1. Mellinger Lesson5 Einstein coefficient & HI line Toshihiro Handa Dept. of Phys. & Astron., Kagoshima University Kagoshima Univ./ Ehime Univ. Galactic radio astronomy

2. Mellinger Energy level ▶ Schrödinger equation of an electron ▶ Steady state = energy eigen value ■ Parameter separation ▶ Schrödinger equation for steady state

3. Mellinger Energy eigenvalue & bound states ▶ Solution depends on the boundary condition ■ Continuous E is possible if E>0. ■ Discreet values if E<0 (bound state) ▶ Continuous solution in quantum mechanics! ▶ In many cases, we consider bound states. ■ Discreet eigenvalues and eigenfunctions

4. Mellinger Electron in an atom/molecule ▶ Electron in an atom/molecule ■ Bound state → discreet energy levels ▶ Energy state

5. Mellinger Energy transition and matter ▶ Electron transition between energy levels ■ Emission & absorp of EM wave ■  E=h ▶ Structure of energy levels=matter identify ■ Wavelength of emission & absorption lines ■ Matter identification with spectrum

6. Mellinger Einstein coefficient(1) ▶ Emission & absorption: 2 level model ■ Transition probability of emission A Independent of input intensity ■ Transition probability of absorption B Proportional to input intensity dI = n 2 A-n 1 B I

7. Mellinger Einstein coefficiant(2)

8. Mellinger Stimulated emission(1) ▶ Add another process ■ Difficult to see the existence ▶ Introduction of “stimulated” emission ■ spontaneous emission A 21, absorption prob. B 12 ■ stimulated emission B 21 Emission proportional to input intensity! dI = n 2 A 21 -n 1 B 12 I+n 2 B 21 I = n 2 A 21 -(n 1 B 12 -n 2 B 21 ) I Seems to reduce the effective absorption coeff.

9. Mellinger Stimulated emission(2)

10. Mellinger Relation between Einstein coff.

11. Mellinger Maser(1)

12. Mellinger Maser(2) ▶ We can make T<0 for 3 level system pomping inverse population maser seed photon

13. Mellinger Maser(3) ▶ MASER Microwave Amplification by Stimulated Emission of Radiation ■ Developed by Towns in 1954 He found ammonia in space, too. ▶ LASER ■ Microwave →Light ▶ Characteristics of stimulated photon ■ Same freq., phase, polarization as the seed photon First detected molecule with 3 atoms in space

14. Mellinger Excitation temperature

15. Mellinger Emissivity

16. Mellinger Absorption coefficient(1)

17. Mellinger Absorption coefficient(2)

18. Mellinger Source function

19. Mellinger Neutral atomic hydrogen ▶ proton + electron ■ Proton is a particle with spin 1/2  2 values ■ electron is a particle with spin 1/2  2 values spin of a particle=should be related with mangetizm Interaction between two spins A 10 =2.86888 × 10 -15 [s -1 ],  =1.420405751786[GHz]

20. Mellinger HI emission(1)

21. Mellinger HI emission(2)

22. Mellinger HI emission(3)

23. Mellinger What is the natural width  ( )? ▶ Duration in quantum transition  t ■ Not 0 ∵ emitted EM wave is not  (t) time profile ■ Not ∞ ∵ finish the transition in finite time span ▶ Gradually increase and gradually decrease ▶ Give a width after Fourier transformation wave packet wave particle

24. Mellinger report ▶ Attach to your e-mail. Deadline : 13 Nov. ■ Submit to handa@sci.kagoshima-u.ac.jp ▶ Questions 1.Show relations between Einstein coeff. 2.How long the mean time to transit a neutral hydrogen atom?