Y2 Neutrino Physics (spring term 2016)
Lecture 4
How to detect a neutrino?
Dr E Goudzovski [email protected] http://epweb2.ph.bham.ac.uk/user/goudzovski/Y2neutrino
Previous lecture
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.
1 This lecture
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. 2 Nuclear reactors as e sources Nuclear fission: splitting of a nucleus into smaller nuclei. Discovered by Otto Hahn in 1938 (Nobel Prize in chemistry 1945). n
An example of a neutron-induced fission reaction:
+ 200 MeV
92p+144n 98p+138n ~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 Effectively, 9892=6 neutron to proton conversions: 140 94Zr Ce Antineutrino production rate in a reactor: (typical modern commercial reactor power is ~1 GW) n
−13 20 1 1 n F / Pth ~ 6 / 200 MeV = 6 / (200×1.602×10 J) ~ 10 s GW .
Nuclear reactors and bombs: first artificial high intensity antineutrino sources3 Neutrinos or anti-neutrinos? The chart of nuclides Neutron-to-proton ratio grows as a function of atomic number.
238U Reason: mutual Coulomb repulsion of 208Pb the protons. Examples: 16 O = 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 94Zr Nuclear fission necessarily leads to neutron-to-proton conversion.
By electric charge and lepton flavour conservation, anti-neutrino production: 16O 4 Inverse beta-decay (1) Beta decays:
(mn > np: free neutron is unstable, = 882 s)
(proton is stable; can occur within nuclei) Neutrinos are created in beta-decays. Could they be absorbed in the reverse process?
(recall bremsstrahlung and photon conversion )
Crossing symmetry:
antiparticles are equivalent to particles going backwards in time.
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. 5 Inverse beta-decay (2)
Inverse beta decays:
Q1: Is antineutrino detection via the following reactions possible?
(a) NO: does not conserve electric charge
(b) NO: does not conserve lepton flavour
Q2: Is neutrino detection via the following reaction possible?
NO: does not conserve lepton flavour 6 Reactor e detection via IBD
Energy threshold for : (see lecture 1)
Reactor e energy spectra
Detection rate Antineutrinos/fission
Flux Cross-section Eth
Antineutrino energy, MeV Antineutrino energy, MeV 7 Interaction cross-section
Number of “interaction centres” in a volume:
n: constant density of the “interaction centres” [cm–3]
Area S The fraction of area covered by interaction centres: (=probability for an incoming particle to interact)
Thickness L : geometrical cross-section of an interaction centre [cm2]
Fluence : the number of particles that intersect a unit area [cm2]
The number of interactions per interaction centre:
Differential equation for the fluence:
8 Beam attenuation
;
Beam attenuation law:
Mean free path: [ (cm–3×cm2)1 = cm ]
Physical meaning of the mean free path:
A beam is attenuated by a factor of e=2.71 over the mean free path 9 (e+ehadrons) & quarkonia 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. Nobel Prize 1976 (charmonium) (e+ehadrons)
Nobel Prize 2008 microbarn (CKM mechanism) (1034 m2)
3 DD Nobel Prize 1984 bound states of (Z boson) light quarks charmonium (“hidden charm”) nanobarn bottomonium 37 2 states (10 m ) states
10 picobarn (1039 m2) Centre-of-mass energy ECM, GeV
4 2 2 Cross-section energy-dependence: ~ 1/ECM × ECM ~ 1/ECM
photon propagator phase space 10 Neutrino interaction cross-section 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, 11 The numerical result
Natural units: [unit: GeV2]
Practical units: [Unit: GeV2 × (GeV×cm)2 = cm2]
The cross-section has a linear energy-dependence Numerically,
(a non-assessed problem)
This computation is for electron-neutrino scattering. Neutrino-nucleon interaction cross-sections are of the same order of magnitude. 12 scattering cross-section We expect: (1 MeV) ~ 1043 cm2, (1 GeV) ~ 1040 cm2 in agreement with data!
e scattering cross-section
)
2 Rev.Mod.Phys. 84 (2012) 1307
cm
27
1037 cm2
1040 cm2 (1mb = 10 = (1mb The Glashow 1043 cm2 resonance at E=6.3 PeV:
(a non-assessed problem)
1 MeV 1 GeV
Neutrino energy, eV 13 Neutrino mean free path Mean free path of a typical reactor antineutrino (E=3 MeV) in water:
(~10x distance to Centauri) n: density of free protons [cm3]; : density of matter [g cm3]; 1 H2O molecule: about 1/9 of the nucleons are free protons (i.e. H nuclei).
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) 14 Designing a neutrino detector Reactor antineutrino production rate per unit of thermal power:
20 1 1 F / Pth ~ 10 s GW .
20 1 Consider a typical reactor: Pth = 1 GW, therefore F = 10 s .
Let’s place a detector at a distance L=10m from the reactor core.
Antineutrino flux at the detector:
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:
That is ~20 interactions / hour
Most reactor antineutrinos are below IBD threshold. Typical detection rate in real life: ~ few interactions / hour. 15 Summary
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. 16