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Radioactivity lecture 2

Fedor Danevich Institute for Nuclear Research, Kyiv, Ukraine http://lpd.kinr.kiev.ua [email protected] [email protected]

1 F.A. Danevich Univ. Tor Vergata October 09, 2015 Brief summary of Lecture 1 • Observation of radioactivity was one of the crucial steps to discover atomic nuclei

Antoine Uranium salt (1852 –1908) in the lab Photographic plate covered by opaque paper

2 F.A. Danevich Univ. Tor Vergata October 05, 2015 Brief summary of Lecture 1 • occur if energy of the initial state is higher than that of the final state (principle of minimum energy, the Necessary condition) and there is no conservation law forbidding the transition (the Sufficient condition) • Due to the mass–energy equivalence concept (E=mc2) the mass of atoms, nuclei and particles is a measure of its energy • Measurements of atomic mass allow to estimate radioactive decay possibility of the atomic nuclei

3 F.A. Danevich Univ. Tor Vergata October 05, 2015 Brief summary of Lecture 1 • Probability of the decay is higher for higher energy of decay

2.3 m  decay,  decay

187 W: Q = 1311 keV  24 h 242 10 Pu: Q = 4984 keV  4.410 y 242 Am: Q = 5583 keV  141 y 242Cm: Q = 6216 keV  163 d 187 10  Re: Q = 2.7 keV  4.410 y

4 F.A. Danevich Univ. Tor Vergata October 05, 2015 Brief summary of Lecture 1 • There are several types of radioactive decay, in many cases a combination of a few modes occurs (branching)

• Gamma emission, electron conversion • β- decay n  delayed emission • β+ decay  2n  delayed 2- + + • Electron Capture (EC) p delayed emission + 2p + delayed 2- • β-delayed particle emission    delayed  emission • Neutron decay + + delayed  emission • Double β decay  d  delayed deuteron emission   • Proton decay  t  delayed triton emission +SF + delayed fission •  SF  delayed fission • Cluster decay • (SF) 2 double  decay EC/EC EC+ electron capture with + emission 2+ double + decay 5 F.A. Danevich Univ. Tor Vergata October 05, 2015 Brief summary of Lecture 1 • Large enough number of radioactive nuclei undergoing exponential decay.

The decay rate of a radioactive substance is characterized by half-life (T1/2), or decay constant (), or mean lifetime ()

The half-life T1/2 is the time at which the number of nuclei is reduced to 1/2 times its initial value: t ln 2 T1/2 N N0 e

The three parameters ,  and T1/2 are related in the following way: ln 2 T   ln 2 1/2 

6 F.A. Danevich Univ. Tor Vergata October 05, 2015 questions on lecture 1: 1-2

1. Which kind of was observed by Becquerel from uranium?

2. Does radioactive decay always change composition of the nucleus?

7 F.A. Danevich Univ. Tor Vergata October 09, 2015 questions on lecture 1: 3

3. Why the probability of decay is higher for higher energy? (how a nuclei “know” that the energy release is large?) Stone 1

2.3 m  decay, electron capture

Stone 2 187 W: Q = 1311 keV  24 h

187 10 Re: Q = 2.7 keV  4.410 y

8 F.A. Danevich Univ. Tor Vergata October 09, 2015 questions on lecture 1: 4

4. how do we know that the nuclei decay spontaneously?

9 F.A. Danevich Univ. Tor Vergata October 09, 2015 in this lecture:

• Measurements of half-life • Non-exponential decay • Branching ratio, Investigations of decay schemes • Natural radioactivity • Radioactive decay chains

10 F.A. Danevich Univ. Tor Vergata October 09, 2015 Measurements of half-life

113 15 212 -6  decay of Cd with T1/2 = 810 y  decay of Po with T1/2 = 0.310 s

Natural cadmium contents 12% of  active 113Cd

Spectrum accumulated with CdWO4 scintillator (434 g) at the Gran Sasso Lab over 2758 h [1]

113 T1/2 = ln2 η N (t/S), where N is number of Cd nuclei in the crystal, η is efficiency of registration of the  Fit of the data by exponential function to decay of 113Cd, and t is the time of measurements. determine T1/2 [1] P.Belli et al., Investigation of β decay of 113Cd, PRC 76 (2007) 064603

[2] P.Belli et al., Investigation of rare nuclear decays with BaF2 crystal scintillator contaminated by radium, EPJA 50 (2014) 134 11 F.A. Danevich Univ. Tor Vergata October 05, 2015 Half-life of very short living nuclei

41.5 ps 19Mg 2p 12 < 40 ns

-12 T1/2 = 4.00.5 ps (1 ps = 10 s)

SIS facility at GSI Darmstadt [1] I. Mukha (for the S271 Collaboration), Experimental studies of nuclei beyond the proton drip line by tracking technique, EPJA 42 (2009) 421 12 F.A. Danevich Univ. Tor Vergata October 05, 2015 Very short living nuclei

Nuclei Half-life Decay mode The very short half-lives can be estimated using the Heisenberg's 12 Li < 10 ns n ? uncertainty principle 16Ne 910-21 s 2p : 100.00 % Position and momentum cannot be measured with absolute accuracy. The 10He 300200 keV n : 100.00 % product of standard deviations of 15  F 1.0 0.2 MeV p : 100.00 % position σx and momentum σp cannot be 4Li 6.03 MeV (910-23 s) p : 100.00 % less than:   , xp 2 h where is reduced Planck constant 6.582119514 401 016 eV s 2 With some care the principle can be applied also to standard deviations of energy and time:

 . Et 2 For some nuclei, the half-life (T1/2) is deduced from the total level width (cm) by using the equation: -22 T1/2 (s)  4.562 10 / cm (MeV).

13 F.A. Danevich Univ. Tor Vergata October 05, 2015 Limits on half-lives for “marginal” nuclei

# 186Po For most of the neutron reach nuclei only limits on their half-lives are known Nuclei Half-life Decay mode # 204Ir 15Be < 200 ns n ? 28O < 100 ns n ? 43Al > 170 ns - n 120Tc > 394 ns β-2n ? β-n ? N, number of β- 233Fr > 300 ns - Finally, there are nuclei (e.g. 204Ir – neutron reach, or 186Po – proton reach) experimentally not studied (unknown half-life)

14 F.A. Danevich Univ. Tor Vergata October 05, 2015 Half-life of very long living nuclei

The half-life of nuclei can be then estimated by using the formula: ln 2 NZA ( , ) TT2  1/2 NZA( 2, ) where N(Z,A) is amount of 96Zr, N(Z+2,A) is Measurement of double of amount of its daughter 96Mo, (measured by 96 Zr by geochemical method [1] mass-spectrometry), T is age of the mineral Possible mimic of the 2 decay: 238 Zircon samples were obtained from The spontaneous fission of U mineral sand mining operations at Capel, Thermal Western Australia. The average age of Electron capture of Tc the zircons was (1.8220.003) 109 yr as effects. 18 measured by U-Pb dating techniques T1/2 = (9.43.2)10 yr [1] 19 Result of direct counting experiment: T1/2=[2.35 ± 0.14 (stat) ± 0.16 (syst)] × 10 yr [2] [1] M.E. Wieser, J.R. De Laeter, Evidence of the double β decay of zirconium-96 measured in 1.8 × 109 years-old zircons. Phys. Rev. C. 64 (2001) 024308 [2] J. Argyriades et al., Measurement of the two neutrino half-life of Zr-96 with the NEMO-3 detector. A 847 (2010) 168–179. 15 F.A. Danevich Univ. Tor Vergata October 05, 2015 The longest decays ever observed

 decay of 209Bi 22 decay of 128Te analysis half-life of geological samples

Geological age of the ore formation is between 61 and 89 Myr. From the concentration of 128Xe by mas- 19 T1/2 = (1.90.2)  10 yr [1] spectrometry: 24 T1/2 = (2.4 ± 0.4) · 10 y [2]

A great difference: 810-23 s (4Li) vs 81031 s (128Te) (54 orders of magnitude; it is not a bound)

[1] P. de Marcillac et al., Experimental detection of -particles from the radioactive decay of natural bismuth, Nature 422 (2003) 876 130 128 [2] A.P. Meshik et al., Te and Te double beta decay half-lives, NPA 809 (2008) 275 16 F.A. Danevich Univ. Tor Vergata October 05, 2015 Nonexponential decay theoretical preditions

• It was pointed out that the exponential nature of the radioactive decay law is only an approximation [see, e.g., 1-3]

• The decay of a nonstationary state usually starts as a quadratic function of time and ends as an inverse power law (possibly with oscillations). Between these two extremes, the familiar exponential decay law may be approximately valid [4]

[1] L. A. Khalfin, Zh. Eksp. Teor. Fiz. 33, 1371 (1958) [Sov. Phys. JETP 6, 1053 (1958)]. [2] P. T. Matthews and A. Salam, Phys. Rev. 115, 1079 (1959). [3] R. G. Winter, Phys. Rev. 123, 1503 (1961). [4] A. Peres, Nonexponential decay law, Annals of Physics 129 (1980) 33 17 F.A. Danevich Univ. Tor Vergata October 05, 2015 Nonexponential decay experiments

Numbers of y rays observed from 60Co source Composite decay curves for the 847- and 1811-keV in time bins of (a) 10 ms, (b) 100 ms, (c) 1 s, y rays observed from the decay of 56Mn. The straight and (d) 10 s. The straight line drawn through lines are the results of least-squares fits with the each data set is the result of a least-squares fit assumption of purely exponential decay with the with the assumption of purely exponential known 56Mn half-life. decay with the known 60Co half-life.

[1] E.B. Norman et al., Tests of the Exponential Decay Law at Short and Long Times, PRL 60 (1988) 2246 18 F.A. Danevich Univ. Tor Vergata October 05, 2015 Nonexponential decay experiments

The experiment was criticized in [1]: “nuclear-decay experiments are roughly 18 to 20 orders of magnitude less time sensitive than required to constitute a meaningful search for pre-exponential Behavior”

[1] F.T. Avignone III, Comment on "Tests of the Exponential Decay Law at Short and Long Times", PRL 61 (1988) 2624 19 F.A. Danevich Univ. Tor Vergata October 05, 2015 Branching ratio The branching ratio is the fraction of individual decays of the certain mode with respect to the total number of the decay For Decay Radiation, intensities are listed per 100 decays of the parent nucleus. Examples:

In some data bases (as e.g. NNDC) for the Gamma rays intensities correspond to gamma branching ratios for each level, assigning 100 to the strongest

20 F.A. Danevich Univ. Tor Vergata October 05, 2015 Investigation of decay scheme: 190Pt [1]

[2]

Energy spectrum of the Pt sample measured during 1815 h and the background spectrum measured during 1046 h (normalized) [1] P. Belli et al., First observation of α decay of 190Pt to the first excited level (Eexc = 137.2 keV) of 186Os, PRC 83 (2011) 034603 [2] http://www.nndc.bnl.gov/chart/ 21 F.A. Danevich Univ. Tor Vergata October 05, 2015 Rare nuclear decays beta decays

22 F.A. Danevich Univ. Tor Vergata October 09 , 2015 Investigation of decay scheme: 180mTa

The part of the γ -ray spectrum collected for 170 d that encompasses the energy regions with the γ rays expected from the decay of 180Tam. The peaks are all from background of the naturally occurring decay chains and the being the major contributors to those peaks are indicated. 15 The new limit was set as T1/2 > 7.1 × 10 y

[1] M.Hult et al., Underground search for the decay of 180Ta m , Phys.Rev. C 74 (2006) 054311 23 F.A. Danevich Univ. Tor Vergata October 05, 2015 Investigation of decay scheme: 50V

Total time = 3487 h, V sample 955 g

Copper shield HPGe S1554 = 625  30 counts S783 < 31 counts 1 +0.14 17 18 T1/2 = 2.75 0.1310 y T1/2 > 7.510 y (90% CL) (only stat. uncertainties) Vanadium HPGe sample 2 Plexiglass

Hades Belgium 24 F.A. Danevich Univ. Tor Vergata October 05, 2015 Search for proton decay

Many theoretical models predict decays of p, n (B=1), n to –n oscillations (B=2): GUT, Supersymmetry, … These predictions to construction of massive detectors and to experimental searches of N decays: Kamiokande, SuperKamiokande, IMB, Frejus, Soudan, HyperKamiokande… The efforts were mainly concentrated on searches for N decays to particles which interact with a detector strongly of electromagnetically: pe+0, pK+, n –n with subsequent annihilation of –n, etc. These processes were not observed to-date, and only  limits were established, in particular the most stringent (SK): pe+0, >1.0e34 yr; p+0, >6.6e33 yr; pK+, >2.0e33 yr; n –n, >1.9e32 yr.

25 F.A. Danevich Univ. Tor Vergata October 05, 2015 Search for decay

Really massive detectors: SuperKamiokande 50 kt of water 10,000 20” PMT Physicists in boat inside SK checking PMTs

26 F.A. Danevich Univ. Tor Vergata October 05, 2015 Search for nucleon decay

Limits on 79 modes of proton decay: Particle Data Group [1]

In case if proton is unstable all the ordinary matter composed of atoms and a substantial part of the Interstellar medium becomes to be unstable

[1] K.A. Olive et al. (Particle Data Group), Chin. Phys. C, 38, 090001 (2014). 27 F.A. Danevich Univ. Tor Vergata October 05, 2015 Main characteristics of nuclei

• A: (number of nucleons: p + n) • Z: charge (number of ) • Mass excess (mass excess values [in keV], defined as being differences between the atomic mass [in mass units] and the ) • Spin and Parity (J) • Half-life • Decay modes and intensities (%)

28 Natural radioactivity There are plenty of radioactive elements

K, Ca, V, Ge, Se, Ru, Ze, Mo, Cd, In, Te, Xe, La, Nd, Eu, Sm, Gd, Lu, Hf, W, Rh, Os, Pt, Bi, Ra, Th, U Assume you have a nice house with 3030 m garden. Uranium concentration varies in different soils is 0.7 ppm – 11 ppm (ppm part per million) = (0.7 – 11) 10-6 g/g 

~15 kg of uranium in 1 m layer ~0.1 kg of 235U  37 MW / day (enough to provide power for 3-5 103 houses)

29 F.A. Danevich Univ. Tor Vergata March 05, 2015 30 Ф.А.ДаневичF.A. Danevich Хімічний факультет КНУ ім. Т.ШевченкаUniv. Tor Vergata 6 грудня 2013 March 05, 2015 31 Ф.А.ДаневичF.A. Danevich Хімічний факультет КНУ ім. Т.ШевченкаUniv. Tor Vergata 6 грудня 2013 March 05, 2015 32 Ф.А.ДаневичF.A. Danevich Хімічний факультет КНУ ім. Т.ШевченкаUniv. Tor Vergata 6 грудня 2013 March 05, 2015 33 Ф.А.ДаневичF.A. Danevich Хімічний факультет КНУ ім. Т.ШевченкаUniv. Tor Vergata 6 грудня 2013 March 05, 2015 34 Ф.А.ДаневичF.A. Danevich Хімічний факультет КНУ ім. Т.ШевченкаUniv. Tor Vergata 6 грудня 2013 March 05, 2015 Elements containing primordial radioactive isotopes

Element Radioactive Isotopic Half-life (yr) Activity in Mass of element , abundance 1 g of (g) corresponding decay (%) element (Bq) to activity of a modes radioactive isotope 1 mBq/kg Potassium 40K, ,  0.0117(1) 1.248(3)  109 31.0 3.22  10-8 Calcium 48Ca, 2 0.187(21) 4.4  1019 1.17  10-8 85 Vanadium 50V 0.250(4) 1.4(4)  1017 4.7  10-6 0.21 Germanium 76Ge, 2 7.83(7) 1.5(1) 1021 9.1  10-9 110 Selenium 82Se, 2 8.73(22) 9.2(7)  1019 1.53  10-7 6.5 Rubidium 87Rb,  27.83(2) 4.81(9)  1010 881 1.14  10-9 Zirconium 96Zr, 2 2.80(9) 2.3(2)  1019 1.68  10-7 6.0 Molybdenum 100Mo, 2 9.67(20) 7.1(4)  1018 1.80  10-6 0.55 Cadmium 113Cd,  12.22(12) 8.04(5)  1015 1.78  10-3 5.62  10-4 116Cd, 2 7.49(18) 2.8(2)  1019 3.05  10-7 3.28 Indium 115In,  95.71(5) 4.41(25)  1014 0.250 4.0 10-6 Tellurium 128Te, 2 31.74(8) 2.0(3)  1024 1.6  10-11 62 000 130Te, 2 34.08(62) 6.8(1.2)  1020 5.1  10-8 20 Lanthanum 138La, ,  0.090(1) 1.02(1)  1011 0.846 1.182  10-6 Neodymium 144Nd,  23.8(3) 2.29(16)  1015 9.6  10-3 1.05  10-4 150Nd, 2 5.6(2) 8.2(9)  1018 6.0  10-7 1.66 35

F.A. Danevich Univ. Tor Vergata March 05, 2015 Elements containing primordial radioactive isotopes

Element Radioactive Isotopic Half-life (yr) Activity in Mass of element isotope, abundance 1 g of (g) corresponding decay (%) element (Bq) to activity of a modes radioactive isotope 1 mBq/kg Samarium 147Sm,  14.99(18) 1.06(2)  1011 127 7.85  10-9 148Sm,  11.24(10) 7(3)  1015 1.4  10-3 7  10-6 Gadolinium 152Gd,  0.20(1) 1.08(8)  1014 1.61  10-3 6.2  10-4 Lutetium 176Lu,  2.59(2) 3.78(7)  1010 51.5 1.94  10-8 Hafnium 174Hf,  0.16(1) 2.0(4)  1015 6.08  10-5 0.016 Tungsten 180W,  0.12(1) 1.8(2)  1018 4.9  10-8 20 Rhenium 187Re,  62.60(2) 4.12(11)  1010 1075 9.3  10-10 Osmium 186Os,  1.59(3) 2.0(11)  1015 6  10-4 0.0018 Platinum 190Pt,  0.014(1) 6.5(3)  1011 0.0150 6.7  10-5 Bismuth 209Bi,  100 1.9(2)  1019 3.3  10-6 0.30 Radium 226Ra,  100 1600(7) 3.6581010 2.734  10-17 Thorium 232Th,  100 1.40(1)  1010 4 070 2.456  10-10 Uranium 234U,  0.0054(5) 2.455(6)  105 12400 8.0  10-11 235U,  0.7204(6) 7.04(1)  108 575.9 1.736  10-9 238U,  99.2742(10) 4.468(3)  109 12 346 8.100  10-11

36 F.A. Danevich Univ. Tor Vergata March 05, 2015 environmental radioactivity

2615 keV  208Tl (232Th) most energetic natural gamma line

The most valuable gamma quanta come from 40K and daughters of Th, U Gerd Heusser, Annu. Rev. Nucl. Part. Sci. 45 (1995) 543 37 F.A. Danevich Univ. Tor Vergata October 09, 2015 Potassium (K) is one of the most radioactive elements

Isotopic abundance of 40K is very low: 0.01171 % Activity of one gram of potassium is 31 Bq

38 Radioactive decay chains (families)

Nuclei heavier than A = 208 are unstable, mainly relatively to alpha decay due to increase of Coulomb interaction. The nuclei with A >> 208 belong to four decay chains beginning from 232Th, 235U, 238U, 237Np Chain Atomic number Half-life 232Th …  … 208Pb 4n 1.40(1)1010 yr 238U …  …. 206Pb 4n + 2 4.468(3)109 yr 235U (239Pu *) …  …. 207Pb 4n + 3 7.04(1)108 yr 237Np …  …. 205Tl ** 4n + 1 2.144(7)106 yr

239 4 * T1/2( Pu) =2.411(3) 10 yr ** The family decayed almost completely

39 F.A. Danevich Univ. Tor Vergata October 09, 2015 schedule of the lessons

October 09, Friday, 14:30-16:30 October 12, Monday, 14:30-16:30 October 16, Friday, homework October 21, Wednesday, 14:30-16:30

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