Question

It is intended to use a charged mono-energetic hyperon beam to perform scattering experiments off liquid hydrogen. Assuming that the beam transport system must have a minimum length of 20m, calculate the minimum momentum of a Σ beam such that 1% of the hyperons accepted by the transport system arrive at the hydrogen target (τ = 0.8 × 10⁻¹⁰ s, m_Σ = 1.19GeV/c²). What measurements would you make to identify the elastic scattering in a (Σ⁻ p) collision?

Answer 1

I/I₀ = 1/100 = exp(−d/βc γτ) 

Put d = 20m, c = 3 × 10⁸m/s and τ = 0.8 × 10⁻¹⁰s and take loge on both sides to solve for βγ . We find βγ = 181. Therefore, the momentum of hyperon,

cp = mβγ = 1.19 × 181 = 215 GeV 

Thus, the minimum momentum required is P = 215 GeV/c 

The elastic scattering of Σ⁻ hyperons with protons can be recorded in the hydrogen bubble chamber from the kinematical fits of events.

It may be noted that the beams of sigma hyperons are available only in recent times. This has been possible because of time dilation for high momenta particles. Even beams of omega minus have been used.