Experiments with ultracold neutrons
Ultracold neutrons (UCN) form a tiny low-energy fraction in Maxwelian spectrum of thermal neutrons in moderators of nuclear reactors and spallation sources. Their energy is extremely small (~10⁻⁷ eV), their velocity is a few meters per second, and their effective temperature is as low as ~1 mK. Spec...
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irk-123456789-1185432017-05-31T03:07:41Z Experiments with ultracold neutrons Nesvizhevsky, V.V. 8th International Conference on Cryocrystals and Quantum Crystals Ultracold neutrons (UCN) form a tiny low-energy fraction in Maxwelian spectrum of thermal neutrons in moderators of nuclear reactors and spallation sources. Their energy is extremely small (~10⁻⁷ eV), their velocity is a few meters per second, and their effective temperature is as low as ~1 mK. Specific feature of UCN consists of their nearly total elastic reflection from nuclear-optical potential of many materials at any incidence angle; therefore they could be stored in closed traps for many minutes, thus they could be used for extremely sensitive measurements. A fraction of UCN in the thermal neutron flux is as low as 10⁻¹¹–10⁻¹², and serious efforts are undertaken all over the world to produce UCN in larger amounts. UCN are widely used in precision particle physics experiments. Applications of UCN are emerging in surface and nanoparticle physics. Here we will focus on recent advances in the field. 2011 Article Experiments with ultracold neutrons / V.V. Nesvizhevsky // Физика низких температур. — 2011. — Т. 37, № 5. — С. 471–476. — Бібліогр.: 107 назв. — англ. 0132-6414 PACS: 14.20.Dh, 03.75.Be, 29.25.Dz http://dspace.nbuv.gov.ua/handle/123456789/118543 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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8th International Conference on Cryocrystals and Quantum Crystals 8th International Conference on Cryocrystals and Quantum Crystals |
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8th International Conference on Cryocrystals and Quantum Crystals 8th International Conference on Cryocrystals and Quantum Crystals Nesvizhevsky, V.V. Experiments with ultracold neutrons Физика низких температур |
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Ultracold neutrons (UCN) form a tiny low-energy fraction in Maxwelian spectrum of thermal neutrons in moderators of nuclear reactors and spallation sources. Their energy is extremely small (~10⁻⁷ eV), their velocity is a few meters per second, and their effective temperature is as low as ~1 mK. Specific feature of UCN consists of their nearly total elastic reflection from nuclear-optical potential of many materials at any incidence angle; therefore they could be stored in closed traps for many minutes, thus they could be used for extremely sensitive measurements. A fraction of UCN in the thermal neutron flux is as low as 10⁻¹¹–10⁻¹², and serious efforts are undertaken all over the world to produce UCN in larger amounts. UCN are widely used in precision particle physics experiments. Applications of UCN are emerging in surface and nanoparticle physics. Here we will focus on recent advances in the field. |
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Article |
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Nesvizhevsky, V.V. |
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Nesvizhevsky, V.V. |
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Nesvizhevsky, V.V. |
| title |
Experiments with ultracold neutrons |
| title_short |
Experiments with ultracold neutrons |
| title_full |
Experiments with ultracold neutrons |
| title_fullStr |
Experiments with ultracold neutrons |
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Experiments with ultracold neutrons |
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experiments with ultracold neutrons |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2011 |
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8th International Conference on Cryocrystals and Quantum Crystals |
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http://dspace.nbuv.gov.ua/handle/123456789/118543 |
| citation_txt |
Experiments with ultracold neutrons / V.V. Nesvizhevsky // Физика низких температур. — 2011. — Т. 37, № 5. — С. 471–476. — Бібліогр.: 107 назв. — англ. |
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Физика низких температур |
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| fulltext |
© V.V. Nesvizhevsky, 2011
Fizika Nizkikh Temperatur, 2011, v. 37, No. 5, p. 471–476
Experiments with ultracold neutrons
V.V. Nesvizhevsky
Institut Laue-Langevin, 6 rue Jules Horowitz, Grenoble F-38046, France
E-mail: nesvizh@ill.fr
Received December 12, 2010
Ultracold neutrons (UCN) form a tiny low-energy fraction in Maxwelian spectrum of thermal neutrons in
moderators of nuclear reactors and spallation sources. Their energy is extremely small (~10–7 eV), their velocity
is a few meters per second, and their effective temperature is as low as ~1 mK. Specific feature of UCN consists
of their nearly total elastic reflection from nuclear-optical potential of many materials at any incidence angle;
therefore they could be stored in closed traps for many minutes, thus they could be used for extremely sensitive
measurements. A fraction of UCN in the thermal neutron flux is as low as 10–11–10–12, and serious efforts are
undertaken all over the world to produce UCN in larger amounts. UCN are widely used in precision particle
physics experiments. Applications of UCN are emerging in surface and nanoparticle physics. Here we will focus
on recent advances in the field.
PACS: 14.20.Dh Protons and neutrons;
03.75.Be Atom and neutron optics;
29.25.Dz Neutron sources.
Keywords: ultracold neutrons, fundamental physics, quantum phenomena.
Introduction
The present contribution is based on a talk given at the
School of Young Scientists carried out during 8th Confe-
rence on Cryocrystals and Quantum Crystals in Chernogo-
lovka, Russia, on 26–31 July 2010. This contribution
presents the physics with ultracold neutrons; particular
attention is paid to recent advances related to the domain
of interest of the author of present contribution.
Ultracold neutrons (UCN) [1–4] form a tiny low-energy
fraction in Maxwelian spectrum of thermal neutrons in
moderators of nuclear reactors and spallation sources.
Their energy is extremely small (~10–7 eV), their velocity
equals a few meters per second only, and their effective
temperature is as low as ~1 mK. Specific feature of UCN
consists of their nearly total elastic reflection from the nuc-
lear-optical potential of many materials at any incidence
angle; therefore they could be stored in closed traps for
extended period of time, thus they could be used for ex-
tremely sensitive measurements. UCN characteristic pene-
tration depth is close to its wavelength and equal to a few
tens nanometers. Very cold neutrons (VCN) with typical
energy of 10–7–10–4 eV are totally reflected from flat sur-
face only if the incidence angle is sufficiently small; so
that the neutron longitudinal velocity component is lower
than the material critical velocity. As a fraction of UCN in
the thermal neutron flux is as low as 10–11–10–12, serious
effort are undertaken all over the world to produce UCN in
larger amounts, using super-thermal UCN sources or even
equilibrium cooling of neutrons [5–20]. UCN are widely
used in precision particle physics experiments [21], such
as, for instance, searches for additional fundamental short-
range forces [22–28], searches for non-zero neutron elec-
tric dipole moment [29,30], precision neutron lifetime
measurements [31–36] and constrains for the neutron elec-
tric charge [37,38]. Applications of UCN are emerging in
surface and nanoparticle physics [39,40]. We focus on re-
cent advances in the field including observation of the cen-
trifugal quantum states of neutrons. Combined with obser-
vation of the gravitationally bound quantum states of neu-
trons, this phenomenon provides the first demonstration of
the weak equivalence principle for an object in a quantum
state [41,42]. Also we will present a new spectrometer
GRANIT constructed for precision studies of the gravita-
tionally bound quantum states of neutrons and for other ap-
plications in particle physics, quantum optics, and in sur-
face studies [43]. A promising methodical development in
the field consists of building neutron reflectors based on
nanostructured materials [44–46]. Finally, unique proper-
ties of UCN allow using them for experimental studies of
motions of weakly bound nanoparticles [13,47].
V.V. Nesvizhevsky
472 Fizika Nizkikh Temperatur, 2011, v. 37, No. 5
Centrifugal and gravitational quantum states of
neutrons
Lift a ping-pong ball to a height 0H above table and let
it gently falling down. The ball will accelerate in the
Earth’s gravity field to the velocity 0 02V gH= , g is the
gravitational acceleration; then it will reflect from the table
surface. In case of perfectly elastic reflection in vacuum,
the ball would return back to surface due to gravity after
the period of 0 0 0( ) 8 / ;H H gΔτ = then it would continue
bouncing with the frequency 0 0 0 0( ) 1/ ( )H Hν = τ =
0g / 8 H= . The smaller 0 ,H the larger 0ν : 0 (1 m)ν ≈
010≈ Hz, 1
0 (1 cm) 10ν ≈ Hz, 2
0 (100 μm) 10ν ≈ Hz. The
frequency 0ν does not depend on the ball mass M.
Imagine another experiment (Fig. 1). A table is moving
together with a spaceship with the acceleration = −a g far
from large gravitating masses; the table surface is perpen-
dicular to g. An observer in the spaceship will see a ball
bouncing on the table with the same frequency 0ν as it
does in the previous experiment (an observer in the rest
frame will see the table accelerating towards the ball). This
is a consequence of the weak equivalent principle verified
with amazing accuracy of 12~ 10− for macroscopic objects
[48], and with the accuracy of 4~ 3·10− for a classical ele-
mentary particle [49].
What would happen in the two experiments at very
small heights 0 ?H Would be these two problems still
equivalent? Would the frequency seek to infinity? No, the
frequency would increase only if 0H exceeds the quan-
tum-mechanical limit 0
QMH that could be estimated using
Heisenberg coordinate-momentum uncertainty relation:
00 2 2QM QMM gHH ≈ π , where is the Planck constant.
For a ball in the Earth’s gravitational field the value 0
QMH
is too small. However, quantum effects for an elementary
particle, for instance, for a neutron, could be observed at
relatively large height of 0 10QMH m≈ μ [41,50,51]. The
condition separating quantum and classical behavior of
UCN above mirror is defined by a ratio of a neutron quan-
tum state width nEδ (reciprocal neutron lifetime 1
n
−τ in nth
quantum state) and an energy difference between neighbor
quantum states 1, 1n n n nE E E+ +Δ = − (i.e. the energy-time
uncertainty relation , 1 2 )n n nE +τ Δ ≈ π . The transition from
a classical case to a quantum one is considered, for in-
stance, in Refs. 52,53.
In a quantum limit, we do not consider trajectories,
heights, velocities; a frequency is defined by an energy as
00 /(2 )QM Eν ≈ π , and a characteristic height 0
QMH de-
pends on mass. In accordance with the weak equivalence
principle, an effective centrifugal potential [42,54] is local-
ly equivalent to gravity. Thus objects do not fall in gravita-
tional field and they do not move in an accelerated refer-
ence system universally: massive objects could behave
classically while light objects exhibit quantum properties at
equal distances to mirror. Nevertheless, the weak equiva-
lence principle holds: it means in our case that neutron
quantum states in gravitational and centrifugal potentials
are equivalent if accelerations are equal.
A general solution of Schrödinger equation for a par-
ticle above mirror attracted by linear potential was found in
1920th [55]. Nevertheless, it was regarded for a long time
just as a beautiful quantum-mechanical text-book problem
[56–62]. However, conditions corresponding to this idea-
lized problem have been realized recently in experiments
with slow neutrons in gravitational [41] and centrifugal [42]
potentials in Institut Laue-Langevin, Grenoble, France. Due
to limited space, we do not present these experiments in
detail here, but refer our readers to detailed overviews [63,64],
or/and to many other relevant publications [50,51,65–78].
GRANIT spectrometer
Further, more precise studies of gravitational and cen-
trifugal quantum states of neutrons will continue in an ad-
vanced GRANIT spectrometer that is currently under com-
missioning in Institut Laue-Langevin in Grenoble, France
[43,79]. GRANIT is a follow-up project based on a second-
generation UCN gravitational spectrometer with ultra-high
energy resolution. The studies will focus on applications of
these phenomena in fundamental particle physics, surface
studies, methodical applications, and reflectometry with
UCN as well as in quantum optics.
Basic advantages of the new GRANIT spectrometer in-
clude 1) much longer observation time of neutrons in a
closed specular trap [72,80–82] thus much better precision
in energy measurements; 2) the method of resonance tran-
sitions between the gravitationally bound quantum states of
neutrons [72,79]; 3) increase in UCN density using dedi-
cated 4He UCN source [20] delivering UCN to the spec-
trometer with no significant dilution of phase-space density
Fig. 1. The quantum behavior of an object above mirror in the
gravity field and that in the accelerating reference system is illu-
strated schematically. The ball heights correspond to its most
probable positions; the scale corresponds to the neutron mass, we
consider 5th quantum state.
Height over
mirror
40 m�
30 m�
20 m�
10 m�
Experiments with ultracold neutrons
Fizika Nizkikh Temperatur, 2011, v. 37, No. 5 473
[83,84]; 4) profiting from a permanent installation of the
spectrometer in a more comfortable experimental envi-
ronment; 5) using polarized neutrons and polarization
analysis.
Nanoparticle reflectors for slow neutrons and studies
of weakly bound nanoparticles
Significant advance in using nano-structures in UCN
physics on one hand and in studying nanoparticles and
nano-structures using UCN on the other hand is due to
fortunate coincidence of some their characteristic parame-
ters [13]. Thus, under certain conditions, the neutron wave-
length is close to nanoparticles size, simultaneously the
neutron velocity is about equal to the thermal velocity of
nanoparticles.
Recently, powders of diamond nanoparticles have been
used efficiently as the first VCN reflectors in the complete
velocity range from UCN to up to ~160 m/s, thus bridging
the energy gap between efficient reactor reflectors for
thermal and cold neutrons, and optical neutron-matter po-
tential for UCN (see Fig. 2) [13,44,85]. Moreover, VCN
could be stored in traps with nano-structured walls in some
analogy to storage of UCN in traps [45]. Diamond, with its
exceptionally high optical nuclear potential and low ab-
sorption cross-section, is a particularly suitable material for
this application. Formation of diamond nanoparticles by
explosive shock was first observed 50 years ago [86].
These particles measure a few nanometers. They consist of
a diamond nucleus (with a typical diamond density and
optical nuclear potential) within an onion-like shell of a
complex chemical composition [87] (with significantly
lower optical potential). The use of nanoparticles with the
characteristic size of a few nanometers is needed to pro-
vide a sufficiently large cross-section of coherent interac-
tion and inhomogeneity of the reflector density on a spatial
scale of about the neutron wavelength. A large number of
diffusive large-angle neutron-nanoparticle scattering events
needed to reflect VCN from powder constrains the choice
of materials: only low absorbing materials with high opti-
cal potential are appropriate.
Studying so-called anomalous losses [88] of UCN from
traps (providing an obstacle for precision neutron lifetime
experiments) we observed a surprising phenomenon: the
energy of stored UCN increased by ~10–7 eV with the
probability of ~10–8–10–5 per collision [89]; this value
exceeded any theoretical expectations by many orders of
magnitude. If the neutron energy after such inelastic scat-
tering exceeds some critical value it would escape from the
trap. This small heating of UCN has been studied over the
last years both on solid surfaces (stainless steel, copper,
beryllium etc) and on liquid surfaces (different kinds of
hydrogen-free oils) [47,89–98]. Only the scattering of
UCN at weakly bound nanoparticles on surface with a size
of ~10 μm can explain the experimental data obtained [13].
To our knowledge, such quasi-elastic scattering of UCN
provides unique opportunity to measure slow motions of
nano-objects as well as to study their interaction with sur-
faces and with each other. Impurity gels [99–105] provide
an interesting object to study using neutron techniques, as
well as a tool to reflect and even to slow down neutrons
[13,106,107] using the observed earlier quasi-elastic ref-
lection of slow neutrons.
Summary
We presented recent experiments with UCN and dis-
cussed further prospects in the field. These studies as well
as many other applications of slow neutrons are rapidly
progressing.
The author is sincerely grateful to all colleagues contri-
buted to the studies overviewed here, in particular to
GRANIT collaborators. These experiments are supported
in part by GRANIT collaboration, by ANR (Agence Na-
tionale de la Recherche, France), and the Federal program
“Scientific and pedagogical cadres of innovative Russia”.
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