Beta decay: energy relations
2 ' 2 2 atomic mass Mc = M c + Zmec − Bel nuclear mass electron binding energy
P(arent) D(aughter) - A A − a) β decay Z XN → Z+1 XN−1 + e +νe ' 2 ' 2 2 Nuclear recoil is very small Q − = T − +T = M c − M c − m c β e νe P D e 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 c2 M c2 β − = P − D
- Consequently, the β decay process is possible whenever MP>MD
+ A A + b) β decay Z XN → Z−1 XN+1 + e +νe ' 2 ' 2 2 Q + = T + +T = M c − M c − m c β e νe P D e 2 2 2 = M Pc −(M Dc + 2mec )
+ 2 Consequently, the β decay process has a threshold 2mec c) Electron capture Atomic electron is captured by a proton. This process leaves (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 X e− A X Z N + → Z−1 N+1 +νe cascade 2 2 QEC = M Pc −(M Dc − Ben ) examples…
mass relationship in electron capture between the parent and daughter atom energy relations in various beta β+ decay can occur when the mass of parent decay processes 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 therea er 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
h ps://www.phy.anl.gov/mep/a a/research/a a.html 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 so ware isn’t related to atomic decay, but there are some similari es in that an atom that decays is unstable and decays a er a period of me to something more stable e.g. Carbon14 to Nitrogen14. In the Microso 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) week ending PRL 111, 222501 (2013) PHYSICAL REVIEW LETTERS 27 NOVEMBER 2013
Improved Determination of the Neutron Lifetime
A. T. Yue,1,2,3,* M. S. Dewey,2 D. M. Gilliam,2 G. L. Greene,3,4 A. B. Laptev,5,6 J. S. Nico,2 W. M. Snow,7 and F. E. Wietfeldt5 1Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA 2National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA 3University of Tennessee, Knoxville, Tennessee 37996, USA 4Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 5Tulane University, New Orleans, Louisiana 70118, USA 6Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 7Indiana University, Bloomington, Indiana 47408, USA (Received 6 September 2013; published 27 November 2013) The most precise determination of the neutron lifetime using the beam method was completed in 2005 and reported a result of 886:3 1:2 stat 3:2 syst s. The dominant uncertainties were attributed n ¼ð Æ ½ Æ ½ Þ to the absolute determination of the fluence of the neutron beam (2.7 s). The fluence was measured with a neutron monitor that counted the neutron-induced charged particles from absorption in a thin, well- characterized 6Li deposit. The detection efficiency of the monitor was calculated from the areal density of the deposit, the detector solid angle, and the evaluated nuclear data file, ENDF/B-VI 6Li n; t 4He thermal ð Þ neutron cross section. In the current work, we measure the detection efficiency of the same monitor used in the neutron lifetime measurement with a second, totally absorbing neutron detector. This direct approach does not rely on the 6Li n; t 4He cross section or any other nuclear data. The detection ð Þ efficiency is consistent with the value used in 2005 but is measured with a precision of 0.057%, which represents a fivefold improvement in the uncertainty. We verify the temporalNeutron stability of beta the neutron decay monitor through ancillary measurements, allowing us to apply the measured neutron monitor efficiency to the lifetime result from the 2005 experiment. The updated lifetime is 887:7 1:2 stat h p://physics.aps.org/synopsis-for/10.1103/PhysRevLe .111.222501n ¼ð Æ ½ Æ 1:9 syst s. ½ Þ DOI: 10.1103/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 À nucleosynthesis during the big bang, while par cle physicists use it to constrain The accurate determination of the mean lifetime of the not only improve the experimental limits on n but to also free neutron addresses fundamentallyfundamental parameters of the standard model. Yet measured life mes have varied by important questions carefully study systematic effects in all methods. We have in particle physics, astrophysics,about a percent (or 8 sec), depending on the experimental technique. and cosmology [1,2]. To completed an investigation into the dominant systematic date, two distinct experimental strategies have been used to uncertainty in the most precise beam neutron lifetime accurately measure the neutron lifetime. In the first, or measurement, resulting in confirmation of the accuracy beam method, the rate of neutron decayNIST: dN=dt andPhys. Rev. Le . 111, 222501 (2013): the of the fluence measurement technique andT a=(887.7±1.2[stat]±1.9[syst]) reduction in s number of neutrons N in a well-defined volume of a the total uncertainty in the lifetime result. n neutron beam are determined. The neutron lifetime is determined from the differential form of the exponential 896 decay function dN=dt N= . In the second, or bottle Bottle n Beam method, neutrons of sufficiently¼À low energy are confined in 892 a trap or bottle established by some combination of mate- 888 rial walls, magnetic fields, and/or gravity. The number of Ref. [3] [8] [9] neutrons in the bottle at various times t is measured and fit 884 [4] [7] t= [6] to the exponential decay function N t N 0 eÀ n in ð Þ¼ ð Þ Neutron lifetime (s) 880 order to extract n. Measurements used to form the 2013 Particle Data [5] 876 Group (PDG) world average value for n include the five 1995 2000 2005 2010 bottle and two beam measurements shown in Fig. 1 [10]. Date published While there is currently reasonable internal consistency among the bottle and among the beam determinations, FIG. 1 (color online). The neutron lifetime measurements used the two sets differ from each other by 2:6 (where is in the 2013 PDG world average. The weighted mean and 1 one standard deviation). Historical discrepancies among uncertainty (inflated by scale factor 2=d:o:f: 1:53, follow- ¼ independent bottle experiments and between bottle and ing PDG procedures) of the data set isp representedffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi by the dashed beam measurements suggest that it is highly desirable to line and shaded band.
0031-9007=13=111(22)=222501(4) 222501-1 Ó 2013 American Physical Society Neutron radiative beta decay
h p://physics.aps.org/synopsis-for/10.1103/PhysRevLe .116.242501 According to QED, the neutron decay also produces photons, most of which come from the decelera on 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 Na onal Ins tute of Standards and Technology (NIST), Maryland. The measurement comes close to the level of precision needed to look for devia ons from QED predic ons, which would signal a break from standard model physics.
In 2006, the NIST team used this setup to measure the photon branching ra o (the frac on of radia on-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, collec ng more photons, and using new techniques to characterize the detectors. Based on 22 million electron-proton events, the researchers report an average branching ra o of 3.35×10−3 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 predic ons that go beyond QED.
h p://journals.aps.org/prl/abstract/10.1103/ PhysRevLe .116.242501 Beta decay: spectrum and life me
2 2π dn − W = φ f Vint φi e ,νe i→ f ! dE ( )
product wave function of the wave function of the parent nucleus daughter nucleus, electron, and ! ! antineutrino pD, ED pe− , Ee− ! ! ! pD + pe− + pν = 0
TD +Te− +Tν = Q = 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:
2 2 4 ! 2 dn − V 2 mv c pν , Eν e ,ν = p − E − E − 1− dp − ( e ) 6 3 e ( e ) 2 e dE 4π! c E E ( − e− )
! ! ! ! ! ! ˆ V ≈ gδ r − r δ r − r − δ r − r O(n → p) zero-range int ( n p ) ( n e ) ( n υ ) Depends on nuclear wave functions
2 ' 2 4 M fi 2 m c p dp F Z , p p2 E E 1 v dp Wi→ f ( e− ) e− = 3 7 3 ( D e− ) e− ( − e− ) − 2 e− 2π ! c E E ( − e− )
2 2πη Ze positive (negative) sign Fermi function: F Z, p − = , η ≡ ± ( e ) −2πη used for β- (β+) decay 1− e !ve− KATRIN neutrino experiment h p://www.katrin.kit.edu
Deviations around the endpoint due to nonzero neutrino mass…
h ps://www.youtube.com/watch?v=dmmVb779NP4 If we assume that the matrix element does not depend on Ee-, and a er taking out the strength g of the weak interac on, one obtains:
3 7 2π ! ˆ fT = 0.693 2 , M ' fi ≡ gM ' fi 2 5 4 ˆ g me c M ' fi
w0 2 f Z ,w = F Z , w 2 −1 w 2 −1 w − w wdw f-function ( D 0 ) ∫ ( D ) ( 0 ) 1
2 where and w = Ee − / mec w0 is the reduced max. electron energy.
positrons
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