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PHY211 - KTI Exercise Sheet 6

Herbstsemester 2017 Prof. N. Serra

P. Owen, D. Lancierini

http://www.physik.uzh.ch/de/lehre/PHY211/HS2017.

html

Issued: 6.12.2017 Due: 8.12.2017 10:15

Exercise 1: The τ neutrino interaction with a nucleus

• There are two types of neutrino interaction with a nucleus: The neutral-current interaction (mediated by the Z boson) and the charged current interaction (mediated by the W boson).

Draw a Feynman diagram for each of these interactions for a τ neutrino interacting with a neutron.

• If the neutron is at rest, what is the minimum incident energy of the τ neutrino needed for the charged-current interaction to occur? (hint: the mass of the τ lepton is around 1.8 GeV)

• If the incident neutrino has an energy of 5PeV (P = 10 15 ) and the out-going particles take equal energy, what is the mean decay length for the τ lepton in the lab frame? (the lifetime of the τ lepton is 0.3ps).

• What is the decay width of the τ lepton?

The attenuation length of a particle in a material is given by l 0 = 1

where D is the nuclear density of the material and σ is the cross section.

• The cross-section of the τ neutrino charged-current interaction with an iron nucleus is approx- imately 0.1fb (femto-barn). If the mass density of iron is 7800kg/m3, what is the attenuation length of the neutrino? You can assume that the mass of an iron nucleus is 56 atomic mass units (around 54 GeV).

With a given l 0 , the probability of finding a particle at distance l of the material is P(l) = e −l/l

0

.

• At the centre of a spherical neutron star with diameter of 2 meters, 10 9 neutrinos are produced

isotropically per second. If the density of the neutron star is 10 17 kg/m 3 , what is the neutrino

flux at the surface of the star? You can take the mass of the neutron to be one atomic mass unit

(940 MeV) and you can assume that the cross-section for a neutrino interaction with a neutron

to be the same as for an iron nucleus.

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