1000 Solved Problems in Modern Physics

504 9 Particle Physics – I 9.4 In natural unitsτ= 2 /mα^5. Introduce the factorsandc Letτ= 2 xcy/mα^5 Find the dimensions: [] ...

9.3 Solutions 505 9.7 If a particle m 1 moving with total energyE 1 collides with the target of mass m 2 , then the total energy ...

506 9 Particle Physics – I 9.12 (a) In elastic scattering, total kinetic energy is conserved. Life-time means mean-life-time i.e ...

9.3 Solutions 507 = 6. 02 × 1023 × 7. 9 × 600 × 10 −^27 / 55. 95 = 0 .051 cm−^1 I/I 0 = 1 / 500 =exp(− 0. 051 x) Take logeon bot ...

508 9 Particle Physics – I Q^2 = 2 EiEf(1−cosθ) Thus, the approximation is valid when the particle mass is much smaller than the ...

9.3 Solutions 509 En= ( mΣ^2 +mn^2 −mμ^2 ) / 2 mΣ=(1, 1892 + 9392 − 1062 )/ 2 × 1 , 189 = 960 .6MeV ThereforeTn=En−mn= 960. 6 − ...

510 9 Particle Physics – I Eμ=Eμ∗γπ(1+βμ∗βπcosθ∗) Eμ∗= 105. 7 + 4. 0 = 109 .7MeV;γμ∗= 1 .0378;βμ∗= 0. 2676 γπ= 5 / 0. 1395 = 35 ...

9.3 Solutions 511 It may be noted that the beams of sigma hyperons are available only in recent times. This has been possible be ...

512 9 Particle Physics – I The integration of the expression ∫ mμ 2 c^2 0 E^2 e ( 1 − 4 Ee/ 3 mμc^2 ) dEe gives (mμc^2 )^3 /48 s ...

9.3 Solutions 513 or n 1 +n 2 =n 12 −B (1) Now, for each particle that is counted, on an average there will be a dead timeτdurin ...

514 9 Particle Physics – I 9.41 Slope= 2% 100 V = 0 .1% 5 V The voltage should not vary more than±5 V from the operating voltage ...

9.3 Solutions 515 whereτis the dead time.τ= 100 μs= 10 −^4 s. n 0 = 104 /min= 166. 7 /s n=(10^4 /min)/(1− 166. 7 × 10 −^4 )= 10 ...

516 9 Particle Physics – I Eπ= ( P^2 +mπ^2 ) 1 / 2 =(1. 192 + 0. 142 )^1 /^2 = 1 .198 GeV βπ=P/Eπ= 1. 19 / 1. 198 = 0. 9933 tπ=d ...

9.3 Solutions 517 9.55 LabelAis due to photopeak of 1.275 MeVγ-rays. Some of the primary pho- tons will be absorbed within the c ...

518 9 Particle Physics – I Atx ̄, p(x ̄)= ( σ √ 2 π )− 1 (2) Let the HWHM points be located at x ̄−x=kσ (3) Thenp(kσ)= ( σ √ 2 π ...

9.3 Solutions 519 cosθ= 1 /βn (1) wherenis the refractive index andβcis the particle velocity. The threshold corresponds toθ= 00 ...

520 9 Particle Physics – I 9.63 Number of photons emitted per unit length N= 2 πα(1− 1 /β^2 n^2 )(1/λ 1 − 1 /λ 2 )(1) Pions:βπ=p ...

9.3 Solutions 521 depend on the composition of emulsions,zis the charge of the ion andMits mass in terms of proton mass. The dat ...

522 9 Particle Physics – I = 1. 13 × 10 −^11 T = 1. 13 × 10 −^7 G Fig. 9.9 9.69 Electric force=qE Magnetic force=qvB If these tw ...

9.3 Solutions 523 Fig. 9.10 9.72t= 2 usinα α = 2 usinα Ee .m Where the accelerationα=Ee/m t= 2 × 8 × 105 sin 30◦× 9. 1 × 10 −^31 ...