A.V. Ramayya and J.H. Hamilton

Vanderbilt University

EXPERIMENTAL METHODS• Lawrence Berkeley National Laboratory• Gammasphere Detector Array with 101

Compton-suppressed Ge Detectors• 252Cf Source of 62 mCi is sandwitched

between two iron foils.• Total of 5.7x1011 triple – and higher –fold g-g-g coincidence events (in cube)

• Radware software package to analyze data• Angular correlation of cascades of gamma

rays.

I1

I2

I3

g1(L1L1)

g2(L2L2)

W A P A P( ) ( ) (co s ) ( ) (co s )ex p exp 1 2 2 4 4

1

2

A A A A I I A I I2 2 1 2 2 2 1 2 1 2 2 3 2ex p ( ) ( ) ( , , ) ( , , ) g g

W A G P A G Pth eory theory( ) (cos ) (co s ) 1 2 2 2 4 4 4

N A A P A Pn n n( ) ( (co s ) (co s ))ex p ex p ex p 0 2 2 4 41

GA

A k qkk

ktheory

q

k

exp

( )12 1

1 2 11 2 2

0

• If the intermediate state interacts with a magnetic field of sufficient strength for a sufficient length of time, then the experimentally observed correlation will be attenuated.

• Specifically, for a constant magnetic field, B, a nucleus with spin I and magnetic moment m will precess about the direction of B with the Larmor precession frequency.

m

LN gB

-

m

LN gB

-

mean precession angle, f

m

- N H FL

gB

The Larmor Precession frequency, L

BHF : nuclear hyperfine field

: mean life time

Detector response function1. For a typical angular correlation measurement, it is necessary

to calculate a solid angle correction Qk for each parameter Ak.2. However, for very low intensity transitions, the sensitivity of

the angular correlation measurement can be improved by the detector response function Rn (q, E1, E2).

3. For a given detector pair, the response function describes the distribution of possible angles about the central angle of the pair as a function of energy. The response functions for each pair can then be summed to find the response function of each angle bin.

1. We calculate the response function using a simple Monte Carlo simulation, with the g ray transport simulated up to the first collision. This is equivalent to the traditional calculation of Qk.

2. The mean free path, l(E), of g-rays was calculated using the known Gammasphere detector properties.

3. The energy dependence of Rn (, E1, E2) is negligible, and so only Rn () was calculated.

• 17 groups of 64 bins

(1,2), (3,4,5,6), (7,8,9,10), (12,13,14,15), (16,17,18), (19,20,21,22,23), (24,25,26), (27,28,29), (30,31,32,33,34), (35,36,37), (38,39,40), (41,42,43,44,45), (46,47,48),(49,50,51,52), (54,55,56,57),(58,59,60,61), (62,63)

f f

t1/2=0.2 ps

462.8 keV

0+

1435.8 keV

4+

2+

138Ba

A2(theory) = 0.102 A4(theory) = 0.0089

Mixing ratios of DI=1 transitions within a rotational band

gR = ½(Z/A), gK : intrinsic g factor

a: Nilsson coefficients, gl=0, gseff=-2.296

a a

g( / ). ( )

||

.

( )

/

, / , /

E MK

E Qg g

I K I KI K I K

QZ A

g gg g

K

K R

f i

f i

K ls l

l K l K

2 1 51 2

11 2 1 0

2 01 0

9 1 7

2

30

02 3

1 22

1 22

-

-

- Ref.: S,G. Nilsson, Nat. Fys. Medd. Dan. Vis. Selsk., 29 (1955).

138.3

9/2 -

5/2 -

95.3 7/2 -

13/2 -

11/2 -

390.6

283.2

138.3

95.3

232.8

9/2 -

5/2 -

7/2 -

150.2

5/2+

7/2+

9/2-

166.6

NucleusEnergy (keV)

Configurations

(cal)(exp)

101Zr98.2

3/2[411]-0.13

-0.15(6)

Qo=2.84 3/2[422] 0.44

3/2[402] 0.22

Nucleus Energy (keV) Configurations (cal)(exp)

107Mo 152.1 5/2[413] 0.79

Qo=3.09 5/2[402] -0.20-1.0(7)

110.2 7/2[523] -0.16-0.18(9)

103Mo 102.8 3/2[411] -0.15-0.19(5)

Qo=3.02 3/2[422] 0.50

3/2[402] 0.25

124.9 5/2[532] -0.15-0.49+14

-22

105Mo 95.3 5/2[532] -0.15-0.12(3)

Qo=3.06 138.3 5/2[532] -0.17-0.25(4)

Nucleus Energy (keV)

Configurations (cal)(exp)

109Ru 185.1 5/2[413] 1.07

Qo=3.28 5/2[402] -0.26-0.25(6)

222.7 5/2[413] 0.98

5/2[402] -0.24 -0.35(10)

111Ru 150.2 5/2[413] 0.85

Qo=3.32 5/2[402] -0.21-0.32(2)

Summary

Nucleus Bands Previously assigned Conf.

Present work

101Zr Ground band 3/2[411] confirmed

103Mo Ground band 3/2[411] confirmed

Excited band 5/2[532] confirmed

105Mo Ground band 5/2[532] confirmed

107Mo Ground band 5/2[413] 5/2[402]

Excited band 7/2[523] confirmed

109Ru Ground band 5/2[413]5/2[402]

5/2[402]

111Ru Ground band 5/2[413]5/2[402]

5/2[402]