PHY20004NuclearPhysicsClass3:Radioactivity

Inthisclasswewilldescribethebasictypesofnuclearradioactivedecay,thatproduce𝛼,𝛽 and

𝛾 particles

Introducingradioactivity

• Radioactivityisthespontaneoustransformationofanunstablenucleus,involvingtheemissionofradiation

• Radioactivedecaycanoccurifthenucleonsarearrange-ableinalowerenergystatethantheircurrentconfiguration

Wewilldiscussthethreecommontypesofnuclearradioactivedecay,whicharelabelled𝛼, 𝛽, 𝛾 decays

𝛼 decays

Heliumnucleusconsistsof2protonsand2neutrons

(+energy𝑄)

• 𝛼-decayoccurswhenanucleusistoolargetobestable,anddisintegratestoalower-energystatebyejectingaheliumnucleus,whichisalsoknownasan𝛼-particle

• 𝛼-decayrequirestheparenttohavemassnumber𝑨 ≳ 𝟏𝟓𝟎 inorderthatthedecayisspontaneous(i.e.energy𝑄 > 0)

𝛼 decays↵ Decay

↵ decay is due to the emission of a 42He nucleus.

42He is doubly magic and very tightly bound.

↵ decay is energetically favourable for almostall with A�190 and for many A�150.

Why ↵ rather than any other nucleus?Consider energy release (Q) in various possible decays of 232U

n p 2H 3H 3He 4He 5He 6Li 7Li

Q/MeV -7.26 -6.12 -10.70 -10.24 -9.92 +5.41 -2.59 -3.79 -1.94

↵ is easy to form inside a nucleus 2p "# + 2n "#(though the extent to which ↵ particles really exist inside a nucleus is stilldebatable)

Dr. Tina Potter 15. Nuclear Decay 9

(+energy𝑄)

• Althoughothertypesoffissionarepossible,𝛼-decayisdominantbecause He/

0 isverytightlybound(doublymagic!)

• Considertheenergyreleasedfromthefollowingdecaysof𝑈/2/ : theonlyspontaneousdecay(with𝑄 > 0)is 𝐻𝑒0

𝛼 decays

• Theescapeofan𝛼-particlefromthenucleusisanexampleofquantumtunneling

• Tunnelingisaquantumphenomenonwhichallowsthe𝛼-particletoviolateenergyconservationforabriefperiodoftime,owingtothequantumuncertaintyprinciple

• Havingtunneledoutofthenucleus,the𝛼-particleisejectedbyCoulombrepulsion

• Themeanlifetimeoftheunstablenucleusishighlysensitivetotheheightofthepotentialbarrier andcanvarybetween1067s and10:;<yr!(see:theGeiger-Nuttalllaw)

Credit:https://www.nuclear-power.net/

Calculatingtheenergyreleased

• Asthenucleusdisintegratestoalowerenergyconfiguration,𝛼-decayreleasesenergy𝑄 whichtakestheformofthekineticenergyofthedecayproducts

• 𝑄 canbecalculatedasthedifferenceinthebindingenergy𝐵 betweenthedecayproductsandtheinitialnucleus

𝑄 = 𝐵 𝛼 + 𝐵 𝐴 − 4, 𝑍 − 2 − 𝐵(𝐴, 𝑍)

Bindingenergyof𝛼-particleis

𝐵 𝛼 = 28.3𝑀𝑒𝑉

𝛽 decays

• 𝛽-decayisthetransformationofaneutron-rich(orproton-rich)nucleusbythedirectconversionofaneutronintoaproton (orviceversa)

Neutrontransformsintoproton

Protontransformsintoneutron

Credit:https://education.jlab.org

𝛽 decays

• 𝛽-decaytransformsthenumberofprotons𝑍 andneutrons𝑁 inanucleusclosertothelineofstability𝑍~𝑁

• Thereare3formsof𝛽-decay:§ 𝜷6 decay:𝑁 istoolargeforstability,andaneutronbecomesa

protoninvolvingtheemissionofanelectronandanti-neutrino

§ 𝜷: decay:𝑍 istoolargeforstability,andaprotonbecomesaneutroninvolvingtheemissionofapositronandaneutrino

§ Electroncapture:𝑍 istoolargeforstability,andanatomicelectronstraystooclosetothenucleusandreactswithaproton,producinganeutron(withinthenucleus)andaneutrino

𝑛 → 𝑝 + 𝑒6 + �̅�V 𝑋XY → 𝑌:X:;Y + 𝑒66;

< + �̅�V

𝑝 → 𝑛 + 𝑒: + 𝜈V 𝑋XY → 𝑌6X6;Y + 𝑒::;

< + 𝜈V

𝑝 + 𝑒6 → 𝑛 + 𝜈V 𝑋XY + 𝑒66;< → 𝑌6X6;

Y + 𝜈V

Neutrinos

• Theproductionofnewparticlescalledneutrinos isaninterestingfeatureof𝛽-decay

• Neutrinosareweakly-interacting,electrically-neutralparticleswithnear-zeromass

• Theirexistenceisrequiredtoensureenergyandmomentumconservationduring𝛽-decay

• We’llhearmuchmoreaboutneutrinoslaterinthecourse!

TheSuper-Kamiokande detectorinJapan,anunderground

neutrinodetector

Note:aprotoncannotdecayinfreespace(sinceit’sthelightestbaryon),butinsideanucleusitcandecaybyborrowingsomeenergyfromthebindingenergy

𝛾 decays

• 𝛾-decayoccurswhenanucleusisinanexcitedstate–oftenfollowing𝛼- or𝛽-decay– andrevertstothegroundstate,emittingaphoton(alsoknownasa𝛾-ray)

• 𝛾-decayissimilartoatomicde-excitation,butoccursatmuchhigherenergy(~MeV vs.~eV)

𝑋∗XY

Radioactivedecaychains

• Theproductsofradioactivedecaymaythemselvesbeunstabletodecay– creatingadecaychain

• Here’sthedecaychainforUranium-235 – noticetheverydifferenthalf-livesofdifferentsteps!

• We’lldiscussthisinmoredetailinthenextclass

Credit:http://hyperphysics.phy-astr.gsu.edu/

Keytake-aways

• Radioactivedecayisaspontaneousprocesswhichoccurswhennucleonsre-arrangethemselvesintoalower-energyconfiguration

• Wecandistinguishthreemaincases:

• 𝜶-decay:transformationofalargenucleus(𝐴 ≳ 150)bytheemissionofa 𝐻𝑒/

0 particle,viaquantumtunneling

• 𝜷-decay:transformationofaneutronintoaproton(orviceversa),emittinganelectron(orpositron)andneutrino

• 𝜸-decay:de-excitationofanucleus,involvingtheemissionofaphoton