E2-M1 mixing ratios in 2′ → 2 → 0 transitions

" 1.D 2 : I Nuclear Physws 11 (1959) 691--695, (~) North-Holland Pubhshzng Co, Amsterdam 1E 4

] N o t to be reproduced by photoprmt or mtcrofilm without written perrmssmn from the publmher

E2--M1

MIXING

S S MALIKt,

RATIOS V

R

I N 2' --* 2 - * 0 T R A N S I T I O N S

P O T N I S t¢ and C E

MANDEVILLE??t

Bartol Research Foundat,on o/ the Franhhn Instztute, Swarthmore, Penna * Receaved 16 March 1959 A b s t r a c t The results of twelve p u b h s h e d angular correlation e x p e r l m e n t s h a v e been analyzed, and the E2---M1 m i x i n g ratios of the 2' -~ 2 t r a n s l t m n s have been obtained for twelve different even nuclei Particular a t t e n t i o n has been given to e~aluatlon of the errors in the m e a s u r e d values of the m i x i n g ratios The available d a t a range from A = 56 to A = 198 W h e n (J/ET)2 is plotted against Z * A t , three of the experimentally observed points, those for Fe 5., Zr 9z and H g lss, deviate s h a r p l y from a curve calculated from the theoretical consaderatlons of D a v y d o v and Ffllppov

1. I n t r o d u c t i o n

From spatial correlation functaons of the cascade emissions, the mlxang ratios, values of 82 of the 2' -+ 2 transition of the 2' -+ 2 -+ 0 spin sequence of even nuclei can be obtained The quantaty 6 is here defined as

5 = ±~/I(E2)/I(M1)

(1)

In the case of 2'--> 2--> 0 transitions, A =

3 + 8 782(~+0 715(52 7 - - 2 927~±9 286(~

(2)

where A, the anlsotropy, is given b y l+A2+A4 A - - I _ _ ½ A , + a A * --1

(3)

In eq (3), A S and A4 are the coefficients of the Legendre polynomials of the correlation function whmh m ay be written

W (O) = l + A 2 P 2 ( c o s O)+ A4 P4(cos O)

(4)

2. R e s u l t s

Values of ~ have been discussed and estimated m a number of recent pubhcatlons 1-4) More recently, values of ~ have been calculated from theory b y D a v y d o v and Fxhppov 5) In order to make proper comparisons wath the t P e r m a n e n t address Muzaffar N a g a r (U P ), I n d i a tt P e r m a n e n t address G w a h o r (M P ), I n d i a tit At present a t the D e p t of Physics, U m ~ e r s l t y of Alabama, Tuscaloosa, A l a b a m a * This research w a s s u p p o r t e d b y the U S Air Force t h r o u g h the Air Force Office of Scaentlfm Research of the Air Research and D e v e l o p m e n t C o m m a n d 691

692

s

s

MALIK,

V

R

POTNIS

AND

C

E

MANDEVILLE

theoreUcal predictions, a series of e x p e r i m e n t s whereto (5 was o b t a i n e d for 2' -~ 2 -~ 0 transitions in even nuclei h a v e been considered In m o s t instances (5 has been r e - e v a l u a t e d from the d a t a of the angular correlation measurem e n t s with emphasis upon p r o p e r e s t l m a t l o n of error In these cases, the independence and n o n - i n d e p e n d e n c e of errors m all quantltles concerned was t a k e n into account in c o m b i n i n g errors to obtain the error in (5 The results of these calculations are s u m m a r i z e d in table 1 I t will be n o t e d t h a t according to eq (2), (5 is a double-valued f u n c t i o n of the a s y m m e t r y A To d e t e r m i n e which value of (5 is applicable, the experim e n t a l l y d e t e r m i n e d values of A S and A 4 are c o m p a r e d with theoretical values of these coefficients given b y the following equatlon~: 1 Ag. - - ~ 1+(5 (0 2 5 0 + 0 732(5--0 077(5s),

(5)

0 326(59 A,

--

(6)

1+(53

In this manner, the value of (5 which is c o m p a t i b l e with the observed values of b o t h As a n d A4 can be selected Values of A S and A4 are p l o t t e d along with eqs (5) a n d (6) in fig 1 The a p p r o p r i a t e values of (5 so obtaaned are Indic a t e d b y an asterisk in table 1 Values of (5 for Sn 11e a n d P t 191 a n d t h e i r i

u

'

' ' ' ' I

'

,

,

,

, | . , I

06

,

H

F,~*

n98

|

,

i

'

FeS8

Q

' ' ' ' I PI

-

I -e

122

,

.

.

.

, . .

I°e -

[

us

188

04

\

/

\

;

;

i

;

02

A2 1-8)

V

-

•

~

_

_

_

O0 -0 2

-0 4

-0 6 *

001

,

,

.

, , , . I

oI

J

,

,

,

. i . n l

Io lSI

'

'

'

'

J ' ' l |

IOo

Fig 1 Coeffmmnts A z and .4~ plotted as a function of

I

|

I

l

I

I

.

iooo

E2--M1

MIXING

RATION

IN

2' ~

TABLE

693

2 --~ 0 T R A N S I T I O N S

1

Values of 6 Element and Isotope

E7 (keY)

zsFess

1810

26Fe5s

,4 z

A~

A

8

Reference

0 346

0 025

0 6410 1

0 15 1 89

-~ 0 075* ! 0 39

i)

805

026 1 0 0 3

028 q-005

058±010

232 011

1 047* :[: 007

b)

14Se7'

643

--021 +003

4oZrts

900

~0Sn11'

800

6=TeIn

693

0 14 ! 0 05

0 32 ± 0 025

0 3 9 1 0 044

s~TeIH

740

006 ! 0 0 1

030 t 0 03 0 27 t 0 014

~Os ls8

478

--004010002

035 t 0 0 2

TsPt 19s

296

~sPt1°~

293

--0 042-4-0 002

~sPtl"

331

0 0 7 3 1 0 004

0 2 3 6 1 0 049

024610045

--0134-007

0 0 3 6 1 0 068

0 4 2 ! 0 15

(--371) t 1 8 6 ' (-053) t 0 13

e)

( - 0 0047) t 0 106" 312 4- 163

¢)

35

q- 1 5

d)

3 21 (-001)

I t

0 48* 003

e)

026!005

637 ( - 0 14)

t I

090" 0 02

~)

0141003

1569 q- 701" (--0207) I 0021

s)

(-- 6 5)

4- 1 5

h)

29 1 (--024)

t 2 5 8* t 002

1)

t

J)

0 30 1 0 02

0 11-4-0 02

0 2 8 6 1 0 015

0 27 ± 0 02

5 43

0 53*

(--0112) 4- 0015 soHg IH

675

i) ~) e) d) e) l) g) h) l) J) k)

F H C R T M V j C V C

--0 261 t 0 023

0 137___0 012

--0 2 6 1 0 03

( - - 0 96) (-- 1 60)

R Metzger and W B Todd, Phys Rev 92 (1953) 905 Frauenfelder et al, Phys Rev 103 (1956) 352 F Coleman, Nuclear Physxcs 7 (1958) 488 Schaxenberg et al, Phys Rev 101 (1956) 689 Lmdqumt and I Marklund, Nuclear Physics 4 (1957) 189 Sakal, private commumcatxon R Potms et al, Phys Rev 102 (1956)459 Mraz, Nuclear Physics 4 (1957) 457 E Mandevflle et al, Phys Rev 98 (1955) 94 R Potnm, Inchan J Phys 30 (1956) 375 D Shrader, Phys Rev 92 (1953)928

t 0 22* ± 0 42

k)

6q4

S

S

MALIK, V

R

POTNIS AND C

E

MANDEVILLE

respective errors have been taken arbitrarily as quoted b y the authors of the indicated references Because of insufficient data concerning As and A4 In these two cases, no critical evaluation of ~ was attempted 3. D i s c u s s i o n

In their theory of axially asymmetrical nuclei, D a v y d o v and Flhppov 5) have given the expression for 6z as ~ = -~E~,2ZZAIx

(7)

10 -10

with E r in keV A log-log plot of this expression appears in fig 2 Experimentally determined values of (~/E~,) z have been calculated from the data ,

,

l

' I

I

I

I

t I

*

I

l

pt I g 4

10 4

Os 188

103

Io 0

%-..

10 2

, Te 126 Se 7 6

Te 122 I0 t

t

I0 0 r

,

,

,I

,

5

,

I

,!

rig

198

,

50

A2Z4/3X 10-5

1

56

ge

92

Zr

F i g 2 Comparison of measured values of (6/E~,) ~ w i t h the t h e o r y of D a v y d o v and F f l ] p p o v Values or the o r d i n a t e are decades smaller for Fete(7 × 1 0 - 3 + 7 × 10 -3) and Zrg2(2 × 10 -5 ± ] 3 × 10 -~)

E2--M1 MIXING RATIOS IN 2' --->2 -+ 0 TRANSITIONS

695

table 1 and are shown in fig 2 along with their associated probable errors. It is evident from fig 2 that with certain exceptions, there appears to be a general trend of agreement between experiment and theory The extreme variations from the theory evidenced by Hg 19S, Zr 9~ and Fe 5. are perhaps related to shell effects In the case of Zr 92, there is not absolute certainty t h a t the level from which the mixed transition occurs is the 2' (second 2 + ) level References 1) I Bergstrom and G Andersson, Arklv f Fys 12 (1957) 415 2) T Lmdqulst and I Marklund, Nuclear Physms 4 (1957) 189 3) Mltsuo Sakal, Report on Even-Even Nuclei, Institute for Nuclear Study, University of Tokyo, Japan INS-J-6 (February 24, 1958) 4) V :R Potnls and C E Mandevllle, J Frankhn Inst 26b (1958)226 5) A S Davydov and G P Ffllppov, Nuclear Physms 8 (1958) 237