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

ISSN 2229-5518

π±

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 π

π

method**. **The results are compared with other references

π

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

π

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

π

Key word: population parameter**, Ξ³**-ray transition,

π

method, multiple mixing ratios**.**

Introduction:

35 35 90

Angular distribution experiment using the reaction 28 ππ (17πΆπ ,3ππΎ)42ππ

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 ππ (17πΆπ ,3ππΎ)42ππ

constant statistical tensor and least square fitting methods **.**

by using **a**2 βratio**,**

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π

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

π

method **[3] .**This method depends on the

Gaussian distribution with its half-width **Ο, **where determined using the experimental angular distribution coefficients obtained for a selected number of well-known **Ξ³-ray **transitions from levels with different spin **J**i 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 **J**i and magnetic quantum number

P(mRiR)= β¦β¦β¦..(1)

Ji

m= -Ji

Where p**(mi) **represents the population parameters and **Ο **is the half-width of the Gaussian distribution**.**

In the present work, the half βwidth **Ο, **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 ΟR 2R(Ji) from the following equation [5]

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

aR2R = ΟR 2R (JRiR) QR2R __ __ β¦..(2) (1+ Ξ΄ 2 )

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Where **Ξ΄ **is the multiple mixing ratio **J**i and **J**f 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 **F**2 **-coefficients **are tabulated in ref**. [4,5,6] **for integer and half

β integer **J **-values **.**

And

(JRoR JRoR ΧKRoR) for integer J β¦β¦.(4)

J-Β½

(JR1/2R J- Β½ KRoR) for half βinteger Jβ¦β¦(5)

The **Ξ±**R2R **(J**R iR**) **values are tabulated in ref**. [6] **for integer values of **J**RiR from 1 to 26 and half β integer values from **3/2 **to 51/2 for

π

values from 0.1

π

to 2.0 each **J**R iR value .from these tables **, **the half β width **, Ο **was determined for the **J**R iR values and was used in eq**. (1) **to calculate population parameters **p(mi). **The population parameters of levels in 90**Mo**( computed by using computer program in mat lab language) **, **were it is almost constant for level **, **with the same **J**RiR value for both positive and negative parities **, **it **, **may**, **there for **, **be stated that population parameters of levels with the same **J**RiR 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 statistical tensors were then used with **F**2 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 πΏ- value for this transition 3367.4 keV (7--5-) from 818.4 keV

level equal (0.04) ,this πΏ - value is very small even it will be negative or positive by using Ξ΄2= π3 when we use , | J -J |β€ Lβ€ |

πΈ2

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 πΏ- 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 πΏ-value , results for 6643.1 keV (15--14+) from 1018.1 keV are true and by using Ξ΄2= π2 ,the

πΈ1

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 πΏ-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 πΏ-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 π

π

π

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

π

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 Ο/J Method

RiR

RΞ³R

π’ π

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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) | β ( π. ππ+π.ππ ) βπ.ππ (π. π+π.π ) βπ.π |

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) - (ππ. π+π.π ) βπ.π |

5625.0 | 1069.1 | + 14 -12+ | 0.35(2) -0.11(33) | -1.0312 | E2 | 0.00(2) | 0.01(2) | - (π. ππ+π.ππ ) βπ.πππ (π. π+π.π ) βπ.π |

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. π+π.π ) βπ.π |

6643.1 | 1018.1 | - + 15 β 14 | -0.23(2) 0.03(3 | -0.92332 | 0.01(6) | 0.00(2) | 0.01(2) | β (π. πππ+π.πππ ) βπ.πππ - (ππ. π+π.π ) βπ.π |

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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) | (π. ππ+π.ππ ) βπ.πππ 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) | (π. πππ+π.πππ ) βπ.πππ - (ππ. π+π.π ) βπ.π |

8525.4 | 1779.2 | + + 18 -16 | 0.33(4) -0.05(4) | -0.89717 | E2 | 0.00(5) | -0.02(3) | (π. ππ+π.ππ ) βπ.ππ (π. π+π.π ) βπ.π |

9319.1 | 1804.0 | - - 19 -17 | 0.34(6) -0.02(6) | -0.97766 | E2 | 0.00(7) | -0.01(5) | (π. πππ+π.πππ ) βπ.πππ (π. π+π.π ) βπ.π |

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]

ππ’

β ππ

οΏ½π±

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6643.1 | 1018.1 943.5 | 15- -14+ 15- β 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 |

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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 β 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 βlying 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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