Y2 Neutrino Physics (spring term 2016)

Lecture 4

How to detect a neutrino?

Dr E Goudzovski eg@hep.ph.bham.ac.uk

http://epweb2.ph.bham.ac.uk/user/goudzovski/Y2neutrino

Previous lecture

1

The rates of weak processes in the low energy regime are

proportional to the Fermi constant squared .

Example: weak decays of leptons.

Free quarks have not been observed

(“colour confinement”; “asymptotic freedom”).

Most known hadrons are bound states of

2 (anti-)quarks [mesons] or 3 (anti-)quarks [(anti-)baryons].

The energy spectrum of the two- (three-) body decays

is discrete (continuous).

The neutrino hypothesis was put forward in 1930; one of the

reasons was to explain the continuous beta-emission spectrum.

This lecture

2

How to detect a neutrino?

Nuclear reactors as anti-neutrino sources.

Neutrino detection via the inverse beta-decay.

Cross-section, mean free path and beam attenuation.

Cross-section of the inverse beta-decay.

Designing a reactor anti-neutrino detector.

Reading list:

B.R. Martin and G. Shaw. Particle physics. Chapter 2.

D. Perkins. Introduction to high energy physics. Chapter 7.4.

C. Sutton. Spaceship neutrino. Chapter 3.

N. Solomey. The elusive neutrino. Chapter 4.

94Zr 140Ce

n

n

n

Nuclear reactors as e sources

3

92p+144n 98p+138n

+ 200 MeV

Effectively, 9892=6 neutron to proton conversions:

Antineutrino production rate in a reactor: (typical modern commercial reactor power is ~1 GW)

F / Pth ~ 6 / 200 MeV = 6 / (200×1.602×10−13 J) ~ 1020 s1GW1.

Nuclear fission: splitting of a nucleus into smaller nuclei.

Discovered by Otto Hahn in 1938 (Nobel Prize in chemistry 1945).

An example of a neutron-induced fission reaction:

~106 times greater than

in chemical reactions

Neutron production: chain reaction

First nuclear reactor: December 1942, University of Chicago, US

First atomic bomb: July 1945, New Mexico, US

Nuclear reactors and bombs: first artificial high intensity antineutrino sources

Neutrinos or anti-neutrinos?

4

208Pb

238U

Neutron-to-proton ratio grows

as a function of atomic number.

Reason: mutual Coulomb repulsion of

the protons.

94Zr Nuclear fission necessarily leads

to neutron-to-proton conversion.

By electric charge and

lepton flavour conservation,

anti-neutrino production:

Examples: 16O = 8p + 8n; N(n)/N(p)=1 94Zr = 40p + 54n; N(n)/N(p)=1.35 208Pb = 82p + 126n; N(n)/N(p)=1.54 238U = 92p + 146n; N(n)/N(p)=1.59

16O

The chart of nuclides

Inverse beta-decay (1)

5

Inverse beta decay (IBD): related to the beta-decay by crossing symmetry

IBD: production of charged particles (e).

A possible tool for indirect (anti)neutrino detection.

Beta decays:

(mn > np: free neutron is unstable, = 882 s)

(proton is stable; can occur within nuclei)

Crossing symmetry:

antiparticles are equivalent to particles going backwards in time.

Neutrinos are created in beta-decays.

Could they be absorbed in the reverse process?

(recall bremsstrahlung and photon conversion )

Inverse beta-decay (2)

6

Q1: Is antineutrino detection via the following reactions possible?

(a)

(b) NO: does not conserve lepton flavour

NO: does not conserve electric charge

Q2: Is neutrino detection via the following reaction possible?

Inverse beta decays:

NO: does not conserve lepton flavour

7

Reactor e detection via IBD

Reactor e energy spectra

Energy threshold for :

Flux Cross-section

Detection rate

(see lecture 1)

Antineutrino energy, MeV

Anti

neutr

inos/

fiss

ion

Antineutrino energy, MeV

Eth

Interaction cross-section

8

Number of “interaction centres” in a volume:

n: constant density of the “interaction centres” [cm–3]

The fraction of area covered by interaction centres:

(=probability for an incoming particle to interact)

: geometrical cross-section of an interaction centre [cm2]

Thickness L

Area S

Differential equation for the fluence:

Fluence : the number of particles that intersect a unit area [cm2]

The number of interactions per interaction centre:

Beam attenuation

9

Mean free path:

;

Beam attenuation law:

Physical meaning of the mean free path:

A beam is attenuated by a factor of e=2.71 over the mean free path

[ (cm–3×cm2)1 = cm ]

(e+ehadrons) & quarkonia

10

Cross-section unit: barn. Definition: 1 b = 1028 m2 = 1024 cm2 = 100 fm2.

Geometrical cross-sections of nuclei: (p)1 fm2=0.01 b; (U)1 b.

Centre-of-mass energy ECM, GeV

(e+ehadrons)

microbarn

(1034 m2)

nanobarn

(1037 m2)

10 picobarn

(1039 m2)

Cross-section energy-dependence: ~ 1/ECM4 × ECM

2 ~ 1/ECM2

photon propagator phase space

charmonium

(“hidden charm”)

states bottomonium

states

bound states of

light quarks

DD

3

Nobel Prize 1976 (charmonium)

Nobel Prize 1984 (Z boson)

Nobel Prize 2008 (CKM mechanism)

Neutrino interaction cross-section

11

Weak elastic scattering:

Dimensional estimate assuming :

(ECM is the only available Lorentz-invariant scale parameter)

Dimensional analysis:

Energies in the CM frame (ECM) and the lab frame (E) [see lecture 1]:

Therefore,

The numerical result

12

[unit: GeV2] Natural units:

The cross-section has a linear energy-dependence

Practical units:

[Unit: GeV2 × (GeV×cm)2 = cm2]

Numerically,

(a non-assessed problem)

This computation is for electron-neutrino scattering.

Neutrino-nucleon interaction cross-sections are of the same order of magnitude.

scattering cross-section

13

We expect:

(1 MeV) ~ 1043 cm2, (1 GeV) ~ 1040 cm2

Rev.Mod.Phys. 84 (2012) 1307

1037 cm2

1040 cm2

1043 cm2

1 MeV 1 GeV

Neutrino energy, eV

in agreement with data!

e scattering cross-section

(a non-assessed problem)

(1m

b =

1027cm

2)

The Glashow

resonance

at E=6.3 PeV:

Neutrino mean free path

14

(~10x distance to Centauri)

Consider a ~1 MeV neutrino produced in the Solar core.

Probability of interaction before leaving Sun:

(average solar density = 1.4 g/cm3)

Low energy neutrinos are direct probes into

the Sun’s (and Earth’s) interior (but not into neutron stars)

n: density of free protons [cm3];

: density of matter [g cm3];

H2O molecule: about 1/9 of the nucleons are free protons (i.e. 1H nuclei).

Mean free path of a typical reactor antineutrino (E=3 MeV) in water:

Designing a neutrino detector

15

Reactor antineutrino production rate per unit of thermal power:

F / Pth ~ 1020 s1GW1.

Consider a typical reactor: Pth = 1 GW, therefore F = 1020 s1.

Let’s place a detector at a distance L=10m from the reactor core.

Antineutrino flux at the detector:

That is ~20 interactions / hour

Most reactor antineutrinos are below IBD threshold.

Typical detection rate in real life: ~ few interactions / hour.

Interaction rate per free proton (remember, E=few MeV):

Consider a water detector with an active mass of mdet = 100 kg.

Rate of IBD interactions in the detector:

Summary

16

In 1940s, nuclear reactors became the first powerful

continuous artificial anti-neutrino sources

(production rate: ~1020 s1GW1; typical energy: few MeV).

Anti-neutrinos are detectable via the inverse beta decay (IBD)

reaction , with a threshold of Eth=1.8MeV.

We have defined the reaction cross-section and mean free

path , and found how they are related:

For MeV-energy neutrinos, the interaction cross-section is tiny

(~1043 cm2), free path in matter is astronomical (light years).

Design of the reactor anti-neutrino experiment:

the expected detection rate is ~0.01/hour/kg.