probability of surviving through at least time t
DESCRIPTION
probability of surviving through at least time t. mean lifetime = 1/. For any free particle ( separation of space-time components ). Such an expression CANNOT describe an unstable particle. since. Instead mathematically introduce the exponential factor:. then. - PowerPoint PPT PresentationTRANSCRIPT
NdtdN teNtN )0()(
tet )(Pprobability of surviving
through at least time t
mean lifetime = 1/
For any free particle (separation of space-time components)
/0)0()( tiEet
Such an expression CANNOT describe an unstable particle
since2//22 )0()0()( 00 tiEtiE eet
Instead mathematically introduce the exponential factor:
2//0)0()( ttiE eet
/22 )0()( tet
2//0)0()( ttiE eet
then
a decaying probabilityof surviving Note: =ħ
/)2/(0)0()(
tiEiet
Also notice: effectively introduces an imaginary part to E
/)2/(0)0()(
tiEiet
Applying a Fourier transform:
0
/)()( dtetEg iEt
0
]/)(2
[
0
/)2/(/
0
0
)0(
)0()(
dte
dteEg
tEEi
tiEiiEt
)](2
[0
EEit
e
2/)()(
0
iEEEg
still complex!
What’s this represent?
E distribution ofthe unstable state
4/)(
4/)(
220
2
max
EE
E
Breit-Wigner Resonance Curve
Expect
4/)(
4/)()(*~)(
220
2
max
EEEgEgE
some constant
Eo E
1.0
0.5
MAX
= FWHM
When SPIN of the resonant state is included:
4/)(
4/
)12)(12(
)12()(
220
2
max
EEss
JE
ba
130-eV neutron resonancesscattering from 59Co
Transmission
-ray yield for neutron radiative
capture
+p elastic scattering cross-section in the region of the Δ++ resonance.
The central mass is 1232 MeV with a width =120 MeV
Cross-section for the reaction
e+e anything
near the Z0 resonanceplotted against
cms energy
Cross section for the reaction B10 + N14* versus energy.The resonances indicate levels in the compound nucleus N14*.[Talbott and Heydenburg, Physical Review, 90, 186 (1953).]
Spectrum of protons scattered from Na14 indicating its energy levels.[Bockelman et al., Physical Review, 92, 665 (1953).]
Resonances observed in the radiative proton capture by 23Na.[P.W.m. Glaudemans and P.M. Endt, Nucl. Phys. 30, 30 (1962).]
