ultracold neutrons and interaction of waves with moving...

Ultracold neutrons and

interaction of waves

with moving matter

FLNP of JINR, Dubna, Russia

[email protected]

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


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


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


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


8

19972009


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


10 15 20 25 30 35

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

Count/

s


Decreasing of intensity and displacement 1997-1999гг

1010E eV


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


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. 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. 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


2. Nonstationary

diffraction by a moving

grating


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.


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


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


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)


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


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)


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


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


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


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


Multiwave dynamic theory V.А. Bushuev, A.I. Frank, G.V. Kulin.

JETP , 122, 32 (2016)


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)


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


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


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


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


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


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)


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


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.


2 2

maxw A 60m / s

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


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


38

Where is region of validity of the usual dispersion law?


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)


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


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)


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


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

ultracold neutrons and interaction of waves with moving...

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