MeV above En and up to E,, the cross section o(y, n) is equal to otO,within several per cent [the (y, y) and (y, y’) reactions], i.e. one might normalize the atomic cross sections using the cross sections o(y, n) known for a given nucleus or a nucleus adjacent to it in this energy range. Such a tentative normalization is common practice. However, the real spread of experimental data obtained by various authors is fairly great and the error in this case can be up to 5&60 mb. In order to reduce errors, the normalization was carried out in the region where otO,decreases drastically, i.e. in the energy range 2 or 3 MeV below or near the threshold E,(a,,,, = a(y, y)+o(y, y’)). The cross sections gtot in this case were determined from the Lorentz curves fitting the photoneutron cross sections. (An analysis of the limited number of data on the cross sections for the (y, y) and (y, y’) reactions shows that the total cross sections for these reactions are well described by Lorentz curves extrapolated to this energy region.) With the same relative spread of experimental data obtained for a(y, n) in l&14 MeV energy range the absolute normalization errors considerably diminish with the decrease of otot. In the 8 to 9 MeV range the normalization accuracy is approximately f 10 mb, being k3 mb at 6 MeV. The normalization errors for the investigated nuclei listed in table 1 were, on average, 3 to 5 mb. The correction factors for the calculated atomic cross sections are given in table 1.
3. Results Fig. 2 presents the total nuclear absorption cross sections gtot obtained using the above procedure for the following twelve isotopes: ’ 54Sm, 156Gd, “j5Ho, 168Er, 174Yb, 178Hf, “‘Hf, ‘*lTa, “‘W, 184W, 186W and lg7Au. The errors shown are the rms values. The solid lines correspond to the best fits of the respective cross sections with two Lorentz curves (one Lorentz curve in the case of lg7Au):
The obtained values of the fit parameters are listed in table 2. For all the nuclei from ‘54Sm to 186W the shape of the cross-section curves is typical for strongly deformed rigid nuclei. The ratios of the areas under the Lorentz curves a2~2/ol~l are given in the eighth column of table 2. According to the OkamotoDanos model 11,12) in the cas e of axially symmetric prolate nuclei the area under the high-energy Lorentz curve should be twice as large as that for the low-energy
261
G. M. Gurecich et al. / Total nuclear photoabsorption
300
200 loo 0 !200
IO
I5
t,naJ
__
2oE,nev
Fig. 2. Total nuclear y-absorption cross sections (CT,,,)measured by the absorption method for “%m, IsbGd, lh5Ho ‘68Er, 1’4Yb I’sHf, lsoHf, “‘Ta, lszW, la4W, ‘86W and “‘AU. Rms error bars are shown.
curve. The average of the a,T,/a,T, values in table 2 is 1.90&0.07. Table 3 gives the ratios of the nuclear ellipsoid axes (k), the deformation parameters (/I) and the intrinsic quadrupole moments (QJ calculated using Danos’ formula 12) + from the ratios of the resonance energies E2 and El given in table 2. Lorentz
+ E,/E, = 0.91 lkf0.089; p z $Jz/S(k’I)//c”~; Q0 = fZriA2’3(k2charge and mass number of the nucleus and r0 = 1.2fm.)
I)//c~‘~. (2 and A are the
G. M.
262
Gurerich
et al. 1 Total
nuclear photoabsorption
TABLE 2
Parameters of Lorentz curves fitting the experimental data on (I,,, Nucleus ’ %rn ’ 56Gd IasH rb8Er r7’Yb ‘=Hf ‘*‘Hf ‘arTa tszw
184W ISbW 19’Au Average error
E, (McV)
(rnij
12.2 12.3 12.3 11.9 12.3 12.2 12.2 12.1 11.9 11.9 12.0 13.7
188 206 202 222 297 291 286 272 267 315 246 535
1.4%
Il.Z”i,
Ez (MeV)
(I&
(M6;)
3.4 3.2 2.3 3.2 2.9 3.1 3.2 3.0 3.2 2.9 3.3 5.2
15.7 15.7 15.2 15.5 15.5 15.5 15.3 15.0 14.8 14.8 14.5
207 220 239 275 320 334 324 316 303 321 332
5.7 5.5 4.8 4.5 4.9 4.9 5.1 5.i 5.6 4.7 5.1
9.3 %
1.50/o
1.85 1.81 2.47 1.73 1.80 1.80 1.81 1.97 2.01 1.65 2.07
8.1 7.7 7.0 7.4 7.1 7.2 7.1 6.8 6.8 6.8 6.4
0.22
0.2 MeV
-9.7 yd
4.6 %
The integral characteristics of the El giant resonance (cl0 = ~~~~~(~)d~, CJ~= &r,,,W)tlIE)d& c-2 = fo,,,(E)( 1/E2)dE) obtained in the energy range 8 to 20 MeV from the experimental values for gtOtare given in table 4. This table also gives the integral characteristics calculated from the Lore&z line parameters of table 2: (zoL= f: o,(E)dE, C_ rL = j: o,(E)(l/E)dE and o_~,_ = f; oL(E)(1/E2)dE (or = oL1 + crL2) +. As can be seen from table 4, the integral cross sections crOexpin the range from 8 to 20 MeV for nuclei with A - 150-170 and A - 170-200 constitute respectively about 90 y0 and 110 y0 of the value given by the classical dipole sum rule [ref. 14)]. The ratios 0,,/0.06 NZ/A constitute, in the same (TOtheor = 0.06 NZ/A nuclear mass ranges, - 1.3 and - 1.5, respectively, which supports the assumption that the fraction of two-particle exchange forces K must be about 0.5 (crO= 0.06 (NZ,/A)( 1 -i- 0.8 K)). The energy-weighted integral cross sections CT_,L calculated from the Lorentz line parameters (column 7) lie slightly lower than the theoretical values (~_r obtained by Levinger Is) within the framework of the shell model with a harmonic oscillator potential (ET_, = 0.36 A4j3 mb) and on the basis of the independent-particle model with a square well of finite depth (G- 1 = 0.30 A4’3 mb). Taking into account the roughness of the model assumptions this discrepancy must not be considered essential. Changes in the proportionality factors in the expressions for G_ lr (column 8) and c._~~ (column 11) for nuclei around A - 170 seem to be more interesting. The values LT._ 2L obtained for A - 170-200 nuclei agree quite well with the Levinger empirical value (T_~ = 3.5 A513 pb/MeV [ref. “)I. The width of the giant resonance. Table 2 (column 9) gives the FWHM values r t For nuclei with A > 150 the cross section a,(El) [ref. r3)].
(T+
I)
giant resonance contribution
is less than * 2 % of the integral
19’Au
I84W ISbW
1s%m l%d ‘65H~ “*Er 174Yb ‘78Hf ‘*‘Hf ‘*‘Ta lSZW
1.302
156(-&j
6.2 +0.3
5.8 +0.8
0.87 0.91 0.78 0.92 1.07 I.11 1.05 1.09 1.09 I.05 1.08 1.10
_. .~~. 2.86 2.95 2.53 3.07 3.82 3.99 4.03 3.81 4.01 3.80 3.95 4.37
7.0 kO.6
0.296 iO.024
1.289
‘14Yb
7.5 +0.8
0.303 + 0.032
I .296
“sHf
1.2 +0.9
0.288 + 0.036
1.281
‘s”Hf
1.29 1.30 1.06 1.26 1.52 1.55 1.56 1.46 1.52 I .43 I .48 1.54
eot.; 0.06h’Z A
l43k4.6 155+4.4 I61 54.3 195h3.4 208k4.9 20054.4 21Ok5.3 2111_5.3 207) 5.3 214k5.3 229k4.2
117+3.5
0-1 (mbf 156 163 I60 197 240 247 250 245 256 251 256 276
C-tL tmb)
0.189 0.194 0. I77 0.212 0.247 0.247 0.246 0.239 0.248 0.240 0.241 0.241
(mb)
K,,,A-43
Integral characteristics of El giant resonance
7.5 kO.7
0.334 + 0.032
1.327
lhsEr
*oL (MeV b)
0.266 iO.036
1.259
lh5Ho
00 exp! 0.06NZ A
0.309 iO.016
1.94kO.06 2.07+0.07 1.86*0.06 2.24kO.06 2.69kO.05 2.85 + 0.07 2.72iO.06 2.84kO.07 2.865 0.07 2.78+0.07 2.90+ 0.07 3.12+0.06
.-
(M~~b)
k3
PO
Nucleus
0.326 kO.017
B
+0.3
1.320
1 “4Sm
k
Nucleus
TABLE3
9. I & 0.3 10.5+0.4 10.1+0.3 12.0+0.3 14.540.3 15.3Ito.4 15.1+0.3 16.0+0.4 16.2kO.4 15.9iro.4 16.2kO.4 18.6+0.4
(mb.?$V-‘)
6.9 +0.7
0.270 i 0.026
I .263
‘sITa
14.9 12.6 16.0 19.2 20.2 20.7 20.0 21.6 20.9 21.6 23.3
14.3
I .268
IWj&l
7.1 kO.8
D_.2L‘4-5’3
6.2 +0.9
0.235 + 0.033
I .229
l8hW
3.30 2.54 3.13 3.54 3.59 3.61 3.45 3.70 3.51 3.56 3.49
3.23
(pb.MeV-‘)
0.214 k 0.032
(rnb~~~-~)
7.2 kO.8
0.278 + 0.030
I.271
lSlW
Ratios of nuclear ellipsoid axes (k), deformation parameters (s) and intrinsic quadrupole moments (QJ, calculated from El/E,
!z
3
+, F i? *o 2 8
s
B
r” cr
c, g CI
264
G. M. Gurevich et al. / Total nuclear photoabsorption
Fig. 3. El giant resonance widths f for oLOtof this work and ref. “) (0) and for o, measured with “monochromatic” Is-beams (Saclay 0. Livermore A). Crosses are the deformation parameters [I (scale on the right).
of the cto, curves for the investigated deformed nuclei with E,,, = $(E, +2E,). Fig. 3 contains the r-values for A > - 140 obtained for crtotin this work and in ref. 16) by the absorption method as well as the widths r obtained in the same A-region for the total photoneutron cross sections (cr, = ~$7, n) +a(?, pn) + a(~, 2n)+. .) measured with “monochromatic” y-beams by the Saclay and Livermore groups +. As is well known, for deformed axially symmetric rigid nuclei (e.g., for 150 < A < 190) the El giant resonance width r should be determined from the widths I-r and r2 of the resonances corresponding to vibrations of nucleons along and across the deformation axis and from the energy separation between these resonances (E, -E,). This separation is a function of deformation and generally determines the resonance broadening with increase of the deformation parameter fi: E,/E,
&-El
= I +0.91 l(k-
1) z
z 80A +p( 1 -$+$‘)
1+0.91 I,$ - const A -+/?.
+ The results of measurements of the total neutron cross sections 4, made with the bremsstrahlung spectrum in the energy region above E,,,,,, have a much lower accuracy. Therefore they are not used in the discussion of the resonance widths I’.
265
G. M. Gureckh et al. / Total nuclear photoahsorption
In fig. 3 the crosses represent p-values (scale on the right) taken from ref. I’). The zero position for p corresponds to r = 4 MeV (spherical nuclei with fi = 0), p z 0.3 being correlated with the curve r = j(f(A) in the vicinity of A = 155. Fig. 3 shows that for nuclei with N 155 < A < - 180, the expected correlation between the deformation parameter fi and the resonance width is violated. While fi remains approximately constant, the widths r decrease rather drastically by a value of about 1 MeV. In the case of strongly deformed nuclei the full resonance width r can be qualitatively represented as a sum r z (+r, ++r,)+(E, -E,). Therefore, to explain the absence of a correlation between r and /I in this atomic mass region the changes in the first and second terms of this sum must be considered separately as a function of A. Fig. 4 gives the differences of the positions of the Lorentz maxima (E, -E,) obtained for 159 < A < 190 nuclei from the data of this work and from the photoneutron cross sections measured with quasimonochromatic y-beams. The crosses represent the deformation parameters B (scale on the right); /I z 0.3 corresponds to the (E2-Ei) values at A - 155. As fig. 4 implies, the experimental values (E, -E,) are in good correlation with the behaviour of fi. Thus, the discrepancy found must be associated with the behaviour of the widths ri and r2. Figs. 5 and 6 give the values dT = r-(E, -E,) and the widths of the Lorentz curves r1 and r2 obtained from cto, and cn of the works used in figs. 3 and 4. Fig. 5 I
1
AL=
EL-E,,
P
MeV
- 0.3 3-
2-
- 42
+
++
+* ++ + +
t
i 1.
3.
150
I.
4.1.
a.
1.
200
II
A
Fig. 4. Differences of the resonance energies (E, - E,) for deformed nuclei for 150 < A K 190. 0, from the otO, curves of this work; l and A, from photoneutron cross section curves measured respectively in Saclay and Livermore; +, deformation parameters /?.
G. M. Gurevich et al. 1 Total nuclear photoabsorption
266
I
I
Cl0
I
160
I
170
I
(80
'!m
A
Fig. 5. Experimental AT = T-(E, -E,) values for deformed A = 1533186 nuclei: 0, this work, Saclay group; A, Livermore group. Ordinates are shifted by 0.15 MeV up and down respectively the Saclay and Livermore data due to the small systematic difference in the absolute values.
0, for
co-
so-
40-
90-
20-
150
I60
170
180
A
Fig. 6. rr and r2 widths of the Lorentz curves fitting clot for deformed 153 5 A s 186 nuclei: q , Saclay group, A, Livermore group, 0, this work. rI values obtained from 6, are superposed on r, values from o,,, of this work for A = 1533154.
G. M. Gurrcich et al. )/_Totul nuclear photoabsorption
267
shows that AT z +r, +$Tz really decreases by about 1 MeV with A increasing from 153 to _ 175. This is confirmed by the behaviour of the experimental values rI and TZ given in fig. 6. The relative changes in the widths U/T, and N,/T, are approximately equal and constitute about 20 %. For nuclei with A > 175 the deformation parameters /3 tend to decrease and, consequently, the Lorentz curves come closer and overlap more strongly. As a result AT becomes somewhat smaller than f(r, + r,). This fact as well as the behaviour of experimental points for AT (plateau in the interval A - 175-186) and for rI and TZ allows one to assume that the resonance widths rI and r2 have a minimum at A - 175 and then slightly increase. As was mentioned earlier ‘*), this observed effect has not been discussed in the literature until recently and no explanation has been suggested. One of the possible causes of such behaviour of the widths r, and r2 may be the presence of a subshell with neutron number N = 108 in this A-range 19,20) (the “‘Hf, 181Ta, lE2W and 1840s nuclei). The decrease of the widths rI and r2 in this case would mean a decrease in the number of possible dipole transitions or a larger concentration of transitions in the resonance energy region due to the filling of the deformed N = 108 subshell. It is interesting to note that it is precisely in the same region of A where the correlation between the El resonance width and the deformation parameter /I is violated the experiments on inelastic electron scattering have revealed specific features in the behaviour of the charge density inside nuclei 21) (166Er and 176Yb). A comparison between the data for the widths rl and r2 presented by different authors (fig. 6) shows that the absolute values of r2 obtained from the absorption cross sections and the photoneutron cross sections on are in good agreement whereas the absolute values of rl obtained from the photoneutron data are 15 to 20 % smaller. This could be explained by the fact that near the (y, n) threshold (down from energies 2-3 MeV above E,) (T, falls off much more steeply than ctot giving a systematic error in the rI values obtained from the photoneutron cross sections c,,.
References I j B. Btilow and B. Forkman, Technical reports series No. 156, Handbook on nuclear activation cross sections, IAEA, Vienna (1974) p. 475; B. L. Berman, Atomic Data and Nuclear Data Tables 15 (1975) 319 2) 0. V. Vasihjev, G. N. Zalesny, S. F. Semenko and V. A. Semenov, Phys. Lett. 30B (I 969) 97; S. F. Semenko, 0. V. Vasilijev and V. A. Semenov, Phys. Lett. 31B (1970) 429; 0. V. Vasilijev, V. A. Semenov and S. F. Semenko, Yad. Fiz. 13 (1971) 463; P. Carlos, H. Beil, R. Bergere, A. Lepretre and A. Veyssiere, Nucl. Phys. Al72 (1971) 437; P. Carlos, H. Beil, R. Bergere, A. Lepretre, A. de Miniac and A. Veyssiere, Nucl. Phys. A225 (I 974) I71 3) A. M. Gorjachev, G. N. Zalesny, S. F. Semenko and B. A. Tulupov, Yad. Fiz. 17 (1973) 463; A. M. Gorjachev and G. N. Zalesny, JETP Lett. 26 (1977) 107 4) G. M. Gurevich, V. A. Zapevalov, M. N. Kostin, L. E. Lazareva and G. V. Solodukhov, INR preprint, Moscow (1971) 5) G. M. Gurevich, V. A. Zapevalov, L. E. Lazareva, G. V. Solodukhov and V. I. Yavorovsky, PTE N4 (1973) 35 6) J. M. Wyckoff and H. W. Koch, Phys. Rev. 117 (1960) 1261
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G. M. Gurerich et al.
)I Total nuclear photoahsorption
7) G. M. Gurevich, V. M. Mazur and G. V. Solodukhov, PTE N2 (1975) 59 8) E. Storm and H. 1. Israel. Nucl. Data Tables 7 (1970) 565 9) L. C. Maximon, NBS Technical Note 955 (1977): H. A. Gimm and J. H. Hubbell, NBS Technical Note 968 (1978) IO) G. M. Gurevich. L. E. Lazareva. V. M. Mazur and G. V. Solodukhov. Proc. 111 Seminar on electromagnetic interactions of nuclei at low and medium energies. Moscow, 1975 (Nauka, Moscow. 1976) p. 60 II) K. Okamoto, Progr. Theor. Phys. 15 (1956) 75; K. Okamoto. Phys. Rev. 110 (1958) 143 12) M. Danos, Nucl. Phys. 5 (1958) 23 13) E. Hayward, B. F. Gibson and J. S. O’Connell, Phys. Rev. CS (1972) 846 14) J. S. Levinger and H. A. Bethe, Phys. Rev. 78 (1950) I15 15) J. S. Levinger, Nuclear photo-disintegration (Oxford University Press, 1960) p. 54 16) G. M. Gurevich. L. E. Lazareva. V. M. Mazur, G. V. Solodukhov and B. A. Tulupov, Nucl. Phys. A273 ( 1976) 326 17) K. E. G. Liibner. M. Vetter and V. Honig, Nuclear Data Tables A7 (1970) 495 18) G. M. Gurevich. L. E. Lazareva, V. M. Mazur and G. V. Solodukhov, JETP Lett. 23 (1976) 411 19) S. G. Nilsson. C. Fu Tsang, A. Sobiczewski, Z. Szymanski, S. Wycech, C. Gustafson, 1. L. Lamm, P. Moller and B. Nilsson. Nucl. Phys. A131 (1969) I 20) J. Jastrzebski, Acta Phys. Pol. B3 (1972) 397 21) W. Bertozzi, Proc. 111 Seminar on electromagnetic interactions of nuclei at low and medium energies, Moscow, I975 (Nauka, Moscow, 1976) p. 213