Cox, J. A. M.
Groot, S. R. de,
Hartogh, Chr. D.
1953
NUMERICAL
DISTRIBUTION
Physica XIX
1119-1122
CALCULATIONS
FOR THE
OF GAMMA RADIATION
BY ORIENTED
“Co NUCLEI
ANGULAR
EMITTED
by J. A. M. COX *), S. R. DE GROOT and CHR. D. HARTOGH
Instituut
voor
theoretische
natuurkunde,
Universiteit,
Utrecht,
Nederland
Synopsis
In this note the theoretical
results for the angular distribution
of y-radiation emitted by oriented
radioactive
nuclei are applied to the case of
5sCo nuclei. The angular distribution
function of the y-radiation
has been
calculated for an arbitrary
degree of nuclear orientation
and in dependence
of a parameter,
which describes the character of the /If-transition
or the
K-capture
preceding the y-transition.
5 1. Introduction. When the quantisation axis ‘1 is an axis of
rotational symmetry of the initial “Co nuclei, the state of orientation of the nuclei can be described by 2j,, independent parameters
fk(j,,) (cf. ‘) formula 25 and 32). j0 is the spin quantum number of
the nuclei. These parameters f&) are completely determined by j,,
and by the relative populations LZ,,,~
of the magnetic sublevels m,
fkm=~k(io)
zn,<
f%lel %>(-uia-mo-G3+%~ io-?I Ihio) k 0 >.
(1)
In the special case under consideration the nuclei are contained in a
tutton salt “) “) “) “) wh ere due to the orientation mechanism the
levels m, and - m, are equally favoured. This is expressed also in
the formula for a,, by
a
m0
= C cash (j3nz0),
where C is determined by the normalization
c m0 atno=l
(4
condition
-
(3)
In (2) p is considered as a parameter which can vary from 0
(random orientation) to CXJ(total orientation). We assume the “COnuclei to decay according to the scheme “) ,shown in fig. 1.
~l ) Present
address:
Van der Waals
laboratorium,
-
1119 -
Universiteit,
Amsterdam,
Nederland
1120
J. A. &I. COX,
S. R. DE GROOT
AND
CHR.
D. HARTOGH
For the calculation of the angular distribution
radiation we can use the formula (cf. i) formula
of the y quadrupole
93)
w(6)=2[1-(+)N21ii)
fdfii)
fifii)
p2(cos8.)k55N4(ii)
p4
lcos
s)l9 C4)
where 6, is the angle between the direction of emission k of the
y-quantum
and q. The functions P, (cos 6) and P, (cos 6) are normalized Legendre polynomials.
The distribution
function W(6) is
normalized to
J-W(S) df2 = 87~.
(5)
In order to find the distribution
function (4) we have calculated
the orientation
parameters fk(ji) from the initial
parameters fk(jO)
before the flf-transition
or K-capture. The relation between them
is given by (cf. ‘) formulae 28, 29)
SEC0
fZ(ii)
=
4
(*
fd(ii)
=
4
(-
+
I)
2
+
(6)
f2(jO)p
5il)
---J--J
f4bO)*
(7)
Kwcopt”;;:
1
!Y
“Fe
Fig.
A
1. Decay-scheme
jf=
0
of 5BCo.
Here il (0 < I < 1) is a parameter, which describes the character
of the transition j0 -+ ii. When this process is determined
by the
squared nuclear matrix element I/ 11’ the parameter 1= 1 (Fermi
type interaction).
For Gamow-Teller
interaction
only [/crj” occurs
and then Iz = 0.
Ultimately
we obtain an expression for. W(6) which depends on
the parameters /? and 1. The procedure of the calculations and the
numerical results will be given in section 2.
9 2. Procedure of the calculations and numerical results. Since only
fR with k even are needed we can use instead of (2) the Boltzmann
distribution
4Q = C exp (pm,).
(8)
GAMMA
RADIATION
EMITTED
BY
ORIENTED
58c0
1121
NUCLEI
We have calculated a,,,0 for several values of /? (0 + m). With these
values f&,) and f,&) are calculated from (1) with the quantum
number i0 = 2 for 58Co (fig. 1). With (6) and (7) this leads to the
parameters fi(ii) and f4(ji). If we write formula (4) as
W(6) = 2 [ 1 -
&(A, p) P, (cos 8) -
C,(l, /?) P, (cos 6) -J
(9)
it is now possible to evaluate the coefficients &(A, ,!?) and C,(I, fi).
In the table the results for these coefficients have been given as a
function of p for values of ;Z = 0, 4 and 1. On account of the strong
dependence on il it might be possible to determine 1 experimentally
as has been indicated before (cf. “) pages 8 and 9).
TABLE
J0
0,04
0,os
0,lO
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0,50
0,55
0.60
0,70
0,80
0,90
I .oo
I,25
I ,50
I ,75
w
2,5
3,O
4,O
580
co
Jlasimum
l&cc-ived
Physica
c‘, (0, B)
o,oooo
Cd (0, B)
-o,oooo
-o,oooo
-o,oooo
-o,oooo
-o,oooo
-0,000 I
0,0004
0,0006
O,OG25
0,0055
0,0098
0,o 150
0,0213
0,0284
0,0363
0,0449
0,054o
0,0635
0,0733
0,0936
-0,0001
-0,0003
-0,0005
-0,0009
-0,0013
-0,0020
-0.0028
-0,0038
-0,0064
-0,0098
--0,0142
-0,0193
-0,0353
-0,0539
-0,0734
-0,092l
-0,124l
-0,
I475
-0,
I737
0,l I40
0,134o
0,1532
0,196s
0.2320
0,2601
0,282O
0,312l
0,330 I
0,3473
0,353s
0,357 I
error
-0,184l
-0,1905
I unit
of the last
I
c* tt,/%
o,oooo
0,0006
0,0009
0,0037
0,0083
0,O I46
0,0225
0,0319
0,0426
0,0545
0,0673
0,081O
0,0953
0,1100
0,1403
0,1709
0,201o
0,2298
0.2947
0,3479
0,390l
0,423O
0,468 I
0,495 I
0,5209
0,5303
0.5357
I
Cd ct, B)
o,oooo
o,oooo
o,oooo
o,oooo
o,oooo
o,oooo
o,oooo
0,0001
0,000 I
0,0002
0,0003
0,0005
0,0007
0,0010
0.00 I6
0.0025
0,0035
0,0048
0,0088
0,0135
0,0183
0,023O
0,031o
0,0369
0,0434
0,046O
0.0476
C*Cl,B)
o,oooo
0,0008
0,oo I2
0,005o
0,Ol I I
0,019s
0,030 I
0,0426
0,0569
0,0727
0.0898
0,108O
0,127O
0,1467
0,187l
0,2279
0,268O
0,306s
0,393o
0,4639
0,520 I
0,564O
0,6242
0,660 I
0,694s
0,707o
0,7143
(‘6 (l,B,
o,oooo
o,oooo
o,oooo
o,oooo
0.0000
0,000 I
0,0002
0.0004
0,0008
0,0013
0,002o
0,0029
0,004 I
0,0058
0,0095
0,o I47
0,0213
0.0290
0,0529
0,0809
0,I 100
0,138l
0,1862
0,2213
0,2605
0,2762
0,2857
decimal.
22-8-53.
S 1N
71
1122
GAMMA
RADIATION
EMITTED
BY
ORIENTED
58cO
NUCLEI
REFERENCES
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