Beta decay: energy relations

Size: px

Start display at page:

Download "Beta decay: energy relations"

Gary Austin Morgan
6 years ago
Views:

Beta decay: energy relations atomic mass Mc 2 = M ' c 2 + Zm e c 2 B el nuclear mass electron binding energy P(arent) D(aughter) a) β - decay A Z X N A Z+1 X N 1 + e +ν e Nuclear recoil is very small

1 Beta decay: energy relations atomic mass Mc 2 = M ' c 2 + Zm e c 2 B el nuclear mass electron binding energy P(arent) D(aughter) a) β - decay A Z X N A Z+1 X N 1 + e +ν e Nuclear recoil is very small Q β = T e +T νe = M P ' c 2 M D ' c 2 m e c 2 In the following, we assume that the neutrino mass is ~zero and that the very small differences in electron binding energy between the parent and daughter atoms can be neglected. This gives: Q β = M P c 2 M D c 2 Consequently, the β - decay process is possible whenever M P >M D b) β + decay A Z X N A Z 1 X N+1 + e + +ν e Q β + = T e + +T νe = M P ' c 2 M D ' = M P c 2 ( M D c 2 + 2m e c 2 ) c 2 m e c 2 Consequently, the β + decay process has a threshold 2m e c 2

2 c) Electron capture (inverse beta decay) A Z X N + e A Z 1 X N+1 +ν e ( ) Q EC = M P c 2 M D c 2 B en Atomic electron is captured by a proton. This process leaves the atom in an excited state: a vacancy has been created! The vacancy is quickly filled by producing the characterisdc X-ray cascade

3 examples mass relationship in electron capture between the parent and daughter atom energy relations in various beta decay processes β + decay can occur when the mass of parent atom exceeds that of daughter atom by at least twice the mass of the electron

Radiocarbon dating half-life of 5730 years Radiocarbon dadng is a radiometric dadng method that uses 14 C to

The technique was developed by Libby and his colleagues in 1949.

The level of 14 C in plants and animals when they die approximately equals the level of 14 C in the atmosphere at

4 Radiocarbon dating half-life of 5730 years Radiocarbon dadng is a radiometric dadng method that uses 14 C to determine the age of carbonaceous materials up to about 60,000 years old. The technique was developed by Libby and his colleagues in In 1960, Libby was awarded the Nobel Prize in chemistry for this work. The level of 14 C in plants and animals when they die approximately equals the level of 14 C in the atmosphere at that Dme. However, it decreases thereaser from radioacdve decay. Atmospheric nuclear weapon tests almost doubled the concentradon of 14 C in the Northern Hemisphere. The date that the ParDal Test Ban Treaty (PTBT) went into effect is marked on the graph.

5 Radiokrypton dating 81 Kr half-life is y Guarani Aquifer, Brazil h[ps://

6 Other applications J h[p://blogs.technet.com/b/andrew/archive/2010/05/28/beta-decay.aspx I am pre[y sure the term beta in sosware isn t related to atomic decay, but there are some similarides in that an atom that decays is unstable and decays aser a period of Dme to something more stable e.g. Carbon14 to Nitrogen14. In the MicrosoS world, the Dme to decay is usually 180 days (compared to a half life of 5,730 years for Carbon 14 to decay) and this results in fallout- the loss of bugs idendfied during the beat period, and some performance improvements and small enhancements leading to a very stable released product. (Andrew.Fryer)

7 Neutron beta decay h[p://physics.aps.org/synopsis-for/ /physrevle[ Astrophysicists rely on a precise value of the free neutron lifedme to calculate the rate of nucleosynthesis during the big bang, while pardcle physicists use it to constrain fundamental parameters of the standard model. Yet measured lifedmes have varied by about a percent (or 8 sec), depending on the experimental technique. NIST: Phys. Rev. Le[. 111, (2013): T n =(887.7±1.2[stat]±1.9[syst]) s Neutron lifetime (s) Ref. [3] [4] [6] Bottle Beam [7] [8] [9] 876 [5] Date published FIG. 1 (color online). The neutron lifetime measurements used in the 2013 PDG world average. The weighted mean and 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uncertainty (inflated by scale factor 2 =d:o:f: ¼ 1:53, following PDG procedures) of the data set is represented by the dashed line and shaded band.

Neutron radiative beta decay h[p://physics.aps.org/synopsis-for/10.1103/physrevle[.116.

Now the spectrum of these photons has been measured with the greatest precision to date in an experiment at the NaDonal InsDtute of Standards and Technology

The measurement comes close to the level of precision needed to look for deviadons from QED predicdons, which would signal a break from standard model

$In 2006, the NIST team used this setup to measure the photon branching rado (the fracdon of radiadon-producing decays) with an uncertainty of about 10% over$

8 Neutron radiative beta decay h[p://physics.aps.org/synopsis-for/ /physrevle[ According to QED, the neutron decay also produces photons, most of which come from the deceleradon of the emi[ed electron. Now the spectrum of these photons has been measured with the greatest precision to date in an experiment at the NaDonal InsDtute of Standards and Technology (NIST), Maryland. The measurement comes close to the level of precision needed to look for deviadons from QED predicdons, which would signal a break from standard model physics. In 2006, the NIST team used this setup to measure the photon branching rado (the fracdon of radiadon-producing decays) with an uncertainty of about 10% over a limited energy range. The new experiment reduces this uncertainty to less than 5% by measuring more neutrons, collecdng more photons, and using new techniques to characterize the detectors. Based on 22 million electron-proton events, the researchers report an average branching rado of for product photons with energies between 14.1 and 782 kev. They are now working on reducing the experimental uncertainty to the 1% level needed to test predicdons that go beyond QED. h[p://journals.aps.org/prl/abstract/ / PhysRevLe[

9 Beta decay: spectrum and lifedme W i f = 2π! φ 2 dn f V int φ i ( de e,ν e ) product wave function of the daughter nucleus, electron, and antineutrino! p D +! p e +! p ν = 0 T D +T e +T ν = Q = E wave function of the parent nucleus! p D, E D! p e, E e The expression for the density of final states of en electron emi[ed with a given energy and momentum (integrated over all angles) is: dn ( de e,ν e ) = V 2 4π! 6 c p 2 3 e ( E E e ) 2 1 m 2 v c 4 ( E E e ) dp 2 e! p ν, E ν V int gδ ( r! n r! p )δ ( r! n r! ) δ! e ( r n r! )Ô(n p) υ zero-range

10 Depends on nuclear wave functions W i f ( p e )dp e = M ' 2 fi 2 ( ) p e 2π 3! 7 c 3 F Z D, p e ( E E e ) 2 1 m 2 v c 4 ( E E e ) dp 2 e Fermi function: F ( Z, p e ) = 2πη 1 e, 2πη η ± Ze2!v e positive (negative) sign used for β - (β + ) decay

11 KATRIN neutrino experiment h[p:// Deviations around the endpoint due to nonzero neutrino mass h[ps://

12 If we assume that the matrix element does not depend on E e-, and aser taking out the strength g of the weak interacdon, one obtains: 2π 3! 7 ft = g 2 m 5 e c 4 ˆM, ˆM ' 2 fi gm ' fi ' fi ( ) = F Z D, w 2 1 ( ) 2 wdw f-function f Z D,w 0 w 0 1 ( ) w 2 1 w 0 w where w = E e / m e c 2 and w 0 is the reduced max. electron energy. electrons positrons

( ) c) Electron capture (inverse beta decay)

( ) c) Electron capture (inverse beta decay) c) Electron capture (inverse beta decay) A Z X N + e A Z 1 X N+1 +ν e ( ) Q EC = M P c 2 M D c 2 B en Atomic electron is captured by a proton. This process leaves the atom in an excited state: a vacancy