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TOFI
ORNL P
1419
.
.
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.
MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS -1963
.
.
LEGAL NOTICE
This report was prepared as an account of
Government sponsored work. Neither the
United States, nor the Commission, nor any
person acting on behalf of the Commission:
A. Makes any warranty or representa-
tion, expressed or implied, with respect to
the accuracy, completeness, or usefulness
of the information contained in this report,
or that the use of any information, appa-
ratus, method, or process disclosed in this
report may not infringe privately owned
rights; or
B. Assumes any liabilities with respect
to the use of, or for damages resulting from
the use of any information, apparatus,
method, or process disclosed in this report.
As used in the above, “person acting on
behalf of the Commission” includes any em-
ployee or contractor of the Commission, or
employee of such contractor, to the extent
that such employee or contractor of the
Commission, or employee of such contractor
prepares, disseminates, or provides access
to, any information pursuant to his employ-
ment or contract with the Commission, or
his employment with such contractor.
.
ORNU-P-1419
(Paper presented at the International Conference on the Internal
onversion Process, Vanderbilt University, Nashville, Tennessee,
May 10-13, 1965)
CONF-650525-57
JUL 20 1965
s roport, or that the use
LEGAL NOTICE -
Tais report was prepared u aa account of Goversiacot spuogored work. Neither the United
seatos, por the Commiuloa, oor way per a acud oo bebell of the coamula:
A. Makes vynrraty or reprowauauan, exprenod or implied, with respect to the acou-
rny, completeness, or urlaloon of the talcrmina coatalood lo
of way information, apparatus, method, or procos, discloned to the report my not lofringe
B. AsR003 any latives with respect to the wee of, or for damages resuuns from the
've of Lay laloration, oppurtu, dethod. or proceu disclosed to be report.
Au urod in tbe adoro, "parko atto co be ball of the Coomlusion" includes by em-
ployoc or coatractor of the Conclusion, or onployee of such coatractor, to the extent that
such employoe or coaluctor of the Commiuko, or employee of such coauructor prepares,
dienominator, or provides seculo, any lalorquatica pureaat to do coployment or coolract
with the Commiulov, or his espayment wild such contractor.
princely owned ricco; or
Information on Conversion Coefficients from Coulomb Excitati I HAI
and Life-Time Measurements*
P. H. Stelson
Oak Ridge National laboratory
Oak Ridge, Tennessee
Several pepers have pointed out that information on total internal
conversion coefficients for E2 transitions can be obtained from the com-
parison of B(E2)'s found from life-time measurements with those obtained
from Coulomb excitation results (either inelastic scattering, cross sections
or y-ray yields). From such a comparison for 10 rare-earth nuclei,
Fossån and Herskind' concluded that the experimental a's differed from the
theoretical a's by an average of (12 + 7)%. Bernstein? had previously
suggested that the deviations from theory exhibit an N/Z dependence. From
a similar comparison for 19 rare-earth nuclei, Elbek
concluded that there
was an average 9% difference between experimental and theoretical a's.
On the other hand, Goldring and Vager,“ who used a different set of
experimental information, concluded there was agreement between theoretical
and experimental a's for several rare-earth nuclei. Quite recently,
Pancholi? has analyzed the available experimental information and also
concludes that there is agreement with theory to within the existing experi-
mental uncertainties.
In the course of compiling a list of B( E2) values for nuclei, we
have once again studied this problem of the E2 conversion coefficients
since it is desirable to use the large amount of precise information avail-
able from lifetime measurements to supplement the Coulomb excitation
Research sponsored by the U.S. Atomic Energy Commission under contract
with the Union Carbide Corporation.
PATENT CLEARANCE OBTAINED. RELEASE TO
THE PUBLIC IS APPROVED. PROCEDURES
ARE ON FILE IN THE RECEIVING SECTICN.
- 2 -
results. Comparisons between theory and experiment are made for the
rare earth nuclei and for the very heavy nuclei. The extraction of B( E2)'s
from life-time measurements is an especially important problem for the
very heavy nuclei since there are only a few suitable targets in this
region for making Coulomb excitation measurements.
In Fig. 1 we summarize the quantities obtained from the three types
of measurements and indicate how one obtains experimental values for
(1. + 0). A direct measurement of the inelastically scattered particles
which result from Coulomb excitation (method A) allows the extraction of
a B( E2) which does not depend on the knowledge of a. Furthermore, the
results are quite accurate because the experimental arrangement can be
calibrated by the assumption that the strong elastic scattering peak is
given by the Rutherford cross section. Elbek and co-workers at Copenhagen
have used this method to obtain accurate B(E2) values for most of the rare
earth nuclei, The absolute error in B(F2) is typically 5%. Recently,
Friedman et al. reported some very useful new measurements based on the
inethod A for several uranium and plutonium nuclei.
From the knowledge of the mean life of the 2+ state one can extract
the quantity (1 + a)B(E2) (method B). A typical mean life in the rare earth
is 2 ns and absolute accuracies for mean-life determinations in recent
years are 2 to 5%. One should recall that the mean life for an E2 transition
also depends on the energy of the transition to the fifth power. Fortunately,
for most rare-earth nuclei the y-ray energies are known to 0.1 to 0.2% and
hence little error is introduced from the energy uncertainty. The typical
mean life of the 2+ state for very heavy nuclei is only a fraction of a
nanosecond and, as a result, the accuracy of mean-life measurements for
- 3 -
heavy nuclei is not as high as those for the rare earth nuclei; 10% is a
characteristic error.
Finally, from a measurement of the y-ray yield resulting from
Coulomb excitation (method C), one extracts the quantity B(E2)/(1 + a),
Measurements of this quantity are not as extensive as those for methods A
and B and, furthermore, the accuracy is poorer (typically 15%). However,
in comparing Y-ray yields with life-time measurements, one finds (1 + a)"
and therefore the error in (1 + a) is roughly 1/2 che error from the combi -
nation of the errors in the quantities B and C.
The experimental a's deduced by the methods just summarized are
now to be compared to theoretical values for a. Just what does one take
for the theoretical a? In table I we have listed some theoretical a values
quoted in the recent literature for 5 rare earth nuclei. An inspection of
the table reveals a considerable spread in the values quoted for theoretical
a's. On the one hand, the 7 values quoted for +3°ga show only a 3%
variation, whereas those for 152ga show 10% spread. The other three cases
have 5 to 8% variation. It is a little difficult to account for this
much variation in the quoted values for theoretical a's. The differences
between the theoretical values of Rose' and those of Sliv and co-workers
for (one + Cy) for F2 transitions in the energy range of interest are, on.
the average, about 2% (sliv's values are the higher ones). Good theoretical
conversion coefficients for the higher shells are not yet available and
one must therefore depend on the limited experimental information to estimate
the contributions from the higher shells. It is customary to take either
0.30 or 0.330 for this contribution. In table II we have listed con-
version coefficients for 3 representative rare-earth nuclei and we indicate
- 4-
the percentage contribution from the various shells. For _'*Yb, a 2%
difference in a results if one uses 0.30, instead of 0.3304: A final
source of variation in quoted theoretical values for a is the reading
0
error caused by the necessity for interpolatir.g from values listed in
tables for one and Oly. It would be desirable to have a finer mesh of
theoretical values.
The theoretical a values which we have used were obtained by
taking Sliv's values for all and Oy and by taking the contribution of the
higher shells as 0.3304. These theoretical values are listed in the last
column of table III (rare-earth nuclei) and the third column of table VII
(very heavy nuclei).
It is interesting to compare our values to those
of Fossan and Herskind who used an identical prescription for theoretical
a values. For the 10 rare-earth nuclei which they have given values, the
two sets of values differ on the average by less than 1/2%.
In table III we have summarized the values taken for the mean life
and energy for 23 2+ states in rare-earth nuclei. In some cases there
are as many as 7 reported measurements of a given mean life. The available
measurements for 6 nuclei are shown in Figs. 2 and 3. We also show the
weighted average value we have used. In general, the weighting values are
taken as inversely proportional to the quoted error rather than inversely
proportional to the square of the quoted error, which is the statistically
correct procedure. We believe the weighting procedure used gives more
reliable average values. Furthermore, the assigned error to the weighted
value is never taken to be less than the smallest error assigned to an
individual measurement in the set being averaged. Finally, in cases where
there are only two accurate measurements which disagree, the assigned
- 5-
error is large enough to cover the extent of the disagreement (see ***Er
in Fig. 2).
Table IV summarizes the information obtained on 23 rare-earth nuclei
from the application of methods A, B and C outlined above.
The values
deduced for anat moon from the use of quantities A and B are plotted in
Fic. 4 28 open circles.
The corresponding values given by Fossan and
Herskind are shown as solid dots. In several cases, our values are somewhat
different from those of Fossan and Herskind. The largest difference is
that for 102w and there are lesser differences for 170Hf, 17°yb, 150ga and
1525m. For all these cases our values for exp/atheor are lower. These
differences are caused by different values taken for the mean life. Fossan
and Herskind used their own measurements whereas we have taken weighted
average values of all the available measurements. However, for the 3 cases
which exhibit a large positive value for dexolatheor, viz. 154ga, loºdy
ana 10+Er, we agree with values given by Fossan and Ferskind.
It is interesting to note that there are a few rare-earth nuclei
lo
in which direct measurements of a have been reported. Lu and Dingus
have reported results with quite small errors for 1525m, 154Ga and 160dy.
Their values for dex/theor are 0.96 + .01, 0.99 + .02, and 0.95 + .03
for 1525m, 154ga ana 15° Dy, respectively. Lewin1 has reported a similar
type of measurement for 16°Dy and finds @exo/Otheor is 1.00 +.03, in
agreement with the result of Lu and Dingus.
Recalling that the values for a ratheon from measurements A and
B (see Fig. 4) gave 1.22 + . 16 and 1.19 + .10, respectively, for +54d and
Dy, we see there is not good agreement with the direct measurements,
but this disagreement is not severe. For these two cases, most of the
-
-6-
error in the indirect determination is due to the error assigned by
Elbek and co-workers to the direct measurement of the B(E2). The errors
they assign to tnese two cases are somewhat larger than their usual error
because of additional experimental difficulties experienced for these
targets. Since it seems unlikely that the mean-life values for these
two nuclei are in error by more than 3 or 4% (see Figs. 2 and 3), one
concludes that the Copenhagen values for B( E2) are possibly about 10% and
15% low for +3460 and 4°°Dy, respectively, if one accepts the correctness
of the direct measurements of a. Alternatively, there could be a
systematic error in the direct measurements for a.
Taking all the information on the determination of a values by
the indirect methods for rare-earth nuclei, we have carried out least
squares analyses to see how the total set of experimental values compared
with our set of theoretical values. The results of these statistical
analyses are given in table V.
The best values for
1
B. (equal to
ex
) are shown in colum 2 for the three possible
1 + Otheor
combinations of experimental quantities. It is seen that the B, values
derived from the 3 possible combinations are in approximate agreement.
The most precise Bz, based on the A, B combination, indicates remarkably
good agreement between the theoretical and experimental sets of a. The
combinations A, C and B, C suggest that the theoretical a's are a little
higher than the experimental a's. If we combine the three B; values, we
find that the experimental and theoretical sets of a values agree to
within 1
The errors given to the B, values in table V must be treated with
some caution. These errors result from a statistical analysis of the
-7-
errors associated with the input quantities. Certain types of systematic
errors would not be properly taken into account. However, since each of
the possible combinations is independent of one of the three types of
measurements, the fact that all 3 Bvalues are in approximate agreement
suggests that there are no important systematic errors in the original
measurements.
The above results indicate that there is, on the average, good
agreement between experimental and theoretical a values. There might
still be individual nuclei which have anomolous a values (such as an N/?
dependence). One mighi expect this to be revealed by a large "x2" value
upon application of a "x2" test. A large "x2" value could also be the
result of optimistic error assignments. The results of "x2" tests are
given in tabīe V for the 3 possible combinations. The most accurate
results (combination A, B) give a "x-" value which indicates that the
observed fluctuations are about what one would expect from the errors
assigned to the original data. The less accurate A, C and B, C combinations
give "x"" values which are somewhat large from a statistical point of view.
In summary, we have tried to review all the available information
on total E2 conversion coefficients for even-even 2+ - O transitions for
rare-earth nuclei.
Our own interpretation of these results is, first,
there is no very compelling evidence for the existence of anomolous
individual a values. Second, our set of theoretical a values show an
average good agreement with experimental a values. To assign an absolute
accuracy to this agreement is difficult; our best judgment is that the
absolute accuracy is 3 to 4%.
Next, we consider the situation for the very heavy nuclei. Until
recently, there were only two measurements of type A available; those for
- 8 -
232th and 23&y (ref. 3). Results are now also available for 2340, 236,
and 24°ru (ref. 6). The corresponding quantities of type B are summarized
in table VI in the last colum. The energies used are given in column 2
and the half-lives of Bell, et al. are given in column 3. The resulting
experimental a values are given in column 2 of table VII. The theoretical
a values (taken to be 1.33%) are given in column 3 of table VII.
The
last column shows the ratio anather and the associated error. For
these 5 heavy nuclei with their very large El conversion coefficients, one
finds there is approximate agreement between experimental and theoretical
a values. The absolute accuracy of this agreement is about 1.0%. A least
squares fit indicates that, on the average, the experimental values are
7% lower than the thecretical values.
-9-
References
1. D. B. Fossan and B. Herskind, Nucl. Phys. 40, 24 (1963).
2. E. M. Bernstein, Phys. Rev. Letters 3, 100 (1962).
B. Elbek, "Determination of Nuclear Transition Probabilities by
Coulomb Excitation," Copenhagen, Ejnar Munksgaards Forlag (1963).
4. G. Goldring and 2. Vager, Nucl. Phys. 26, 250 (1961).
5. S. C. Pancholi, to be published in Nucl. Phys.
ܩܶ_h
6. A. M. Friedman, J. R. Erskine and T. H. Braid, Bull, Ain. Phys.
Soc. 10, 540 (1965).
7. M. E. Rose, Internal Conversion coefficients (North-Holland Publishing
Co., Amsterdam, 1958).
8. L. A. Sliv and I. M. Band, Internal-conversion coefficient tables
circulated by the University of Illinois.
9. Individual references are given in the B(E2) compilation to be
published (P. H. Stelson and L. Grodzins).
10. D. C. Lu and R. S. Dingus, Phys. Lette.s 3, 44 (1962).
11. W. H. G. Lewin, Reported at International Conference on the Internal
Conversion Process, Vanderbilt University, May 10-13 (1965).
12. R. E. Bell, S. Bjørnholm and J. C. Severiens, Mat. Fys. Medd.
Dan. Vid. Selsk. 32, No. 12 (1960).
- 10 -
Table Captions
Table I.
Theoretical values quoted in the literature for me
Table II.
Total theoretical conversion coefficients for 3 representative
rare-earth nuclei.
The percentage contribution from the
different shells is also given.
Table III. Columns 2 and 3 summarize the energies and weighted mean
life values taken for 23 rare-earth nuclei. The last colum.
shows the theoretical total internal conversion coefficients
which we have used to compare with the experimental values.
Table IV. Columns 2, 3 and 4 summarize the quantities A, B and C,
respectively, (see Fig. 1) for the 23 rare-earth nuclei.
The units on B(E2) are understood to be 10-40 cm-e?.
Summary of the results of a statistical analysis of the 3
Table V.
possible combinations (A,B), (B,C) and (A,C) for obtaining
experimental total 12 conversion coefficients.
Table VI.
Summary of the energy (column 2), half-life (column 3)
and quantity B (column 4) for 5 heavy even-even nuclei.
Tahle VII. Summary of experimental a (column 2), theoretical a (column
3) and the ratio andat noon for five 2+ - O+ transitions in
heavy nuclei,
ORNL DWG. 65-4949
TABLE !
12
THEORETICAL VALUES QUOTED IN THE
LITERATURE FOR a.
156Gd 152Gd 160Dy 162Dy 166Er
3.95 1.21 4.75 6.09 6.91
3.93 1.23 4.62 5.96 6.64
3.93 1.13 4.60 6.09 6.73
3.97 1.20 4.43
6.55
3.84 1.21 4.62 6.27 6.86
3.93 1.24 4.75
5.81
ORNL DWG. 65-4946
TABLE 11
Nucleus
154 Gd
168Yb
174Yb
OT
ay aK
1.21 54%
5.46 24%
9.49 16%
al
34%
57%
63%
M+ N +...
12%
19%
21%
- 13 -
Table III
Nucleus
E24- )
(key)
Tx 109
Otheor.
0.84
2.22 + 10
2.04 + .05
1.18
150
Sn152
Sn154
Ga154
131 + 1
121.85 + .03
81.99 + .02
123.1 :
89.00
3.95 + .35
1.70 + .04
1
Ga 156
Gal58
Gabo
795
75.3
5.05
1.21
3.95
6.07
7.48
4.75
6.27
9.05
86.7
80.6
73.4
90.5
80.6 +
79.8
1 1 1 ? 고 ​고 ​, 고
​+-+-+-+-+=+=+=+=+=+=+=+=+=+=+=+
고 ​고 ​고 ​고 ​고 ​고 ​고 ​고 ​고
​8
ů i
2 9 8
2 8
+1 +1 +1 +1 +1 +1 ++ + +
" į ii m ů in i į į ý ù ù ù ù
+1 +
8 2 & 8 2 8 8 8 8 2 1 && 885
8
+1 +1 +1 +1 +1 ++1 +1 +1 +
0 8
ù ù ii i
0 8
6 8
8
+1
1 51 3 6 7 4 6 94 6 7 6 8 9 7 54 4 3 0 1
6.86
7.22
6.38
8. 38
9.49
82.1
17.08
Yb17e
YB174
rs176
176
Fir178
Ep180
93.3 +
28746
5.85
4.72
4.68
3.99
2.65
1.84
100.1
187년
​111.1
고
​122.5
고
​- 14 -
Table IV
Nucleus
Bộ )
B( E2)(1 + a)
B(E2)
(1 + a)
Na150
Sm252
+1
1 +
0.59 + 0.09
+1
Smy254
Ga 254
Ga256
+1
1+
+1
0.73 + 0.11
0.64 + 0.10
Ga258
Ga 160
Dy 260
Dy 162
0.70 + 0.11
Dy264
Er 164
2.67 + 0.10
3.46 + 0.12
4.61 + 0.20
3.43 + 0.30
4.53 + 0.25
5.40 + 0.25
5.76 + 0.25
4.46 + 0.30
5.11 + 0.15
5.64 0.25
5.04 + 0.35
5.66 + 0.25
5.72 + 0.20
5.53 + 0.25
5.89 + 0.20
5.75 + 0.25
5.78 + C.20
5.27 + 0.25
4.58 + 0.20
4.35 + 0.20
4.00 + 0.20
3.62 + 0.20
3.57 + 0.25
4.78 + 0.28
7.43 + 0.18
27.90 + 2.50
8.48 + 0.20
23.75 + 0.62
37.1:0 + 1.67
46.30 + 2.55
29.00 + 0.87
36.90 + 1.14
54.90 + 5.49
29.60 + 2.80
45.90 + 1.38
46.30 + 1.53
43.40 + 2.00
59.30 + 3.70
56.80 + 6.20
37.80 + 2.60
37.90 + 1.10
25.90 + 1.03
26.30 + 0.88
20.40 + 0.41
12.75 + 0.47
9.87 + 0.40
0.88 + 0.15
0.90 + 0.15
-1
Er 168
88270
76272
10274
86276
HP276
Hp278
Hp 180
+1
0.65 + 0.10
+1
+
1+
w282
0.76 + 0.13
0.76 + 0.13
0.90 + 0.11
1.22 + 0.12
1.29 + 0.13
1+
+
w284
w86
ORNL DWG. 65-4943
TABLE V
TABLE V
Ratio B:
B/A 1.001 +0.013
[B/C)" 0.925 + 0.046
A/C 0.948 + 0.046
x2
20.5
17.9
14.6
Degrees of
Freedom
23
11
11
ORNL DWG. 65.4947
TABLE VI
Nucleus
E (2+)
1/2 (sec)
B(E2) (1 +a ») (cm^)
x 10-10
x 10-45
232Th
238 U
234U
50 +1
44.7
43.5
45.28
42.9
3.45 + 0.15
2.25 + 0.20
2.66 + 0,20
2.32 = 0.20
1.67 + 0.15
2.52
7.03
6.83
6.41
11.60
236 U
240PU
ORNL DWG. 65-4948
TABLE VII
Nucleus
(ar) Theora Exp/a Theor
232Th
238 U
(az) Exp
260 + 30
558 = 60
702 +
575 120
868 + 78
234 U
80
307
625
717
586
897
0,85 = 0.12
0.89 0.115
0.98 + 0.11
0.98 +0.21
0.97 + 0.09
236 U
240 Pu
- 18 -
Figure Captions
for (1 + a).
Fig. 2. Graphical summary of available mean-life measurements for the
first 2+ states of 154Ga, 5°ga and 104Er. Also shown are the
164
weighted average values used for extracting a values.
Fig. 3. Graphical summary of available mean-life measurements for the
first 2+ state of 16°Dy, 166er, and 1820. Also shown are the
weighted average values used for extracting a values.
Fig. 4. Graphical summary of the values for Qaynar hoor obtained by
the use of the quantities A and B. Our values are shown as
open circles. The values given by Fossan and Herskind are shown
by the solid dots.
ORNL DWG. 65-4944
(A) Inelastic-scattering cross section B(E2)
(B) Lifetime
(1 + a2) B(E2)
(C) Gamma-ray yield
B(E2)/(1 + a)
(1 + a !Exp. from B/A, (B/C]V2, A/C
(1 + a T'Exp
= B;
(1 + at Theor
FIG. 1
ORNL-DWG 65-4781
2+ STATE 154 Gd
2+ STATE 156 Gd
2+ STATE 164 Er
SUNYAR
NATHAN
(1958)
BROWN, et al.
(1954)
BIRK, et al.
(1959)
BIRK, et al.
(1959)
FCSSAN, et al.
(1962)
STIENING, et al.
BELL, et al.
(1959)
CO
de BOER
(1963)
BURDE, et al.
(1963)
BAUER, et al.
(1962)
WEIGHTED
AVERAGE
FOSSAN, et al.
FOSSAN, et al.
(1963)
WEIGHTED
AVERAGE
WEIGHTED
AVERAGE
4.4
1.6 1.8
Tinsec)
2.0
2.2
3.4
1.0
1.4
1.8
tInsec)
2.2
2.6 3.0
T(nsec)
FIG. 2
2.6



ORNL-DWG 65-4782
2+ STATE 160 Dy
2+ STATE 166 Er
2+ STATE 182 w
MCGOWAN
(1952)
MCGOWAN
(1950)
SUNYAR
(1954)
FOSSAN, et al.
(1962)
GRAHAM
(1955)
BIRK, et al.
(1959)
RICHTER, et al.
(1963)
BIRK, et al.
(1959)
BIRK, et al.
(1962)
de BOER
(1963)
BAUER, et al.
(1962)
BASHANDY, et al.
(1963)
BERLOVICH, et al.
(1963)
de BOER
(1963)
FOSSAN, et al.
(1963)
Ll, et al
(1963)
FOSSAN, et al.
(1963)
DORIKENS, et al.
(1965)
WEIGHTED
AVERAGE
LI, et al.
(1963)
SCHARENBERG, et al.
(1964)
WEIGHTED
AVERAGE-
WEIGHTED
AVERAGE-
20
2.4
2.8
(nsec)
3.2
3.6
1.8
3.0
4.2
2.2 2.6
r(nsec)
FIG. 3
4.6 2.0
ilnsec)
2.4




ORNL-DWG 65-3994
Go
КО
Ipold
The
EXP/Q THEOR.
&
+
boy lot
Sm
load
i sm1 sm
w...
Erl
Tool Loy Dy
at
WHW-
TGT
150
160
170
180
A
FIG. 4
----
---
--
-----
----------
-
ILA
9) 161 / 165
DATE FILMED
--
END


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D
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