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1 ดร. สมศ กด แดงต บ ห องพ ก 617 โทร 5777 ห องว จ ย k46 โทร Psonal Wbsit : Cous (1 st alf wbsit: Lctu 6 Raioactiv Dcay ค าถามทบทวน July 9 SCPY 415: Nucla Pysics Lctu 1

2 การสลายต ว// ร งส อ ลฟ า รงสอลฟา ร งส แกมมา ร งส บ ตา July 9 SCPY 415: Nucla Pysics Lctu 1 Ala cay Consi T Z9 fm R7.6 fm E4 V E Z Z 1 4πε c c R Engy of α: E α 4.8 V Qustion: How os t α sca? Answ: Q tunnlling July 9 SCPY 415: Nucla Pysics Lctu 1 4

3 Ala cay aial wav function in ala cay I II III Exonntial cay of ψ nuclus bai (ngativ KE small flux of al α July 9 SCPY 415: Nucla Pysics Lctu 1 5 ψ I x( ikx + Ax( ikx ψ B x( Kx + C x( Kx II ψ III D x(ikx Q tunnlling k me K m ( V E E t BC B.C. at x an xt fo Kt>>1 an k~k Kgivs fo 1D ctangula bai ticknss t givs T D x( Kt Intgat ov Coulomb bai fom R to t July 9 SCPY 415: Nucla Pysics Lctu 1 6

4 Ala cay ΔE s 6V nuclon fo avy nucli ΔE bin ( 4 α8. V > 4*6V Nutons Potons Alas July 9 SCPY 415: Nucla Pysics Lctu 1 7 T t x K( x R Z V ( 4πε E α Z 4πε t Ala cay ( V ( E 1/ t 1/ Z G πε R 1/ 1 Z 1/ G t sin ϑ ϑ πε α x( G ( 1/ 1/ t ; t cos ϑ t cosϑ sinϑϑ ϑ sin ϑ ϑ (1/ ϑ sinϑcosϑ [ ] 1/ Z t >> ;cos ϑ / ; cosϑ ; ϑ π /; 4 πε t R R t G π July 9 SCPY 415: Nucla Pysics Lctu 1 8

5 Ala cay ats 1/ Z t π G Gamow facto 4 πε t Z 4πε E α Z G 4ε E α 1/ Numb of its, on sufac of nuclus aius R ~ v/r.dcay at (Eα / m ω RR x( G July 9 SCPY 415: Nucla Pysics Lctu 1 9 Eximntal tsts Pict log cay at ootional to (E a 1/ Ags ~ wit ata fo nucli. Angula momntum ffcts: Aitional bai l(l l + 1( c E l c Small coma to Coulomb o but still gnats lag agta xta xonntial sussion. E.g l1, R15 fm E l ~.5 V cf fo Z 9 Ec~17 V. Sin/aity i ΔJL aity cang( L July 9 SCPY 415: Nucla Pysics Lctu 1 1

6 Eximntal tsts 1 18 Half-lif (s Engy E (V July 9 SCPY 415: Nucla Pysics Lctu 1 11 Fmi Bta Dcay Toy Consi simlst cas: n cay. At quak lvl: l u+w follow by cay of vitual W. n ν ; n u u u - u ν W - ( ν July 9 SCPY 415: Nucla Pysics Lctu 1 1

7 Fmi Toy 4 oint intaction (low ngy aoximation. if * * * Gβ ψ ( ψν ( ψ ( ψ n ( ψ ( x( ik. ; ( x( ik. ; q k + k ( ψ ν ν ν q ~ 1 V / c R ~ 5 fm > q. ~ 1/ 4 > x( iq. 1 if G β * ψ ( ψ ( n July 9 SCPY 415: Nucla Pysics Lctu 1 1 Fmi Toy istibution tmin by as sac (nglct nucla coil ngy N N 4π / ; Nν 4πν ν / ( 4π / ( 4π / ν ν ( E f E / c ; / E f 1/ c ν ν N 16π 6 c ( E f E E f Us FGR : as sac &.E. cay at July 9 SCPY 415: Nucla Pysics Lctu 1 14

8 Kui Plot I( A I ( ( E f E A( E f E Coulomb coction Fmi function K(Z, Continuous sctum nutino En oint givs limit on nutino mass Intnsity Titium β cay (I I(/ K(Z, 1/ Elcton ngy (kv 18 Elcton ngy(kv July 9 SCPY 415: Nucla Pysics Lctu 1 15 Fmi Tansitions: Slction Ruls n coul to giv sin: ΔS Allow tansitions ΔL ΔJ. Gamow Tll tansitions: n coul to giv 1 unit of sin: ΔS o ± 1. Allow tansitions ΔL ΔJ o ± 1. Fobin tansitions: x( iq. 1 + ( iq. + O ( q Hig o tms coson to non zo ΔL. Tfo suss ning on (q (q. L Usual Q uls giv: JL+S July 9 SCPY 415: Nucla Pysics Lctu 1 16

9 Can comt wit β + cay Elcton catu + if G n + ν R β * * ψ ( ψ ( ψ n ( ψ ν ( Fo allow tansitions. ii if * Gβψ ( ψν ( ψ ( ψ n ( R Only l. n1 lagst. ψ ( / 1 / Zm x( ik. π ; ( / 4 ψν πε L if Gβ Zm πl 4 πε F F R * ψ n ( ψ ( July 9 SCPY 415: Nucla Pysics Lctu 1 17 Dnsity of stats: Elcton catu (II N 4π q N N q L L ; ; Eν qc ν q E q E N E 4π q L c q L Fmi s Goln Rul: ππ w w G β F N E 16π E c ν 4 Zm 4 πε July 9 SCPY 415: Nucla Pysics Lctu 1 18

10 Discovy of Anti nutino + Invs Bta Dcay n ν ; ν n Sam matix lmnts 6 β F G L Fmi Goln Rul: w w π N E π N Gβ F E July 9 SCPY 415: Nucla Pysics Lctu 1 19 Discovy of Anti nutino(ii Pas sac facto Nglct nucla coil Combin wit FGR N E 4π L E ; E / c E 4 E c + m c w π G πe c L F c / L ; R 4 β F σ G Fσ 16π E β F 4 c July 9 SCPY 415: Nucla Pysics Lctu 1

11 Eximnt to vify Anti nutino Fo E~ 1 V s~1 47 cm Pauli iction an Cowan an Rins. ν + n + γ (omt n + C γs(9v,lay Liqui Scint. 1 GW Nucla Racto H +CCl PTs Siling July 9 SCPY 415: Nucla Pysics Lctu 1 1 Paity Dfinitions ; P[ ψ ( ] ψ ( P [ ψ ( ] ψ ( Pv ( v ; Pvv ( 1. vv 1. L x P( L L Eignvalus of aity a ± 1. If aity is consv: [H,P] ignstats of H a ignstats of aity. If aity violat can av stats wit mix aity. If Paity is consv sult of an ximnt soul b uncang by aity oation. July 9 SCPY 415: Nucla Pysics Lctu 1

12 Paity Consvation If aity is consv fo action a+b c+. η L a η b ( 1 η c η ( 1 IN L FINAL Nb absolut aity of stats tat can b ouc fom vacuum (.g. otons can b fin. Fo ot aticls w can fin lativ aity..g. fin η +1, η n +1 tn can tmin aity of ot nucli. If aity is consv <suo scala> (s nxt tansancy. July 9 SCPY 415: Nucla Pysics Lctu 1 < > O ψ Oψ ψ POψ ψ ψ ψ ψ * * < O > ψ PO P ψ * * < O > ( η ψ Oψ < O > ψ O ψ <O > QED * July 9 SCPY 415: Nucla Pysics Lctu 1 4

13 Is aity consv? Fynman s bt. Ys in lctomagntic an stong intactions. Big suis was tat aity is violat in wak intactions. July 9 SCPY 415: Nucla Pysics Lctu 1 5 Paity Tst: m Wo s Eximnt 6 6 * Co(J 5 Ni (J 4 ν ; Ni Ni+γ 6 * 6 Align sins of 6 Co wit magntic fil. Aiabatic magntisation to gt T ~ 1 mk asu angula istibution of lctons an otons lativ lti to B fil. Cla fowa backwa asymmty Paity violation. July 9 SCPY 415: Nucla Pysics Lctu 1 6

14 T ximnt July 9 SCPY 415: Nucla Pysics Lctu 1 7 Imov aity tst ximnt θ is angl wt sin of 6 Co. July 9 SCPY 415: Nucla Pysics Lctu 1 8

15 Gamma cay Wn o ty occu? Nucli av xcit stats cf atoms. Don t woy about tails E,J P (n sll mol to unstan. E intaction << stong intaction Low ngy stats E < 6 V abov goun stat can t cay by stong intaction ti E. Imotant in casca cays α an β. Pactical consquncs Fission. Significant ngy las in γ cays. Raiotay: γ fom Co 6 cays. ical imaging g Tc. July 9 SCPY 415: Nucla Pysics Lctu 1 9 Gamma cay β cay lavs Tc in xcit stat. Usful fo mical imaging July 9 SCPY 415: Nucla Pysics Lctu 1

16 Gamma cay toy ost common cay mo fo nucla xcit stats (blow tsol fo bak u is γ cay. Liftims vay fom yas to 1 16 s. nb long liftims can asily b obsv unlik in atomic. Wy? Angula momntum consvation in g cays. intinsic sin of g is1 an obital angula momntum intg J is intg. Only intg cangs in J of nuclus allow. Q aition of J: J J J J + J i f Absolutly fobin (wy?: i f July 9 SCPY 415: Nucla Pysics Lctu 1 1 Gamma cay Elctic tansitions E E x[ i ( k. ω t ] E E (1 + ik. + ( k. + O( k. Tyically k~1 V/c ~ 1 fm k~1/ k.~1/ us multiol xansion. Lowst tm is lctic iol tansitions, L1. H * ψ f ψ i Paity cang fo lctic iol. July 9 SCPY 415: Nucla Pysics Lctu 1

17 Fobin Tansition If lctic iol tansitions fobin by angula momntum o aity can av fobin tansitions, g lctic quaool. Rat suss cf iol by ~ (k. agntic tansitions also ossibl: Classically: E μ.b 1 tansition at small tan E1 by ~ 1. Hig o magntic tansitions also ossibl. Paity slction uls: Elctic: Δ( 1 L agntic: Δ( 1 L+1 July 9 SCPY 415: Nucla Pysics Lctu 1 Intnal convsion absolutly l fobin: Wat ans to a + xcit stat? Dcays by it: Intnal convsion: nuclus mits a vitual oton wic kicks k out an atomic lcton. Rquis ovla of t lcton wit t nuclus only l. Pobability of lcton ovla wit nuclus incass as Z. Fo ig Z can comt wit ot γ cays. Intnal ai convsion: nuclus mits a vitual oton wic convts to + ai. July 9 SCPY 415: Nucla Pysics Lctu 1 4

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