Cross Sections for Cross Sections for Positrons Colliding Positrons Colliding

with H , Hwith H , H2 2 , He, He

Department of PhysicsDepartment of PhysicsNational Tsing Hua UniversityNational Tsing Hua University

G.T. ChenG.T. Chen2007/6/122007/6/12

OutlineOutline

IntroductionIntroduction Cross sectionsCross sections

- H- H

- H- H22

- He- He Discussion and Future WorkDiscussion and Future Work

IntroductionIntroduction

Some problems for the 511 keV annihilSome problems for the 511 keV annihilation line had been reported.ation line had been reported.

In order to understand the evolution oIn order to understand the evolution of positrons in our galactic center regiof positrons in our galactic center region, we first have to know cross sections n, we first have to know cross sections of positrons colliding with H , Hof positrons colliding with H , H2 2 , He., He.

N. Guessoum et al. 2005 A&AN. Guessoum et al. 2005 A&A ““The live and deaths of positrons in the interstellThe live and deaths of positrons in the interstellar medium”ar medium”

IntroductionIntroduction

The varieties of cross sections:The varieties of cross sections: Charge ExchangeCharge Exchange IonizationIonization ExcitationExcitation Direct annihilation with free electronsDirect annihilation with free electrons Radiative combination (with free electroRadiative combination (with free electro

n) n) Direct annihilation with bound electronsDirect annihilation with bound electrons

IntroductionIntroduction

Charge Exchange (CE):Charge Exchange (CE):

P+

Positronium

Atom or Molecule

e+

Positron

IntroductionIntroduction

Ionization (ION):Ionization (ION):

Atom or Molecule

e+

Positron

e+

e-

P+

IntroductionIntroduction

Excitation (EX):Excitation (EX):

Atom or Molecule

e+

Positron

e+

*

IntroductionIntroduction

Threshold energy of each process Threshold energy of each process

CE

EX

IONH

H2

He

Cross SectionsCross Sections

H H2 He

Cross sections (H-CE)Cross sections (H-CE)

Cross sections (H-ION)Cross sections (H-ION)

40eV

Cross sections (H-EX)Cross sections (H-EX)

Cross sections (H)Cross sections (H)

Cross SectionsCross Sections

H H2 He

Cross Sections (HCross Sections (H22-CE)-CE)

Cross Sections (HCross Sections (H22-ION)-ION)

Cross Sections (HCross Sections (H22-EX)-EX)

Cross Sections (HCross Sections (H22-EX)-EX)

Cross Sections (HCross Sections (H22))

？

Cross SectionsCross Sections

H H2 He

Cross Sections (He-CE)Cross Sections (He-CE)

Cross Sections (He-ION)Cross Sections (He-ION)

150eV

Cross Sections (He-EX)Cross Sections (He-EX)

Cross Sections (He)Cross Sections (He)

？

Discussion and Future Discussion and Future WorkWork

Study other processes and energy loss Study other processes and energy loss processesprocesses

Calculate the evolution of positrons in Calculate the evolution of positrons in the galactic center region by diffusion the galactic center region by diffusion equationequation

Produce spectrum with 511 keV annihProduce spectrum with 511 keV annihilation lineilation line

>>Thank You<<>>Thank You<<

IntroductionIntroduction

Problems:Problems: The production of positronsThe production of positrons The galactic map of the annihilation The galactic map of the annihilation

line line The propagation/evolution of the The propagation/evolution of the

positrons between their production positrons between their production sites and annihilation placessites and annihilation places

IntroductionIntroduction

IntroductionIntroduction

After thermalization of positrons, some rAfter thermalization of positrons, some reactions occur: eactions occur:

charge exchange with H, Hcharge exchange with H, H22, He, He direct annihilation with free electronsdirect annihilation with free electrons radiative combination (with free electroradiative combination (with free electro

n) n) direct annihilation with bound electronsdirect annihilation with bound electrons

e e Ps

e e

e H p

e H Ps H

Diffusion EquationDiffusion Equation

, ,i k ii i i i k

k i

N dE ND N N Q r E t

t E dt