Importance of The Doppler Effect for The Precision Measurement of The 29 Si Binding Energy Yongkyu Ko and Kyungsik Kim School of Liberal Arts and Science, Korea Aerospace University, Korea 1. Abstract 2. Motivation 3. Neutron capture reaction 4. Deuteron binding energy 5. Binding energy of 29 Si 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 29 Si 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 Motivation

Principle of Penning trap measurement Cyclotron frequency

Comparison of the two experiments Flat crystal spectrometer Penning Trap

Energy levels of 29 Si Neutron Capture Reaction

Binding energy of neutron Decay Scheme of 29 Si Feynman diagram for neutron capture reaction Separation of binding energy into two parts

Deuteron Binding Energy Nonrelativistic calculations Velocity of the center of mass system Relativistic calculations Energy-momentum conservation :

Binding energy for 29 Si Velocity of the center of mass system Binding energy for the excited state of 29 Si Energy-momentum conservation for the capture reaction Binding energy of the excited state

Energy-momentum conservation for the decay of the intermediate state Binding energy of the intermediate state Total binding energy Velocity of the intermediate nucleus

Angular correlation Angular correlation function For 0  1  0 dipole-dipole For 1/2  3/2  1/2 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 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. A coincidence measurement of gamma rays with angular correlation would be a good solution.