Neutrons with Energy

Guillaume.Pignol@ lpsc.in2p3.fr ESIPAP, febuary 2019 1. Neutrons and the precision frontier 2. Neutron optics, ultracold neutrons 3. Neutron detection 4. Fundamental physics with UCNs • Neutron lifetime • Electric dipole moment • Gravity with neutrons Two frontiers of particle physics

Energy frontier (LHC): producing Precision frontier: detecting the effect heavy unstable particles at of virtual particles. colliders, e.g. The neutron beta decay, lifetime of 15 . W boson, 푚푊 = 80 GeV minutes, proceeds via the exchange of . Higgs boson, 푚퐻 = 125 GeV the virtual W. . Dark matter particle? Fundamental structure of the Standard Model inferred from properties of the decay (e.g. parity violation). New physics at the precision/intensity frontier

New particles could induce super-rare decays. 15 Example: a new boson with m푋 = 10 GeV could induce the proton decay with a lifetime of 푀4 휏 ≈ 푋 ≈ 1033 years 푝 2 5 훼 푚푝 It would violate the conservation of baryon and lepton number.

New particles could induce exotic couplings. An electric dipole moment (EDM) is an interaction of the spin of a particle with the electric field. This coupling violates time reversal symmetry, and is connected with the matter-antimatter asymmetry of the Universe.

The search for the EDM of the neutron is highly sensitive to interesting new physics. Detecting the neutron electric dipole moment

퐻 = −푑푛 퐸 ⋅ 휎

−27 If the neutron EDM is 푑푛 = 10 푒 cm And the electric field is 퐸 = 15 kV/cm The neutron spin will make one full turn in a time 휋ℏ = 1.4 × 106 s = 4 years 푑푛퐸

In order to detect such a tiny coupling we need: • The slowest possible neutrons to maximize the interaction time in the electric field • An intense source of such neutrons to maximize the statistical sensitivity Large neutron factories Future European Spallation Source ILL high flux reactor Scheduled 2025 since 1967 Lund, Sweden Grenoble, France

multi-disciplinary facilities

Biology Chemistry Material sciences Magnetism Nuclear physics Particle physics A typical neutron scattering experiment Fission or Spallation sources

FISSION • steady chain reaction • ~ 2 neutron/fission • Energy ~ 2 MeV

SPALLATION • Accelerator driven

• Pulsed or steady G.J. Russell, Spallation physics–an overview, • ~ 20 neutrons/proton Proceedings of ICANS-XI, KEK-Report Vol. 90-25, 291–299, 1991 • Energy ~ 20 MeV About 20 Big neutron sources in the world

S R R S R R S SR S R R S R R

High flux reactors with cold neutron High intensity spallation sources source available for users (there are 246 operational research reactors worldwide) Compare the flux

ILL high flux reactor 58 MW Thermal neutron flux ~ 1.5 x 1015 n/cm2/s

PWR power reactor 3 GW SNS pulsed source (60 Hz) Thermal neutron flux Thermal neutron flux 14 2 ~ 10 n/cm /s Peak ~ 3x1016 n/cm2/s Average ~ 4x1013 n/cm2/s Thermalization of fast neutrons

Fast neutron Thermal neutron E = a few MeV E = kT = 25 meV

Moderator material with hydrogen or deuterium. In heavy water the mean free path is about 2 cm and it takes about 35 collision to thermalize. ILL reactor

Heavy water moderator and reflector Ø2.5 m Fuel: HEU (93.3% 235) Hot source Cold source: 20 L of Liquid D2 at 20K 1. Neutrons and the precision frontier 2. Neutron optics, ultracold neutrons 3. Neutron detection 4. Fundamental physics with UCNs • Neutron lifetime • Electric dipole moment • Gravity with neutrons Neutron spectrum

Fission ~ 2 MeV 1 MeV fast 휆 < 0.1 nm 1 keV “PARTICLE”

Resonant capture ~ 10 eV 1 eV De Broglie wavelength

epithermal 2휋 ℏ Thermal neutrons: 휆 =

kT = 25 meV @ T =300 K 1 meV 2 푚 퐸 cold 휆 > 0.1 nm 1 μeV Fermi potentials ~ 100 neV “WAVE”

ultracold 1 neV Mirror effect at grazing incidence Particles and waves Neutron interaction with a single nucleus

Potential scattering described by nonrelativistic quantum scattering theory. For nonrelativistic neutrons, nuclei look point-like ( 푘푅nucl ≪ 1 ): • Isotropic scattering • Energy-independent A

Neutron wave function corresponding to the scattering process 푒푖 푘 푟 휓 푟 = 푒푖 푘 푥 − 푏 For a catalog, see 푟 www.ncnr.nist.gov/resources/n-lengths scattering X-section Surprisingly, almost all nuclei have 푏 > 0. 휎 = 4휋 푏2 Neutron interaction with a collection of nuclei

Incident neutron with energy E = ℏ푘 2/2푚

Nucleus number 푗

at position 푅푗

푖푘 푟 −푅푗 푖 푘 푥 푒 Self consistency of the wave function 휓 푟 = 푒 − 휓 푅푗 푏 푗 푟 − 푅푗

푖푘 푟 −푅푗 2 푒 Using the relation Δ + 푘 = −4휋 훿 푟 − 푅푗 푟 − 푅푗

2 We find the wave equation Δ + 푘 휓 푟 = 4휋 푏 훿 푟 − 푅푗 휓 푟 ≈ 4휋 푏 푛 휓 푟 푗 푛 is the nuclear density of the medium Neutron Fermi potential

Defining the Fermi potential of a medium The wave equation is a Schrodinger equation with the potential V 2 2휋ℏ ℏ2 푉퐹 = 푏 푛 − Δ + 푉 휓 푟 = 퐸 휓 푟 푚 2푚 퐹

For cold neutrons, bulk matter is characterized by its Fermi potential. We expect wave phenomena (refraction, reflection, tunnel transmission..).

Condition for total reflection of neutrons of energy E (Fermi & Zinn 1946) 2 퐸 sin 휃 < 푉퐹 Solid matter characterized

by the Fermi potential VF Exercises 1. Calculate the Fermi potential of Nickel 2. What is the maximum reflection angle on a Nickel surface for a cold neutron of wavelength 0.9 nm? Application: neutron guides ILL High Flux Reactor

Guide Hall Neutron distribution channel at ILL Many guides at the ILL, up to 100 m long Ultracold neutrons (UCNs)

Thermal neutrons, E=25 meV

Cold neutrons, E<25 meV

Neutrons with energy < 200 neV, are totally reflected by material walls. Ultracold neutrons E< 200 neV They can be stored in material bottles for long times (minutes). They are significantly affected by gravity.

23/22 UCN plumbing

UCNs are guided through evacuated stainless steel pipes (about 10 cm diameter) and bends. Losses are generally percents/meter Exercises

1. Calculate the velocity for an UCN with an energy of 200 neV

2. Calculate the De-Broglie wavelength of the same UCN

3. What is the proportion of UCNs (say E < 300 neV) in a Maxwell spectrum of thermal neutrons at 300 K?

4. A neutron is dropped at rest from a height of h = 1 m. What is the kinetic energy of that neutron when hitting the ground at h = 0? UCN and gravity

UCNs feel gravity 푉 푧 = 푚푔 푧 푉 푧 = 1 m = 102 neV

Very important for UCN techniques • We accelerate UCNs to detect them (otherwise they would bounce off the detector window). • Some UCN traps do not need a roof. • Lifting an experiment by 50 cm can modify significantly the outcome! Example: the “U” filter

If you want to remove UCNs with energy E<80 neV, Just set h = 80 cm UCNs and magnetic fields

Magnetic fields act on the Neutron magnetic moment spin ½ neutron 휇푛 × 1 T = 60 neV 푉 = −휇 푛 퐵

Input: unpolarized UCNs Magnetized foil Output: polarized UCNs

−휇푛퐵

+휇푛퐵 Summary about UCN interactions

UCNs can be manipulated using

• The nuclear force (Fermi potentials ~ 100 neV) • The gravitational force (1 m = 100 neV) • Magnetic fields (1T = 60 neV)

They are used to study the fundamental interactions and symmetries

• Weak interaction (beta decay period 10 min) • Electromagnetic properties of the neutron (EDM) • Gravitational effects UCN source at ILL

Turbine with counter rotating blades to decelerate the neutrons Superthermal production of UCNs in superfluid He

Input: intense beam of cold neutrons with a wavelength of 8.9 A The superfluid Helium needs to be cooled down to 0.7 K UCN source at the Paul Scherrer Institute

pulsed UCN source One kick per 5 min 600 MeV online since 2011 2.2 mA Worldwide comparison of UCN sources

3 techniques

• selection out of a thermal flux ILL PF2 source

• Superthermal production and accumulation in superfluid He ILL SUN-2, ILL GRANIT, TRIUMF

• Superthermal production in solid deuterium PSI, Los Alamos, Mainz (TRIGA)

Diter Ries standard stainless steel bottle 1. Neutrons and the precision frontier 2. Neutron optics, ultracold neutrons 3. Neutron detection 4. Fundamental physics with UCNs • Neutron lifetime • Electric dipole moment • Gravity with neutrons Importance of neutron detection

• Monitoring in nuclear reactors • Radiation safety • Detection of special nuclear materials (233U and 239Pu) • Cosmic ray detection, monitoring the flux

• Neutrino detectors 휈 + 푝 → 푒+ + 푛 • Most serious background in WIMP direct searches WIMP-induced nuclear recoil 휒 + 푁 → 휒 + 푁 similar to fast neutron – induced recoil n + 푁 → 푛 + 푁

Remember: You can’t directly detect neutrons… Neutrons should be converted in a detectable particle first. Neutron inelastic reactions

• Neutron capture 푛 + 퐴X → 퐴+1X∗ + 훾 a. k. a. X 푛, 훾

• Charged reactions 푛 + 퐴X → 푝 + 퐴Y a. k. a. X 푛, 푝 Y 푛 + 퐴X → 훼 + 퐴−3Y a. k. a. X 푛, 훼 Y

• Fission 235 푛 + U → 푃퐹1 + 푃퐹2 + 휈 푛 a. k. a. U 푛, 푓

One finds in tabulated THE 1/v LAW neutron data the 푣 휎(푣) = 휎 푣 0 thermal cross sections 0 푣 휎th = 휎 2200 m/s 퐴 퐴+1 (n,γ) capture: 푛 + 푍X → 훾 + 푍X

2 ퟒ Energy release 푄 = 푚푋 + 푚푛 − 푚푊 푐 All stable nuclei have Q>0 EXCEPT for 퐇퐞. a.k.a. the neutron separation energy Thus, ퟒ퐇퐞 is the only stable element with zero of the nucleus W. capture cross section for slow neutrons. 퐴 퐴 (n,p) reaction 푛 + 푍X → 푝 + 푍−1Y

Coulomb barrier ℏ푐 푍 − 1 퐵푐 = 훼 1/3 푅0 1 + 퐴

2 Energy release 푄 = 푚푋 + 푚푛 − 푚푝 − 푚푌 푐 Only one possibility 3 Slow neutrons undergo (n,p) reaction only if 푄 > 퐵푐 푛 + He → 푝 + 푡 퐴 퐴−3 (n,α) reaction 푛 + 푍X → 훼 + 푍−2Y ℏ푐 2 (푍 − 2) Coulomb barrier 퐵푐 = 훼 1/3 1/3 푅0 4 + (퐴 − 3)

Only two possibilities Energy release 푄 = 푚 + 푚 − 푚 − 푚 푐2 푋 푛 훼 푍 6 Slow neutrons undergo (n,α) reaction only if 푄 > 퐵푐 푛 + Li → 훼 + 푡 푛 + 10B → 훼 + 7Li Validity of the 1/v law

Capture on Cadmium

푣 휎(푣) = 휎 푣 0 0 푣 Three possible neutron convertors

3He (n,p) 6Li (n,훂) 10B (n,훂) Abundance 0.014 % 7.6 % 19.9 % 휎th 5330 barn 937 barn 3837 barn p 764 keV 훂 2.056 MeV 훂 1.47 MeV Kinetic energy t 191 keV t 2.728 MeV Li 0.84 MeV of products γ 0.48 MeV

Gaseous detectors 3 proportional counters filled with He or BF3

Solid detectors scintillators LiF silicon detectors with Boron solid conversion layer Exercises 1. Calculate the kinetic energy of the products for the reaction 푛 + 3He → 푡 + 푝 2. Consider a 1 cm thick multiwire proportional chamber filled with 1 bar of 3He. What is the detection efficiency for thermal neutrons? 3. The same detector is filled with 10 mbar of 3He, what is the detection efficiency for UCNs? For thermal neutrons? 1. Neutrons and the precision frontier 2. Neutron optics, ultracold neutrons 3. Neutron detection 4. Fundamental physics with UCNs • Neutron lifetime • Electric dipole moment • Gravity with neutrons The neutron beta decay lifetime

• Particle physics extracting CKM matrix element

• Astrophysics and Neutrinos Calculating weak semi-leptonic processes like + 푝 + 푝 → 푑 + 푒 + 휈푒 + 휈휇 + 푝 → 휇 + 푛

− 푛 → 푝 + 푒 + 휈푒 + 782 keV • Cosmology Predicting the Free neutron lifetime yields of the 휏푛 = 880.0 9 s BigBang [PDG 2013] Nucleosynthesis Two complementary experimental methods

Counting the dead neutrons: BEAM METHOD A detector records the decay products in a well defined part of a neutron beam. A neutron beam is indeed radioactive due to beta decay. 푑푁 푁 − = 푑푡 휏푛

Counting the surviving neutrons: BOTTLE METHOD UCNs are stored in a bottle, the number of neutrons remaining in the bottle after a certain storage time t is measured. 푁(푡) = 푁 0 푒−푡/휏푛 Early beam method: counting the electrons

Christensen et al (1972) Modern beam method: counting the protons

Nico et al (2005) Protons produced almost at rest (endpoint energy = 800 eV) are accumulated in a Penning trap. Principle of a bottle UCN measurement

STORAGE VOLUME Typical sequence 1. Switch moved to FILL position, VALVE Valve OPEN for 20 s 2. Close Valve, UCN Switch moved to EMPTY position SWITCH 3. Wait period T 4. OPEN Valve, count neutrons DETECTOR Repeat the sequence with different T UCN storage curve

Example: measured storage curve in the 20 L chamber of the EDM experiment

Problem: UCN losses 1 1 1 at wall reflection are = + not negligible. 휏푠푡 휏푛 휏푤푎푙푙 Estimating the wall losses

−4 The probability for a UCN to be lost at a wall collision 휇 ≈ 10 can be of the order of

The mean free path between collisions is of the order of 휆 ≈ 30 cm

The frequency of wall collisions for a velocity of 3 m/s 푣 is of the order of 푓 = ≈ 10 Hz 휆 The partial lifetime due to wall losses is thus of the 1 order of 휏 = ≈ 1000 s 푤푎푙푙 푓휇 Useful Clausius law

When mechanical equilibrium is Consider a bottle with achieved (isotropic velocity arbitrary shape, of distribution) the mean free volume V and surface S. path between wall collisions is 4 푉 휆 = 푆

Results valid 2푑 without gravity! 휆 = 3 푑ℎ 2푎푏ℎ 휆 = 휆 = 푑 2 + ℎ 푎푏 + 푎ℎ + 푏ℎ More on wall losses (complicated topic)

• The wall loss probability is energy- dependent 푉 퐸 푉 휇 퐸 = 2휂 asin − − 1 퐸 푉 퐸

• It depends on temperature (the colder the better) • Losses can be calculated from absorption and inelastic scattering cross section data. But measured losses are generally higher, due to surface impurities (hydrogen, in particular) Example: MAMBO 1 (ILL, 1989)

The trap geometry is varied, one extrapolates the storage time to infinite mean free path Current status on the neutron lifetime

The current situation There is a 3.8 σ discrepancy between the bottle method combination and the beam method combination.

To be continued… 1. Neutrons and the precision frontier 2. Neutron optics, ultracold neutrons 3. Neutron detection 4. Fundamental physics with UCNs • Neutron lifetime • Electric dipole moment • Gravity with neutrons Electric and Magnetic Dipoles

Spin precession due to Spin precession due to the magnetic dipole 흁풏 the electric dipole 풅풏?

퐻 = −휇푛 퐵 휎 푧 − 푑푛 퐸 휎 푧 56/25 Electric dipole violates time reversal invariance!

> PLAY > > PLAY >

< REWIND < < REWIND < Hunting the neutron Electric Dipole Moment

One measures the neutron Larmor precession frequency 풇푳 in weak Bagdetic and strong Electric fields 2 푓 ↑↑ − 푓 ↑↓ = − 푑 퐸 퐿 퐿 휋ℏ 푛 Neutron EDM

The most sensitive experiments use Ramsey’s method with polarized ultracold neutrons stored in a “precession” chamber Here a cylinder, Ø47 cm, H12 cm. 58/25 CP violation and baryogenesis

symmetric phase 1015 GeV 흓 = ퟎ Sakharov’s Baryogenesis Inflation ends? recipe (1967) T = 300 GeV • Baryon number not 100 GeV conserved Electroweak transition • Universe out of equilibrium boiling • Violation of CP symmetry 1 MeV > nEDM

1 eV T ≃ 100 GeV Decoupling of CMB Current nEDM bound 1 meV broken phase T = 20 GeV constrains many Today 흓 ≠ ퟎ scenarios of BSM electroweak baryogenesis

59 First EDM experiment with a neutron beam

Smith, Purcell and Ramsey, Phys. Rev. 108, 120 (1957) −20 푑푛 = −0.1 ± 2.4 × 10 푒 cm D: counter

A’: spin analyzer

Vary the RF frequency and measure the resonance C’ :Second RF pulse curve to extract 푓퐿. Do it for parallel and antiparallel E and B fields. Free precession in E and B fields ... Statistical sensitivity: C: Apply RF pulse ℏ A: spin polarizer π/2 spin-flip... 휎푑 = 푇 ≈ 1 ms 푛 2 훼 퐸 푇 푁 The slower, the better… UCN nEDM apparatus (Sussex/RAL/ILL)

−26 Apparatus installed at the Best limit: 푑푛 < 3 × 10 푒 cm ILL reactor Grenoble obtained with 1998 − 2002 data (1986-2009) [Baker et al, PRL (2006) ; Pendlebury et al, PRD (2015)] Scheme of the High voltage, E = ± 132 kV 12 cm apparatus 4 layers mu-metal shield at PSI Mercury lamp

photomultiplier

SWITCH UCN source 5T polarizer (SC magnet)

Spin flipper Iron analyser Problem: the analyzing foil

What is the optimal height of the analysing foil in the nEDM experiment? Iron, thickness 400 nm

The analyzing foil consists of a thin layer of Aluminum substrate, magnetized iron. The precession chamber, thickness 25 µm situated at height H above the analyzing foil, stores neutrons in the energy range 0 < E < 120 neV. Calculate the Fermi potential of non- magnetized iron. Suppose now that the foil is magnetized to a saturation field of Bs = 2 T. Neutrons with spin aligned with the magnetic field are dubbed low field seekers, those with spin anti-parallel with the magnetic field are dubbed high field seekers. • Calculate the Fermi potential of the magnetized foil for high and low field seekers. • Discuss the optimal height H to maximize the spin-analysis efficiency. • Estimate the transmission of the foil. Typical measurement sequence at PSI, 1 cycle every 5 minutes

Uncorrected neutron frequency 훾 - + - + - + - + - + - + 푓 = 푛 퐵 n 2휋

Mercury-corrected neutron frequency

훾Hg 푓 = 퐵 Hg 2휋

corr 푓푛 푓n ∝ 푓Hg The mercury co-magnetometer compensates for the residual magnetic field fluctuations 1. Neutrons and the precision frontier 2. Neutron optics, ultracold neutrons 3. Neutron detection 4. Fundamental physics with UCNs • Neutron lifetime • Electric dipole moment • Gravity with neutrons Bouncing neutrons

The vertical motion is a

simple quantum well problem Vertical energy (peV) energy Vertical ℏ2 푑2휓 − 2 + 푚푔푔푧 휓 = 퐸 휓 2푚푖 푑푧

Height (µm) We want to test Enstein’s equivalence principle for a quantum particle in a classical gravity field. Discovery of the quantum states at ILL Nesvizhevsky et al Nature 415 (2002) Problem: micrometric position sensitive detector

1. Calculate the Fermi potential of (i) natural boron (ii) pure 10B. Why do we have to use isotopically pure boron?

2. We choose a boron layer thickness of 200 nm. Discuss this choice in terms of neutron conversion efficiency (for UCNs of velocity 3 m/s), Si detector efficiency and spatial resolution.