International Journal of Scientific & Engineering Research, Volume 5, Issue 4, April-2014 1451

ISSN 2229-5518

Transition properties of γ-ray Emitted from levels in 90Mo using 𝝈 method

𝑱

Wafaa Ahmed Azeez, Bashair M.saied, Taghreed A.Younis

Department of Physics, University of Zakho

Department of physics, Dohok University

Department of physics, Baghdad University

Abstract:

The Ξ΄-mixing ratios have been calculated for several Ξ³-transitions in 90Mo using the 𝛔

𝐉

method. The results are compared with other references

𝛔

the agreement is found to be very good .this confirms the validity of the

𝐉

method as a tool for analyzing the angular distribution of Ξ³-ray.

𝛔

Key word: population parameter, Ξ³-ray transition,

𝐉

method, multiple mixing ratios.

Introduction:

35 35 90

Angular distribution experiment using the reaction 28 𝑁𝑖 (17𝐢𝑙 ,3𝑝𝛾)42π‘€π‘œ
has been performed at 120 MeV beam energy by kabadiyski et.at

35 35 90


[1] . Rasha J.T. calculate the multiple mixing ratios ,Ξ΄, of gamma transitions from levels excited in 28 𝑁𝑖 (17𝐢𝑙 ,3𝑝𝛾)42π‘€π‘œ
constant statistical tensor and least square fitting methods .
by using a2 –ratio,

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International Journal of Scientific & Engineering Research, Volume 5, Issue 4, April-2014 1452

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𝛔

In the present work , the angular distribution of Ξ³-rays from this reaction are reanalyzed using

𝐉

method [3] .This method depends on the
Gaussian distribution with its half-width Οƒ, where determined using the experimental angular distribution coefficients obtained for a selected number of well-known Ξ³-ray transitions from levels with different spin Ji Values , the main aim was to confirm the validity of this method as a tool for analyzing the angular distribution of Ξ³-ray.

Data Reduction & Analysis:

Yamaszaki [4] has shown that the population parameters of the magnetic sub states of an initial state with spin Ji and magnetic quantum number

mi may be represented by a Gaussian distribution of the form:-

exp(-mi2 / 2Οƒ2 )

P(mRiR)= ………..(1)

Ji

οΏ½ exp(-mi2/2Οƒ2)

m= -Ji

Where p(mi) represents the population parameters and Οƒ is the half-width of the Gaussian distribution.
In the present work, the half –width Οƒ, was determined as follows:

The experimental value of the angular distribution coefficient aR2R, of a certain and well known Ξ³-transition was used to calculate the statistical

tensor ρR 2R(Ji) from the following equation [5]

F2 (L1L1Jf Ji) + 2 Ξ΄ F2 (L1L2Jf Ji) + Ξ΄ 2 F2 (L2L2Jf Ji)

aR2R = ρR 2R (JRiR) QR2R …..(2) (1+ Ξ΄ 2 )

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Where Ξ΄ is the multiple mixing ratio Ji and Jf are the spin of initial and final states respectively L, is the angular momentum of Ξ³-ray with L2
= L1 +1 and Q is the attenuation factor which is considered here to be unity . The F2 -coefficients are tabulated in ref. [4,5,6] for integer and half
– integer J -values .

The attenuation coefficient,Ξ±2 (Ji),was then calculated from the following relation ship [4-6] :-

a2 (Ji ) = ρ 2 (Ji ) / B2 (Ji )…….(3)

Where B2 (Ji) is the statistical tensor for the complete alignment and its values are given in ref. [4]

B (J) =(2J+1)Β½

And

(-)J

(JRoR JRoR Χ€KRoR) for integer J …….(4)

B (J) =(2J+1)Β½

(-)

J-Β½

(JR1/2R J- Β½ KRoR) for half –integer J……(5)


The Ξ±R2R (JR iR) values are tabulated in ref. [6] for integer values of JRiR from 1 to 26 and half – integer values from 3/2 to 51/2 for

𝛔

values from 0.1

𝐉

to 2.0 each JR iR value .from these tables , the half – width , Οƒ was determined for the JR iR values and was used in eq. (1) to calculate population parameters p(mi). The population parameters of levels in 90Mo( computed by using computer program in mat lab language) , were it is almost constant for level , with the same JRiR value for both positive and negative parities , it , may, there for , be stated that population parameters of levels with the same JRiR value do not depend upon the energy of the level nor upon its parity . Tacking this fact into consideration, the population parameters thus calculated were used to cover all the possible transitions occurring in the present work.

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These population parameters were then, used with statistical tensor coefficients ρ 2 (Ji,Mi) from Ref. [6] in order to calculate statistical Tensor

ρ 2 (Ji) from the following equation:

ρ 2 (Ji ) = βˆ‘ ρ 2 (Ji ,mi ) P (mi ) ……..(6)

These statistical tensors were then used with F2 coefficient values to calculate the multipole mixing ratios of Ξ³-transition.

Result and discussion:-

1- If the differences between J f and Ji =2 and its parity is even, the transition will be pure E2 ,depending upon this fact the transition (7--5-)
must be pure E2, and this is what we reached it in present work , the 𝛿- value for this transition 3367.4 keV (7--5-) from 818.4 keV

level equal (0.04) ,this 𝛿 - value is very small even it will be negative or positive by using Ξ΄2= 𝑀3 when we use , | J -J |≀ L≀ |

𝐸2

Ji+Jf| the magnetic transition will be odd value and the electric transition will be even value and M3+E2 =100% ,this mean that

this transition will be 99.8% E2 and (0.04) M3 ,this indicate that the 𝛿- value in present work is accurate and agreement with that in ref[1
] ,[ 2].
This rule will applied for other transitions:

4192.5keV

(10+-8+) from

1317.7keV

E2=99.999

4555.8 keV

(12+-10+) from

477.0keV

E2=99.998

5699.6 keV

(13--11-) from

857.5keV

E2=99.910

5625.0 keV

(14+-12+) from

1069.1keV

E2=99.990

6643.1 keV

(15--13-) from

943.5keV

E2=99.997

7515.1 keV

(17--15-) from

872.8keV

E2=99.990

8525.4 keV

(18+-16+) from

1779.2keV

E2=99.960

9319.1 keV

(19--17-) from

1804.0ke

E2=99.999

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The results of the present work are agreement with other refs [1,2 ] except that the (20+ -18+) transition.
2-If the difference between Ji and Jf =0 or 1,and have odd parity ,the transition will be pure E1, depending upon this fact the (15-- 14+)
transition must be pure E1 this indicated that our 𝛿-value , results for 6643.1 keV (15--14+) from 1018.1 keV are true and by using Ξ΄2= 𝑀2 ,the

𝐸1

magnetic transition must be even and electric transition will be odd and E1+M2= 100% this mean that E1=99.999% and M2=0.002% ,this
indicate the 𝛿-values present work for this transition are true and in good agreement with that in refs[1,2 ] . and this rules also will be applied
for other transition (17--16+) from 7515.1 keV which have E1=99.99% and M2= 0.004% ,however for (11- -10+ ) 4842.1 keV from 649.6 keV
and 5699.6 keV (13- -12+ ) from 1143.8 keV our results show that this transitions are not pure transition even its they have odd parity .This indicate that the experimental results are inaccurate and this ensured by experimental results from ref[1 ] where presented that this transitions
are not E1 and it may be have small 𝛿-value.

Conclusion:-

The results of the present work are in very good agreement with those of ref. [1,2] from these comparisons, it may be concluded that the 𝛔

𝐉

𝛔

method is a powerful tool for analyzing angular distributions of Ξ³-ray .it should also be mentioned that the calculations based on the

𝐉

can be performed using an ordinary personal computer.
method

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Table (2) Multipole mixing Ratios of Ξ³- transition from level of 90MO Using Οƒ/J Method

RiR

RΞ³R

𝐒 𝐟

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International Journal of Scientific & Engineering Research, Volume 5, Issue 4, April-2014 1457

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5699.6

857.7

- -

13 -11

0.34(2)

-0.09(2)

-1.0513

E2

-0.02(2)

0.01(2)

– ( 𝟎. πŸŽπŸ‘+𝟎.𝟎𝟏 )

βˆ’πŸŽ.𝟎𝟐

(πŸ”. πŸ‘+𝟎.πŸ• )

βˆ’πŸŽ.πŸ”

5699.6

1143.8

13--12+

-0.28(2)

0.03(2)

-1.0513

-0.02(5)

-0.02(2)

-0.03(1)

- 0.29(1)

- (𝟏𝟎. πŸ”+𝟏.πŸ“ )

βˆ’πŸ.𝟏

5625.0

1069.1

+

14 -12+

0.35(2)

-0.11(33)

-1.0312

E2

0.00(2)

0.01(2)

- (𝟎. 𝟎𝟏+𝟎.𝟎𝟐 )

βˆ’πŸŽ.πŸŽπŸπŸ’

(πŸ“. πŸ“+𝟎.πŸ” )

βˆ’πŸŽ.πŸ“

6643.1

943.5

15--13-

0.33(2)

0.04(2)

-0.92332

E2

0.00(2)

-0.01(2)

0.005(0.015)

(πŸ’. πŸ—+𝟎.πŸ“ )

βˆ’πŸŽ.πŸ’

6643.1

1018.1

- +

15 – 14

-0.23(2)

0.03(3

-0.92332

0.01(6)

0.00(2)

0.01(2)

– (𝟎. 𝟎𝟎𝟐+𝟎.πŸŽπŸŽπŸ– )

βˆ’πŸŽ.𝟎𝟏𝟐

- (𝟏𝟐. πŸ–+𝟐.πŸ’ )

βˆ’πŸ.πŸ–

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7515.1

872.0

- -

17 - 15

0,29(2)

-0.05(2)

-0.8003

E2

0.01(3)

-0.05(2)

(𝟎. 𝟎𝟏+𝟎.𝟎𝟐 )

βˆ’πŸŽ.πŸŽπŸπŸ—

4.5(5)

7515.1

768..9

- +

17 -16

-0.19(2)

0.07(2)

-0.8003

0.02(6)

0.01(2)

0.03(1)

(𝟎. πŸŽπŸŽπŸ’+𝟎.πŸŽπŸπŸ” )

βˆ’πŸŽ.πŸŽπŸπŸ’

- (πŸπŸ’. πŸ”+πŸ‘.πŸ— )

βˆ’πŸ.πŸ”

8525.4

1779.2

+ +

18 -16

0.33(4)

-0.05(4)

-0.89717

E2

0.00(5)

-0.02(3)

(𝟎. 𝟎𝟐+𝟎.𝟎𝟏 )

βˆ’πŸŽ.πŸŽπŸ’

(πŸ’. πŸ’+𝟎.πŸ– )

βˆ’πŸŽ.πŸ•

9319.1

1804.0

- -

19 -17

0.34(6)

-0.02(6)

-0.97766

E2

0.00(7)

-0.01(5)

(𝟎. 𝟎𝟎𝟐+𝟎.πŸŽπŸ’πŸ– )

βˆ’πŸŽ.πŸŽπŸ“πŸ

(πŸ’. πŸ”+𝟏.πŸ’ )

βˆ’πŸŽ.πŸ—

10235.2

1709.9

20+-18+

0.37(3)

-0.03(4)

-0.7321

E2

0.00(3)

0.01(3)

0.14(4)

2.7(3)

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Table (1) Statistical tensor coefficient, half width and attenuation coefficients for 90Mo[1,2]


𝐉𝐒
βˆ’ π‰πŸ
�𝑱

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6643.1

1018.1

943.5

15- -14+

15- – 13-

-0.23(2)

0.03(3)

0.33(2)

0.04(2)

-1.119749

0.836220

0.83622

3.75

0.25

-093635(4656)

-0.92332499

7515.1

872.0

768.9

17- -15-

17- -16+

0.29(2)

-0.05(2)

-0.19(2)

0.07(2)

-1.119408

-1.119375

0.728658

0.728677

5.1

0.3

-0.81566(4707)

-0.8003

Table (1) cont.

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8525.4

1779.2

18+ -16+

0.33(4)

-0.05(4)

-1.119270

0.851045

4.5

0.25

-0.95255(11546)

-08971702

9319.1

1804.0

19- -17-

0.34(6)

-0.02(6)

-1.119130

0.88060

3.8

0.2

-0.98551(17391)

0.9776691

10235.2

1709.9

20+ -18+

0.37(3)

-0.03(4)

-1.119057

0.961988

2

0.1

-1.07652(8729)

-0.7321

Reference:-

1- Kabadiyski M.K ., Cross G.J., Harder A.,Lieb K.P.,Rudilph D.,weiszflog M.,ALtamann J.,Dewald A., Eberth J., Mylacus I.,Graw
H.,Heese J.,and Maier K.H.,(1994),phys.Rev.C50,110.
2- Tammy R.J.,(2004) , ph.D.thesis, Multipole Mixing Ratios of gamma – rays from different Nuclear Reactions ,University of AL- Mustansiriyah.
3- Ameen M.M.,(1999) , ph.D.thesis ,University of Baghdad .
4- Yamazaki T. ,(1967) ,Nuclear data ,Tables A3.,1.

5- Poletti A.R. and Warburton E.K. (1965), Study of the low –lying levels of F18 by means of the O16(He3 ,pΞ³) F18 Reaction; Phys. Rev. B595. Volume

137 ,Issue . .

6- Der Mateosain E.,and A.W.sunyar; (1974) , Atomic Data and Nucl .Data tables 13,391.

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