Measurements of the lines λ7852 (5s6p^1P→5s6s^1S) are λ8241 (5s6p^1P→5s5d^1D) of In II show deviations from interval rule. These deviations are satisfactorily accounted for by the presence of a nuclear electric quadrupole moment which from the first of the lines is found to be Q=0.82×10^(−24) cm^2. No trace of lines due to In^(113) was found

Bacher, R. F.

Tomboulian, T. D.

Caltech Authors - Main

OCTOBER 15, 1937 PHYSICAL REVIEW VOLU M E 52
The Electric Quadrupole Moment of In""
R. F. BAcHER AND D. H. TQMBQULIAN
Cornell University, Ithaca, New York
(Received August 16, 1937)
Measurements of the lines X7852 (5s6P 'P~Ss6s 'S) are X8241 (Ss6P 'P~SsSd 'D) of In II
show deviations from interval rule. These deviations are satisfactorily accounted for by the
presence of a nuclear electric quadrupole moment which from the first of the lines is found to
be Q=0.82)&10 ' cm'. No trace of lines due to In"' was found.
' EASUREMENTS on the hyperfine struc-
ture of the lines of indium II by Paschen
and Campbell' have shown that the nuclear spin
is 4-,' from the use of the interval rule. Several
terms of the Ssns and Ss6p configurations lead
uniquely to this value for the nuclear spin.
Further work by Paschen' has showed that the
interval rule is followed more closely by the
low 'S terms than by the 'P and 'D terms. The
higher '5 terms show marked deviations from
the interval rule. These deviations and those in
the 'P and 'D terms are due mainly to the
presence of nearby levels so that perturbations
occur between terms of the same total angular
momentum F. Paschen has discussed these devi-
ations for higher series members in some detail.
In order to ascertain whether there w'ere also
deviations from interval rule which were not due
to perturbations of this sort but which might
arise if the nucleus possessed an electric quad-
rupole moment, lines involving the Ss6p 'I' and
SsSd 'D terms w'ere investigated. ' The Ss6p 'P
term is su%ciently removed from the 'P term
of the same configuration so that perturbation
of the type mentioned is negligible. This is also
true for the SsSd 'D term but, due to a different
type of perturbation from the Sp''D, it is not
useful for determining the quadrupole moment.
This latter perturbation does not affect the
interval rule how'ever, and the observed devia-
tions may be attributed to electric quadrupole
moment. '
The indium spectrum was excited in a hollow-
cathode discharge tube operated under a variety
of conditions. The cathode was run hot and the
' Paschen and Campbell, Naturwiss. 22, 136 (1934).
2 Paschen, Sitzungsbericten der Preussischen Akademie
der Wissenschaften 456 (1934); 431 (1935).
' Bacher and Tomboulian, Phys. Rev. SO, 1096 (1936).
83
current in the lamp frequently exceeded one
ampere. This did not seem to broaden the lines
appreciably. The radiation was studied with a
Fabry-Parrot etalon with fixed separators used in
conjunction with a Zeiss three prism spectro-
graph. The interferometer and the spectrograph
were kept in a constant temperature room and
the interferometer remained in adjustment for
days at a time though the exposures were never
longer than two hours. For accurate measure-
ments, it was found advisable to use small grain,
high contrast plates, though when weaker com-
ponents were sought the faster plates were used.
Most attention was confined to the lines ) 7852
Ss6p 'I' —+Ss6s 'S and ).8241 Ss6p 'P +SsSd 'D. —
For the first of these lines a rather large number
of photographs were taken and the separations
reduced in order to get an idea of the deviations
which might be expected in measurements on a
simple well resolved line. For this purpose 3,
5 and 8 mm separators were used. The separators
completely change. the relative spacings of the
components as can be seen in Fig. 1. For this
line about ten orders of the interference pattern
were measured on each plate.
Table I shows the results obtained for different
plate separations for the three component line
X7852. The separations show maximum devia-
tions from the mean of 2)&10 'cm 'and 3)&10 '
cm ' for the larger and smaller intervals respec-
tively. There does not seem to be any dependence
of the measured interval on the interferometer
separator which was used. Such a dependence
might have been expected had certain systematic
errors which were due to the relative spacing of
the observed components, been present in the
measurements. It seems that the measurements
of a completely resolved and well separated
pattern are really very accurate. The measure-
6
QUADRUPOLE MOMENT OF INDIUM 837
I l~
FIG. 1. Interferometer patterns of X7852 (Ss6P 'P~Ss6s 'S) taken with 8
(bottom), 5 (middle) and 3 mm separators,
ments of ) 7852 give the hyperfine separations of
the 'P term directly as seen from Fig. 2. The
separations of the 'P state show definite devi-
ations from the interval rule. Using the same
over-all separation, the central level wouM
necessarily be so placed that the two hfs.
separations would be 357.7 and 437.1 X10—' cm '
(Fig. 2) if the interval rule holds. The values
differ from the observed separations by 5.2)&10 '
cm ' which is respectively 17 and 26 times the
maximum deviation found in these - measure-
ments.
The interval rule follows directly from the
simple form of interaction betw'een the nuclear
magnetic moment and the electrons. A deviation
from the interval rule does not mean that this
form of the interaction is insufficient or incorrect.
Such deviations are frequently found where two
states of different angular momentum Japproach
each other. If the distance of such states ap-
proaches the hyperfine separations, then large
deviations are expected. The deviations are
appreciable for separations of the states of differ-
ent J of 100 cm ' or more. In the present case
of Ss6p 'P the nearest states are those of the
Ss6p 'P. All of these should perturb the 'P
slightly but the effect of the 'Po would be greatest
since it would affect only the central hyperfine
SEPARATOR
MM
3.1226
3.1223
5.0136
8.0083
Mean
INTERVAL
11/2-9/2
10 3 cM i
432.0
431.9
432.0
431.7
432.1
431.7
431.7
431.9
432.1
432.0
431.9
DEV. FROM
MEAN
103CMr
+0.1
0.0
+0.1
—0.2
+0.2
—0.2
—0.2
0.0
+0.2
+0.1
INTERVAL
9/2-7/2
10-3 cM-~
363.2
362.8
362.8
362.9
362.7
362.6
363.0
362.8
363.2
362.9
36Z.9
DEv. FRQM
MEAN103cM~
+0.3
—0.1
—0.1
0.0
—0.2
—0.3
+0.1
—0.1
+0.3
0.0
level of 'P». This perturbing effect would be less
than 10—4 cm ' and is therefore neglected here.
No other perturbations are expected and it
appears that the deviations from the interval
rule are due to the inadequacy of the interaction
term. They can be accounted for by assumption
of an electric quadrupole moment for the nucleus
as found in other cases.
That this explanation is plausible will be seen
from the measurements on the nine component
line 48241 (Ss6p 'P&~5sSd 'D2) This line is
considerably more complex and the measure-
ments of the intervals less accurate. Fig. 3 shows
the level scheme and pattern of the line and
TABLE I. Separati ons of the 5s6P 'P& state of IrI II.
The separations of the 'Pr state mere measured from X785Z
(5s6p 'P~5s6s 'S).
R. F. BACHER AND D. H. TOMBOULIAN
F
/7
F
7/
362.9 35 7.7
43 l.9
I I I
I
I I
I I
I
8/
li/
D 9/,
7/g
W2
f27 3
IOI ~ 6
Fr@. 2. Level scheme and line structure observed for X7852.
Table II gives the measured separations of the
'Dg level. Component 3 was too weak for accurate
measurements and components 8 and 9 were
resolved only in one or tw'o cases and their
measured separations thus unreliable. Fig. 4
shows the separations of the 'Dg level observed,
and also by using the over-all separation to
determine the interval factor and assuming the
interval rule to be correct. The center of gravity
found from the two unresolved lines was used.
These deviations are not due to perturbations
for there are no perturbing levels nearer than
3700 cm '. The 5s5d'D is, how'ever, perturbed
by the Sp' 'D but the interval rule is not affected
thereby. The deviations must be due to a differ-
ent form for the interaction energy presu'mably
from the presence of an electric quadrupole
moment. Such a moment gives rise to a charac-
teristic change in the hyperfine separations. The
separation of any two hyperfine levels I" and I"'
can be written4
h(F F') = -,'A (X—X')—
+ ,'HIE:(%+1)—X-'(E'+1) I, (1)
where E=F(F+1) I(I+'1)—J(7+1)—
'See H. B. G. Casimir "On the Interaction between
Atomic Nuclei and Electrons. " Prize Essay published by
"Tyler's Tweede Genootsckap. "
I 2
I$6
FIG. 3. Level scheme and line structure observed for X8241.
SEPARATOR
MM
INTER-
VAL
13/2-
11/2
10 3
CM 1
DEv.
FROM
MEAN
10 3
CM-1
INTER-
VAL
11/2-
9/2
10 3
CM
DEv.
FROM
MEAN
10 ~
CM 1
INTER
VAL
9/2-
7/2
10 3
GM-1
DEv.
FROM
MEAN
10 ~
CM 1
3.0015
3.1223
127.1
128.1
126.9
3.1226 127.7
126.6
Mean 1W'.8
—0,2
+0.8
-0.4
+0.4
017
101.0
101.S
103.5
102.2
100.0
202.8
—0.6
-0.1
+1.9
+0.6
—1.6
79.2
83.0
76.0
79.2
78.8
l
—0.1
+37
3e3
-0.1
and A and 8 are constants, the first associated
with the separation due to the nuclear magnetic
moment and the second arising from the con-
tribution of the electric quadrupole moment.
The observed. values of the two largest separa-
tions of 5s5d 'D2 have been used to determine
2=18.47 and 8=0.0615)&10 ' cm ' and the
remaining separations and over-all separation
determined from them. In Fig. 4 the levels on
the right show the separations so determined.
The agreement indicates that the assumption of
an electric quadrupole moment is justified. The
determination of the moment itself from the
above value of 8 cannot be carried out with any
TABLE II. T he seParations of the 5s5d 'D& state of In II as
measured from the line X8Z41 (Ssdp 'I'~Ss5d 'D).
QUADRUPOLE MOMENT OF INDIUM 839
degree of accuracy for this level due to the per-
turbation by 5ps 'D which makes the character
of the level uncertain.
The value of the nuclear electric quadrupole
moment can be found from a consideration of the
5s5p 'P~ level. From the observed separations
using (1), A = —79.37&&10 ' cm ' and 8=0.141
)&10 ' cm '. In the case of only three levels there
is no check on the value of B. The value of the
quadrupole moment4 in terms of 8 is found to be
—8J(2J—1)I(2I—1)
7.9(((3 cos' ti —1)/r') ~~)« (2)
where
cr=cos (0 —8s); cs ——sin (Hs —8),
es —arctan [l/(1+1)]&
F
I3g.
I 27.3 I ZO.O l27 3
lOI S. 3+O3 IOI 5 IOI 6 3~3
798
s/%~A%%%%&"
83.I
646
789
32 5
26 8
FIG. 4. Measured lintervals of Sssd 'Ds are shown on the
left. The center sketch shows the separations obtained
assuming the interval rule and with the separation con-
stant determined from the over-all separation. On the right
are the calculated levels found by using the two larger
level separations for the determination of A and B.
where (((3 cos' 8 —1)/r')qq)«depends upon the
electron configuration, the coupling and upon
relativistic corrections and 8 is given in units
10 ' cm—' For sp'P~
(3 cos' 8 —1)
r )~z «
(2l —1)(l+2) 2l 1
C 2(l+1)(2l+1)(21+3) r'
12c,cs[l/(1+1)]i 1
(2l+1)(21+3) r' «
The factors c~ and c2 depend on the coupling
and sin' 0= 5/d, 6 being the deviation of the sPt
term from its position if the interval rule held
exactly and d the sPt —'Pr separation. (1/r')«' '
and (1/rs)«' " are equal to certain relativistic
correction terms' times (1/r')«.
For indium 5s6p, ct —0.915 and cs ——0.404
(((3 cos' 0 1)/—r') ~~)« ——0—.425(1/r')«.
The value of (1/rs)«can be obtained in terms of
the doublet separation, or here, in order to
include the screening of the Ss electron, from the
5s6P Psseparation. (1/r')A„can be found to be
(1/rs)« —8/ I IIZ, (l+ ts)Rns}. -
Here 5 is the separation, H a relativistic cor-
rection factor' 1.06, Z; is taken as (Z —4) and
(1/rs)« —1.84 which gives
Q= 0.82)(10 cm'.
This value of'Q is essentially the same as the
value R'= 1. .0)&10 ' cm' reported previously, '
since Q= 2IR'/(2I+3).
Q=0.82+10 ss cm' is also in agreement with
the value Q = 0.8&0.2 recently reported by
Schuler and Schmidt' from a study of the
Sp 'P3~2 term of In I.
A considerable search was made to find evi-
dence of In'" expected' to be present to the
extent of about 4.5 percent. Though long ex-
posures of several lines were made which clearly
show'ed components w'hose intensity represented
only 2 percent of the total intensity of the line,
no trace of components attributable to In'" was
found. This indicates that the components of
In'" are probably concealed under those of In"'
which means that the angular momenta and
magnetic moments are probably the same for the
two isotopes; I=9/2, p=5.7 nuclear magnetons.
Such a value for the nuclear spin of In'" is quite
adequate' to explain the stability of this isotope
and Cd'", since the change from one to the other
would be highly forbidden with AI=4.
'Schuler and Schmidt, Zeits. f. Physik 104, 468 (1937).
'Aston, Proc. Roy. Soc. 149, 396 (1935); Sampson and
Bleakney, Phys. Rev. 50, 456 (1936).
7 Bethe and Bacher, Rev. Mod. Phys. 8, 200 (1936).



The Electric Quadrupole Moment of In^(115)

https://authors.library.caltech.edu/51302/1/PhysRev.52.836.pdf

The Electric Quadrupole Moment of In^(115)

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main