X ray energy measurements in 5g yields 4f pionic transitions of Th-232 and U-23

Jenkins, D. A.

Kunselman, A. R.

Powers, R. J.

English

NASA Technical Reports Server

General Disclaimer 
One or more of the Following Statements may affect this Document 
 
 This document has been reproduced from the best copy furnished by the 
organizational source. It is being released in the interest of making available as 
much information as possible. 
 
 This document may contain data, which exceeds the sheet parameters. It was 
furnished in this condition by the organizational source and is the best copy 
available. 
 
 This document may contain tone-on-tone or color graphs, charts and/or pictures, 
which have been reproduced in black and white. 
 
 This document is paginated as submitted by the original source. 
 
 Portions of this document are not fully legible due to the historical nature of some 
of the material. However, it is the best reproduction available from the original 
submission. 
 
 
 
 
 
 
 
Produced by the NASA Center for Aerospace Information (CASI) 
https://ntrs.nasa.gov/search.jsp?R=19710006578 2020-03-11T23:51:07+00:00Z
r ._0
.o
oe
O ^
rr
a (w
..
—	
. ^^>	
- ^ Y = -	 .--	 -	 - -
^	 -
_=
_^	 The 5g^4f Pionic Transition in Th232 and U238 ^s^
N G^ ^ - ¢ -7- v o S/ —
 Q o'6
-	 D. A. Jenkins and R. J. Fonvera
_	 ^
^^'.^	 Virginia Polytechnic Institute, Blacksburg, Virginia
and
-	 A. R. Kunselman
-'	 University of Wyoming, Laramie, Wyoming
ABSTRACT
-_	 Earljr measurements of pioaic x-rqy energies and widths in Th 232 sad
-_=	 U238 have suggested the possibility or an aao^malous effect for the interaction
between high Z nuclei and a pion in the 4r-atas►ic state. We have remeasured
==	 the 5g^+4f x-ray energies and ^ridths in these isotopes and we compare them to a
-^	 calculation which considers the distortion of the nucleus. A small dis^ee-
--
^'	 went between theory and experiment persists, but it is probablyr due to ur.cer-
:
tainties in the calculation of the strong interaction effects.
.	 5 3' .l► T^ ^ 1
>CCESSION—^ ►^tKT	 —	
(THRU)
( G 51
	 n
^^	
(_
CR OR TMY. OR AD NUMBER) 	 (CATEG RY)
t^i^RSS e
^^. R- .^ ;
<^^^ Q
	
J	 ,.
^^^ -^^^ $\^^c^
y^^ t^,ZZZ ^Z^
-2-
1. Introduction
In comparing available pionic x-ray data with present theory, one finds
two areas of disagreement. The experimental widths for the 2p^ ►le transition in
nuclei with Z (atomic number) greater than 8 are leas than the predicted valuesl,
and the experimental energy shifts and widths for the 5g^4f transition for
Z > 90 are greater than the predicted values 2. The present situation for the
2p-►ls transitions is ambiguous because of disagreementi among the different mea-
surements; the measurements are difficult because the x-rays have a low yield
and nuclear gammas from pion capture fall near the x-rays in the energy epec-
tram. An early measurement of the nuclear shift and width for the 58^4f x-ray
in high Z nuclei gave results which were three times larger than values pre-
dicted in s perturbation calculation2 . Krell and Ericson calculated the nuclear
shift and width by integratir$ the Klein-Gordon equation sad obtained results
which are larger than the perturbation calculation but still significantly leas
than experiment3 . However, these results were somewhat ambiguous because the
nuclear size was not well known. Atypical example is the measured energy
shift in U238 of 5.96 ± 1.1 keV which can be compared to Krell and Ericaon's
result of 3. 48 keV.
Recent results of McKee4 from mLOnic atoms provide parameters which
describe the distorted shape of the nuclear densities of Th232 and U238 . With
this nuclear density, we can construct an optical model potential which is free
of the ambig^:ities in au^leer size present in earlier calculations. In this
paper we present more accurate measureme^rta of tihe shift and widtk for the
5gi4f transition in rjrh232 and U238, sad we compare the results with a theoret-
ical calculation which includes the distortion of the nuclear shape.
-3-
2. Experimental Method
X-rays we=e detected by a k0 cc lithium-drifted germanium detector, and
^	 the x-ray spectrum was analyzed with an 8192 channel analog-to-digital coaverter
which al]_owed us to observe all pionic x-rays with energy above 100 keV. The
gain was stabilized on peaks which were present in the x-ray spectr^un. The ex-
perimental arrangement for a similar measurement has been given in a recent
s
papers
We used the element fn metallic form for target materials; each weighed
about 200 grams and was at least 99^ isotopically pure. The linearity of the
pulse height spectrum was checked with many gammas oP known energy, and the
^	 gammas in the region oP interest are given in Table I. With these sources, we
were able to make non-linearity corrections of 0.7 keV to an accuracy of t 0.15
keV.
Our data for the 5g^4f peak in Th232 had about 7500 counts with a peak
height of 290 counts on top of a background of 200 counts. The U238 peak had
7800 counts with a peak height of 266 counts on top of a background of 310
counts. A calculation of muonic x-ray energies for thorium and uranium does
not reveal any lines near in energy to the 5g^f pion transition, therefore,
xe did not con3ider the problem of interference from muonic x-rays in our pion
data.
The dynamic quadrupole effect obBerved when muons form stoma with
Th232 and U238 is not expected to make a significant coirtribution to our tran-
sitions since the pion is in a bf ataoiic state.
i-4-
3. X-ray F^ergy and Width
f
	
	 The peaks in the pulse height spectrum were analyzed for their posi-
tion and width by fitting the peaks with a Voightian profile. The method of
anal,}►sis has been described 8 . The data is shown in Fig. 1 with a best Pit
Voightian profile which determined the centroid and width of the peaks. Com-
pared to the spectra given in ReP. 6 for lower Z isotopes, the peak to valley
ratio fur the pion transitions is good and the background is relativeljr smooth.
The small peak at 718 keV appeared in all of our spectre and is resolved from
the pionic x-ray peaks. However, we did add a small Gaussian to fit this pow
while analyzing the uranium data.
The centroid positions were found to be (in channels)
r^23z 2407.9 ± 0.25, and
U238	 2522.1 t 0.45,
w:^ere the errors reflect uncertainties in statistics and background. The energy
scale was determined from the 511 keV annihilation gsarma and the 1273 keV gamma
from Na22
 decay which appear in the spectrum, and the slope of the calibration
line was found to be 0.285 keV/channel. The resulting energies are
Th232 698.15 t 0.22 keV, and
U238	 730.88 t 0.25 keV.
The errors are tabulated in Table II. These results are in good agreement with
the earlier measurements 2 of 698.0 t 0.6 for Th232 and 731.4 t 1.1 for U238.
The energies of other pionic x-rays from these targets agreed with the values
caQnputed for a point nucleus.
s
Using a value of 3.8 t 0.3 keV for the instrumental resolution, we
found for the widtiia
Th232 3.53 ! 0.46 keV, and
U23e	 4.05 t o.86 kev.
- 5-
The errors are due to uncertainties in background, jtatistics and inst.^+imental
resolution. These widths are significantly l^^^rer than earlier results 2 of .ri.0
_^
t 0.9 keV ^'or Th232 and 6.1 t 1.0 keV fcr U239. Reexamining the earlier data,
we find that the errors were not evPivated correctly sad should have been t 3.0
keV for Th232 and *_ 2.0 keV for U2 ^ 8 . The width oP pu239 should have been qu^^ted
with an error of f 3.0 KeV. With ^^hese corrections, there is good agreement
between the two sets of measurements.
1-6-
4. Optical Model Analysis
To calculate the expected x-ray energies and widths for the 5g•►4f
transition in Th232 and U239, we use an optical model potential with strong
interaction parameters determined Pram other pionic x-ray data 9 and with the
charge distribution derived by HcKee^ from muonic x-rays in Th 232 and U238.
McKee found that the distorted charge distribution of these nuclei can be
represented by the density
n(r - 1)
with
^
2_	 2
R = a/[1 - b^ cos20]1/2
;=
where A is the polar angle and p o is a normalization constant.	 The parameters
a, b, and a are given in Table III.
	 Since the ground states of Th 232 and U23.'
have zero spin, there is no coupling between the nuclear sad pion coordinates.
We derived the shape of the mass density Prom McKee's charge density by
ad^ustiag the skin thickness parameter n
	
such that the mesa-square mass den-
sity be equal to the difference of the mean-square charge density and the mean-
^# square proton charge density (.60 F2 ).	 The resulting distribution is given by
the parameters a, b and n^ of Table III.
	
We assumed that the mass densities
^_
of the protons and neutrons have the same shape, and the shape was averaged
over the polar angle A
P(r) = Iol p(r,A) d (cos A)
to find a density p(r) to use in the opl;ical potential given in I. 	 The re-
^ sults of the calculation are given in Table IV.
Tabel IV lists the Klein-Gordon energy computed for n point nucleus
with reduced mass, and the vacuum polarization computed to 2nd order (in e)
i_ --	
T^^	 ^_
-7-
by perturbation theory fo: a finite nucleus using wave functions distorted by
the nuclear interaction. The vacuum polarization was computed in the same way
by McKee and he obtained good agreement between his calculated and measured 4f
energies for muons. The nuclear shift listed in the table is the difference
between the Klein-Gordon point value and the solution of the Klein-Gordon eque-
tfon with the optical potential described in I. It inclu3es effects from both
the strong interaction and the finite distribution of charge.
A measured nuclear shift is derived by subtracting the point Klein-
Gordon value and the vacuum polarization correction from the measured value.
This measured nuclear shift then contains effects due to both the strong inter-
action and the finite Coulomb size of the nucleus, but the finite Coulomb size
effect is small and reduces the total nuclear shift by about 100 ev.
Calculations of the nuclear shift and width are less than the measured
values by about 2514 for both nuclei. Increasing the rms radius of the neutron
distribution would only reduce the calculated values. However, we believe that
	^ the difference between theory sad experiment is probably not significant when
uncertainties in the optical potential are considered.
i-^
CONCLUSION
We have measured the 5^4f pionic x-ray energy and width in Th232
and U238. The results are found to be greater than, but still in fair
agreement with, s prediction made from an optical modal snal,}rsis. The
large disagreement of a factor of tit ►ree between theory and experiment
reported in an earlier measurement has been largely resolved by (1) more
reliable optical-model potential parameters, (2) an improved measurement
of the x-r^r width, and (3) abetter knowledge of the charge distribution.
We attribute the remaining difference between theory and experiment to
uncertainties introduced by the optical model.
-^£
^€
T
S
'F
i-9-
ACI^Q^IOWLEDGEMF^VT3
We thank members of the William and Mary physics group for help
in the data collection, Mr. J)uane cieaugh for help in the data analysis,
Dr. David Anderson for eesiatance in the theoretical calculations, and
the staff of the NASA Space Radiation Effects Laboratory for their
assistance during the experiment.
•-10-
FOOTNOTES
"Work supported by the National Aeronautics and Space Administration.
1. G. H. Miller, bi. Eckhause, W. W. Sapp and R. E. Welsh, Physics
Letters 2^8, 663 (1968). This article contains references to
other work.
2. D. A. Jenkins sad R. Kunse Lnan, Fhys. Rev. Letters 17, 1148 ( 1966).
3. M. Krell and T.E.O. Ericson, Nuclear Physics B11, 521 ( 1969)•
1a. R. J. t9cKee, Phys. Rev. 180, 1139 (1969).
5. D. A. Jenkins, R. J. Pacers and A. R. Kunselman, "The 4f^3d Pionic
Transition in Ba138^ Ce l ^^ and Ce 142 , to be published ( 1970).
6. C. M. Lederer, J. M. Hollander end I. Perlman, Table of Isotopes,
(John Wiley and Sons, Inc., New York, 1957), 6th Ed., Appendix II,
Table 3, p. 561.
T. S. M. Brahmavar, J. H. Hamilton, A. V. Rameyya, E. F. Zgan^ar and
C. E. Bemis, Nuclear Physics Alm , 217 (196y).
8. D. A. Jenkins, R. J. Pacers and G. H. Miller, P`^ya. Rev. lam, 1508 (1969).
9. D. K. Anderson, D. A. Jenkins and R. J. Pacers, Phys. Rev. Letters
24, 71 (1970). FTeresfter refernd ico as I.
.`
. 
__ =—
t
-11-
Table I. Calibration Sources. The energies are taken frcm
Ref. 6 except for Ag110m from Ref. 7.
Source	 Energy (keV)
Ir 192 612.435 t 0.017
^11om 626.22 t 0.03
pgllom 686.80 t 0.03
ag 110m 706.68 t 0.04
1131 722.91 t 0.05
A^^ = ^ 744.19 t 0.04
a ^
t
-12-
Table II. Errors in energy analysis (in keV).
^2 32
Statistics and background	 0.07
Gain	 0.15
Non-linearity	 0.15
Total	 0.22
U2 3 8
0.13
0.15
0.15
0.25
z
,,
-13-	
1
Table III. Parame;ers for the charge distribution.a
r^2 32
a	 6.506 ± 0.28 F
b	 8.189±o.038 F
n	 14.9	 ± 0.7
n'	 16.7
U238
6.501 ± 0.024 F
8.396 ±0.033F
14.9	 ± 0.6
16.0
a. From Ref. 4.
-14-
Table IV. Comparison of prediction with experimental results (in keV).
^2 32 LJ2 38
Energies
Klein-Gordon 689.54 721.15
Vacuum polarization 4.27 4.54
Nuclear shift 3.40 4.09
Total Calculated 697.21 729.78
Measured total 698.15 ± 0.22 730 . 88 ± 0.25
Measured nuclear shift 4.34 ± 0 . 22 5.19 ± 0.25
Widths
Calculated
	
2.82	 3.45
Measured	 3.53 ± 0.46	 4.05 ± 0.86
-15-
FIGURE LEGENDS
Fig. 1.
	 Pulse height spectra of the 5p; ►4f pionic x rey. The
^'^	 solid line is a least-squares-fit to the data, and the
dashed line is the assumed shape of the background.
`1'he gain on the horizontal scale is 0.57 keV/channel.
1200
800
T h 232
680	 700	 7 20
ENERGY (keV)
800
..
740
.•
..
...	 ..	 .	 .	 ...
...
^^^^^ ^^^ t1
 ^^^^^^ ^^~
	 ^^M
U 238
^	 .'
400
I
Z 0
O
U 1200


The 5g yields 4f pionic transition in Th 232 and U 238

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server