1 Recoilless Resonant Capture of Antineutrinos: Basic Questions and some Ideas Walter Potzel Technische Universität München SNOW2006, Stockholm, 5th May

1

Recoilless Resonant Capture of

Antineutrinos:

Basic Questions and some Ideas

Walter Potzel

Technische Universität München

SNOW2006, Stockholm, 5th May 2006

2

Papers

Two papers:

R. S. Raghavan, hep-ph/0511191 and follow-up paper hep-ph/0601079

Earlier papers:

W. M. Visscher, Phys. Rev. 116, 1581 (1959)

W. P. Kells and J. P. Schiffer, Phys. Rev. C 28, 2162 (1983)

3

Outline

I) -decay:1) Usual -decay2) Bound-state -decay: resonant character

II) Promising example: 3H – 3He system

III) Recoilless emission and absorption

1) Recoilfree fraction2) Linewidth3) Relativistic effects: Second-order Doppler shift

a) temperatureb) zero-point motion

IV) Consequences – some Ideas, mission impossible?

V) Conclusions

e

4

I) -decay

1) Usual β-decay

3-body process: show (broad) energy spectra

Maximum energy:

where

is the end-point energy

)()1( eeZAZA neutron transforms into a proton

occupy states in continuum

e

ee ,

e QEev

max

21 )( cMMQ ZZ

5

I) -decay

2) Bound-state -decay

)()1( eeZAZA

J. N. Bahcall, Phys. Rev. 124, 495 (1961)

Bound state atomic orbit.Not a capture of e- initially created in a continuum state (less probable).

Example:

33eeHeH

Atomic orbit in 3He

2-body process, has a fixed energy:

e

Rzv EBQEe

where

21 )( cMMQ ZZ end-point energy

zB binding energy

RE recoil energy

sourcee

eHe3 recoils

6

I) -decay

)1(eA(Z) - ZAe

Reverse process (absorption):

in atomic orbit

etarget for

Example:

HHee3-3 e

in atomic orbit of 3He

energy required for : e

Rzv EBQEe

Bound-state -decay has a resonant character which is (partially) destroyed by the recoil energy ER.

H3recoils

7

I) -decay

3) Resonance cross section

2

2/1

20

41)(

1018.4 cmft

Eg

res

e

32

3

0 13744

Z

mcg

for low Z, hydrogen-like ψm: electron mass ψ 2: probability density of e in A(Z)

)( resve

E : resonant spectral density, i.e., number of in an energy interval of 1MeV around

eresve

E

2/1ft value logft

10002/1 ft : super-allowed transition

L.A. Mikaélyan, et al.: Sov. J. Nucl. Phys. 6, 254 (1968)

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II) Example: 3H-3He system

resve

E2/1ft CB /Decay

HeH 33 18.60

keV

1132

sec

6.9x10-3

(80% ground state,

20% excited states)

3H (source) and 3He (target): gases at T=300K→thermal motion, Doppler energy profile

eVMcTkEKFWHM Bresve

16.0)/2(22:)300( 22

→ resonant spectral denstiy ρ≈106/0.16≈6x106

recoil energy:

eVEMc

E

R

rese 06.02

2

2

)(

2ER≈0.12eV; 2Δ≈0.16eV→reduced overlap

Resonance cross section: σ ≈ 1x10-42 cm2

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III) Recoilless antineutrino emission and absorption

1) Recoilfree fraction

Stop thermal motion!Make ER negligibly small!

recoil energy:

2

2

2

)(

Mc

E

R

reseE

3H as well as 3He in metallic lattices:freeze their motion →no Doppler broadening.M→Mlattice>>MLeave lattice unchanged, leave phonons unchanged.

Energy of lattice with N particles:

N

sssL nE

3

1

)2/1( ,...2,1,0sn

max

0

)(2/1)(

dZnEL with 1)/exp(/1)( Tkn B

zero-point energy

:)( dZ number of oscillators with frequency ω between ω and ω + dω

10

Phonon density of states

Zn metal

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III) Recoilless antineutrino …

Recoilfree fraction f:

2

2

xc

E

ef

dTk

Z

NMc

ETf

B

11/exp

2)(

3

1

2exp)(

max

02

2

1f

Debye model:

BkMc

ETf

2

3

2exp)0(

2

2

T0:

Example: 3H – 3He

17.0)0( f for Θ=600KEmission and absorption:f2 ≈ 0.03 for T0

f depends on: transition energy E mass M of the atom Debye temperature Θ

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2) Linewidth

minimal width (natural width): / natE lifetime

3H: = 17.81 y eVE nat 241017.1 (extremely narrow)

More important: electromagnetic relaxation effects.

Magnetic interactions: a) 3H, 3He with atoms (nuclei) of metallic latticeb) 3H – 3H magnetic dipolar spin-spin interaction

Measurements: 3H (Pd), 3H (Ti-H) Typical relaxation times: T2~2ms

Energy width: eVE 13103.3 Cross section: 232109 cmres

13


homogeneous broadening

Transitionenergy 18.6keV

10-13eV

Relaxation between the sublevels affectsthe lineshape and the total linewidth.

The linewidth is determined by the relaxation rate.

Magnetic interactions:a) 3H, 3He with atoms (nuclei) of metallic latticeb) 3H – 3H magnetic dipolar spin-spin interaction

3.3x10-13eV = H

~ 3x1011

14


3) Relativistic effects

Second-order Doppler shift due to mean-square atomic velocity <V2>

Time-dilatation effect: 2)/(1

'

cV

tt

moving system

stationary system

2

2'2'

21)/(1

c

VcV Frequencies:

Second-order Doppler shift:2

2'

2c

V Reduction of

frequency (energy)

15


Within the Debye model:

s

tt

s

ss

Bts

B TfT

TfT

Mc

k

Mc

k

E

E22 2

3

16

9

T

dxx

xTTf

/

0

33

1exp3

where

1 ts TTIf

Zero-point energy

degree → 500010/ 13 EE linewidths

Low temperatures: 0 ts TT 0.....

If 1 ts degree → 1000102/ 14 EE linewidths

However, zero-point energyremains!

Energy levels (also the groundstate) depend on the surrounding atoms.

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IV) Real experiments: some thoughts

1) Preparation of source and target

Source:3H chemically loaded into metals to form hydrides (tritides), e.g., Pd: in octahedral interstitial sites (IS).

Target:3He accumulates with time: tritium trick:

Pd3Hxtime Pd3Hx-y

3Heydischarge Pd3Hey

Remove (discharge) 3H by slightly heating (in vacuum)

17


How much metal for source and target?

Source:1 kCi of 3H (~100mg 3H): ~5g of Pd3H0.6

for NMR studies: 0.5 kCi 3H in 2.4g PdH0.6

Target:100mg of 3He implies ~50g of Pd3H0.6

(3He/3H)~0.13He is not mobile

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2) Event rates for 3H – 3He recoilless resonant capture of antineutrinos

Base

line 3H 3He

Antineutrino

capture per day

R(t=30d)

per day

10 cm

10 m

1 kCi

1 MCi

100 mg

1 g

1.5x104

1.5x104

75

75

R(t)/day: Reverse -activity rate after growth period t

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Energy width: eVE 13103.3 Cross section: 232109 cmres

a) Ultra-short base lines for neutrino-ocillation experiments

Oscillatory term: )/(sin 02 LL

Oscillation length:eVm

MeVE

m

EcL

/

/480.24

220

[m]

Determination of Θ13: E=18.6 keV instead of 3 MeV.

Base line of 9.3 m instead of 1500 m

b) Gravitational redshift experiments within distance of ~20cm (Earth)

H. Nunokawa et al., hep-ph/0503283, H. Minakata et al., hep-ph/0602046Accurate measurement of m2 atmosph.: determination of mass hierarchy

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IV) Real experiments: some thoughtsProblems:

1) Recoilfree fraction:

How are 3H and 3He bound in the metallic matrix?Difficult problem, needs inelastic neutron scattering experiments.Recoilfree fraction may be smaller by a factor of ~5, this means a loss by a factor of ~25.

Model: Particles in a box with steep walls.

2) Use low temperatures (liquid He) to achieve stability and to avoid temperature differences between source and target.Make sure to get rid of the heat generated by the decay in the source.

21


3) Source and target should be as similar as possible:

No chemical shift ts

Difference of 1 degree in Debye temperatures: energy shift ~ 1000 linewidths

Source contains 3H, whereas target contains mainly 3He.

Interaction (chemical bonds) of 3H and 3He with themetal atoms may be different.

However:

ts

22


This is connected to the questions:

a) How well can 3H be discharged?

b) Source contains 3H in the neighborhood of 3He which has just formed after decay.Target contains 3He in the neighborhood but no 3H.

Possible solutions to b):

Use stable 2H (D) to replace the discharged 3H.Use highly diluted systems only.

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Both types of line broadening will be important

4) Linewidth

Two types of line broadening:

a) homogeneous broadening b) inhomogeneous broadening

due to fluctuations, e. g. ofmagnetic fields

due to stationary effects,e.g. impurities, lattice defects

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a) homogeneous broadening

Transitionenergy 18.6keV

10-13eV

Relaxation between the sublevels affectsthe lineshape and the total linewidth.

The linewidth is determined by the relaxation rate.

Magnetic interactions:a) 3H, 3He with atoms (nuclei) of metallic latticeb) 3H – 3H magnetic dipolar spin-spin interaction

3.3x10-13eV = H

~ 3x1011

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b) inhomogeneous broadening

In the best crystals: (1 +a) ~10-13 eV corresp. to 1011 or larger

Both types of broadening reduce the resonant reaction intensity

Many individual resonancesdisplaced from the nonper-turbed resonance energy E0

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B. Balko, I. W. Kay, J. Nicoll, J. D. Silk, and G. Herling,Hyperfine Interactions 107, 283 (1997).

H

H

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V) Conclusions

1) Recoilless resonant emission and absorption of antineutrinos:3H – 3He system is the prime candidate.

2) Experiment is very difficult:a) Recoilfree fraction might be smaller than expectedb) Temperature difference between source and target (temperature shift)c) Different Debye temperatures of source and target (chemical shift)d) Homogeneous and inhomogeneous broadening of linewidthe) Discharge of 3H from the metal matrix

Rate estimates given by R. S. Raghavan are probably too optimistic,possibly by a factor of more than 1000.

3) If successful, ultra-short (~10m) baseline experiments feasible as wellas gravitational redshift experiments within a distance of ~20 cm (Earth).

28

Extra slides

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Candidates for recoilless neutrino absorption

W. P. Kells and J. P. Schiffer,Phys. Rev. C 28, 2162 (1983)

Line broadeningRecoilless fraction

30

Determination of neutrino mass

Gravitational redshift experiment: 2c

gh

E

E

ghc2

Assumption: experimental linewidth eV13103.3

where h is height corresponding to 1 experimental linewidth

ghc

E2

'' with 42

022' cmcpE

For :20 pccm

220

22

420'

2

11

2

11

cm

cp

cmpcE

220

2'

2

11

cm

c

ghand

220

2

''

2

11

cm

c

gh

Ec

v A larger Dopplervelocity is neededfor the same height

To have '

220

220

2

11

21

1

'

E

cmh

Ecm

hh

If :00 m

31

Determination of neutrino mass

220

2

11

'

E

cm

h

h

Some numbers: meVcm 5020 12106.31

'

h

h

cmh 18 Angströmcmhh 311 105.6105.6'

meVcm 50020 Angströmhh 65.0'

Doppler velocity: 12'

106.31/

/ cv

cv

R. W. Kadel: hep-ph/0603211 has been withdrawn (wrong approximation)

32

Frequency modulation

a) homogeneous broadening


tmti

ttE sin

2exp)( 0

lifetime: carrier frequency modulation frequencym: modulation index

m = (max. frequ. deviation)/

Radiation field:

Long-lived state: (1/)>>

Intensity:

n

n

n

mJI 22

0

2

2/

)()(

Instant. frequency: tmi cos0

Sum of Lorentzians, all with natural width /2,located at n=0±nwith intensity Jn

2(m).Jn: Bessel funct. 1st kind,order n.

33


Modulation index detemines the number of sidebands.

34


Frequency modulation in source and target are not exactly equal.Natural linewidth: =1.2x10-24 eV corresp. 2.8x10-10 Hz.Modulation frequency: ~100 Hz (T2~2ms)

Spacing between sidebands is enormously large compared to No perfect match of sideband spectra, i. e. strongly reduced overlap

Reason: inhomogeneities in the samples

b) inhomogeneous broadening

in the best crystals: ~10-13 eV ~1011

Both types of broadening reduce the resonant reaction intensity

35

Emission spectrum much broader than natural.This is being looked at with a high-resolution target.Tremendous reduction of intensity.


Source

Target

36

FM sidebands

37

FM sidebands m=2.0

38

FM sidebands m=10.0

39

Red(blue)shift 67ZnO

gravitational redshift

gravitational blueshift

difference in height: 1min gravitational field of Earth

accuracy: (=1x10-18

W. Potzel et al., Hyp. Interact.72, 197 (1992)

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Gravitational Redshift Experiment

Documents

1 Recoilless Resonant Capture of Antineutrinos: Basic Questions and some Ideas Walter Potzel Technische Universität München SNOW2006, Stockholm, 5th May