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Endpoint spectra of tritium and rhenium beta decays for massive neutrinos
Rastislav DvornickЩ Department of Nuclear Physics & Biophysics Comenius University, Bratislava Slovakia supervisor - Fedor Simkovic

14-th Lomonosov conference on Elementary Particle Physics


Neutrino
Neutrino was suggested in y. 1930 by Pauli to explain the continuity of spectrum as a spin 1/2 particle obeying Fermi-Dirac statistics

I have done a terrible thing I invented a particle that cannot be detected W. Pauli

TЭbingen


Neutrino oscillations

Pontecorvo -Maki-Nakagawa-Sakata matrix

Zh.Eksp.Teor .Fiz.,32(1957)

Maki,Nakagawa,Sakata. Prog.Theor.Phys.28(1962)870

oscillations massive neutrinos

Flavor eigenstates

Mass eigenstates

m 2 P( e ) = sin 2 2 sin 2 ( ) 4 Et


Absolute mass scale of neutrinos ?

0-decay
3

H decay

Cosmology
We need 3 mass eigenstates To explain 2 different m2 Solar neutrinos m22-m12=msol2 3.10-5 eV2 m32-m22=matm2 2.10-3 eV2 Atmospheric neutrinos

1968 Homestake

1998 SuperKamiokande


Double beta decay
H = G


2

e ( x) (1 - 5 ) e ( x) j ( x) + h.c.

Enrico Fermi 1934

~ (Z - 2, A) (Z , A) + 2e- + 2 e

Maria GЖppert Mayer 1935

Observed for 10 isotopes: 48Ca, 76Ge, 82Se, 96Zr,100Mo. 116Cd. 128Te, 130Te, 150Nd, 238U, T 18 24 1/2 10 -10 years


0 decay

( Z - 2, A) ( Z , A) + 2e

-

L = 2

neutrino origin

0 m

2

m = Ue1 m1 + Ue2 e m2 + Ue3 e m3

2

2 i 21

2 i31


Tritium ­ 3H
1. low endpoint ­ Q=18.6 keV 2. super-allowed nuclear transition (spectrum shape) 3. short half-live T1/2 = 12.32 y 4. simple molecular structure


KATRIN experiment Direct measurement of neutrino mass Measuring last 300 eV of endpoint KArlsruhe TRItium Neutrino experiment 2010 ­ start data taking
Weinheimer, Nucl.Phys. Proc.Suppl. 168,5(2007)


Tritium beta decay
3

~ H He + e +
3 -

Q=18.6 keV Differential spectrum

Kurie plot

Both ­ Fermi & Gamow-Teller transitions (T1/2=12.32 y)

M =g M
2 V

2

2 F

+g M
2 A

2 GT


Tritium beta decay
Spin ­ isospin properties are identical
3

~ H He + e +
3 -

1/ 2 1/ 2

+

+

~ n p + e +
-

Elementary particle treatment (Kim & Primakoff, Phys.Rev. 139, B 1447(1965)) Exact relativistic treatment of tritium decay. Recoil effect taken into account (3.4 eV less than standard Q value)
E
max e

1 = 2M

[M
f

2 i

+ me2 - M 2 - m2 f

(

)]

E

max e

M i - M f - m


Nucleus as elementary particle

Beta decay on free nucleons. Relativistic calculation. No nuclear matrix elements.

Simkovic, DvornickЩ, Faessler: Phys. Rev. C77,055502(2008)


Tritium beta decay
Approximation with keeping dominant terms

Relativistic Kurie plot

K ( y ) = BT

(

y ( y + 2m ) ( y + m )

)

1/ 2

BT =
T1
exp /2

GFVud 2
3

2 gV + 3 g

2 A

= 12.32 y g A = 1.247


Rhenium beta decay

1. the lowest known Q value 2.47 keV 2. T1/2= 4.35 x 1010 y ~ age of universe 3. natural abundance 187Re is 63%


MARE experiment Re-187 calorimeter source=detector -we don't bother with energy loses -no corrections for atomic or molecular structure

ъ

i,

Os-187 calorimeter source=detector

T1/2=4.35 в 1010 y - low radioactivity

Microcalorimeter Arrays for a Rhenium Experiment


Rhenium beta decay

whole spectrum is measured
187

Re 187Os+e-+e 5/2+1/2-

J = 2

-

first unique transition

higher partial waves of leptons


Rhenium beta decay J = 2
-

=>

p-waves have to be taken into account


H =

G

2

e ( x) (1 - 5 ) ( x) j ( x) + h.c.
plane wave expansion -

( x) = (1 + ik .r )v(k )
s wave p wave

e

ik . r

1 Z 0 ^ e ( x) = u ( p) F0 ( Z , E ) (1 - i .r ) - i F1 ( Z , E ) ( p.r + . p .r ) 2 3
s
1/2

wave

p1/2 wave

p

3/2

wave


Rhenium beta decay

J = 2

-

=>

leptons have to take

L=2

Amplitude = e (s1/2) & (p) + e(p3/2) & (s)

1 -1/ 2

+

1 +1/ 2

e (p1/2) & (p) => no change of parity


Rhenium beta decay first unique transition
22 d GFVud 2 = M pE( E0 - E ) ( E0 - E) 2 - m2 dE 2 3

122 в R p F1 (Z , E ) + k 2 F0 (Z , E ) 3

(

)

for allowed trans. only F0 survives = s waves of both leptons

4 g 187 M= < Os || 2Ji +1 3
2 2 A


n

rn ( n Yn ) 2 ||187 Re > R
+ n

2


Rhenium beta decay
electron kinetic energy spectrum normalized to unity

T1

/2

4 = 4.35 *10 y < J f || 3
10


n

rn ( n Yn ) 2 || J i > = 0.0523 R


Rhenium beta decay
22 d GFVud 22 = M R pE( E0 - E) ( E0 - E) 2 - m2 p2 F1 (Z , E) + k 2 F0 (Z , E) dE 6 3

(

)

d

dP dS = + dE dE dE

S / P = 1.027 в10

-4

electron P wave is dominant => important


Rhenium beta decay plane wave limit => neglecting the Coulomb interaction

F0 ( Z , E ) 1 F1 ( Z , E ) 1

k

max

= 2.47keV

p

max

50keV

kinematics is enhancing the P wave


Rhenium beta decay

Temax = Q - m

Y = Te - Temax

Q - highest electron kinetic energy to obtain in case of zero neutrino mass

S and P wave contributions near the endpoint


Rhenium beta decay The goal is that we can define (similar as for tritium)

k 2 = ( E0 - Ee ) 2 - m2

- negligible

F1 ( Z , Ee ) p F0 ( Z , Ee )
2

- almost constant due to small Q value in comparison with m

e


Rhenium beta decay Kurie plot properly scaled is the same for 3H &
187Re

m2 K ( Ee ) / BRe ( E0 - Ee ) 4 1 - ( E0 - Ee )
theory

2

experiment

y=E

max e

-E

e

Arnaboldi, PRL 96, 042503 (2006)


Conclusions
· Exact relativistic treatment of 3H beta decay including recoil · Dominance of P wave of electron in 187Re first unique decay · Linearity of Kurie plot in 187Re decay under discussion with Milano group