Beta decay Coupling between nucleons and weak field
One of the puzzles in understanding beta-­‐decay was the emission of par:cles (electron, positron, neutrino) that are not present in the atomic nucleus. • 1899 Rutherford discovers beta radiation!
• 1900 Becquerel suggests that beta particle is an electron!
• 1901 Rutherford and Soddy discover that beta radioactivity involves transmutation!
• 1911 Meitner and Hahn show that beta spectrum is continuous!
• 1930 Pauli postulates neutrino!
• 1931 Fermi names the new particle neutrino!
• 1933 quantum theory of radiation developed!
• 1934 Fermi theory of beta decay (based on relativistic formalism). The original
Fermi’s idea was that the weak force responsible for beta decay had essentially zero
range. !
• 1934 Wick develops theory of electron capture!
• 1937 Electron capture observed by Alvarez!
• 1956 Neutrino detected by Cowan and Reines!
• 1957 Fall of parity conservation. Fermi theory revisited.!
• 1961 Glashow, introduces neutral intermediate boson of weak interactions!
• 1962 Three types on neutrino (Lederman, Schwartz and Steinberger)!
• 1974 Pati-Salam GUT model!
• 1984 GUT. Georgi and Glashow!
• 1983 W and Z bosons discovered at CERN!
Dear radioac:ve ladies and gentlemen, As the bearer of these lines [...] will explain more exactly, considering the 'false' sta:s:cs of N-­‐14 and Li-­‐6 nuclei, as well as the con:nuous β-­‐spectrum, I have hit upon a desperate remedy to save the "exchange theorem" of sta:s:cs and the energy theorem. Namely [there is] the possibility that there could exist in the nuclei electrically neutral par:cles that I wish to call neutrons, which have spin 1/2 and obey the exclusion principle, and addi:onally differ from light quanta in that they do not travel with the velocity of light: The mass of the neutron must be of the same order of magnitude as the electron mass and, in any case, not larger than 0.01 proton mass. The con:nuous β-­‐spectrum would then become understandable by the assump:on that in β decay a neutron is emiUed together with the electron, in such a way that the sum of the energies of neutron and electron is constant. […] But I don't feel secure enough to publish anything about this idea, so I first turn confidently to you, dear radioac:ves, with a ques:on as to the situa:on concerning experimental proof of such a neutron, if it has something like about 10 :mes the penetra:ng capacity of a γ ray. I admit that my remedy may appear to have a small a priori probability because neutrons, if they exist, would probably have long ago been seen. However, only those who wager can win, and the seriousness of the situa:on of the con:nuous β-­‐spectrum can be made clear by the saying of my honored predecessor in office, Mr. Debye, [...] "One does best not to think about that at all, like the new taxes." [...] Therefore one should seriously discuss every way of rescue. Thus, dear radioac:ve people, scru:nize and judge. -­‐ Unfortunately, I cannot personally appear in Tübingen since I am indispensable here in Zürich because of a ball on the night from December 6 to 7. With many gree:ngs to you, also to Mr. Back, your devoted servant, W. Pauli n → p + e− + ν e
The bilinear combina:ons ("currents") of the fermion fields are Lorentz four-­‐vectors, similarly to the electromagne:c current (coupled to vector four-­‐poten:al) familiar from QED: (Fermi)
µ
µ
Four-fermion Lagrangian
Lint
= −G (ψ pγ ψ n ) (ψeγ ψυ ) + h.c.
Why is it called antineutrino?
an annihilation operator for particle
or
a creation operator for antiparticle
Nuclear beta decay is one of the many facets of weak interac:on. The basic reac:ons involving weak interac:ons in nuclei may be characterized by the decay of a neutron and a (bound) proton: n
pbound
→
p + e− + ν e
→ n + e+ + ν e
A free proton cannot beta decay since a free
neutron is more massive (939.566 MeV) than
a free proton (938.272 MeV).
There are many other examples of weak decays: a) semi-leptonic processes (both hadrons and leptons are involved)
π+ →
µ+ + νµ
e+ + ve
π− →
µ− + νµ
e− + ve
b) purely-leptonic processes
µ− → e− + v e + ν µ
The coupling constant (Fermi coupling constant):
Force carriers: GF = 1.16639(2) ×10 −11 (!c)3MeV-2
mW c 2 = 80.36 ± 0.12 GeV
mZ c 2 = 91.187 ± 0.07GeV
interaction range is very short ~10-3 fm
(weak interactions can be considered as zero-range
in nuclear physics!)
Beta decay: energy relations
Z
Mc = M c + Zmec − ∑ Bei
2
atomic mass
'
2
2
i=1
nuclear mass P(arent)
a) β- decay
A
Z
electron binding energy D(aughter)
X N → Z+1A X N−1 + e− + ν e
Qβ − = Te− + Tν e = M P' c 2 − M D' c 2 − mec 2
Nuclear recoil is very small 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 = M c 2 − M c 2
β−
P
D
Consequently, the β-­‐ decay process is possible whenever MP>MD b) β+ decay
A
Z
X N → Z−1A X N+1 + e+ + ν e
Qβ + = Te+ + Tν e = M P' c 2 − M D' c 2 − mec 2
= M P c 2 − ( M D c 2 + 2mec 2 )
Consequently, the β+ decay process has a threshold 2mec2 Atomic electron is captured by a proton. This process leaves c) Electron capture
(inverse beta decay) the atom in an excited state: a vacancy has been created! The vacancy is quickly filled by producing the characteris:c X-­‐ray A
−
A
cascade Z X N + e → Z−1 X N+1 + ν e
QEC = M P c 2 − ( M D c 2 − Ben )
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 da:ng is a radiometric da:ng method that uses 14C to determine the age of carbonaceous materials up to about 60,000 years old. The technique was developed by Libby and his colleagues in 1949. In 1960, Libby was awarded the Nobel Prize in chemistry for this work. The level of 14C in plants and animals when they die approximately equals the level of 14C in the atmosphere at that :me. However, it decreases thereamer from radioac:ve decay. Atmospheric nuclear weapon tests almost doubled the concentra:on of 14C in the Northern Hemisphere. The date that the Par:al Test Ban Treaty (PTBT) went into effect is marked on the graph. Radiokrypton dating
81Kr half-­‐life is 2.293·∙105y Guarani Aquifer, Brazil
hUps://www.phy.anl.gov/mep/aUa/research/aUa.html Other applications J
hUp://blogs.technet.com/b/andrew/archive/2010/05/28/beta-­‐decay.aspx “I am preUy sure the term beta in somware isn’t related to atomic decay, but there are some similari:es in that an atom that decays is unstable and decays amer a period of :me to something more stable e.g. Carbon14 to Nitrogen14. In the Microsom world, the :me 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 iden:fied during the beat period, and some performance improvements and small enhancements leading to a very stable released product.” (Andrew.Fryer) es not rely on the 6 Liðn; tÞ4 He cross section or any other nuclear data. The detection
consistent with the value used in 2005 but is measured with a precision of 0.057%, which
fivefold improvement in the uncertainty. We verify the temporal stability of the neutron
ugh ancillary measurements, allowing us to apply the measured neutron monitor efficiency to
result from the 2005 experiment.
The updated lifetime is !n ¼ ð887:7 # 1:2½stat% #
hUp://physics.aps.org/synopsis-­‐for/10.1103/PhysRevLeU.111.222501 Neutron beta decay
PhysRevLett.111.222501
PACS numbers: 21.10.Tg, 14.20.Dh, 23.40.'s, 26.35.+c
Astrophysicists rely on a precise value of the free neutron life:me to calculate the rate of nucleosynthesis during the big bang, while par:cle physicists use it to constrain not only improve the experimental limits on !n but to also
nation of the mean lifetime of the
fundamental p
arameters of the standard model. Yet measured life:mes have varied by undamentally important questions
carefully study systematic effects in all methods. We have
physics,
and cosmology
[1,2].dTo
completed
investigation
into the dominant
systematic
about a percent, epending on anthe experimental technique. Neutron lifetime (s)
mental strategies have been used to
uncertainty in the most precise beam neutron lifetime
neutron lifetime. In the first, or
measurement, resulting in confirmation of the accuracy
of neutron decay
dN=dt and
the Rev. of the
fluence
measurement
and
reduction in
NIST: Phys. LeU. 111, 222501 technique
(2013): T a=(887.7±1.2[stat]±1.9[syst]) s in a well-defined volume of a
the total uncertainty in the lifetime result. n
rmined. The neutron lifetime is
896
ferential form of the exponential
Bottle
¼ 'N=!n . In the second, or bottle
Beam
892
ciently low energy are confined in
ed by some combination of mate888
Ref. [3]
ds, and/or gravity. The number of
[8] [9]
various times t is measured and fit
884
[4]
[7]
[6]
y function NðtÞ ¼ Nð0Þe't=!n in
to form the 2013 Particle Data
rage value for !n include the five
asurements shown in Fig. 1 [10].
y reasonable internal consistency
among the beam determinations,
each other by 2:6" (where " is
. Historical discrepancies among
eriments and between bottle and
ggest that it is highly desirable to
=222501(4)
880
876
[5]
1995
2000
2005
2010
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.
222501-1
! 2013 American Physical Society
Can proton beta-decay? Discuss.
Discuss beta decay of doubly-magic nuclei
•  48Ni
•  78Ni
•  100Sn
•  132Sn
Provide decay equations. Find Q-values.