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physics
elementary particle physics

Questions and Answers of Elementary Particle Physics

For each of the following reactions establish whether it is allowed or not; if it is not, give the reasons.(a) p → n+e+;(b) μ+→ νμ + e+;(c) e++e→ νμ + νμ;(d) νμ + p →
Which of the following processes is allowed and which forbidden by strangeness conservation?(a) π- + p → K+ +p;(b) π- + p → K+ + Σ-;(c) K- p → K+ + Ξ0 +
Give the reasons forbidding each of the following decays: (a) n → p + e-; (b) n → π+ + e-; (c) n → p + π- ; (d) n → p + γ.
For each of the following reactions establish whether it is allowed or not; if it is not, give the reasons:(1) μ+→e+ + γ;(2) e → νe + γ;(3) p + p→ Σ+ K+;(4) p+p → p+Σ+ +
For each of the following reactions (a) establish whether it is allowed or not, (b) if it is not, give the reasons (they may be more than one), (c) give the types of interaction that allow it:(1)
The existence of the anti-hyperons was proven by the discovery of an anti-lambda by M. Baldo-Ceolin and D. J. Prowse in 1958. A beam of negative pions with energy Eπ = 4.6 GeV hit an emulsion stack.
Consider a π- beam impinging on a liquid hydrogen target. Find the threshold energy for K- production.
Consider a π+ beam of momentum p = 200 GeV at a proton accelerator facility. We can build a muon beam by letting the pion decay in a vacuum pipe. Calculate the energy range of the muons.
In 1933, Blacket and Occhialini discovered several e+e- in the electromagnetic showers from cosmic rays in a Wilson chamber. The magnetic field was B = 0.3 T. In one event both the negative and the
In the event discovered by Anderson, a positive track emerged from the lead plate with measured momentum p = 23 MeV. Calculate its kinetic energy assuming it to be: (a) a proton and (b) a positron.
In the SLAC linear accelerator electrons were accelerated up to the energy Eel = 20 GeV. To produce a high-energy photon beam a LASER beam was back scattered at 180° by the electron beam. Assuming
A photon of energy Eγ = 511 keV is scattered backwards by an electron at rest. What is the value of the energy of the scattered photon? What is the value if the target electron were moving against
Calculate the energy thresholds (Eν) for the processes (1) νe + n → e- + p, (2) νμ + n → μ- + p and (3) ντ + n → τ- + p.
A hydrogen bubble chamber was exposed to a π- beam of 3 GeV momentum. We observe an interaction with secondaries that are all neutral and two V0s pointing to the primary vertex. Measuring the two
We wish to produce a monochromatic beam with momentum p = 20 GeV and a momentum spread Δp/p = 1%. The beam is 2 mm wide and we have a magnet with a bending power of BL = 4 Tm and a slit d = 2 mm
We calculated the energy threshold for the reaction p + p → p + p + p + p on free protons as targets in Problem 1.9. Repeat the calculation for protons that are bound in a nucleus and have a Fermi
Calculate the ratio between the magnetic moments of the electron and the μ and between the electron and the τ.
Consider the decay π0→γγ in the CM. Assume a Cartesian coordinate system x*, y*, z* >, and the polar coordinates ρ*, θ*, ϕ*. In this reference frame, the decay is isotropic. Give the
A photon converts into an e→e-1 pair in a cloud chamber with magnetic field B = 0.2 T. In this case, two tracks are observed with the same radius ρ = 20 cm. The initial angle between the tracks is
A π+ is produced at an altitude of 30km by a cosmic ray collision with energy Eπ=5GeV. What is the distance at which the pion sees the surface of the Earth in its rest reference frame? What is the
Two μ are produced by a cosmic ray collision at an altitude of 30 km. The two energies are E1 = 5 GeV and E2 = 5 TeV. What are the distances at which each of the muons sees the surface of the Earth
A π0 decays emitting one gamma of energy E1=150 MeV in the forward direction.What is the direction of the second gamma? What is its energy E2? What is the speed of the π0?
Consider the decay K → μ + ν. Find(a) The energy and momenta of the μ and the ν in the reference of the K at rest;(b) The maximum μ momentum in a frame in which the K momentum is 5 GeV.
Compute the energies and momenta in the CM system of the decay products of π→μ+ν.
Consider the head-on collision of two photons, γ1 and γ2, of energies E1 > E2 respectively. If γ1 is produced by a LASER of wavelength λ=690 nm, what is the minimum value of E2 to produce a
Neutrons originated from radioactive elements in the ambient have kinetic energies up to a few MeV. We want to detect such neutrons with a TPC containing 40Ar. If the neutron energy is low enough,
Portable neutron generators are commercially available based on the d–t fusion. These devices contain a source of deuterium ions, an accelerator that accelerate the ions up to about Td=130 keV
(1) What is the maximum energy of a cosmic-ray proton to remain confined in the Solar System? Assume R=1013 m as the radius of the system and an average magnetic field B=1 nT.(2) What is the maximum
Consider a Cherenkov apparatus to be operated as a threshold counter. The pressure of the N2 gas it contains can be varied. The index n depends on the pressure π, measured in pascal, as n=1+3 x
Considering the Cherenkov effect in water (n¼1.33), determine: (1) the minimum velocity of a charged particle for emitting radiation, (2) the minimum kinetic energy for a proton and a pion to do so,
Superman is travelling along an avenue on Metropolis at high speed. At a crossroad, seeing that the lights are green, he continues. However, he is stopped by the police, claiming he had crossed on
A Cherenkov counter containing nitrogen gas at pressure Π is located on a charged particle beam with momentum p = 20 GeV. The dependence of the refraction index on the pressure Π is given by the
Consider two particles with masses m1 and m2 and the same momentum p. Evaluate the difference Δt between the times taken to cross the distance L. Let us define the base with two scintillator
We wish to measure the total π+p cross-section at 20 GeV incident momentum. We build a liquid hydrogen target (ρ = 60 kg m-3) that is l = 1 m long. We measure the flux before and after the
In the experiment of O. Chamberlain et al. in which the antiproton was discovered, the antiproton momentum was approximately p = 1.2 GeV. What is the minimum refraction index needed in order to have
A particle of mass m, charge q = 1.6 x 10-19 C and momentum p moves in a circular orbit at a constant speed (in absolute value) in the magnetic field B normal to the orbit. Find the relationship
Find the ratio between the Mott and Rutherford cross-sections for the scattering of the same particles at the same energy at 90°.
If E = 20 GeV electrons scatter elastically emerging with energy E' = 8 GeV, find the scattering angle.
An α particle beam of kinetic energy E = 6 MeV and intensity Ri = 103 s-1 goes through a gold foil (Z = 79, A = 197, ρ = 1.93 X 104 kg m-3) of thickness t = 1 μm. Calculate the number of
Geiger and Marsden observed that the alpha (ɑ) particles, after having hit a thin metal foil, not too infrequently bounced back. Calculate the ratio between the scattering probabilities for θ >
A proton with momentum p1 = 3 GeV elastically diffuses on a proton at rest. The diffusion angle of one of the protons in the CM is θ*ac= 10°. Find,(a) The kinematic quantities in the L frame;(b)
Consider the collision of a ball on an equal ball at rest. Compute the angle between the two final directions at non-relativistic speeds.
A Λ hyperon decays as Λ → p + π- ; its momentum in the L frame is pΛ = 2 GeV. Take the direction of the Λ in the L frame as the x-axis. In the CM frame the angle of the proton
Find the expressions of the energies and momenta of the final particles of the decay M → m1 + m2 in the CM if m2 mass is zero.
Electrons with 10 GeVenergy are scattered by protons initially at rest at 30°. Find the maximum energy of the scattered electron.
Consider an electron beam of energy E= 2 GeV hitting an iron target [assume it is made of pure Fe56]. How large is the maximum four-momentum transfer?
A π- beam is brought to rest in a liquid hydrogen target. Here π0 are produced by the ‘charge exchange’ reaction π- + p → π0 + n. Find the energy of the π0, the kinetic energy of the n,
The primary beam of a synchrotron is extracted and used to produce a secondary monochromatic π- beam. One observes that at the distance l=20 m from the production target 10% of the pions have
A ‘charmed’ meson D0 decays D0→K- π + at a distance from the production point d=3 mm long. Measuring the total energy of the decay products one finds E=30 GeV. How long did the D
In a monochromatic π beam with momentum pπ a fraction of the pions decays in flight as π→μνμ.We observe that in some cases the muons move backwards. Find the maximum value of pπ for this to
Consider the process γ + p → p + π0 (π0 photoproduction) with the proton at rest.(a) Find the minimum energy of the photon Eγ. The Universe is filled by ‘background electromagnetic
Consider the weak interaction lifetimes of π±: τπ=26 ns, of K±: τK=12 ns and of the Λ: τΛ = 0.26 ns and compute their widths.
Evaluate the energies and momenta in the CM frame of the two final particles of the decays Λ → pπ-, Ξ- → Λπ-.
Consider a particle of mass M decaying into two bodies of masses m1 and m2. Give the expressions of the energies and of the momenta of the decay products in the CM frame.
The Universe contains two types of electromagnetic radiation:(a) the €˜micro-wave background€™ at T = 3 K, corresponding to photon energies E Î³, 3K ‰ˆ 1
In the LHC collider at CERN two proton beams collide head on with energies Ep = 7 TeV. What energy would be needed to obtain the same centre of mass energy with a proton beam on a fixed hydrogen
The Bevatron was designed to have sufficient energy to produce antiprotons. What is the minimum energy of the proton beam for such a process? Take into account that because of baryonic number
In the collision of two protons, the final state contains a particle of mass m besides the protons.(a) Give an expression for the minimum (threshold) energy Ep for the process to happen and for the
An accelerator produces an electron beam with energy E=20 GeV. The electrons diffused at θ=6° are detected. Neglecting their recoil motion, what is the minimum structure in the proton that can be
Consider the strong interaction total widths of the following mesons: ρ, Γρ=149 MeV; ω, Γω=8.5 MeV; ϕ, Γϕ=4.3 MeV; K*, ΓK*=51 MeV; J/ψ, ΓJ/ψ=93 keV; and of
Three protons have momenta equal in absolute value and directions at 120ο from one another. What is the mass of the system?
Estimate the energy of a Boeing 747 (mass M=400 t) at cruising speed (850 km h-1) and compare it with the energy released in a mosquito–antimosquito annihilation.

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