Neutrino Resonance and Applications R. S. Raghavan Virginia Tech NDM-09

1. Neutrino Resonance and Applications R. S. Raghavan Virginia Tech NDM-09 Madison Wis Aug 31 2009

2. Neutrino Resonance --Some Milestones Resonant Nu Capture— Conceptual Beginnings: Kells & Schiffer, Phys. Rev. C28 (1983) 2162 Technology: Neutrino Osc. on the Table Top Recoilless resonant capture of antineutrinos from tritium decay, hep-ph/0601079 --first experimental design with potential-(hydrogen storage tech.); (“WIDE”) “conventional” linewidths of “classical” Mőssbauer Effect Linewidth in Nu Capture—Conceptual Advance: Hypersharp Resonant Capture of Anti-Neutrinos, hep-ph 0805.4155; hep-ph 0806.0839--- New insights on line narrowing! Final paper : Much refined. Hypersharp Resonant Capture of Neutrinos as a Laboratory Probe of the Planck length Phys. Rev. Letters 102 (2009) 0918040 Quantum mechanical Time Energy Uncertainty in Nu Resonance hep-ph 0907.0878(July 09) Why Neutrino Lines are Hypersharp ?(Reply to Comments) –hep-pharXiv:0908.2980 v2 (Aug 09)

3. Quest for resonance reaction of neutrinos from Tritium-- Analogy to γ-ray resonance (Mőssbauer Effect) Good part Low Energy of Tritium Nus—good ME efficiency 2 basic problemsNeutrino Lines (β-decay emits continua)! Resonance lifetimes very long--- β-decay ! Electron Capture another natural possibility (W. Visscher 1960)

4. Remedies Step 1 Make monoenergeticneutrinos in beta decay of T–  “Bound State” β-decay—JohnBahcall (1962) ; Electron appears in an atomic orbit (2-body decay)instead of into the continuum -- Monoenergetic Neutrino LINES! ----branching in T decay = 0.54% to 1s state—OK since it has a vacancy for one more electron T  neutral 3He (with e- in 1s orbit) + ν̃e(18.6 keV) Step 2 Detection of 18.6 keV ν̃e ν̃ecapture by inverse beta sets capture threshold at 1.022 MeV to create positron  ν̃e+ 3HeT +e+threshold too high Induced Orbital Electron Capture (Mikaelyan 1968) by antineutrnos from tritium Reverse of BB decay: ν̃e +3He +e- ( 1s )  T • Resonance capture of T antineutrinos:T ↔ 3He+ ν̃e ; Eνmin = 18.6 keV • a pair of time-reversed processes with really low threshold

5. Resonance Linewidth and Cross Section Line widths determine the resonance cross section inversely  σ = σo/ (ΔE/Γ) Γ- natural width (~10-24 eV in tritium). e.g. linewidth for T Nus from NMR data for broadened lines ~ 13 kHz  σ ~ 10-33 cm2 For natural linewidth ΔE = Γ For hypersharp nus σ = σo  “geometrical” cross section ~10-17 cm2  Very High σ and very small ΔE High priorities for New Physics Applications-- Prime mover for the quest for natural linewidth in resonance transitions.

6. Linewidths in Short lived & long lived states Linewidth estimates for short lived (~nsec to μsec) ME cases usually taken from other techniques such as NMR—fluctuation ~kHz to MHz in ME levels. First pass assumption-used in in previous work (R. S. R hep-ph/06 1079 (2006)  13kHz  σ ~10-33 cm2 Is this correct for LONG LIVED LEVELS ? --Is the linewidth physics different for long life times? In “classical” ME experience, the answer is usually NO

7. Ω But….Early hint for “yes”---from theory of ME itself if viewed in different, more basic perspective of ME—not the usual one • ME is a problem in FREQUENCY MODULATION (Shapiro 1960) • (emphasis not on the conventional view as condensed matter problem—Debye excitations etc.) • Doppler shifts due to lattice vibrations modulate the energy of γ-ray—Result • Carrier and sidebands: Nu energy spectrum with central unshifted line (ME line) with natural width and sidebands Eo±nΩ (also of natural width) where Ω is the phonon frequency • Condition for ME:non overlapping first bands • nuclear lifetimeτ >> lattice vibrational time 1/Ω ~ 10-14 sec • (noted already 1961 byH. Frauenfelder)-  • This condition always satisfied in • every ME isotope so far(>1010s) • nuclearlifetime-linewidth connection •  General LessonLong lifetimes need new perspective •  MODULATION of nu linesdue to energy fluctuations

8. Quantitative linewidth in modulated long lived states Theoretical treatment of ME lineshape that explicitly includes role of the nuclear lifetime: ---(Salkola, S. Stenholm 1990-extension of Shapiro theory) Illustration: Modulating fluctuation = Ωo cos Ωt The line shape is a familiar FM series : Jk (x) are Bessel functions, η = Ωo /Ω [Ωo is the energy spread of fluctuation Ω= frequency of fluctuation ξ = Ω/ Γ , δ is the external detuning for scanning the line shape.  Central line and sidebands of index ±k, all with the natural width. Crucial Feature: Broadening occurs due to overlap of k= ± 1 peaks. They are ξ linewidths separated from central line. k= ± 1 overlap small if separation ξ is LARGE or Ω/ Γ is large • Line approches natural width as Γ becomes v. small • For T decay (τ = yrs—Γ always << Ω for conceivable extranuclear fluctuations) • ν̃e linewidth is necessarily  Γ • Intensity of central unbroadened line is Jo2 (η)

9. Generalized Hypersharp Fraction of Emitted Neutrinos Question: What is the intensity of the sharp line after loss to sidebands? A hypersharp fraction (analogous to ME recoilless fraction) H = J02 (<x>/ λ) ∏KJ02 (Δ K/ Ω K) where K runs over the different types of fluctuations with width ΔK and rate ΩK with the specific hypersharp fraction J02 (Δ K/ Ω K). f = J02 (<x>/ λ) the first term  Debye-Waller factorRecoilless fraction • Parameter of interest to experiment is hypersharp intensity • determined by Δ K/ Ω K for each type K of energy fluctuation

10. η = Ωo/Ω ~`1 τ>> 1/Ω τ ~1/Ω Modulation in Long lived levels -- broadening in short lived levels Under same fluctuations –example Long lifetime Modulation  narrow central line Resolved from sidebands Short lifetime Broadening  Wide central line unresolved from central line broadening Basic Lesson—In long lived levels fluctuations affect the line energy only by modulation all effects that broaden line in short lived cases are relegated to side bands in the modulation. Then the only concern is how much of central intensity is transferred away to sidebands.

11. Nu spectrum Modulating spectrum Einstein Debye Stochastic Relax Kubo Gaussian

12. Sources of Nu Energy Fluctuations • Periodic • Doppler effect due to lattice vibrations • Mechanical Vibrations • Gravitational Waves (!!) • Stochastic • Diffusion--Collisions • Hyperfine relaxation • Inhomogeneous distributions • Dipolar magnetic fields from neighbours • Electric fields due to Lattice imperfections • Other distributed field inhomogeneties • …….

13. Stochastic fluctuations—Only correlation methods used—not FM Effect is general—not dependent on FM picture Line narrowing Via Stochastic Energy Fluctuations by collisions In a gas.: Narrow peak riding on top Of familiar Doppler broadened line profile Dicke—1952 (6 years before Mossbauer !) Narrowing not restricted to periodic modulation

14. Line Narrowing by Magnetic Relaxation, Exchange narrowing of magnetic moments (paramagnetic relaxation) What happens in ME. Modulating spectrum Fourier Transform of random fluctuation or two state relaxation Explicitly shown as Gaussian by Kubo…. Each freq component of Gaussian modulates like single freq: Then the modulated spectrum looks like fig below Results confirmed by general correlation physics treatments Specific case: magnentic relaxation of TNb. Line remains hypersharp; many orders of magnitude (~1011) taller) But intensity is reduced by Jo2 ~ 0.4 transferred to side bands overall by Jo4 = 0.2 for T in metals. Very different from estimate from classical ME(~ μsec). Reduction is x1011 = ratio of relaxation width/natural width !! η = Ωo/Ω ~`1 Ω

15. Inhomogeneously distributed Perturbations —Balko et al PR (1997) 12080—not based on FM FM and non FM methods equivalent

16. Doppler Effect due to External fluctuations • :Mechanical Vibrations • δE/E = v/c = 1/c (δl/l) f L = 3x10-11x 10x10-17 ~3x10-27 • L is the baseline (~10 cm) and (δl/l) the fractional length change at the frequency f ; From LIGO development the (δl/l) f ~ 10-17 Hz • δE/E ~3x10-27 or ~60 linewidths. • This appears not as resonance detuning but a modulation with • η = ( Ωo/ Ω) = δE/(h f ) ~10 -5 to 10 -11 for f ~ 10-3 to 103 Hz. •  [Jo (η)]4 ~ 1 even for much higher freq and vib amplitudes • No effect on the hypersharp Nu fraction. Gravitational Waves— universal periodic wave-would this be detectable? • Effect is identical to above for the same baseline since GW strain changes of L produces Doppler effect identical to above for :δE/E ~ 1/c (δl/l) f L = 3x10-11x 10x10-17 ~3x10-27 since (δl/l) f from typical GW are also the same as above—NO Effect Too bad!! 

17. Emitter-Target Energy BalanceSelf-compensation Energy SHIFTS ET and EHe specific to the T and the He, in general, different. • Atomic (Binding energies already considered) • Chemical & lattice bonding (T and He chemically different and sit in isosymmetric interstitial traps with different trap depths—see below) Atomic dynamics and excitations only to discrete levels in traps  Recoil free fraction determined only by the trap levels—not the Debye spectrum of the lattice.  first trap level ~800 K- no lower energy excitations no temperature dependent shift at normal temp. BUT Zero Point Energy ZPE remains and is different in the two traps But in every decay both T and He participate • Energy gain in Emission is COMPENSATED in absorption: net ΔE changes sign in emission/absorption • Motional averaging via fluctuating coordinates r  • Compensation is PRECISE because each shift is averaged to unique sharp values

18. Experimental---Basic Embedding Technique Tritides and the “Tritium Trick” He is a noble gas. Tricky problem to embed in a solid. How to embed T and He in solids • Metal tritides —Best approach visible • Tritium gas reacts with metals and alloys and forms metal tritides –(PdT, TiT, NbT...) embeds T in lattice uniformly in the bulk  Tritium decays and He grows—distributed uniformly (Tritium Trick (TT)) Problems: • T and He lattice Sites in TT—Unique? Identical for T, He? • Must Remove T from absorber to improve S/N –replace T by H

19. Tritium and He sites in metals He T HeMicrobubbles: 1-2nm diam; 4000 atoms Solid under pressure ~10 GPa at <100K He atoms closer than in IS sites TInterstitial Sites Octahedral – fcc metals Tetrahedral—bcc metals Quest for matrix and conditions where IS sites dominant –not bubbles T and He should occupy same type of INTERSTITIAL site  Search for metal matrix and conditions

20. Niobium- Unique Discovery Niobium as Matrix choice: • Calculations show that at <200K He is sited ONLY in TIS sites Same as T • No bubbles are formed indefinitely •  Uniqueness and identical site requirement satisfied • Nb is unique in providing these features • Most significant advance in 25 years

21. Recoil free fractions in local Potential Wells In Nb TIS the sizes of T and He result in local deformations that create potential wells in which T and He oscillate. Simple picture—T and He ignore the general lattice. • Recoil free fractions from local excited vibrational states Ei , not general lattice excitations outside well. (No Debye Model !) • Ei have been measured via n-inelastic scttering. • Exact calculations • Then f = exp-[ER (=62 meV)(Σ1/Ei )] =0.125 with Ei =72 and 2x 101 meV f = 0.15 • f = f(T)f(He) ~1.5%.

22. Detection of ν̃e Resonance– ν̃e Activation Analysis Source T and absorber 3He made by tritium trick. Resonance signal is the ν̃e induced activity of betas (Rβ) (similar to Davis) The TT method implies some T content in the absorber which will create a background (Tβ). A chief design goal is to maximize Rβ/Tβ. The background due to T in absorber can be minimized by replacing T with H via efficient exchange process. The resonance activation signal, Rβ of 18.6 keV betas grows with time ( t /τ_) while the background Tβ decays ( exp-t/τ ). Rate deviation from the exponential decay is the signature of the resonance.

23. Applications of Hypersharp neutrinos • Novel Tools • Low Energy (18.6 keV) • Extreme Energy precision (ΔE/E ~5x10-29) • Very large resonance cross section σ ~10-17 cm2 • Novel Experimental landscapes---Bench top scale neutrino experiments • Neutrino Oscillations • 1-3 mixing---”long” baseline 10m • Sterile-Active mixing—very short baseline 1-10 cm • Mass Heirarchy (Intermediate baselines?) • Time Energy Uncertainty • Quantum mechanics • Ultimate energy measurement—Fundamental Length in nature

24. Neutrino Oscillations • Text book expts—with monoenergetic nu lines • Theoretical Questions oscillatiion (or not?) addressed by numerous papers • Experimentally, low energy crucial for new landscape • Compare Reactor baselines • E = 18.6 keV vs 1.8 MeV baseline 1m vs 1km • Reaction cross sections—10-43 cm2 vs 10-20 cm2 • Bench top baselines from km scale with gm scale materials vs kiloton targets  1-3 mixing • Active- Sterile Osc for Sterile masses in much extended range with • higher sensitivity to oscillation amplitudes • Much shorter baselines ( tens of cms) • Little systematic Errors • Initial experimental focus on <1m baselines

25. Quantum Mechanical Time -Energy Uncertainty ΔE Δt ~ h/2π The energy of a decaying state has a width determined by the time of observation. If Δt is uncontrolled, Δt is the mean life time τ and the measurement yields an energy spread ΔE = natural width of the decaying state ΔE ~ (h/2π) /τ = ΔE (nat) If Δt is artificially determined say as T, then the energy spread is more, given by ΔE ~ (h/2π)/ T >> ΔEnat  Directly affects cross section  (1/ ΔE) So, What is Δt in a resonance reaction? E.g. in Mossbauer experience? in the tritium resonance reaction ? According to QM Δt is counted from the point of CREATION of the state Question can be probed if lifetimes of decaying states in both cases are long Enough for external control of T

26. ME in 14.4 keV state of 57Fe • Lifetime = 140 ns • Δt can be controlled since the time of creation • of the ME state can be tagged by the 122 keV • Signal and the ME of the 14.4 keV γ can be observed • After a delay T in coincidence. • Time filtered resonance • T is the relevant time- detection of gamma at T fixes both final and initial measurement defining the “time of expt” • Expts done in 60’s by Wu et al and Lynch et al 122 keV 140 ns 14.4 keV Question already addressed in 1960 in ME work

27. TEU in Fe57 ME Observed basically the cross section at resonance Any broadening reduces this cross section relative to the geometrical value for natural linewidth. . TIME FILTERED RESONANCE Observed width is QM limited width only if the nu is observed without limitation on the time of emission; i.e. the full lifetime is operational If the time of emission is limited to times < τ the line is broadened, again because of QM, to a broadening a factor T / τ  Time filtering effect – Abs. at resonance max:  1-Jo2 (√(βT)  t with T=t/τ <<1 β = Nσ f = resonance thickness of absorber In mfp units Wu et al (1960)

28. Time filtered Resonance in Tritium No need for coincidence Abs. at resonance max:  1-Jo2(√(βT)  t with T=t/τ Calibrates the prevailing width directly by signal rate controllable by the time window of emission since creation of state • Easy for tritium –T is very long so that each day of measurement T increases naturally spontaneous signal growth with time predictable directly by the decay rate of tritium • In- vivo rate increases as source ages; • Activation time and T age dependence produce in practice  t2 rate dependence Signal Rate at Resonance vs time t Nu act. + time filter effect  t2 Nu Activation t (corrected for decay) Bgd tritium Decay 1/t Time t<< τ

29. β=1 ΔEnat β=1 ΔE = 10ΔEnat The signal growth rate depends on β i.e the cross section at zero detuning- thus the state width. The two curves show that the growth rate can lead to the prevailing width of Tritium state in particular if it is > ΔEnat τ=6600 d

30. The hypersharp width basis presumes of the tritium resonanceis controlled by the NATURAL width ΔEnat Growth rate of signal in time-filtered resonance is controlled by the prevailing width in experiment ΔE If ΔE > ΔE nat The experiment might be way to probe violation of the TEU. There may be reason for TEU could be violated because tiny widths at the level of 10-24 eV may be set by a FUNDMENTAL length rather than by TEU

31. Fundamental Length L = (Gh/2πc)3 ~ 10-33 cm How to observe a very tiny length ? Guidance from early work of Mead (1965) Tiny L implies a tiny limiting imprecision of the local potential V(r) Tiny energy imprecision or width of bound states overrides at some level the QM time-energy uncertainty width Test by measuring the very small width ΔE of states with very long τ L effect Planck broadened line width ΔE > QM width h/τ Planck length or not, the test probes the keystone of QM in the untested regime of extremely small energies --Unprecedented precision needed: ΔE/E << 10-20 !

32. Mead Theory of Fundamental Length Ultimate widths of nuclear states i.e. ΔE/E depends on L. Range of predictions from simple arguments of Mead ΔE/E (L) = (L/ R) λ ~ 10-20 (for λ = 1) ΔE/E (L) ~ 10-40 (for λ = L/R) R is the nuclear radius ~10-13 cm used as length scale. Highest precision attainable—Best chance in T hypersharp resonance ΔE/E= 10-29 situated strategically in the predicted range !! Sensitive result could be the empirical milestone or guidestone on the road to Quantum Gravity via an effect depending on the universal constants of Newton and Planck.

33. Summary • The linewidth of neutrino lines from long lived levels such as tritium is a result of modulation of fluctuating perterbations -- Not detuning via broadening as in classical ME • The FM perspective offers a simple picture of motional averaging of perturbations and a central line of natural width • A key experimental discovery --Identical interstitial sites are possible for T and He in Niobium below 200K— • The cross section is “geometrical” ~10-17 cm2-->practicality • Hypersharp neutrinos promise an exciting new landscape for bench top Investigations of fundamental questions in neutrino physics and Quantum mechanics—who knows –even quantum gravity!