Importance of The Doppler Effect for The Precision Measurement of The 29 Si Binding Energy Yongkyu...
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Transcript of Importance of The Doppler Effect for The Precision Measurement of The 29 Si Binding Energy Yongkyu...
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
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.