Post on 04-Feb-2022
Endpoint spectra of tritium and rhenium beta decays for massive neutrinos
Rastislav DvornickýDepartment of Nuclear Physics & Biophysics
Comenius University, Bratislava Slovakia
supervisor - Fedor Šimkovic
14-th Lomonosov conference on Elementary Particle Physics
NeutrinoNeutrino was suggested in y. 1930 by Pauli to explain the continuity of β
spectrum as a spin 1/2 particle obeying Fermi-Dirac statistics
I have done aterrible thingI invented a particle thatcannot bedetectedW. Pauli
Tübingen
Neutrino oscillations
Pontecorvo-Maki-Nakagawa-Sakata
matrix
Flavoreigenstates
Masseigenstates
oscillations ⇒ massive neutrinos
Zh.Eksp.Teor.Fiz.,32(1957)
Maki,Nakagawa,Sakata.Prog.Theor.Phys.28(1962)870
)4
(sin2sin)(2
22
EtmP e
Δ=→ ϑνν μ
0νββ-decay
Absolute mass scale of neutrinos ?
3H decay
Cosmology
Solar neutrinos
Atmospheric neutrinos
1998SuperKamiokande
1968Homestake
We need 3 mass eigenstatesTo explain 2 different Δm2
m22-m1
2=Δmsol2≈ 3.10-5 eV2
m32-m2
2=Δmatm2≈ 2.10-3 eV2
Double beta decay
Observed for 10 isotopes: 48Ca, 76Ge, 82Se, 96Zr,100Mo.116Cd. 128Te, 130Te, 150Nd, 238U, T1/2 ≈1018-1024 years
Enrico Fermi1934
..)()()1()(2 5 chxjxxeG
H e +−= μμβ
β νγγ
Maria GöppertMayer 1935
eeAZAZ ν~22),(),2( ++→− −
0νββ decay
−+→− eAZAZ 2),(),2(
20 m≈Γ νββ 3
232
221
21
3121 meUmeUmUm ie
iee
αα ++=
2=ΔL
neutrino origin
Tritium – 3H
1. low endpoint – Q=18.6 keV2. super-allowed nuclear transition
(spectrum shape)3. short half-live T1/2 = 12.32 y4. simple molecular structure
KATRIN experiment
KArlsruheTRItiumNeutrinoexperiment
Direct measurementof neutrino mass
Measuring last300 eV of endpoint
2010 – startdata taking
Weinheimer, Nucl.Phys.Proc.Suppl. 168,5(2007)
Tritium beta decay
ν~33 ++→ −eHeH
22222GTAFV MgMgM +=
Q=18.6 keV
Differentialspectrum
Kurie plot
Both – Fermi &Gamow-Tellertransitions (T1/2=12.32 y)
Tritium beta decay
ν~++→ −epn
ν~33 ++→ −eHeH
++ → 2/12/1
( )[ ]2222max
21
νmMmMM
E feif
e −−+= νmMME fie −−≅max
Spin – isospin propertiesare identical
Elementary particle treatment (Kim & Primakoff, Phys.Rev. 139, B 1447(1965))
Exact relativistic treatment of tritium β decay. Recoil effect taken into account (3.4 eV less than standard Q value)
Nucleus as elementary particle
Beta decay on free nucleons.Relativistic calculation.No nuclear matrix elements.
Šimkovic, Dvornický, Faessler:Phys. Rev. C77,055502(2008)
Approximation withkeeping dominant terms
Relativistic Kurie plot
22
33
2AV
udFT ggVGB +=
π
( ) 2/1)()2()( νν mymyyByK T ++=
Tritium beta decay
247.132.12exp2/1 =⇒= AgyT
Rhenium beta decay
1. the lowest known Q value 2.47 keV2. T1/2= 4.35 x 1010 y ~ age of universe3. natural abundance 187Re is 63%
MARE experiment
-we don’t bother with energy loses-no corrections for atomic or molecular structure
MicrocalorimeterArrays for aRhenium Experiment
Re-187
Os−187
ßi,
calorimetersource=detector
T1/2=4.35 × 1010 y - low radioactivitycalorimetersource=detector
Rhenium beta decay
Δ Jπ = 2- first unique transition187Re →187Os+e-+νe
5/2+→1/2- higher partial waves of leptons
whole spectrum is measured
Rhenium beta decay
p-waves have to be taken into account Δ Jπ = 2- =>
..)()()1()(2 5 chxjxxG
H e +−= μνμβ
β ψγγψ
)().1()( kvrkix +=νψ
⎟⎠⎞
⎜⎝⎛ +−−= )..
31.(),()ˆ.
21(),()()( 1
00 rprpEZFirZiEZFpuxe γγγγαψ
plane wave expansion - rkie .
s wave p wave
s1/2 wave p1/2 wave p3/2 wave
Rhenium beta decay
Δ Jπ = 2- => leptons have to take
Amplitude = e (s1/2) & ν(p) + e(p3/2) & ν(s)
2/11 − + 2/11 +
Δ L = 2
e (p1/2) & ν(p) => no change of parity
( )),(),(31
02
122 EZFkEZFpR +×
2200
23
22
)()(2 νπ
mEEEEpEMVGdEd udF −−−=Γ
Rhenium beta decay
first unique transition
for allowed trans. only F0 survives = s waves of both leptons
2
1872
1872
2 Re||)(3
4||12
>⊗<+
= ∑ +
nnn
nn
i
A YRrOs
JgM στπ
Rhenium beta decayelectron kinetic energy spectrum normalized to unity
0523.0||)(3
4||10*35.4 210
2/1 =>⊗<⇒= ∑n
innn
f JYRrJyT σπ
Rhenium beta decay
2200
223
22
)()(6 νπ
mEEEEpERMVGdEd udF −−−=Γ ( )),(),( 0
21
2 EZFkEZFp +
dEd
dEd
dEd SP Γ
+Γ
=Γ 410027.1/ −×=ΓΓ PS
electron P wave is dominant => important
Rhenium beta decay
plane wave limit => neglecting the Coulomb interaction 1),(
1),(
1
0
→→
EZFEZF
keVk 47.2max = keVp 50max ≅
kinematics is enhancing the P wave
Rhenium beta decay
νmQTe −=maxQ - highest electron kinetic energyto obtain in case of zero neutrino mass
S and P wave contributions near the endpoint
maxee TTY −=
Rhenium beta decay
- negligible
The goal is that we can define (similar as for tritium)
- almost constant due to small Q value in comparison with me
220
2 )( νmEEk e −−=
),(),(
0
12
e
e
EZFEZFp
Rhenium beta decay
Kurie plot properly scaled is the same for 3H & 187Re
42
0
2
0Re )(1)(/)(
eee EE
mEEBEK−
−−≅ ν
ee EEy −= max Arnaboldi, PRL 96, 042503 (2006)
experimenttheory