Importance of The Doppler Effect for The Precision Measurement of The

29Si Binding Energy

Yongkyu Ko and Kyungsik Kim

School of Liberal Arts and Science, Korea Aerospace University, Korea

1. Abstract2. Motivation3. Neutron capture reaction4. Deuteron binding energy5. Binding energy of 29Si 6. Summary and conclusion

Using a flat crystal spectrometer, the binding energy of the neutron capture reaction can be determined precisely by measuring the -ray energy with the Bragg law.

In a cascade decay such as the 29Si nucleus, the nucleus of the intermediate state has a considerable velocity, because it is recoiling by emitting the primary -ray.

Therefore the precision measurement of the secondary -ray energy should be made by considering the Doppler broadening and shift.

Possible corrections are estimated in determining the binding energy with relativistic kinematics and an angular correlation method is suggested to compensate for the Doppler shifted -ray.

Abstract

Results in the scale of interferometer angle

Measurement of the Bragg angle with the flat crystal spectrometer

Principle of the two axis flat crystal spectrometer

Bdn sin2 law sBragg'

Motivation

Principle of Penning trap measurement

Cyclotron frequencymqB

Comparison of the two experiments

Flat crystal spectrometer

Penning T

rap

Energy levels of 29Si

Neutron Capture Reaction

nAA SXmXmnm )()()( 1

1*1 )()()( b

AA EXmXmnm

21*1 )()( b

AA EXmXm

nbb SEE 21

Binding energy of neutron

Decay Scheme of 29Si

Feynman diagram for neutron capture reaction

Separation of binding energy into two parts

Deuteron Binding Energy

kqpp 21

MMMEb 2

222

eV cos2.1203.07.1317)23(2.2223255

cos)2()(

2

cos)2(2)(2

111122

1111222

M

mKK

MKm

M

mKKKmMMEb

112

111

12

1..

)2(||Kmm

mKK

Emp

v mc

Nonrelativistic calculations

Velocity of the center of mass system

Relativistic calculations

Energy-momentum conservation

eV 056.0 for km/s 6.1 1.. Kv mc

EmE 21 kqp

1:

Binding energy for 29Si

110 kppp

eV cos3.10.09.231)16(3.3538966

cos)2()(

2111112

2

111

M

mKK

MKm

MEb

Velocity of the center of mass system

112

111

12

1..

)2(||Kmm

mKK

Emp

v mc

eV 056.0 for m/s 114 1.. Kv mc

11 EMm

110 kp

Binding energy for the excited state of 29Si

Energy-momentum conservation for the capture reaction

1

2

111

2

1

2

111 2MMMEb

Binding energy of the excited state

cos22 2

21

21

221

2

22

22 MMMMEb

eV cos9.6460.0

9.4509.231)40(3.4933946)16(3.3538966

cos222 2

21

21

221

2

22

1

21

2121

MMMMM

EEE bbb

221 kpp 221 EE

221 kpp

Energy-momentum conservation for the decay of the intermediate state

Binding energy of the intermediate state

Total binding energy

Velocity of the intermediate nucleus

1

2

12int21 2

)(21

Mcv

cMKE

km/s 39int v

Angular correlation

Angular correlation function

max

)(cos)(l

evenlllPAW

)cos1(16

3)( 2

W

)cos73

1(323

)( 2

W

For 010 dipole-dipole

For 1/23/21/2 dipole-dipole

GAMS4 Facility and the Reactor at Institut Laue Langevin

The through tube makes coincident measurements possible

Summary and conclusion

• The velocity of the recoiled nucleus due to the emission of a primary gamma ray is significantly so large (39km/s) that the Doppler shift of the secondary gamma ray reach 647.9 eV.

In the reaction the velocity of the incident neutron does not cause significant Doppler effect so that the recoil term of the intermediate nucleus is easily calculated and is in agreement with a non-relativistic calculation.

• Precision measurement of gamma ray with flat crystal spectrometer should consider such a large Doppler shift and Doppler broadening.

Si),n,(Si 2928

• A coincidence measurement of gamma rays with angular correlation would be a good solution.