Super Kamiokande (Japan) neutrino detector W. Udo Schröder ...Super Kamiokande (Japan) neutrino detector 50,000 t H 2. Electron/Beta Spectrometry W. Udo Schröder, 2009 y

W. Udo Schröder, 2009

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Super Kamiokande (Japan) neutrino detector 50,000 t H2O) Cerenkov counter, 11,200 PMTs

Electron/Beta Spectrometry


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Iron-free “Orange” spectrometer with axially sym-metric toroidal magnetic field inside current loops

Setup used in nuclear reaction studies (counters for coincident particles & g-rays) Different energies correspond to different locations on focal detector

B

60 Helmholtz coils every 60 arranged in a circle. Current: ~1000 A

2 2e

e e e e e e e

e

e e e

Circular e orbit radius in B field

p e B

E p m dE p m dp

mdN dN

dE p dp

a g

b

Active

sample

Ma

gn

et

Radioactive Ra sample in a magnetic field b = e-.

Observed later in decay of neutrons and excited nuclei (internal conversion) or nuclear transmutation (b decay).

Chadwick (1914): Some nuclides emit e- with continuous energy spectra “b rays”

Energy spectrum constructed

from momentum spectrum

Electron and Beta Spectroscopy


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e

dN

dE

eE

max

eE Q

Nuclei can deexcite via photon, (e+, e-) , or atomic-electron emission (internal conversion)

gs

Z,I

1gs

Z ±1,(I,I )

0Q e eject

Nuclei transmute in b decay

Fixed differences Q and |DI| carried by more than one decay product additional “neutrinos” ,

I

1 1gs

I ,I

e

ejecte e

E*

Conversion electron line spectrum for decay of 203Tl state E*=280-keV

Electron binding energies in 203Tl

Ee=E*-EB < 280keV

g

b spectrum is continuous up

to Ee ≈ Q

The Neutrino Hypothesis


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Dilemma: continuous e- spectrum would violate energy/momentum balance in 2-body process. Wolfgang Pauli (1930) postulates unobserved, neutral particle (“neutron” later =“neutrino” (Fermi))

Evidence for Neutrino


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gs

Z,I

1gs

Z ±1,(I,I )

0Q e eject

•Fixed decay energy (Q value Dmc2)

but continuous e- spectrum • e- has spin Ie=1/2

but |Ifinal-Iin|= 0, 1 typically

• Electron capture produces recoil momentum • Direct evidence by neutrino-induced reaction

e-

com

ep

Np

Np

Recoil Experiment

Recoil Detector

Auger e- Detector

37Ar gas cell

TOF distance

37 37Ar e Cl

ii observed

p 0

i Ni observed

p p

Fermi’s Neutrino Hypothesis


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Enrico Fermi (1934): Adapt Dirac’s elm field theory to weak interactions. Weak (beta-decay-type) interaction is similar to elm interaction between currents. Range of weak interaction is rWI ≈ zero (relm )

Electromagnetic Current-Current Interactions

Fermi’s theory accepted as working hypothesis for weak interactions. Neutrino properties predicted: spin=1/2, zero charge, zero mass. Directly observed: 1956(Science)/1959(PR) by Fred Reines & Clyde Cowan

Direct Evidence for Neutrino


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g

g

g

109 110

e

* 110

th

Inverse beta decay

e e annihilation

e e 2 511keV

Delayed n capture rays

n Cd Cd

n

Cd

e

x

p

Savannah River reactor experiment (fission fragments decay

900 hrs with reactor on 250 hrs reactor off

prompt e+-delayed capture g coincidences

Reines Cowan Target tanks H2O

LSc (Cd) tanks

Experiment: s = 7·10-19b

Elementary Modes of b Decay


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Bethge, Kernphysik

b b EC b to K-hole

Nuclear b decay and electron capture

Fermi’s zero-range (point-like) weak interaction, coupling constant GF

e e

Different lepton families : electron, muon, tau

neutrinos : , , ,

All neutrinos have small masses and (only upper limits known)

In energetics of decay, account for electrons. Mass tables apply to neutral atoms. Example: EC “recycles” e-

b + decay of p produces ion


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Beta Decays of Odd-A and Even-A Nuclei

2

2

min 2 3

,

4:

2 2 4

s n p e

A

s C

m A Z A A Z A Z

a m m m c Am m Z

a a A

a b g

b

g

D

Expand around ZA: Mass parabola bottom of valley

2( ) ( ) Am Z A Z Za b D

11.2

0

11.2

MeV o oA

MeV A odd

MeV e eA

D

mc

2

ZA Z

odd-A isobars D = 0

b

b

b

b


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Energetics of b Decay

, 1, | , 1, |

( , ) ( 1, ) ( , ) ( 1, )

, 1, |

( , ) ( 1

2

, )

e

e

e

e

Z A Z A e Z A Z A e

m Z A m Z A m Z A m Z A

Z A e Z A

m Z A m

m

Z

EC

A

b

b

1 extra e+ 1 extra e-

Beta decay and EC (K)-capture

11 116 5: 6 6 eExample C e Be e e Qb

b

Mass balance:

11 2 11 2 2 2

11 2 11 2 2

( ) ( )

( ) ( ) 2

e e

e

m C c m Be c m c m c Q

Q m C c m Be c m c

bb

b

Decay Q-value smaller by 2mec2 for b+ decay than for b-

Qb>0 exotherm

5 1

Fermi Theory of b Decay


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p

core

n

core

EC

i f

Simple example: single nucleon orbiting core of paired nucleons captures atomic 1s electron.

c c p p n nf ri r

c c c c

c

c

c c c c

2

3

3 n n

np

3 p p

p n n p

operators , , anal

Isospin wave functions ,

Iso

ˆ

sp og to spin operat

ˆ

orsˆ ˆ ˆ

1 2 1 2ˆ

n

ˆ

i

initial, final s.p. nuclear states

2

if WI f

2 ˆP f H i E Fermi’s Golden Rule Perturbation theory for i f

d d d WI F p e n p nĤ G r r r r r rˆ

Weak Interaction Hamiltonian (point-like) GF: coupling constant, : Isospin raising operator d : delta distribution

̂

ME of weak interaction H

Density of final states per unit

energy

e- e

Weak Transition Matrix Elements


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3 *

fi WI f i

i e p core

f n co e

F

r

ˆH : f H i d r r r

r r r r

r r r

G ˆ

r

2

2 2 3 *

fi F f i

Nucl

222 22 3 *

F e core core n p

Nucl

H G d r r r

G (0) (0) d r

ˆ

ˆr r

=1 =1, per def

2

pr

2

er

5 fm 104 fm

r

2

nr

2

r

5 fm 104 fm

r

Lepton wave functions vary weakly over nuclear volume

2 2

e, e,r 0

Fermi Transition ME


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2 2 22

fi F eH G (0) (0)

Hydrogen-like e- wave function

B2Zr3

2 a 4

e B31sB

Z(0) 2 e Bohr Radius a 5 10 fm

a

Plane-wave e wave function

i k r

22 i k r

1(r ) e

V

1 1(0) e

V V

32 2

fi F 3

B

2 Z 1H G

Va

Fermi transitions (“super-allowed”): No change in I,

For Pif need to evaluate density (Ef) of final states: neutron-neutrino relative phase space

Normalization volume, drops out in final calculations

Neutrino Phase Space


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3

2

F 3 f

B

if

2 Z2GP E

1

Va

=# final (n, ) states at energy Ef EC: Ef ≈ E neglect nuclear recoil energy

p

pD

Uncertainty Relation

3

24

2 2 3

2

2 3 3

4

2

x y z

dVp dp

f

p p p x y z h

d n p dp dV h p E c

dn EV E

dE c

D D D D D D

22

if gs2 3

3 32 2

F F3 3

B

3 2 4 3

B

E2P V E :

2 c

2 Z 1 2 ZG G

Va ac

Use experimental data for 7Be EC decay to determine GF

GF ≈ 100 eV fm3. More exact average over many data sets:

GF ≈ 88 eV fm3

Branching in EC b Decay


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2

if max2 4 3

2

ma

3

ma

2

x

F 3

B

x

P2 Z

Ga

E E E Qc

E E

7Be

7Li

0.86 MeV

0.48 MeV

0.0 MeV

3

2

3

2

1

2

I

EC 88%

EC 12%

phase space depends on Q = Emax rate increases with Emax

2

ex

2

gs

2

ex

gs

0.478 MeV Q 0.478MeV

Q

0.3820.20

0.861

ex

gs exp

0.115

Experimental value correct magnitude but disagrees

Reason: n ≠ p because of nuclear spin change 3-/2 1-/2

“forbidden” transition

2 e

if fi f f f max e

f

d n n2P H E E E E E E

dE

Shape of the b± Spectrum


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Beta decay other than EC 3-body final state Neglect nuclear recoil energy.

1, 1,

1, 1

e

e

N Z eN Z

N Z e

2 2

2

max

2 2

max

3 3 2 3

4 44 1

( ,, 1

1

)

e

i

e

f

e

e

e p E c

plane wave problemati

dn p dn pVV E E V

dp d

s for e H V

Fixed E dp dE c

ph h

c for e Coul

c h

omb

22 2

4 6 3

222

max4 6 3max

1

4

4

e e e

e e eee f

Vdn dn p dp p dp

c

dn Vdn p E E E

dE cdp dp

22

22max3 7 32

F fie e

e

e

momentum

spectr

G Hp

dN

dE E

p mc u

Shape of b± Spectrum/Coulomb Correction


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22 2max max

22 2 4

22 2

2 22 22 22 2 4

max max3 7 5 3 7 5

( . )

2 2

e e e

ee e

e

ee e

F fi F fie e

E W p c m c E W Q neglect nucl recoil

p cdWp c W

dN

m cdp

p c m c

G H G Hp W W W W W m c W

cWW

cd

Relativistic momentum-energy relation

e

e

dN

dp

b+

b-

Z=0

epBarrier effect

Should use Coulomb e (r) ≠ plane wave. Electron cloud acts as barrier for e+. Non-relativistic numerical correction factor (Fermi function)

b

22

2

2, : 0 0

1 exp 2

: 2

freee e e

e

e Zf

F

or

Z p

22

22max3 7 3

(2

, )F fie e ee

e

G HdNp E E

dp cF Z p

Kurie/Fermi Plot


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Validity of Kurie Plot •|Hfi| ≠ f(Ee) • DI = 0 (allowed transitions) • mc

2≈ 0 eV For DI ≠ 0 additional correction factors Kurie plots for forbidden transitions

22

22max3 7 3

(2

, )F fie e ee

e

G HdNp E E

dp cF Z p

2 max

22

3 7 3

( , )

2

ee e e

e

F fi

Linear

dNF Z p p

Kur

E Edp

G Hfactor

c

ie Plot

64Cu b+ and b- Decays

Owen et al. PR 76, 1726 (1949)

Kurie plot gives extrapolation to Emax of electron spectrum

Neutrino Mass Effect


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Correct decay energy for mc2:

2 2 2 2 2 4max max max

2 2 4max

22 1 222 2 4 2 4

max max3 7 4

,

1 1

2

fie Fe

e

E W E m c p c W m c

dp W

dE c c W m c

HdN GF W m c W W W W m c

dp c

2

e

e e

dN

Fp dp

Ee (keV)

Kurie Plot 3H b - Decay

m ≠ 0 deviations of Kurie plot

from linearity at end point. No direct evidence for mc

2≠ 0 Indirect evidence (neutrino oscillations) mc

2 > 0.1 eV

Total b± Decay Rate


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e

e

e ee

e

e e

e

max

3 7

e0 5 4 2 2

e F e e

2

2fi 2emax

0

e

1 21

p2 W: : :

m c G m c m c

HdN1 for F 1,

dN n2d

d t

m 0d

Seek method to systematize data: Unit conversion

e

2

fi

max

0 1 2

H n2f Z,

t

Universal numerical function, independent of spectrum Tables

e

2

2 2 3 *

fi F f i

Nucl

max 0

Nuclear str

Phas

ucture info

e spac f

rmation

H G d r

e : Z,

ˆ

,

r r

b b

b(Z )

max maxf (Z ,E ) a(Z) E

a(Z) exp 5.553 7.3418exp Z 213.86

b(Z) 4.148exp

Paramete

Z 51.6

Z

rization (Machner ,2005)

0 for ,Z 0 for

e

e e e e e e e max

22

max max

1

f (Z, ) d

Coulomb Corre

F(Z, )

c o

1

ti n :

b± Decay ft-Values


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e

0max 1 2 2

fi

0

2

fi

n2ft : f Z , t

H

B n2 2787 70 s

H B ft

2

fi

Bft :

H

1 2t1s 6·1014 y

Large ft: slow transitions, small|Hfi|2

Experimental task: Emax, and t1/2 combination nuclear matrix element

Meyerhof, 1967

super

allow

ed

allow

ed

1st fo

rbid

den

Frequency of ft Values

Super allowed b transitions: Large matrix elements, small ft observed only for light nuclei (“mirror nuclei”) and DI=0,±1

b 17 177 8

F O log ft 3.38

16

8O

16

8O

p n


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3H Kurie Plot Solid line corresponds to mc

2=100 keV

22

22max3 7 3

(2

, )F fie e ee

e

G HdNp E E

dp cF Z p

2 max

22

3 7 3

( , )

2

ee e e

e

F fi

Linear

dNF Z p p

Kur

E Edp

G Hfactor

c

ie Plot

Allowed and Forbidden b Decays


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Ee (keV)

36Cl Kurie Plot allowed decay

36Cl Kurie Plot 1st forbidden decay

Double b Decay


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Parity Violation in b Decay


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t (min)

Count

Rate

/Count

Rate

warm

Count

Rate

/Count

Rate

warm

e g

g Anisotropy a equatorial counter b polar counter

b Anisotropy

g Anisotropy average of both counters, both field polarities

2 0

2

W W

W

e

Light Guide

Pumping Inlet

Anthracite Scintillator

Ce/Mg Nitrate Container

Equatorial NaI Counter

Polar NaI

Counter

Sample

Documents

Super Kamiokande (Japan) neutrino detector W. Udo Schröder ...Super Kamiokande (Japan) neutrino detector 50,000 t H 2. Electron/Beta Spectrometry W. Udo Schröder, 2009 y