Beta Decays. Beta decays are proton neutrons or neutron proton transitions involve W exchange and are weak interaction
|
|
- Hubert Underwood
- 5 years ago
- Views:
Transcription
1 Bta Dcays Bta dcays ar proton nutrons or nutron proton transitions involv W xchang and ar wak intraction M Z, A M Z 1, A ν ( p nν M Z, A M Z 1, A ν ( n pν M Z, A M Z 1, A ν ( p nν th last raction is lctron captur whr on of th atoic lctrons ovrlaps th nucli. Sa atrix lnt (ssntially bit diffrnt kinatics th si-pirical ass forula givs a iniu for any A. If ass diffrnc btwn nighbors is larg nough, dcay will occur P461 - dcays II 1
2 P461 - dcays II Bta Dcays - Q Valus Dtrin Q of ractions by looking at ass diffrnc (carful about lctron ass 1 MV or Q in EC than bta ission. Mor phas spac BUT nd lctron wavfunction ovrlap with nuclus.. Y X Y Y X A Z A Z Y X Y Y X A Z A Z Y Y X Y Y X A Z A Z AM AM Q Z Z Y X EC AM AM Q Z Z Y X AM AtoicMass Q Z Z Y X ν ν ν ν ν ν β ν β ( ( : ( ( : ( ( : 1,, 1,, 1,,
3 Bta vs Elctron Captur Fwr bta ittrs than bta- in natural nucli (but any in artificial iportant in Positron Eission Toography - PET sotis both bta and EC for sa nucli. Diffrnt widths sotis only EC allowd 4 4 Li 7 B 7 M.0009u B 7 M u M u Li 7 < ν.00055u ononrgtic nutrino. E.87 MV. Iportant raction in th Sun. Not EC rat diffrnt in Sun as it is a plasa and not atos P461 - dcays II
4 Bta vs Elctron Captur fro Particl Data Group p ph ν 8 B 8 B ν 7 B 7 Li ν P461 - dcays II 4
5 Bta Dcay - Body Th nutrino is ndd to consrv angular ontu (Z,A (Z1,A for Avn hav ithr Z,N vn-vn odd-odd or odd-oddvn-vn p,n both spin 1/ and so for vn-vn or odd-odd nucli I0,1,,. But lctron has spin 1/ I(intgr I(intgr 1/(lctron dosn t consrv J nd spin 1/ nutrino. Also obsrvd that lctron spctru is continuous indicativ of > body dcay Pauli/Fri undrstood this in 190s lctron nutrino discovrd 195 (Rins and Cowan uon nutrino discovrd 196 (Schwartz Ldran/Stinbrgr tau nutrino discovrd 000 at Frilab P461 - dcays II 5
6 Body inatics Whil body th nucli ar vry havy and asy approxiation is that lctron and nutrino split availabl Q (nucli has siilar ontu axiu lctron nrgy whn E(nu0 X p ( E xapl y Y ν x ax p E E x 7 p consrv ν Mg 7,1 Al y x lt E ( E p x E y ν Al 0 ontu consrv ( Q y ν 6.984, 0.kV ( x ν 7,1 x nrgy.8mv.75mv, γ sall Q P461 - dcays II 6 y E 5.5
7 Bta dcay rat Start fro Fri Goldn Rul π Rats M ρfinal h * M ψf βψdτ first approxiation (Fri. Btaconstantstrngth of wak forc M βm M * ψz 1ψ Zdτ Rul 1: parity of nuclus can t chang (intgral of odd*vn0 Rul : as antinutrino and lctron ar spin 1/ thy add to ithr 0 or 1. Givs ithr Fri : i 4 Gaow Tllr Sc P S 16 i Ca ZA 0 i Z ± 1A : i ν ν ± ( not 0 P461 - dcays II
8 Bta dcay rat II Orbital angular ontu supprssion of for ach valu of (in atrix lnt calculation 6 Sc 17 6 Ca 18 ν i ± 1 L 1 look at dnsity of stats factor. Want # quantu stats pr nrgy intrval π dnn Rats M ρfinal ρn h de w know fro quantu statistics that ach particl (actually ach spin stat has p dn 4π h body dcay but rcoil nuclus is so havy it dosn t contribut dp p pν dn 4π dp 4π h h p ( Q / c ν P461 - dcays II 8 n dp 0 ν
9 Bta dcay rat III Consrvation of nrgy allows on to intgrat ovr th nutrino (thr is a dlta function Rats π h M dn dp 4πp h π h 4π ( Q ( hc 1/ ( p this givs a distribution in lctron ontu/nrgy which on thn intgrats ovr. (nd point dpnds on nutrino ass F is a function which dpnds on Q. It is alost loqrithic M c Rat M F( E 7 T π h logf Alog ρ Final P461 - dcays II 9 ax ax
10 actual. not linar du to lctron ass logf F Alog 4.4 ax 4.4 log.5 P461 - dcays II 10
11 Bta dcay rat IV FT is just kinatics asuring FT can study nuclar wavfunctions M and strngth of th wak forc at low nrgis lowr valus of FT ar whn M approachs 1 bta dcays also occur for particls π π π 0 0 ν lctron is now rlativistic and Epc. Th intgral is now asy to do. For assiv particls (with dcay asss sall, Eax M/ and so rat gos as fifth powr of ass ν p ax 0 ( Q p dp E 5 ax / 0 P461 - dcays II 11
12 Bta dcay rat V MβM β is strngth of wak intraction. Can asur fro liftis of diffrnt dcays β 6 10 joul 100V F charactristic nrgy β vol 100V * F (10F 0.1V strong nrgy lvls ~ 1 MV β α wak strong 10 7 rlativstrngth for siilar Q, liftis ar about τ τ τ strong EM wak s 10 s s P461 - dcays II 1
13 Parity Violation in Bta Dcays Th Parity oprator is th irror iag and is NOT consrvd in Wak dcays (is consrvd in EM and strong non-consrvation is on th lpton sid, not th nuclar wav function sid spin 1/ lctrons and nutrinos ar (noinally ithr right-handd (spin and ontu in sa dirction or lft-handd (opposit Parity changs LH to RH P( x, y, z ( x, y, z P( r, θ, φ ( r, π θ, φ π RH LH r r P( p p r r r P( L p r L P461 - dcays II 1
14 Handdnss of Nutrinos handdnss is call chirality. If th ass of a nutrino 0 thn: all nutrinos ar lft-handd all antinutrinos ar right-handd Parity is axially violatd As th ass of an lctron is > 0 can hav both LH and RH. But RH is supprssd for larg nrgy (as lctron spd approachs c fraction RH vs LH can b dtrind by solving th Dirac quation which naturally incorporats spin P461 - dcays II 14
15 Polarizd Bta Dcays So nucli hav non-zro spin and can b polarizd by placing in a agntic fild agntic onts of nucli ar sall (1/M factor and so nd low tpratur to hav a high polarization (s Eq 14-4 and i Co Gaow-Tllr transition with S(-nu 1 60 Ni 5 i 4 s ν if Co polarizd, look at angular distribution of lctrons. Find prfrntial hisphr (down 1, 1 Co Pnu p Spin antinu-rh Spin - LH P461 - dcays II 15
16 Discovry of Parity Violation in Bta Dcay by C.S. Wu t al. Tst parity consrvation by obsrving a dpndnc of a dcay rat (or cross sction on a tr that changs sign undr th parity opration. If dcay rat or cross sction changs undr parity opration, thn th parity is not consrvd. Parity rvrss onta and positions but not angular onta (or spins. Spin is an axial vctor and dos not chang sign undr parity opration. 180 ο θ P irror θ nutron P Bta dcay of a nutron in a ral and irror worlds: If parity is consrvd, thn th probability of lctron ission at θ is qual to that at 180 o -θ. Slctd orintation of nutron spins - polarisation. P461 - dcays II 16
17 Wu s xprint Bta-dcay of 60 Co to 60 Ni *. Th xcitd 60 Ni * dcays to th ground stat through two succssiv γ issions. Nucli polarisd through spin alignnt in a larg agntic fild at 0.01 o. At low tpratur thral otion dos not dstroy th alignnt. Polarisation was transfrrd fro 60 Co to 60 Ni nucli. Dgr of polarisation was asurd through th anisotropy of gaa-rays. Bta particls fro 60 Co dcay wr dtctd by a thin anthracn crystal (scintillator placd abov th 60 Co sourc. Scintillations wr transittd to th photoultiplir tub (PMT on top of th cryostat. P461 - dcays II 17
18 Wu s rsults Graphs: top and iddl - gaa anisotropy (diffrnc in counting rat btwn two NaI crystals - control of polarisation; botto - β asytry - counting rat in th anthracn crystal rlativ to th rat without polarisation (aftr th st up was ward up for two orintations of agntic fild. Siilar bhaviour of gaa anisotropy and bta asytry. Rat was diffrnt for th two agntic fild orintations. Asytry disappard whn th crystal was ward up (th agntic fild was still prsnt: connction of bta asytry with spin orintation (not with agntic fild. Bta asytry - Parity not consrvd P461 - dcays II 18
19 Gaa Dcays If sothing (bta/alpha dcay or a raction placs a nuclus in an xcitd stat, it drops to th lowst nrgy through gaa ission xcitd stats and dcays siilar to atos consrv angular ontu and parity photon has spin 1 and parity -1 for orbital P (-1 L first ordr is lctric dipol ont (d. Easir to hav highr ordr trs in nucli than atos N * N γ γ L 0, d 0 γ L 1, quad.. o. P P final γp N ( 1 L ( 1( 1( 1 P461 - dcays II 19
20 5 Gaa Dcays 17 8 Cl 18 8 Ar 6% E MV 11% gaa 5% gaa 0 0 N * N γ GT GT L 1 ( Pchang L P γ 0 1 γ γ L L 0; d 1; q 0 i ; GT L 1 consrv angular ontu and parity. lowst ordr is lctric dipol ont. thn quadrapol and agntic dipol P461 - dcays II 0
21 Mossbaur Effct Gaa dcays typically hav liftis of around sc (larg rang. Givs width: vry prcis 15 h 10 Vs Γ E τ 10 sc if fr nucli dcays, nd to consrv ontu. Shifts gaa nrgy to slightly lowr valu A p * A A γ p γ E γ M M * xapl. Vry sall shift but gratr than natural width M E A * M A.1MV, M γ.1mv A 5 V M (1.005V M M 191*91.5 P461 - dcays II 1
22 Mossbaur Effct II Enrgy shift ans an ittd gaa won t b rabsorbd * A A γ E MV * A γ A E MV but if nuclus is in a crystal lattic, thn ntir lattic rcoils against photon. Mas(latticinfinity and EgaadltaM. Rcoilss ission (or Mossbaur will hav wings on photon nrgy du to lattic vibrations Mossbaur ffct can b usd to study lattic nrgis. Vry prcis. Us as ittr or absorbr. Vary nrgy by oving sourc/targt (Dopplr shift (us Iron. dvlopd by R. Prston, NIU P461 - dcays II
23 Nuclar Ractions, Fission and Fusion Body raction ABCD lastic if C/DA/B inlastic if ass(cd>ass(ab thrshold nrgy for inlastic (B at rst M th th E tot Q Q A p tot A B > ( B ( non rlativistic for nucli nonrlativistic usually O B C B C D D Q M p Q ( u th th H 4(1 H 1 5.8MV ( non rl 5.47MV ( rl H 4.0MV P461 - dcays II
24 Nuclar Ractions (SIP ABCD asurnt of kinatic quantitis allows asss of final stats to b dtrind (p,e initial A,B known 8 unknowns in final stat (E,px,py,pz for CD but E,p consrvd. 4 constraints4 unknowns asur E,p (or ass of D OR C givs rst or asur pc and pd givs asss of both oftn asist to look at angular distribution in C.M. but can always convrt dσ dω Θ CM P461 - dcays II 4
25 Fission ABC A havy, B/C diu nucli rlass nrgy as binding nrgy/nuclon 8.5 MV for F and 7. MV for Uraniu spontanous fission is lik alpha dcay but with diffrnt ass, radii and Coulob (Z/ vs (Z-. Vry low rat for U, highr for largr A inducd fission nabc. Th nutron adds its binding nrgy (~7 MV and can put nucli in xcitd stat lading to fission vn-vn U(9,8. Adding n gos to vn-odd and lss binding nrgy (about 1 MV vn-odd U(9,5, U(9,, Pu(94,9 adding n gos to vn-vn and so or binding nrgy (about 1 MV MV diffrnc btwn U5 and U8 fission in U5 can occur vn if slow nutron P461 - dcays II 5
26 Spontanous Fission P461 - dcays II 6
27 Inducd Fission P461 - dcays II 7
28 Nutron absorption P461 - dcays II 8
29 ( ( ( ( ( 1 8 H 4 H H B 1 C u.01410u u u u Fusion natur would lik to convrt lightr lnts into havir. But: no fr nutrons ( ( H C H nd to ovrco lctroagntic rpulsion high tpraturs ass B > twic ass H. Supprsss fusion into Carbon Idally us Dutriu and Tritiu, σ1 barn, but littl Tritiu in Sun (idal for fusion ractor < 4 ( H < ( 4 H H H n Q 17MV P461 - dcays II 9 4
30 ( ( ( ( ( 1 8 H u 4 H.01410u H B u u C u Fusion in Sun p p H p H H H H 4 γ ν H p p rat liitd by first raction which has to convrt a p to a n and so is Wak σ(pp ~ barn partially dtrins lifti of stars can odl intraction rat using tunnling vry siilar to Alpha dcay (also don by Gaow tunnling probability incrass with Enrgy (Tpratur but particl probability dcrass with E (Boltzan. Hav ost probabl (Gaow Enrgy. About 15,000,000 for Sun but Gaow nrgy highr (50,000,000?? P461 - dcays II 0
31 ( ( ( ( ( 1 8 H H H 4 B 1 C u Fusion in Sun II.01410u u u u 10 1 sc nd H nucli to hav nrgy in ordr to ak B. (thr is a rsonanc in th σ if hav invariant ass(h-hass(b if th fusion window pak (th Gaow nrgy wightd for diffrnt Z,ass is nar that rsonanc that will nhanc th B production turns out thy arn t quit. But fusion to C start at about T100,000,000 with <kt> about 10 V ach H. Gaow nrgy is highr thn this. 4 8 H B τ B B 4 4 H H H 8 1 B C γ 9 V P461 - dcays II 1
32 ( ( ( ( ( 1 8 H H H 4 B 1 C Fusion in Sun III u.01410u u u u 10 sc BHC also nhancd if thr is a rsonanc. Turns out thr is on at alost xactly th right nrgy MV 0. 8MV 7.65 MV MV C 0 * H B τ B B , H H 11, , ,178MV H 1 MV 8 1 B B C γ H 9 V H P461 - dcays II
Chemical Engineering 412
Chical Enginring 4 Introductory Nuclar Enginring Lctur 6 Nuclar Radiation Typs Ky oints Typs of cay Na roprtis athatical scriptions Cavats cay Charts (KNOW HOW TO USE!) Nuclar Equation for cay -Valus for
More informationNuclear reactions The chain reaction
Nuclar ractions Th chain raction Nuclar ractions Th chain raction For powr applications want a slf-sustaind chain raction. Natural U: 0.7% of 235 U and 99.3% of 238 U Natural U: 0.7% of 235 U and 99.3%
More informationfiziks Institute for NET/JRF, GATE, IIT JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics
Atoic and olcular Physics JEST Q. Th binding nrgy of th hydrogn ato (lctron bound to proton) is.6 V. Th binding nrgy of positroniu (lctron bound to positron) is (a).6 / V (b).6 / 8 V (c).6 8 V (d).6 V.6
More informationBETA DECAY VISUAL PHYSICS ONLINE
VISUAL PHYSICS ONLINE BETA DECAY Suppos now that a nuclus xists which has ithr too many or too fw nutrons rlativ to th numbr of protons prsnt for stability. Stability can b achivd by th convrsion insid
More informationWeak Interactions. Feynman Rules for the Muon Decay Fermi s Effective Theory of the Weak Interaction. Slides from Sobie and Blokland
Wak ntractions Fynan uls for th Muon Dcay Fri s Effctiv Thory of th Wak ntraction osons lids fro obi and lokland Physics 424 Lctur 20 Pag 1 ntrdiat ctor osons Lik ED and CD, th wak intraction is diatd
More informationAndre Schneider P621
ndr Schnidr P61 Probl St #03 Novbr 6, 009 1 Srdnicki 10.3 Vrtx for L 1 = gχϕ ϕ. Th vrtx factor is ig. ϕ ig χ ϕ igur 1: ynan diagra for L 1 = gχϕ ϕ. Srdnicki 11.1 a) Dcay rat for th raction ig igur : ynan
More informationChapter 8: Electron Configurations and Periodicity
Elctron Spin & th Pauli Exclusion Principl Chaptr 8: Elctron Configurations and Priodicity 3 quantum numbrs (n, l, ml) dfin th nrgy, siz, shap, and spatial orintation of ach atomic orbital. To xplain how
More informationPair (and Triplet) Production Effect:
Pair (and riplt Production Effct: In both Pair and riplt production, a positron (anti-lctron and an lctron (or ngatron ar producd spontanously as a photon intracts with a strong lctric fild from ithr a
More informationStandard Model - Electroweak Interactions. Standard Model. Outline. Weak Neutral Interactions. Electroweak Theory. Experimental Tests.
Standard Modl - Elctrowak Intractions Outlin ak Nutral Intractions Nutral Currnts (NC) Elctrowak Thory ± and Z and γ Discovry of ± Exprimntal Tsts LEP Z Boson Mass and idth Numbr of Nutrinos ± Boson ±
More informationA 1 A 2. a) Find the wavelength of the radio waves. Since c = f, then = c/f = (3x10 8 m/s) / (30x10 6 Hz) = 10m.
1. Young s doubl-slit xprint undrlis th instrunt landing syst at ost airports and is usd to guid aircraft to saf landings whn th visibility is poor. Suppos that a pilot is trying to align hr plan with
More informationIntro to Nuclear and Particle Physics (5110)
Intro to Nuclar and Particl Physics (5110) March 09, 009 Frmi s Thory of Bta Dcay (continud) Parity Violation, Nutrino Mass 3/9/009 1 Final Stat Phas Spac (Rviw) Th Final Stat lctron and nutrino wav functions
More informationE hf. hf c. 2 2 h 2 2 m v f ' f 2f ' f cos c
EXPERIMENT 9: COMPTON EFFECT Rlatd Topics Intractions of photons with lctrons, consrvation of momntum and nrgy, inlastic and lastic scattring, intraction cross sction, Compton wavlngth. Principl Whn photons
More informationCollisions. In had on lastic collision of two bodis of qual ass ) Th fastr body spds up furthr and th slowr body slows down. ) Th fastr body slows down and th slowr body spds up. 3) Both of th abov. 4)
More informationde/dx Effectively all charged particles except electrons
de/dx Lt s nxt turn our attntion to how chargd particls los nrgy in mattr To start with w ll considr only havy chargd particls lik muons, pions, protons, alphas, havy ions, Effctivly all chargd particls
More information0 +1e Radionuclides - can spontaneously emit particles and radiation which can be expressed by a nuclear equation.
Radioactivity Radionuclids - can spontanously mit particls and radiation which can b xprssd by a nuclar quation. Spontanous Emission: Mass and charg ar consrvd. 4 2α -β Alpha mission Bta mission 238 92U
More informationfiziks Institute for NET/JRF, GATE, IIT JAM, M.Sc. Entrance, JEST, TIFR and GRE in Physics NUCLEAR AND PARTICLE PHYSICS NET/JRF (JUNE-2011)
NUCLEAR AND PARTICLE PHYSICS NET/JRF (JUNE-) 64 Q. Th radius of a 9Cu nuclus is masurd to b 4.8 - cm. (A). Th radius of a 7 Mg nuclus can b stimatd to b.86 - cm (b) 5. - cm (c).6 - cm (d) 8.6 - cm (c)
More informationThe van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012
Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor
More informationUnit 7 Charge-to-mass ratio of the electron
Unit 7 Charg-to-ass ratio of th lctron Kywords: J. J. Thoson, Lorntz Forc, Magntic Filds Objctiv: Obsrv th rsults of lctron ba influncd by th agntic fild and calculat th charg-to-ass ratio of th lctron.
More informationClassical Magnetic Dipole
Lctur 18 1 Classical Magntic Dipol In gnral, a particl of mass m and charg q (not ncssarily a point charg), w hav q g L m whr g is calld th gyromagntic ratio, which accounts for th ffcts of non-point charg
More informationConstituents of the Atom
1 Constitunts of th Atom To b know th constitunts of th atom with thir masss and chargs To b abl to calculat th spcific charg of th constitunts To b abl to xplain what isotops and ions ar Th Nuclar Modl
More informationNeutrinos are chargeless, nearly massless particles Most abundant particle in the Universe Interact with matter via weak nuclear force
By Wndi Wamlr Nutrinos ar charglss, narly masslss articls Most abundant articl in th Univrs Intract with mattr via wak nuclar forc Narly transarnt to mattr Only known ty of articl that can sca from th
More informationForces. Quantum ElectroDynamics. α = = We have now:
W hav now: Forcs Considrd th gnral proprtis of forcs mdiatd by xchang (Yukawa potntial); Examind consrvation laws which ar obyd by (som) forcs. W will nxt look at thr forcs in mor dtail: Elctromagntic
More information22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.
Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M
More informationelectron -ee mrw o center of atom CLASSICAL ELECTRON THEORY Lorentz' classical model for the dielectric function of insulators
CLASSICAL ELECTRON THEORY Lorntz' claical odl for th dilctric function of inulator In thi odl th lctron ar aud to b bound to th nuclu ith forc obying Hook la. Th forc ar aud to b iotropic and daping can
More informationDecay Rates: Pions. u dbar. Look at pion branching fractions (BF)
Day Rats: Pions Look at ion branhing frations (BF τ 0.6 8 s BF BF BF 0% 1. 1.0 139.6MV Th Bta day is th asist. ~Sa as nutron bta day Q 4.1 MV. Assu FT1600 s. LogF3. (fro ot F 1600 gis artia width(-1 T1600/F1
More information1.2 Faraday s law A changing magnetic field induces an electric field. Their relation is given by:
Elctromagntic Induction. Lorntz forc on moving charg Point charg moving at vlocity v, F qv B () For a sction of lctric currnt I in a thin wir dl is Idl, th forc is df Idl B () Elctromotiv forc f s any
More informationMaxwellian Collisions
Maxwllian Collisions Maxwll ralizd arly on that th particular typ of collision in which th cross-sction varis at Q rs 1/g offrs drastic siplifications. Intrstingly, this bhavior is physically corrct for
More informationLecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields
Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration
More informationContemporary, atomic, nuclear, and particle physics
Contmporary, atomic, nuclar, and particl physics 1 Blackbody radiation as a thrmal quilibrium condition (in vacuum this is th only hat loss) Exampl-1 black plan surfac at a constant high tmpratur T h is
More informationPrecise Masses of particles
/1/15 Physics 1 April 1, 15 Ovrviw of topic Th constitunts and structur of nucli Radioactivity Half-lif and Radioactiv dating Nuclar Binding Enrgy Nuclar Fission Nuclar Fusion Practical Applications of
More informationHydrogen Atom and One Electron Ions
Hydrogn Atom and On Elctron Ions Th Schrödingr quation for this two-body problm starts out th sam as th gnral two-body Schrödingr quation. First w sparat out th motion of th cntr of mass. Th intrnal potntial
More informationCoupled Pendulums. Two normal modes.
Tim Dpndnt Two Stat Problm Coupld Pndulums Wak spring Two normal mods. No friction. No air rsistanc. Prfct Spring Start Swinging Som tim latr - swings with full amplitud. stationary M +n L M +m Elctron
More informationHigh Energy Physics. Lecture 5 The Passage of Particles through Matter
High Enrgy Physics Lctur 5 Th Passag of Particls through Mattr 1 Introduction In prvious lcturs w hav sn xampls of tracks lft by chargd particls in passing through mattr. Such tracks provid som of th most
More informationTitle: Vibrational structure of electronic transition
Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum
More informationToday. Wave-Matter Duality. Quantum Non-Locality. What is waving for matter waves?
Today Wav-Mattr Duality HW 7 and Exam 2 du Thurs. 8pm 0 min rcap from last lctur on QM Finish QM odds and nds from ch.4 Th Standard Modl 4 forcs of Natur Fundamntal particls of Natur Fynman diagrams EM
More informationOn the Hamiltonian of a Multi-Electron Atom
On th Hamiltonian of a Multi-Elctron Atom Austn Gronr Drxl Univrsity Philadlphia, PA Octobr 29, 2010 1 Introduction In this papr, w will xhibit th procss of achiving th Hamiltonian for an lctron gas. Making
More informationNeutrino Physics. Caren Hagner, Universität Hamburg
Nutrino Physics Carn Hagnr, Univrsität Hamburg What ar nutrinos? Nutrino mass and mixing Nutrino oscillations Nutrino bams: OPERA Oscillation of acclrator nutrinos Solar Nutrinos: BOREXINO (KamLAND ractor
More informationPHYSICS 489/1489 LECTURE 7: QUANTUM ELECTRODYNAMICS
PHYSICS 489/489 LECTURE 7: QUANTUM ELECTRODYNAMICS REMINDER Problm st du today 700 in Box F TODAY: W invstigatd th Dirac quation it dscribs a rlativistic spin /2 particl implis th xistnc of antiparticl
More informationBackground: We have discussed the PIB, HO, and the energy of the RR model. In this chapter, the H-atom, and atomic orbitals.
Chaptr 7 Th Hydrogn Atom Background: W hav discussd th PIB HO and th nrgy of th RR modl. In this chaptr th H-atom and atomic orbitals. * A singl particl moving undr a cntral forc adoptd from Scott Kirby
More information(A) (C) relation for the Legendre polynomial is α given by Pm. (A) σ = m. (B) σ 2 = m (C) σ + m = 0 (D) σ = m
. h atrix i Only Hritian i is Only Unitary Hritian and Unitary Nithr Hritian nor Unitary. What is th product of ign valus of 6. h first proprty of th orthogonality rlation for th Lgndr polynoial is α 0
More informationAtomic energy levels. Announcements:
Atomic nrgy lvls Announcmnts: Exam solutions ar postd. Problm solving sssions ar M3-5 and Tusday 1-3 in G-140. Will nd arly and hand back your Midtrm Exam at nd of class. http://www.colorado.du/physics/phys2170/
More informationExam 2 Thursday (7:30-9pm) It will cover material through HW 7, but no material that was on the 1 st exam.
Exam 2 Thursday (7:30-9pm) It will covr matrial through HW 7, but no matrial that was on th 1 st xam. What happns if w bash atoms with lctrons? In atomic discharg lamps, lots of lctrons ar givn kintic
More information2. Laser physics - basics
. Lasr physics - basics Spontanous and stimulatd procsss Einstin A and B cofficints Rat quation analysis Gain saturation What is a lasr? LASER: Light Amplification by Stimulatd Emission of Radiation "light"
More informationLecture 28 Title: Diatomic Molecule : Vibrational and Rotational spectra
Lctur 8 Titl: Diatomic Molcul : Vibrational and otational spctra Pag- In this lctur w will undrstand th molcular vibrational and rotational spctra of diatomic molcul W will start with th Hamiltonian for
More informationDerivation of Electron-Electron Interaction Terms in the Multi-Electron Hamiltonian
Drivation of Elctron-Elctron Intraction Trms in th Multi-Elctron Hamiltonian Erica Smith Octobr 1, 010 1 Introduction Th Hamiltonian for a multi-lctron atom with n lctrons is drivd by Itoh (1965) by accounting
More informationSchrodinger Equation in 3-d
Schrodingr Equation in 3-d ψ( xyz,, ) ψ( xyz,, ) ψ( xyz,, ) + + + Vxyz (,, ) ψ( xyz,, ) = Eψ( xyz,, ) m x y z p p p x y + + z m m m + V = E p m + V = E E + k V = E Infinit Wll in 3-d V = x > L, y > L,
More informationDetermination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot
5 J. Phys. Chm G Dtrmination of Vibrational and Elctronic Paramtrs From an Elctronic Spctrum of I 2 and a Birg-Sponr Plot 1 15 2 25 3 35 4 45 Dpartmnt of Chmistry, Gustavus Adolphus Collg. 8 Wst Collg
More informationProblem Set 4 Solutions Distributed: February 26, 2016 Due: March 4, 2016
Probl St 4 Solutions Distributd: Fbruary 6, 06 Du: March 4, 06 McQuarri Probls 5-9 Ovrlay th two plots using Excl or Mathatica. S additional conts blow. Th final rsult of Exapl 5-3 dfins th forc constant
More informationAntonio Pich. IFIC, CSIC Univ. Valencia.
Antonio Pich IFIC, CSIC Univ. Valncia Antonio.Pich@crn.ch Th Standard Modl A. Pich - CERN Summr Lcturs 2005 1. Constitunts & Intractions 2. Quarks 3. Gaug Invarianc 4. Quantum Chromodynamics 5. Elctrowak
More information26-Sep-16. Nuclear energy production. Nuclear energy production. Nuclear energy production. Nuclear energy production
Aim: valuat nrgy-gnration rat pr unit mass. Sun: (chck L /M, human ) nrgy-gnration rat producd from fusion of two nucli a + A: nrgy rlasd pr raction raction rat pr unit volum (includs cross sction and
More informationAPP-IV Introduction to Astro-Particle Physics. Maarten de Jong
APP-IV Introduction to Astro-Particl Physics Maartn d Jong 1 cosmology in a nut shll Hubbl s law cosmic microwav background radiation abundancs of light lmnts (H, H, ) Hubbl s law (199) 1000 vlocity [km/s]
More informationECE507 - Plasma Physics and Applications
ECE507 - Plasma Physics and Applications Lctur 7 Prof. Jorg Rocca and Dr. Frnando Tomasl Dpartmnt of Elctrical and Computr Enginring Collisional and radiativ procsss All particls in a plasma intract with
More informationPhysics. X m (cm)
Entranc xa 006-007 Physics Duration: hours I- [ pts] An oscillator A chanical oscillator (C) is ford of a solid (S), of ass, attachd to th xtrity A of a horizontal spring of stiffnss (constant) = 80 N/
More informationOutline. Thanks to Ian Blockland and Randy Sobie for these slides Lifetimes of Decaying Particles Scattering Cross Sections Fermi s Golden Rule
Outlin Thanks to Ian Blockland and andy obi for ths slids Liftims of Dcaying Particls cattring Cross ctions Frmi s Goldn ul Physics 424 Lctur 12 Pag 1 Obsrvabls want to rlat xprimntal masurmnts to thortical
More informationPH300 Modern Physics SP11 Final Essay. Up Next: Periodic Table Molecular Bonding
PH Modrn Physics SP11 Final Essay Thr will b an ssay portion on th xam, but you don t nd to answr thos qustions if you submit a final ssay by th day of th final: Sat. 5/7 It dosnʼt mattr how smart you
More informationWhy is a E&M nature of light not sufficient to explain experiments?
1 Th wird world of photons Why is a E&M natur of light not sufficint to xplain xprimnts? Do photons xist? Som quantum proprtis of photons 2 Black body radiation Stfan s law: Enrgy/ ara/ tim = Win s displacmnt
More informationIntro to QM due: February 8, 2019 Problem Set 12
Intro to QM du: Fbruary 8, 9 Prob St Prob : Us [ x i, p j ] i δ ij to vrify that th anguar ontu oprators L i jk ɛ ijk x j p k satisfy th coutation rations [ L i, L j ] i k ɛ ijk Lk, [ L i, x j ] i k ɛ
More informationorbiting electron turns out to be wrong even though it Unfortunately, the classical visualization of the
Lctur 22-1 Byond Bohr Modl Unfortunatly, th classical visualization of th orbiting lctron turns out to b wrong vn though it still givs us a simpl way to think of th atom. Quantum Mchanics is ndd to truly
More informationPropagation of Light in a Hot and Dense Medium
Propagation of Light in a Hot and Dns Mdiu Saina S. Masood Dpartnt of Physics Univrsity of Houston Clar La Houston TX 7758 Photons as quanta of lctroagntic filds dtrin th lctroagntic proprtis of an xtrly
More informationMagnetic Neutron Scattering and Spin-Polarized Neutrons
agntic Nutron Scattring and Spin-Polarizd Nutrons Physical origin: potntial of magntic dipol momnt of th nutron in magntic fild gnratd by lctron spins and orbital momnts in th solid. µ n µ H Spcializ to
More informationIV. Weak interaction 1. Phenomenology of weak decays 2. Parity violation and neutrino helicity 3. V-A theory 4. Neutral currents
IV. Wak intraction. hnonology of wak dcays. arity violation and ntrino hlicity 3. V-A thory 4. Ntral crrnts Th wak intraction was and is a toic with a lot of srriss: ast: Flavor violation, and C violation.
More information2008 AP Calculus BC Multiple Choice Exam
008 AP Multipl Choic Eam Nam 008 AP Calculus BC Multipl Choic Eam Sction No Calculator Activ AP Calculus 008 BC Multipl Choic. At tim t 0, a particl moving in th -plan is th acclration vctor of th particl
More informationSCALING OF SYNCHROTRON RADIATION WITH MULTIPOLE ORDER. J. C. Sprott
SCALING OF SYNCHROTRON RADIATION WITH MULTIPOLE ORDER J. C. Sprott PLP 821 Novmbr 1979 Plasma Studis Univrsity of Wisconsin Ths PLP Rports ar informal and prliminary and as such may contain rrors not yt
More informationRadiation Physics Laboratory - Complementary Exercise Set MeBiom 2016/2017
Th following qustions ar to b answrd individually. Usful information such as tabls with dtctor charactristics and graphs with th proprtis of matrials ar availabl in th cours wb sit: http://www.lip.pt/~patricia/fisicadaradiacao.
More informationExact formula of 3 flavor ν oscillation probability and its application to high energy astrophysical ν
Exact formula of 3 flavor ν oscillation probability and its application to high nrgy astrophysical ν Osamu Yasuda Tokyo Mtropolitan nivrsity 1-16 16-5 at Miami5 Contnts 1. Introduction 1.1 Status of ν
More informationThe Death of Stars - II.
Th Dath of Stars - II. Larning Objctivs! How can w us H-R diagrams to masur th ag of star clustrs (and hnc th ag of our Univrs)?! Why do high and low mass stars volv diffrntly? How ar havy lmnts such as
More informationAlpha and beta decay equation practice
Alpha and bta dcay quation practic Introduction Alpha and bta particls may b rprsntd in quations in svral diffrnt ways. Diffrnt xam boards hav thir own prfrnc. For xampl: Alpha Bta α β alpha bta Dspit
More informationBrief Introduction to Statistical Mechanics
Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.
More informationAddition of angular momentum
Addition of angular momntum April, 0 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat th
More informationMagnetic vector potential. Antonio Jose Saraiva ; -- Electric current; -- Magnetic momentum; R Radius.
Magnti vtor potntial Antonio Jos araiva ajps@hotail.o ; ajps137@gail.o A I.R A Magnti vtor potntial; -- auu prability; I -- ltri urrnt; -- Magnti ontu; R Radius. un agnti ronntion un tru surfa tpratur
More informationDavisson Germer experiment Announcements:
Davisson Grmr xprimnt Announcmnts: Homwork st 7 is du Wdnsday. Problm solving sssions M3-5, T3-5. Th 2 nd midtrm will b April 7 in MUEN E0046 at 7:30pm. BFFs: Davisson and Grmr. Today w will go ovr th
More informationCHAPTER 5 FREE ELECTRON THEORY
CHAPTER 5 REE ELECTRON THEORY r Elctron Thory Many solids conduct lctricity. Thr ar lctrons that ar not bound to atos but ar abl to ov through th whol crystal. Conducting solids fall into two ain classs;
More informationBrief Notes on the Fermi-Dirac and Bose-Einstein Distributions, Bose-Einstein Condensates and Degenerate Fermi Gases Last Update: 28 th December 2008
Brif ots on th Frmi-Dirac and Bos-Einstin Distributions, Bos-Einstin Condnsats and Dgnrat Frmi Gass Last Updat: 8 th Dcmbr 8 (A)Basics of Statistical Thrmodynamics Th Gibbs Factor A systm is assumd to
More informationCollisions between electrons and ions
DRAFT 1 Collisions btwn lctrons and ions Flix I. Parra Rudolf Pirls Cntr for Thortical Physics, Unirsity of Oxford, Oxford OX1 NP, UK This rsion is of 8 May 217 1. Introduction Th Fokkr-Planck collision
More informationVoltage, Current, Power, Series Resistance, Parallel Resistance, and Diodes
Lctur 1. oltag, Currnt, Powr, Sris sistanc, Paralll sistanc, and Diods Whn you start to dal with lctronics thr ar thr main concpts to start with: Nam Symbol Unit oltag volt Currnt ampr Powr W watt oltag
More informationCh. 24 Molecular Reaction Dynamics 1. Collision Theory
Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic
More informationElectromagnetism Physics 15b
lctromagntism Physics 15b Lctur #8 lctric Currnts Purcll 4.1 4.3 Today s Goals Dfin lctric currnt I Rat of lctric charg flow Also dfin lctric currnt dnsity J Charg consrvation in a formula Ohm s Law vryon
More informationAddition of angular momentum
Addition of angular momntum April, 07 Oftn w nd to combin diffrnt sourcs of angular momntum to charactriz th total angular momntum of a systm, or to divid th total angular momntum into parts to valuat
More information15. Stress-Strain behavior of soils
15. Strss-Strain bhavior of soils Sand bhavior Usually shard undr draind conditions (rlativly high prmability mans xcss por prssurs ar not gnratd). Paramtrs govrning sand bhaviour is: Rlativ dnsity Effctiv
More informationExtraction of Doping Density Distributions from C-V Curves
Extraction of Doping Dnsity Distributions from C-V Curvs Hartmut F.-W. Sadrozinski SCIPP, Univ. California Santa Cruz, Santa Cruz, CA 9564 USA 1. Connction btwn C, N, V Start with Poisson quation d V =
More informationIV. e + e annihilation experiments 1. Experimental methods Discovery of the Tau-Lepton 5. hadrons 6. Hadronic resonances
IV. annihilation xprimnts 1. Exprimntal mthods. 3. 4. Discovry of th Tau-Lpton 5. (γ ) µ µ (γ ) hadrons 6. Hadronic rsonancs Lit.: H.U Martyn, Tst of QED in Quantum Elctrodynamics, T.Kinoshita (d.) 1.
More informationIntroduction to the quantum theory of matter and Schrödinger s equation
Introduction to th quantum thory of mattr and Schrödingr s quation Th quantum thory of mattr assums that mattr has two naturs: a particl natur and a wa natur. Th particl natur is dscribd by classical physics
More informationGamma-ray burst spectral evolution in the internal shock model
Gamma-ray burst spctral volution in th intrnal shock modl in collaboration with: Žljka Marija Bošnjak Univrsity of Rijka, Croatia Frédéric Daign (Institut d Astrophysiqu d Paris) IAU$Symposium$324$0$Ljubljana,$Sptmbr$2016$
More informationParticle Physics. Dr M.A. Thomson. e + γ. 1 q 2. e - Part II, Lent Term 2004 HANDOUT II. Dr M.A. Thomson Lent 2004
Particl Physics Dr M.A. Thomson µ q 2 µ Part II, Lnt Trm 2004 HANDOUT II Dr M.A. Thomson Lnt 2004 Quantum Elctrodynamics 2 QUANTUM ELECTRODYNAMICS: is th quantum thory of th lctromagntic intraction. CLASSICAL
More informationChapter. 3 Wave & Particles I
Announcmnt Cours wbpag http://highnrgy.phys.ttu.du/~sl/2402/ Txtbook PHYS-2402 Lctur 8 Quiz 1 Class avrag: 14.2 (out of 20) ~ 70% Fb. 10, 2015 HW2 (du 2/19) 13, 17, 23, 25, 28, 31, 37, 38, 41, 44 Chaptr.
More information(most) due to long range e m forces i.e. via atomic collisions or due to short range nuclear collisions or through decay ( = weak interactions)
Spring 01, P67, YK Monday January 30, 01 8 Obsrvabl particl dtction ffcts ar : (most) du to long rang m forcs i.. via atomic collisions or du to short rang nuclar collisions or through dcay ( = wak intractions)
More informationperm4 A cnt 0 for for if A i 1 A i cnt cnt 1 cnt i j. j k. k l. i k. j l. i l
h 4D, 4th Rank, Antisytric nsor and th 4D Equivalnt to th Cross Product or Mor Fun with nsors!!! Richard R Shiffan Digital Graphics Assoc 8 Dunkirk Av LA, Ca 95 rrs@isidu his docunt dscribs th four dinsional
More informationELECTRON-MUON SCATTERING
ELECTRON-MUON SCATTERING ABSTRACT Th lctron charg is considrd to b distributd or xtndd in spac. Th diffrntial of th lctron charg is st qual to a function of lctron charg coordinats multiplid by a four-dimnsional
More informationThe pn junction: 2 Current vs Voltage (IV) characteristics
Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n
More informationPHYS-333: Problem set #2 Solutions
PHYS-333: Problm st #2 Solutions Vrsion of March 5, 2016. 1. Visual binary 15 points): Ovr a priod of 10 yars, two stars sparatd by an angl of 1 arcsc ar obsrvd to mov through a full circl about a point
More informationNeutrino Probes of Dark Energy and Dark Matter
SNOWPAC@Snowbird March 25, 2010 Nutrino Probs of Dark Enrgy and Dark Mattr Shin ichiro Ando California Institut of Tchnology Dark Enrgy and Dark Mattr 2.0 1.5 1.0 No Big Bang SN Most of th nrgy in th Univrs
More informationCompton Scattering. There are three related processes. Thomson scattering (classical) Rayleigh scattering (coherent)
Comton Scattring Tr ar tr rlatd rocsss Tomson scattring (classical) Poton-lctron Comton scattring (QED) Poton-lctron Raylig scattring (cornt) Poton-atom Tomson and Raylig scattring ar lasticonly t dirction
More informationSeptember 23, Honors Chem Atomic structure.notebook. Atomic Structure
Atomic Structur Topics covrd Atomic structur Subatomic particls Atomic numbr Mass numbr Charg Cations Anions Isotops Avrag atomic mass Practic qustions atomic structur Sp 27 8:16 PM 1 Powr Standards/ Larning
More informationDIELECTRIC AND MAGNETIC PROPERTIES OF MATERIALS
DILCTRIC AD MAGTIC PROPRTIS OF MATRIALS Dilctric Proprtis: Dilctric matrial Dilctric constant Polarization of dilctric matrials, Typs of Polarization (Polarizability). quation of intrnal filds in liquid
More informationPhysics 2D Lecture Slides Lecture 12: Jan 28 th 2004
Brian Wcht, th TA, is away this wk. I will substitut for his offic hours (in my offic 3314 Mayr Hall, discussion and PS sssion. Pl. giv all rgrad rqusts to m this wk (only) Quiz 3 Will Covr Sctions.1-.5
More informationNeutrino Mass and Forbidden Beta Decays
NUCLEAR THEORY Vol. 35 016) ds. M. Gaidarov N. Minkov Hron Prss Sofia Nutrino Mass and Forbiddn Bta Dcays R. Dvornický 1 D. Štfánik F. Šimkovic 3 1 Dzhlpov Laboratory of Nuclar Problms JINR 141980 Dubna
More information6. The Interaction of Light and Matter
6. Th Intraction of Light and Mattr - Th intraction of light and mattr is what maks lif intrsting. - Light causs mattr to vibrat. Mattr in turn mits light, which intrfrs with th original light. - Excitd
More informationChapter 6: Polarization and Crystal Optics
Chaptr 6: Polarization and Crystal Optics * P6-1. Cascadd Wav Rtardrs. Show that two cascadd quartr-wav rtardrs with paralll fast axs ar quivalnt to a half-wav rtardr. What is th rsult if th fast axs ar
More informationChapter 7b Electron Spin and Spin- Orbit Coupling
Wintr 3 Chm 356: Introductory Quantum Mchanics Chaptr 7b Elctron Spin and Spin- Orbit Coupling... 96 H- atom in a Magntic Fild: Elctron Spin... 96 Total Angular Momntum... 3 Chaptr 7b Elctron Spin and
More informationWhere k is either given or determined from the data and c is an arbitrary constant.
Exponntial growth and dcay applications W wish to solv an quation that has a drivativ. dy ky k > dx This quation says that th rat of chang of th function is proportional to th function. Th solution is
More information