Measurement of lifetime for muons captured inside nuclei

Content

1. Introduce of the muon capture 2. The difference of the free decay an

d captured decay 3. How to measure the capture event 4. The apparatus of this experiment 5. The analysis of this experiment 6. Summary

Introduce of the muon capture

Muonic atom

1. Muon entering the matter

2. Electromagnetic interactions

3. One electron is replaced by muon and transitions down to the muonic atom K-shell around sec 910

Muonic atom

Due to the relatively high mass of muon, the Bohr radius of muon is 206.7 times smaller than electron orbit

Only negative charged muon can form muonic atom

Muon capture

There are two process of muon capture :

μ+p→n+ν

μ+p→n+ν+γ The process contains no charged particles i

n the results The process is relatively fast Only negative charged muon may be captur

ed

The difference of the free decay and captured decay

About muon lifetime

Muon lifetime is a typical process of radioactive decay.

The radioactive decay is a random process, independent of the previous life of the particle.

Muon lifetime distribution

dttNtdN )()(

The number of decayed muon

The number of muons at time t

is a constant“decay rate”

teNtN 0)(

We call the muon lifetime is

1

The example of muon lifetime measurement

Muon captured lifetime distribution

The capture decay lifetime is also a radioactive decay.

Because of the relative short lifetime of capture process, the lifetime we measured will less than free decay lifetime.

How the muon capture affect the muon lifetime measurement

The free decay lifetime:

The capture decay lifetime:

Here the A and C are constants, B is the mean lifetime of freedecay, D is the mean lifetime of capture decay, E is the randomaccidental coincidence which produced by the noise.

CAey B

x

ECeAey D

x

B

x

The example of muon capture lifetime measurement

How to measure the capture event

How to measure the capture process

The two process of capture are:

μ+p→n+ν

μ+p→n+ν+γ

We can try to measure the n or γ-ray

Measuring the γ-ray

γ-ray are more efficiently detected by high Z materials.

To detect the γ-ray, the material’s cross sections of photoelectric and pair production must large compared to the compton scattering cross section

NaI is a good material to detect the γ-ray.

Measuring the neutron

The most common method to detect neutron is using another charged particles to replace the kinetic energy of neutron.

The neutron in the plastic scintillator or organic scintillator may have a strong probability to collide with the hydrogen's proton and transfer kinetic energy to the proton.

The apparatus of this experiment

The experiment flow chart

The detectorsμ

n

p

Experiment setup

TDC flow chart

ADC flow chart

The good event nim timing chart

μ

n

p

The cross event1 nim timing chart

particle

The cross event2 nim timing chart

particle

Muon flux

The flux of sea level muons is almost

for horizontal detectors For this experiment, the effective area

of the detector is The probability of two cosmic rays co

mes in 10 micro-sec is almost

12 min1 cm

2513cm

10000

1

The analysis of this experiment

The qualitative analysis of adc

The qualitative analysis of tdc

Cu target quantitative analysis

Fe target quantitative analysis

Al target quantitative analysis

Summary

The result

The average result The experiment result