ElectromagneSc (gamma) decay
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Transcript of ElectromagneSc (gamma) decay
Electromagne,c (gamma) decay Coupling between nucleons and EM field
• Electromagnetic and weak interactions can be treated as perturbations • Emission of a γ-ray is caused by the interaction of the nucleus with an external
electromagnetic field • Besides γ-decay, electromagnetic perturbation can also induce nuclear decay
through internal conversion whereby one of the atomic electrons is ejected. This is particularly important for the heavy nuclei.
• The decay can also proceed by creating an electron-positron pair (internal pair creation)
• Since the nuclear wave function has a definite angular momentum, the external EM field has to be decomposed in spherical multipoles. The quantization and multipole expansion of EM field is straightforward by tedious.
Electromagnetic Decay Kinematics of photon emission
€
Ei = E f + Eγ + T0recoil term
€
T0 ≈Eγ2
2M0c2
Ei
Ef
For A=100 and Eγ=1 MeV, the recoil energy is about 5 eV. But the natural linewidth of the radiation is even smaller.
The emission of photons without recoil is possible if one implants the nucleus in a la;ce. In such a case, the recoil is taken by the whole la;ce and not by a single nucleus. If
!ωlattice >> T0then, quantum-‐mechanically, the energy of the emiBed gamma radia,on takes away the total energy difference (Mössbauer effect – 1958 − or recoilless nuclear resonance fluorescence).
�r�r0
s
✓0
P
s = |�r � �r0|
V (⇧r) =
1
4⇥⌅0
1X
n=0
1
rn+1
Z(r0)nPn(cos �0)⇤(
⇧r0)d3r0
V (⇤r) =1
4�⇥0
0
@Q
r+
⇤p · ⇤rr3
+12
X
i,j
Qijxixj
r5· · ·
1
A
Qij =Z
(3x0ix
0j � r02�ij)⇥(⇤r0)d3r0
⇥p =Z
⇥r0�(⇥r0)d3r0 =NX
k=1
qk⇥r0k
Multipole expansion of electrostatic potential
dipole
quadrupole
€
V = −1cjµA
µ
nuclear current
two polarization states
!A(!r, t) = 1
Nb!kη!εηe
i(!k!r−ωt ) + b!kη
+ !εηe−i(!k!r+ωt ){ }
!k ,η∑
external EM field
photon creation operator
!A(!r, t) =
!Aλµ (!r, t)
λµ
∑ multipole expansion
The typical gamma-‐rays in nuclear transi,ons have energies less than 10 MeV, corresponding to wave numbers of the order k~1/20 fm-‐1 or less. The mul,pole operators give contribu,ons only within the nuclear volume. That is, in most cases kr<<1 and the above series may be approximated by the first term in the expansion alone (“The long-‐wavelength limit”). We are now ready to calculate the contribu,on of each mul,pole order to the transi,on probability from an ini,al nuclear state to a final state.
W (λ;Jζ i → J fξ ) =8π (λ +1)k2λ+1
λ (2λ +1)!![ ]2 !B(λ;Jiζ → J fξ )
transition probability reduced transition probability
This contains both electric and magne,c interac,ons
λ=1,2,3…
But what about λ=0?
Electromagnetic Rates
B(λ;Jiζ → J fξ ) = J fM fζ Oλµ JiMiξµM f
∑2=
12Ji +1
J fζ Oλµ Jiξ2
Oλµ (Eλ) = e(i)i=1
A
∑ riλYλµ (Ωi )
Oλµ (Mλ) = gs (i)!si + gl (i)
2!li
λ +1#
$%
&
'(!∇i
i=1
A
∑ riλYλµ (Ωi )#$ &'
!ji =!si +!li
gyromagnetic factors
Selection Rules
J f − Ji ≤ λ ≤ J f + Ji
W (λ +1)W (λ)
~ (kR)2 large reduction in probability with increasing multipolarity order!
POλµ (Eλ)P-1 = (−1)λOλµ (Eλ), POλµ (Mλ)P-1 = (−1)λ+1Oλµ (Mλ)
π iπ f = (−1)λ π iπ f = (−1)
λ+1
Magnetic transitions are weaker than electric transitions of the same multipolarity
6+
4+ E2, (M3, E4,…)
5+
4+ M1, E2, (M3, E4,…) mixed M1+E2 transition
140Gd
A decay scheme: E1, E2 and M1 transitions
Internal conversion
An atomic electron is ejected instead of gamma-‐ray (atomic Auger effect). Atomic electrons, especially those in the inner orbits, such as K-‐ and L-‐orbits, spend a large frac,on of their ,me in the vicinity of the nucleus, the source of the EM field.
Te−= Ei −Ef( )−Bn
Electron kinetic energy
nucleonic wave functions electron wave functions
Electron binding energy
Virtual photon exchange. This process can occur between I=0 states!
Electron spectrum: internal conversion + beta-decay background
Important for heavy nuclei (large Z). The importance of internal conversion goes as Z3 !!!
Important for heavy nuclei (large Z). The importance of internal conversion goes as Z3 !!!
Important for heavy nuclei (large Z): it goes as Z3 !!!
Internal pair production
An electron-‐positron pair is emiBed in the place of gamma-‐ray. This can happen if the energy of the decay
Eγ > 2mec2 =1.02MeV
Usually, this process is several orders of magnitude retarded compared to allowed gamma-‐ray decays. The pair produc,on rate is largest where the internal conversion rate is smallest. That is in the region of low atomic number and high transi,on energies.
electron scattering pair creation
E0 (IC+e+e_)
γγ = 2E1+2M1
Another interesting candidate is 137Ba. Why?
Nucl. Phys. A474, 412 (1987)
2-gamma decay
Provides important structural informa,on about nuclear electric polarizability and diamagne,c suscep,bility.
Best candidates: 16O, 40Ca, 90Zr
M1 and E1 transitions are similar in strength!
γ-ray laser?
hBps://str.llnl.gov/str/JulAug05/Becker.html
178Hf
2008 LLNL report: “Our conclusion is that the u,liza,on of nuclear isomers for energy storage is imprac,cal from the points of view of nuclear structure, nuclear reac,ons, and of prospects for controlled energy release. We note that the cost of producing the nuclear isomer is likely to be extraordinarily high, and that the technologies that would be required to perform the task are beyond anything done before and are difficult to cost at this ,me.”
hBp://defensetech.org/2006/06/13/superbomb-‐or-‐crapshoot/ hBp://www.theguardian.com/science/2008/aug/14/par,clephysics.research
Hafnium-‐178m has a long half-‐life of 31 years and a high excita,on energy of 2.4 MeV. As a result, 1 kilogram of pure 178mHf contains approximately 1012 J of energy. Some es,mates suggest that, with accelerated decay,1 gram of 100-‐percent isomeric 178mHf could release more energy than the detona,on of 200 kilograms of TNT.
hBp://physics.aps.org/synopsis-‐for/10.1103/PhysRevA.84.053429