Post on 29-May-2020
Ultracold neutrons and
interaction of waves
with moving matter
FLNP of JINR, Dubna, Russia
frank@nf.jinr.ru
ISINN 25 , 22-26 May, 2017
A.I. Frank
1
2A. Frank. ISINN 25, Dubna, 23 May 2017
Outline
1. Test of the dispersion law for neutron waves
in matter, “null” Fizeau experiments and
gravity UCN spectrometry.
2. Nonstationary diffraction by a moving grating
3. Accelerating medium effect
4. Neutron waves in accelerating medium
1. Test of the dispersion
law for neutron waves in
matter, “null” Fizeau
experiments and gravity
UCN spectrometry
3A. Frank. ISINN 25, Dubna, 23 May 2017
4
Effective potential is a basis of the
UCN optics
2 2
0k k 4 b
Dispersion law (UCN and VCN)
b b i constb
22U b const
m
A. Frank. ISINN 25, Dubna, 23 May 2017
with t (k)kb
4
Dispersion law (cold and thermal neutrons)
2 2
0k k 4 (C iC )(b ib ) V. F. Sears Phys. Rep., 82, 1 (1982)
M. Warner, J. E. Gubernatis
Phys. Rev. B.32, 6347, (1985)
2 2 3 3
0 0C 1 k a , C k a (k 0) 1/3 interatomic dia stan ce
For UCN 5 6C 10 10 ?) (
Nosov-Frank hypothesis:
region of applicability of the potential0k 4 a
V.G. Nosov, A.I. Frank. Phys. Rev. A. 55, 1129 (1997).
v 10cm / s
5A. Frank. ISINN 25, Dubna, 23 May 2017
2 2
0 (k )k 4 ?b How to test
If 2 2
0k k 4 b
then2 2
0k k 4 b
In the case of validity the potential
dispersion law (and only in this case)
movement the sample parallel to its
border do not affect the normal
component of the k-vector of the
refracted wave
4b
6A. Frank. ISINN 25, Dubna, 23 May 2017
Wafer
Rotating FP
interferometer
UC
N
Idea of the experiment – rotating Fabry-
Perrot interferometer
2
0
2
0
2 2
0
2 2
0
k k 4 b
k k 4 b
(k )
(k )
A.I .Frank, V.G.Nosov. Phys. At. Nuc., 58, 402 (1995)
Fizeau-type experiment with neutron
Interferometer (Arif et al. 1989)
7
UCN spectrometer with Fabry-Perot
interferometersTwo NIFs with variable
distance between them mg=1.02 neV
1 00 200 3 00
0,0
0,2
0,4
0,6
0,8
1,0
Tra
nsm
issi
on
Energy (neV)
0 5 10 15 20 25 30 35
0
5
10
15
20
25
30
Co
un
t ra
te
Distance between the filters (cm)
Mesured in 2007
Detector
A. Frank. ISINN 25, Dubna, 23 May 2017
8
19972009
A. Frank. ISINN 25, Dubna, 23 May 2017
9
Deformation of the scaning curve
at spinning (variation of the lateral neutron velocity)
10 15 20 25 30 35
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6 Filter at rest
Filter is moving
Co
un
t/s
Distance between filters (cm)
10 15 20 25 30 35 40
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4 Filter at rest
Filter is moving
Co
un
t/s
Distance between filters (cm)
10 15 20 25 30 35
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
Count/
s
Distance between filters (cm)
Decreasing of intensity and displacement 1997-1999гг
1010E eV
A. Frank. ISINN 25, Dubna, 23 May 2017
10
Possible explanation of the effect: resonant
scattering and the shift of the transmission line
98 100 102 104 106 108 110 112 114 116
-0,4
-0,2
0,0
0,2
0,4
0,6
0,8
1,0
Tra
nsm
issio
n &
In
t.cro
ss-s
ecti
on
(arb
. u
nit
s)
Energy (neV)
Transmission
Interference cross-section
in Forward direction
k
fk
k
fk
1. The huge enhancement of the scattering
amplitude at inhomogeneities in resonant
conditions
f 12
mf(k ,k) (r)V (r) (r)dr
2
2. The interference of the forward scattering and
transmitted waves
*
ts t t
4Im T f(k ,k )
k
0 2 4 6 8 10 12 14
100
102
104
106
108
110
112
114
Ti/ZrTi/Zr
Ni(N)Ni(N)Ni(N)
En
erg
y, n
eV
Coordinate 10-6 cm
0
12,75
25,50
38,25
51,00
63,75
76,50
89,25
102,0
A.I.Frank et al. JINR Communication E3 -204-216
A. Frank. ISINN 25, Dubna, 23 May 2017
11
Optics of highly absorbed matter
1. Neutron reflection from the Gd mirror and the measurement of the bcoh for Gd
3 4 5 6 7 8
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
Refl
ecti
vit
y
Wave length (A)
Angle 4.88 mrad
Angle 3.78 mrad
Simulation with b0=11.5f
b0 = 11,5 0,7 f
Re(b)UCN = 5.8 0.7f Im(b)=10.4f
22U b V iW
m
V 45 neV, W 82neV
2. Test of the theory – transmission of the Gd samples
I.M.Frank, 1974
A. Frank. ISINN 25, Dubna, 23 May 2017
A. I. Frank, V. I.Bodnarchuk, P. Geltenbort, et al.,. Phys. At. Nuc., 66, 1831 (2003)
A.I.Frank, V.I.Bodnarchuck, G.V.Kulin and O.V. Kulina.
JINR Communication Р3-2002-288 (2002)
12
Test of the 1/v Law for the absorption cross-section
of UCNs in Gadolinium. Rotating sample
A. Frank. ISINN 25, Dubna, 23 May 2017
A. I. Frank, P. Geltenbort, G. V. Kulin and A. N. Strepetov. JETP Letters, 84 (2006), 105–109.
Gd- film
UCN
Si wafer
Monochromator
The capture cross-section of natural Gd satisfies to 1/v law when neutron velocity
increases from 4.5 till approximately 35m/s within the accuracy of 0.5%
Count rate variation at decreasing of the
spinning frequency from 90 to 3 Hz.
22U b V iW const
m
13
G.V.Kulin, A.N.Strepetov, A.I.Frank, et al., Phys. Lett. A, 378, 2553(2014)
New test of the dispersion law for very slow
neutrons
The variation of count rate with increasing rotational
speed of the sample from 3 to 100 rotations per second
For the representation
22 1U m J b J J iJ
33 10J
𝛿𝐽″ ≤ 3 × 10−8
33 10J b b
3n n (0.6 1.4) 10
38 m/s v 6
A. Frank. ISINN 25, Dubna, 23 May 2017
2. Nonstationary
diffraction by a moving
grating
14A. Frank. ISINN 25, Dubna, 23 May 2017
V
0 0exp i k z t
?
J. Felber, R. Gähler, R. Golub, 1988
V.G. Nosov and A.I.Frank, 1991
15
Neutron diffraction by a moving grating.
Initial formulation of the problem.
A. Frank. ISINN 25, Dubna, 23 May 2017
s ss
exp i kx t exp i k x ts
1 1 1
2 2 1
s
(2s 1)
T
Elementary (kinematic) theory
jj
jjj(z,y, t) a exp[i( t ]qk z y )
02
jq j jq
d
1
2
0
0
1j
k jk
2. Galilean transformation of the wave function.
1. Solving the diffraction problem in a moving
system.
d – space period of a grating
0jj
22 2f
T
V
d
0 1 2j , , ....
0(k L 1)
A.Frank, V.Nosov, 1994
V
k
n = -1
n = +1n = 0
k
k
16A. Frank. ISINN 25, Dubna, 23 May 2017
Experimental realization - rotating grating
UCN
Monochromator
Phase π -grating
where N is number of grooves
n
L
h
k(n 1)h
E
1-1
ΔE= ΩΔE= Ω
h = 0.14 mkm
17A. Frank. ISINN 25, Dubna, 23 May 2017
First experimental results
0 5 10 15 20 25 30 35 40 45
0,2
0,4
0,6
0,8
1,0
1,2
Co
un
t/se
c
Distance between the filters, cm
Slow spinning (3Hz)
Fit by Gaussian
Fast spinning (89.6 Hz)
Theory
Splitting of the spectrum
A.I.Frank et al. ILL annual report 2001
Phys.Lett.A 311 (2003) 6
0 5 10 15 20 25 30 35 40 45
0,6
0,8
1,0
1,2
1,4
1,6
1,8
2,0
2,2
2,4
2,6
0 5 10 15 20 25 30 35 40 45
0,6
0,8
1,0
1,2
1,4
1,6
0 5 10 15 20 25 30 35 40 45
0,6
0,8
1,0
1,2
1,4
1,60 5 10 15 20 25 30 35 40 45
0,6
0,8
1,0
1,2
1,4
1,6
A=1.679± 0.022
7Hz
A=1.69± 0.047
60 Hz
A=1.579± 0.033
99 Hz
Co
un
t ra
te (
c/se
c)
Distance between the filters (cm)
A=1.657± 0.076
80 Hz
2
10 383 8
expa . ( )
2
10 405
tha .
A.I.Frank et al.Jetp Lett, 81 (2005) 427
Angular period of grating 0.3325mrad (20μ at the middle diameter)
Detector
Monochromator
grating
Analyzer
18A. Frank. ISINN 25, Dubna, 23 May 2017
Neutron focusing in time
0,00 0,01 0,02 0,03
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
Co
un
t ra
te (
Arb
.un
its)
Time(sec)
19A. Frank. ISINN 25, Dubna, 23 May 2017
Time lens is working!
0 10 20 30 40 50
0
500
1000
1500
2000
2500
3000
CO
UN
TS
Number of channels
Measured in March 2004
Background
Witdth of the channel is 214 sec
10.3 msec
3.8 msec
A. I. Frank, P. Geltenbort, G. V. Kulin et al. JETP Lett. 78, (2003) 188
S.N. Balashov, I.V. Bondarenko, A.I. Frank et al, Physica B, 350 (2004) 246
20A. Frank. ISINN 25, Dubna, 23 May 2017
21
E tm b
t t
a
tt
a
vt t t
a
( ) .
2 0
2 2
1 2, , , - a
bM,M
A.Frank.R.Gähler, 1996
SS
A. Frank. ISINN 25, Dubna, 23 May 2017
Neutron time focusing from the pulse source - re-bunching
Test of the weak equivalence principle for neutrons
(2006)
H
E0 E
E
H
The idea was to compare the change of energy mgH
with energy ħΩ transferred to neutron by a moving grating
g n
ΔΩm g =
ΔH
g
A.I. Frank, P. Geltenbort, M. Jentschel, et al. JETP Letters, 86, 225 (2007)
Frank A.I., Masalovich S.V., Nosov V.G. (ISINN-12). E3-2004-169, 215, Dubna, (2004)
22
3loc
n
g1 (1.8 2.1) 10
g
A. Frank. ISINN 25, Dubna, 23 May 2017
Contradictions with kinematic theory (2006-2012)
1. Intensity of the first order DEPENDS on the velocity of the grating
2. The first order line is remarkably wider than initial spectrum
3. The presence of the zero diffraction order was detected
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44
1,0
1,5
2,0
2,5
3,0
3,5
4,0
Co
un
t ra
te (
c/s
ec
)
Distance betwee the filter (cm)
f=45Hz
f=55Hz
f = 64 Hz
f =75Hz
f =95Hz
f =105Hz
Scanning curves of the -1 diffraction order measured
at different frequencies of the grating rotation
23
E
2E
0E
A. Frank. ISINN 25, Dubna, 23 May 2017
Multiwave dynamic theory V.А. Bushuev, A.I. Frank, G.V. Kulin.
JETP , 122, 32 (2016)
24A. Frank. ISINN 25, Dubna, 23 May 2017
TOF Fourier spectrometer (2014-2016
G.V. Kulin, A.I. Frank, S.V. Goryunov et al.,
NIM A, 869 (2016) 67
70 80 90 100 110 120 130 140 150 160
0
1
2
3
4
5
6
+1 1500 rpm
Int (a
rb.u
n)
Energy (nev)
0
-1
60 80 100 120 140 160 180
0
1
2
3
4
5
3600 rpm
Int (a
rb.u
nits)
Energy (nev)
0
-2
-1 +1
+2
20 40 60 80 100 120 140 160 180 200
0
1
2
3
4
5
4800 rpm
Int (a
rb.u
nits)
Energy (neV)
-2+2
-1 +1
0
TOF Fourier spectrometry and comparing obtained spectra
with dynamic theory of neutron diffraction
Angular period of grating
0.0665mrad
(4μ at the middle diameter)
V.А. Bushuev, A.I. Frank, G.V. Kulin. JETP , 122, 32 (2016)
G.V. Kulin, A.I. Frank, S.V. Goryunov, et al. Phys. Rev.A 93033606, (2016)
25A. Frank. ISINN 25, Dubna, 23 May 2017
26
20 40 60 80 100 120 140 160 180 200
0,000
0,005
0,010
0,015
0,020
0,025
-2
-1
+2Int (a
rb.u
nits)
E(nev)
4800 RPM
0
+1
20 40 60 80 100 120 140 160 180 200
0
1
2
3
4
5
4800 rpm
Int
(arb
.un
its
)
Energy (neV)
-2+2
-1 +1
0
h=0.14 mkm
h=0.22 mkm
A. Frank. ISNN 25, Dubna, 23 May 2017
FLNP Annual report, 2016
Observation of the theoretical predicted dependence of the
diffraction orders on the depth of groves
V.А. Bushuev, A.I. Frank, G.V. Kulin.
JETP , 122, 32 (2016)
3. Accelerating medium
effect
27A. Frank. ISINN 25, Dubna, 23 May 2017
28
n
V=0
0 0exp i k x t 0 0
exp i k x t i
0 0exp i nk x t
0nk L
L 0 0k L
Transmission of wave through a refractive sample
(sample in rest)
After transmission through a stationary sample
wave number is exactly equal to the initial one
A. Frank. ISINN 25, Dubna, 23 May 2017
29
Refraction of wave at the border of the moving matter
Massive particle (neutron)
0
0
11
i
n Vk nk
n v
0 0 vn n(k ) n k k
0
0
mvk
0 01
in k V
Doppler shift
0 0i k x te
V
i ii k x te
n
0
1V
v
0c v
Light
00k
c
ph 2
c 1v v 1
n n
1V
c
Fresnel drag
A. Frank. ISINN 25, Dubna, 23 May 2017
30
Transmission of a wave through the moving sample
(constant velocity)
When the wave enters into the sample from free space, the
frequency of the wave suffers frequency shift. When the wave
comes out of the medium into free space, the frequency of the
wave suffers an inverse frequency shift. For the constant-
velocity motion, these two frequency shifts cancel each other.
V i ii k x te
n
0 0i k x ti (V )e e 00i k x t
e
V=const
A. Frank. ISINN 25, Dubna, 23 May 2017
31
For the accelerated motion, two frequency shifts do not cancel
because the velocity of the medium is not constant.
Transmission of wave through the sample
(accelerated motion)
V=wt
i ii k x te
n
f fi k x ti (t )e e
00i k x te
0f
A. Frank. ISINN 25, Dubna, 23 May 2017
32
Spectrometric experiment
10 15 20 25 30
0,0
0,5
1,0
1,5
2,0
2,5
3,0
= 6,5 nevC
ount
rate
(arb
. u
nits)
Distance between the filters (cm)
Variation of the UCN energy
Variation of the count rate
E ≈ (2-5)10-10 eV
Periodically variation of the neutron energy, caused by the sample
acceleration, leads to the periodical oscillation of the count rate
m
s
a
Detector
A. Frank. ISINN 25, Dubna, 23 May 2017
33
Oscillation of the count rate and
experimental result
0,000 0,005 0,010 0,015 0,020 0,025
0,90
0,95
1,00
1,05
1,10
Point 22.0
Measured 21July
Count rate 7.26 0.08
No
rma
lize
d c
ou
nt ra
te
Time (sec)
f(t) 1 Bsin( t )
Frequency f = 40, 60 Hz
Oscillation period 0.025, 0.017 sec
Time of flight 0.11 sec
0.2 neV
2 1E mA L 1 sin t
nK
0 94 0 06K . . A.I. Frank, P.Geltenbort, G.V.Kulin, et al, Phys. At. Nuclei, 71 (2008) 1656.
A. Frank. ISINN 25, Dubna, 23 May 2017
2 2
maxw A 60m / s
34A. Frank. ISINN 25, Dubna, 23 May 2017
35
2w A sin t
V A cos t
max
max
wV
Observation of the weak time focusing due to
Accelerating Medium Effect
t
L
t
a
t
L
t
a
t
L
t
a
mm
s
DetectorDetector
mm
s
DetectorDetector
mm
s
DetectorDetector
mm
s
DetectorDetector
20 30 40 50 60 70 80 90 100 110
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
Am
plit
ud
e o
f th
e c
.r. m
od
ula
tio
n
1.1 V
Normalised Full geometry
Null geometry
Frequency, Hz
The amplitude of the count rate modulation was measured
for the set of Ω at AΩ2 = const
A. Frank. ISINN 25, Dubna, 23 May 2017
36
• Experimental results obtained by two different
methods manifest that neutron really changes their
energy at the passing the accelerating sample.
Agreement with theory was about ~10% or better
• Existing theory of the acceleration medium effect for
neutrons based on the assumption of an identity of
the dispersion law for neutron waves in a rest and
accelerating media. This assumption is unlikely
correct at large accelerations
4. Neutron waves in
accelerating medium
37A. Frank. ISINN 25, Dubna, 23 May 2017
38
Where is region of validity of the usual dispersion law?
A. Frank. ISINN 25, Dubna, 23 May 2017
2 2
0k k 4 b (??)
Matter in restMatter is moving with acceleration.
Non- inertial system
Waves in accelerating matter
Phase shift kb inkxe
39
Region of validity of the usual dispersion law
in the accelerating medium
for x ≈ interatomic distance d
For UCN E ≈ 100nev (UCN), b ≈ 510-13cm, a ≈ 510-8cm
W crit= 8107 cm/s2 ≈ 8104 g
2
4
Ebw
md
A.I.Frank. (ISINN-21). Alushta, Ukraine, 2013. JINR E3-2014-13, Dubna, 2014, pp. 63-66
A.I.Frank. JETP Letters., 100, 613 (2014)
A. Frank. ISINN 25, Dubna, 23 May 2017
14
critW E(ev) 8 10
The hypothesis is that usual dispersion law is valid if phase distortion
due to accelerating appeared at the interatomic distance is much less
than the phase shift kb due to scattering at the nuclei
mwxkx 1
2E
2
w
mwxk
2E
40A. Frank. ISINN 25, Dubna, 23 May 2017
Is this hypothesis contradict any experimental results ?
Two types
of experiments:
There are not experiments which contradict to the hypothesis of
critical acceleration in neutron optics !
41
2.2 = MHz
A = 5-6 nmAcceleration w ≈ 105 g Wcrit
Proposed experiment 1. (in stage of preparation)
A. Frank. ISINN 25, Dubna, 23 May 2017
Simulation of the wave packet
transmission through the vibrating
Fabry-Perot Interferometer/
See posters of M. Zakcharov et al.
and of S.Goryunov
42
Proposed experiment 2.
Neutron reflection from standing acoustic waves. Acceleration of surface 5 10 10
Thermal neutrons: Wcrit 1012UCN: Wcrit 108
Detector
UCN
Sample with surface
standing waves
Ni foil
Talk of G. Kulin
this afternoon
0,0 0,2 0,4 0,6 0,8 1,0
0,0
0,2
0,4
0,6
0,8
1,0
1,2
+/-
re
flecte
d (
Deg
)
incident
(Deg)
-/+
-/-
Зеркальный
пучок
A. Frank. ISINN 25, Dubna, 23 May 2017
P. Geltenbort, P. Høghøj, M. Jentschel
Acknowledgements to co-authors
V.I.Bodnarchuck, S,V.Gorunov, G.V.Kulin, D.B. Kustov, M.A.Zakcharov.
S.N. Balashov, S.V.Masalovich, S.V.Masalovich, V.G.Nosov, A.N.Strepetov
V.А. Bushuev
Thank you for your attention!43
B. Lauss, P. Schmidt-Wellenburg
A. Panzarella and Y. Fuchs
Yu. Khaydukov
D. Roshchupkin, D. Irzhak