1000 Solved Problems in Modern Physics

524 9 Particle Physics – I 9.76 p=^0.^3 BR (1) wherepis in GeV/c,Bin Tesla andRin metres. Nowθ≈L/R= 0. 3 BL/p (2) whereLis the l ...

9.3 Solutions 525 Furtherp=qBR T=p^2 / 2 m=q^2 B^2 R^2 / 2 m Maximum radius R(max)=(2mTmax)^1 /^2 /qB =(2× 1. 67 × 10 −^27 × 6 × ...

526 9 Particle Physics – I 9.82 (a) Resonance condition for protons is B= 2 πfm/q=(2π× 5 × 106 )(1. 6726 × 10 −^27 )/(1. 6 × 10 ...

9.3 Solutions 527 E=(p^2 +m^2 )^1 /^2 =(900^2 + 9382 )^1 /^2 = 1 ,300 MeV γ= 1 , 300 / 938 = 1. 386 β= 0. 692 Maximum energy tra ...

528 9 Particle Physics – I 9.93 Using the result of Problem 9.92 R= m 0 c qB (n^2 + 2 n) (^12) = m 0 c 0. 0147 q [( 50 940 ) 2 + ...

9.3 Solutions 529 B= 1 .8T;q= 1. 6 × 10 −^19 C;c= 3 × 108 m/s;mc^2 = 938 × 1. 6 × 10 −^13 J Ts=± 2 .5MeV=± 2. 5 × 1. 6 × 10 −^13 ...

530 9 Particle Physics – I 9.98 (a) At injectionγ= 1 + 0.^10511 = 20. 57 β= 0. 9988 At extractionγ= 1 +^50 ,.^000511 = 9 , 786 β ...

9.3 Solutions 531 (b) Power outputW=iV The current is obtained from (a) and the voltageVcorresponding to final voltage of 2 GeV ...

532 9 Particle Physics – I 9.105 (a)E∗^2 =(E 1 +E 2 )^2 −(p 1 −p 2 )^2 =E 12 + 2 E 1 E 2 +E 22 −p 12 + 2 p 1 p 2 −p 22 = ( E 12 ...

9.3 Solutions 533 9.108 The CMS energy is calculated from the invariance ofE^2 −p^2 E∗^2 =E^2 −p^2 = ( Ep+Ee ) 2 − ( pp−pe ) 2 = ...

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Chapter 10 Particle Physics – II 10.1 Basic Concepts and Formulae ................................ Classification of particles T ...

536 10 Particle Physics – II Table 10.1 Mass Common Particle (MeV/c^2 ) τ(s) decay mode Hadrons ⎧ ⎪⎪⎪ ⎪⎪ ⎪⎪⎪ ⎪⎪⎪ ⎪⎪⎪ ⎪⎪ ⎪⎪⎪ ⎪⎪⎪ ...

10.1 Basic Concepts and Formulae 537 Table 10.2Characteristics of the fundamental interactions Strong Electromagnetic Weak Gravi ...

538 10 Particle Physics – II Strangeness and strange particles: Heavy unstable particles such as kaons and hyperons which are pr ...

10.1 Basic Concepts and Formulae 539 Parity(porπ): The concept of parity was mentioned in Chap. 3. The absolute intrinsic parity ...

540 10 Particle Physics – II The TCP theorem: A lagrangian which is invariant under proper Lorentz transfor- mation is invariant ...

10.1 Basic Concepts and Formulae 541 Gellman’s equation is generalized as: Q/e=I 3 +^1 / 2 (B+S+C+B∗+T) (10.8) whereBdenotes Bar ...

542 10 Particle Physics – II wheremis the mass of the exchanged boson. The quantity (q^2 +m^2 )−^1 is known as the propagator te ...

10.1 Basic Concepts and Formulae 543 e=gsinθw (10.10) sin^2 θw= 0. 2319 (10.11) Mw/Mz= 0. 88 (10.12) Feynman diagramsare short-h ...