Study Guide Nuclear and particle physics, Study Guides, Projects, Research of Nuclear Physics

Download Study Guide Nuclear and particle physics and more Study Guides, Projects, Research Nuclear Physics in PDF only on Docsity! NOTES ON NUCLEAR AND PARTICLE PHYSICS STUDY GUIDE FOR NUCLEAR AND PARTICLE PHYSICS IMPORTANT NOTES ON NUCLEAR AND PARTICLE PHYSICS Sangeetha 9/2/2020 THE NOTES CONTAINS IMPORTANT CONCEPT BASED FORMULA LIST WITH THEORY CONTENTS: 1. PARTICLE PHYSICS ------------------n-----0nccenenecnsneneenensnnne 3 = 34 2. NUCLEAR PHYSICS ---++-+:-2:s0+se+cn-soesnescesencnsscescusonsensen 35 = 38 5|Page STRONG INTERACTION:( NUCLEAR INTERACTION ) Strongest force of nature. Exact nature of the force is unknown but following properties are observed: i.e. (a) charge independent nature (b) spin dependent nature (c) orientation dependent (d) velocity dependent nature (e) exchange type force ( Yukawa theory ) Exchange particles are pions ( 77+ , 0) Mass of pions m ~ 134 — 140 MeV Spin = 0 and velocity v<c Strength of interaction is given by : 2 - where g > nuclear coupling constant Characteristic time of interaction is : ty © ts ¥ 1073 sec WEAK INTERACTION: * This force is generally involved in the decay of particles and interactions among leptons. Range R ~ 10-27 — 10-18m Exchange particle : intermediate vector bosons W+, Z° Mass m,,+ * 82 GeV m,» ~ 92 GeV Spin=1andu<c Strength of interaction is given by : 2 Iw » . ae where gy — weak interaction constant Characteristic lifetime is given by: Ty © 10-6 — 10713 sec or ( 10-19 secin general) 6|Page INTERACTIONS — EXCHANGE MASS AND SPIN RELATIVESTRENGTH — CHARACTERISTIC PARTICLE (OF EXCHANGE TIME ( SEC) PARTICLE Gravitational GRAVITON INFINITE m=0;S=2 10-*° = Electromagnetic © GAMMA INFINITE m=0;S=1 1073 ~10-16 — 10-20 PHOTON Strong PIONS 10-5m m=134-140 ~10773 Mev s=0 1072710718 M= 82-92 GeV ~1071 $=1 1 Characteristic time STRENGTH OF INTERACTION o So, Ts < Tey < Tw < ToRaV ELEMENTARY PARTICLES: A particle which has no internal structure is called as elementary or fundamental particle. OR STRUCTURELESS PARTICLE ARE KNOWN AS ELEMETARY PARTICLES BASIC PARAMETERS OF ELEMENTARY PARTICLES: MASS: The mass of elementary particles are represented in terms of energy units PARTICLES MASS (MeV) B. CHARGE: 0.511 105.6 139.5 134.5 493 497 549 938.3 939.6 — Elementary particles may have positive, negative or zero charge. — The members of a multiplet family have different charges. — Some particles are truly neutral while some are not. C. SPIN: PARTICLES | INTEGRAL SPIN (S=0,1,2....) BOSONS HALF ODD INTEGRAL (S=1/2,3/2,5/2....) ! FERMIONS 10| Page —» CLASSIFICATION OF ELEMENTARY PARTICLES: A) ON THE BASIS OF MASS: \ 5: | | J LIGHTER MASS PARTICLES INTERMEDIATE MASS PARTICLES HEAVY MASS PARTICLES ( LEPTONS [ 0 - 134 MeV] ) ( MESONS > 134 MeV < mp) ( BARYONS m > mp) LEPTONS PARTICLE SPIN e 1/2 Ve 1/2 1/2 Ue 1/2 € 1/2 v, 1/2 NOTE: t does not follow strong interaction whereas it only follows electromagnetic and weak interactions. B) ON THE BASIS OF INTERACTION: “y | | LEPTONS HADRONS Those particles which do not feel strong interactions. Particles which feel strong interactions. EM INTERACTION [EM INTERACTION WEAK Ms WEAK STRONG STRONG LEPTONS IST GENERATION 2ND GENERATION 3RD GENERATION €' Ue Wp TU; and their antiparticles and their antiparticles and their antiparticles ee wa, TU HADRONS | MESONS BARYONS te) Pseudo scalar mesons (? =0) NUCLEONS HYPERONS (pn) yo z-0 No ao (sigma) (cascade) (lambda) (omega) = Strong particles = kaons + hyperons C) CONSERVATION LAWS: DIVIDED AS | EXACT CONSERVATION LAWS APPROXIMATE CONSERVATION LAWS | ) UNIVERSAL CONSTANT LAW APPROXIMATE CONSTANT QUANTITY (E, P, J, QL, B, CPT [ charge parity time reversal ] ) (1, Is, S, ¥, P, C, T) > EXACT CONSERVATION LAWS: © Energy conservation : let us consider a reaction as : A+B>C+D = Energy conservation means : E,+Eg=Ect+ Ep (K4+Kg)+ (Mg i" = (Ke +Kp) + (Mg + Mp)e? Kineticenergy —_ rest mass energy For target at rest; then Ks = 0; THEN Ky = (Mc + Mp — Mg — Mg)c? + (Ke + Kp) DIFFERENCE IN REST MASS ENERGY If particles are produced at rest then; Kc = Kp =0;then Kg =(Mc+Mp — Mg —Mg)c? 15|Page » PARITY: * Pir +-?7;sothat Pw,t) = w(-7,0; Then, P? (Ft) = (F,t)i.e.P? = 1 hence P = +1 * Parity operator has two eigen values : ie. P=41( EVEN) AND P=-1(ODD) « Net parity = orbital parity x intrinsic parity se BARYONS Peal PARITY P = —1 p,e,n,y>P= +1 rH 9 A ott P= +1 INTERACTION CONSERVATION OF (P) STRONG ELECTROMAGNETIC WEAK X 16|Page ‘+ Charge conjugation [ C - PARITY] C- charge conjugation operator Ciq>9 Thus operation reverse the sign of electric charge (Q), Lepton no. (L), B, Is, Strangeness (S); Hypercharge of the particle. Let |p > be the particle state ; then c |p >= |p > andc’|p >= |p > ~>c’=1->c= +1 > two eigen values. INTERACTION CONSERVATION OF C - PARITY STRONG ELECTROMAGNETIC WEAK X “TIME REVERSAL ( TIME PARITY ) : Time reversal is an operator in which the direction of time is reversed; (Time reversal operator) T: t--> -t * Ifatime reversal symmetry holds in a system then it will be impossible to know whether the process is running in forward direction or reverse direction. INTERACTION CONSERVATION OF T STRONG ELECTROMAGNETIC WEAK x 17|Page “+ CPT THEOREM ( PAULI'S - LUDERS THEOREM ) : According to this theorern; all interactions are invariant under combined operation of charge conjugation ( C }, inversion of space coordinate about origin ( P ) and reversal of time (T ). FOR ANY REACTION : A+B->C4+D CPT(L-H.S) = CPT(R.H.S) NOTE: If an interaction is not invariant under anyone of operation ( C.P,T ) then other two operations will adjust themselves such that the net value of CPT becomes invariant. Thus CPT is universally conserved quantity. RESONANCE PARTICLES: These are the particles which are produced via strong interaction and their decay occurs via strong interaction also ( r~10-3sec) ‘> Resonances are produced in different hadronic reactions for a very short duration. Since their life time is very small therefore direct method of measure of life time (r) and mass are not applicable, so indirect method are used to measure life time , mass and other properties. Eg: A graph between cross section and the energy of incident particle shows resonance peak at some particular energy. —+ This peak signifies the existence of resonance particles. » The position and width of resonance peak can be used to measure the mass and life time. 20|Page 2. MESON OcTET (J? = 07): PARTICLES 21|Page 3. VECTOR MESONS : (J? = 17) { MESON RESONANCE ) : PARTICLES + | ss 1 2 1 2 1 2 1 Zz 0 22|Page " BARYON DECUPLET (J? = ; ) (BARYON RESONANCE ): PARTICLES att & Y=B+S +1 ibs At fe rl w Nie NI Re NI] we Hoek fe NIRPNI RE “+ COMPOSITION OF HADRONS ON THE BASIS OF QUARK MODEL: HADRONS 1 | | MESONS ( B =0) BARYONS (B = 1) + MESONS = q+ q(2 quarks) = BARYONS = q+ = Quark + antiquark w px24 5g? 1 £ s _ “Begg 9 "Ss NOTE : my © my = 0.4 GeV + doublet — and I, = +3 and ~} m, = 0.51 GeV; mg = 1.65 GeV ; m, = 5 GeV ; m, ~ 180 GeV > singlets > I = 0 and I; = 0 » These have differentness and different charges. > Real world is made up of from up, down and strange quarks. » Heavy quark played an important role during the initial stages of the universe. 1. COMPOSITION OF MESONS : MESONS = QUARK + ANTIQUARK A) PSEUDOSCALAR MESONS (J? = 07 ): PARTICLES CHARGE QUARK CONTENT +1 ud 0 ui, dd A ud +1 us ds 26|Page A) VECTOR MESONS (J? = 17): PARTICLES CHARGE 5; QUARK CONTENT +1 0 ud 0 0 ui,dd -1 0 ud 0 oO ui,dd uu,dd us ds 2. QUARK STRUCTURE OF BARYONS (q+q+q): z A) BARYON ocTET ( J? => ): PARTICLES CHARGE B QUARK CONTENT +1 +1 0 uud 0 +1 0 udd +1 uus +1 uds +1 dds +1 dss +1 uss +1 uds 27 | Page ¥ B) BARYON DECUPLET (J? =3 }: PARTICLES CHARGE B QUARK CONTENT art 42 41 uuu +1 1 uud 0 +1 udd -1 +1 ddd +1 uus +1 uds 41 dds me dss +1 uss +1 SSS * CONCEPT OF COLOURED QUARKS : COLOURED QUANTUM NO. : RED , BLUE, GREEN COLOURED ANTIQUARK NO. : R, B,G —> Let us consider the quark structure of following particles : Att = uuu; At = uud; A = ddd; 9 = sss Since quarks are spin half particles , so they must follow Pauli - exclusion principle. » Butin these quark structures Pauli principles violated. » To solve this problem ; a quantum no. called as coloured quantum no. was introduced. — Quark colours have no any connection with optical visual colours. They are simply quantum numbers. — Incase of mesons colours and anticolour combine to form colourless particle. R+R = colourless; B + B = colourless ;G + G = colourless; 30|Page By quark model also , EN _ 0.68 Up D) The quark model explains the relationship between cross - sections in different hadronic reactions. ONN + ONN _ Onn | Good agreement with experimental data. 3 QUARK POTENTIAL AND COLOUR LINES OF FORCE : — Atasmall distance ; Vi@~) = -£ ; B > constant. ~ Atlarger distances ; this potential /’(1) must be such that it ensures the confinement of quarks within hadrons. V2(7) = ar ; a > constant ; Hence the net potential between two quarks is ; V(r) = er — B 7 31|Page — > UNIFICATION OF INTERACTIONS : GRAVITATION ELECTROWEAK THEORY THEORY OF EVERGREEN GUT 7 GRAND UNIFIED THEORY STRING THEORY Theories of E.W interaction was given by Abul salam and Weinberg. Grand unified theory (GUT) are an effort to unify the strong interaction with electroweak interaction. CONSEQUENCES OF GUT: Very massive magnetic monopoles will exist. Proton will be unstable particle however calculated lifetime is very hight = 1078 years. There will be no difference between quark and leptons at and above unification theory. SU(5) group suit for the theory of unification of strong , EM , and weak interaction. Unification occurs at very high energy and this energy is called as unification theory. “+ HIGGS FIELD AND HIGGS BOSON : In 1967 , Peter Higgs proposed that there exist an universal field which is present everywhere by interacting with particles attain mass. Stronger the interaction with Higgs field , more will be the mass of particle. The quanta of Higgs field is called as Higgs boson. Notation : p2° ; Mass : © 126 GeV /c* t®©1.6 x 10-*sec ( unstable ) J? =0* — scalar particle. + DECAY MODE OF HIGGS BOSON : pos yy > 2z> ww > bs > tt “ SELECTION RULES : TRANSITIONS ALLOWED | =0 140 Dee RELATIVE ANGULAR MOMENTUM OF e~ and v, IFlei 122 1=3 Ist FORBIDDEN 2nd FORBIDDEN 3rd FORBIDDEN ALLOWED TRANSITIONS FERMI GAMOW - TELLER e and v, are e and v, are emitted anti — parallel emitted parallel 35|Page NUCLEAR PHYSICS: 1, GENERAL PROPERTIES OF NUCLEII: A) NUCLEUS: — Anucleus is a quantum system which consists of discrete energy levels. Each energy level has certain spin and parity. Nuclear spin and parity can be predicted using shell model, B) NUCLEAR COMPOSITION: Before the discovery of neutrons; it was assumed that nucleus consists of protons and electrons. This hypothesis is called as p-e hypothesis, There were many objections for the existence of electron inside the nucleus. MOMENTUM AND ENERGY OF NUCLEONS INSIDE THE NUCLEUS: Maximum uncertainty in the position of nucleon is Ax = 2R 36|Page so[ipie=F ] hoh 8P~ OR h —# jAp ~ z= Ap «As 2RoA3 So, the momentum of the nucleon at least will be of this order : so,| =T px As 2 2 Also ,|E = += E « A 3 where m— mass of nucleus whose fixed value is 1.67 x 10-*7kg 2m D) MIRROR NUCLEI: Two nuclei are called as mirror nuclei if no. of protons and neutrons is interchanged. Eg: li and ]Be (p = 3n=3;p=4n=4) In general (Z1, N1) and (Z2, N2) will be mirror nuclei if : Z1 =N2 and Z2 =N1 For such nuclei: 21 - Z2 =1 ( if Z1 >> Z2 ) and N2 - N1 = 1 and also Al = Al ( mass no. is same) NUCLEAR SIZE: Volume « mass no. 4 1 i g mR aA = R3«xA>R« AS => R = RAB MEASUREMENT OF NUCLEAR RADIUS : NUCLEAR CHARGE RADIUS » Based on charge distribution inside the nucleons : Ro ~ 1.2fm + Ex:electron scattering, muon scattering. | NUCLEAR POTENIAL RADIUS + Based on mass distribution Inside the nucleus : Ro ~ 1.3 —1.4fm —> Ex: neutron scattering. 37|Page F) NUCLEAR SPIN : The nuclear spin is the total angular momentum of the nucleus. J=1+8 — Shell model can be used to predict the nuclear spin. Ex: p =6 TL 1) 11;n=61T IT TL; — Foreven-odd and odd - odd nuclei ; net angular momentum will be due to unpaired nucleons. Ex: p=7 Tl T1 Tif); n=6 TT IT TL; UNPAIRED: G) NUCLEAR PARITY: » Total parity = orbital parity x intrinsic parity. > Orbital parity = (—1)' where l — orbital state of nucleon. > Intrinsic parity of both p andn =+1, — > So, for proton ; net parity = (—1)'»x (+1) = (—1)>; for neutron ; net parity = (—1)""* (41) = (-1)»; HH) MAGNETIC MOMENT OF NUCLEONS : iti + fie sti = fy = gil; fi, = 9.8; g > orbital g — factor; g, > spin g — factor; > fi=gil+gs 2. BINIDING ENERGY : » The minimum energy ( or separation energy ) require to dissociate the particles or OR » The binding energy is basically or simply the work which must to be done against the forces that holds the particles together; dissociate them and we have no any requirement of additional work for further dissociation. BINDING ENERGY = Amc? where Am — mass defect; theoritical mass — observed mass Am = Zm, + (A—Z)m, — M(Z,A