potential for measurement of the tensor electric and magnetic polarizabilities of the deuteron and...
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Potential for measurement of the tensor electric and magnetic polarizabilities of the deuteron
and other nuclei in experiments with polarized beams
Alexander J. SilenkoResearch Institute for Nuclear Problems
of Belarusian State University
18th International Spin Physics SymposiumCharlottesville 2008
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OUTLINE
Overview Measurement of tensor electric polarizability of
the deuteron by the resonance method Tensor magnetic polarizabilities of the
deuteron and other nuclei in storage ring experiments
Measurement of tensor electric and magnetic polarizabilities of the deuteron by the frozen spin method
Summary
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Methods of measurement of tensor polarizabilities of the deuteron and other
nuclei
Methods of measurement of tensor polarizabilities of the deuteron and other nuclei have been proposed by V. Baryshevsky and co-workers:
• V. Baryshevsky and A. Shirvel, hep-ph/0503214.• V. G. Baryshevsky, STORI 2005 Conference
Proceedings, Schriften des Forschungszentrums Jülich, Matter and Materials, Vol. 30 (2005), pp. 227–230; J. Phys. G: Nucl. Part. Phys. 35, 035102 (2008); hep-ph/0504064; hep-ph/0510158; hep-ph/0603191.
• V. G. Baryshevsky and A. A. Gurinovich, hep-ph/0506135.
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V.G. Baryshevsky and co-authors:
The tensor electric and magnetic polarizabilities of the deuteron manifest in the EDM experiment
with vector-polarized deuterons and can be measured
•The tensor electric polarizability stimulates the buildup of the vertical polarization of vector-polarized deuteron beam•The tensor magnetic polarizability produces the spin rotation with two frequencies instead of one, beating and causes transitions between vector and tensor polarizations
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The tensor electric and magnetic polarizabilities affect the spin
2 2' ' .T TV
S E S B
'E 'Band are the rest frame fields
2
2 2.T
zT
z z
V B S E S
B S
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There are two resonance frequencies, ω≈ω0 and ω≈2ω0:
2 2 2 20 0 0 0 0 0
2 2 4 40 0 0
0 0
0
0
2
c
cos
2
12 5 3
4
2 t+
os
1 .
t
A. J. Silenko, Phys. Rev. C 75, 014003 (2007).
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We use the matrix Hamiltonian for determining the evolution of the spin wave function:
1
0
1
, .
C tdi H C tdt
C t
Measurement of tensor electric polarizability of the deuteron by the resonance method
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The polarization vector and tensor:
The spin matrices:
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2 2
2
1 0 1 1 0 11 1
0 2 0 , 0 2 0 ,2 2
1 0 1 1 0 1
0 0 1 1 0 0
0 0 0 , 0 0 0 ,
1 0 0 0 0 1
x y
x y y x z
S S
S S S S i S
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Measurement of tensor electric polarizability of the deuteron by the resonance method
E
Y. F. Orlov, W. M. Morse, and Y. K. Semertzidis, Phys. Rev. Lett. 96, 214802 (2006).
Resonance Method of Electric-Dipole-Moment
Measurements in Storage Rings
Oscillating longitudinal electric field stimulates an oscillation of
particle velocity in resonance with spin precession
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Initial matrix Hamiltonian:
0 0
0
0 0
0
0 2 0 ,
0
E
E
E
A B A
H A
A A B
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Connection between the polarization vector and tensor and the spin amplitudes:
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Vector- polarized beam (initial horizontal polarization):
Θ and ψ are spherical angles
Tensor- polarized beam (initial horizontal polarization and Sl = 0):
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Weaker resonance at the frequency ω≈ω0
Stronger resonance at the frequency ω≈2ω0
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Final vertical beam polarization forinitial horizontal vector polarization and ω≈ω0:
Final vertical beam polarization forinitial horizontal tensor polarization and ω≈2ω0:
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Theoretical data
Tensor electric polarizability of deuteron:
αT = −6.2 × 10−41 cm3
αT = −6.8 × 10−41 cm3
αT = 3.2 × 10−41 cm3
J.-W. Chen, H. W. Grießhammer, M. J. Savage, and R. P. Springer, Nucl. Phys. A644, 221 (1998).
X. Ji and Y. Li, Phys. Lett. B591, 76 (2004).
J. L. Friar and G. L. Payne, Phys. Rev. C 72, 014004 (2005).
Tensor magnetic polarizability of deuteron:
βT = 1.95 × 10−40 cm3
J.-W. Chen, H. W. Grießhammer, M. J. Savage, and R. P. Springer, Nucl. Phys. A644, 221 (1998).
X. Ji and Y. Li, Phys. Lett. B591, 76 (2004).
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Estimated expirimental sensitivity of the resonance method
Tensor electric polarizability of deuteron:
δαT ~ 10−45 ÷ 10−44 cm3
(initial tensor-polarized beam)
A. J. Silenko, Phys. Rev. C 75, 014003 (2007).
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Tensor magnetic polarizabilities of the deuteron and other nuclei in storage ring experiments
Tensor magnetic polarizability of the deuteron can be measured without both a resonance field and a restriction of spin rotationOnly vertical magnetic field is used
2 2
2
1,
2
.
zT
zT
B
B
A
B=
A. J. Silenko, Phys. Rev. C 77, 021001(R) (2008).
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When the direction of the initial tensor polarization is defined by the spherical angles θ and ψ,
0
0
2 2
( ) sin 2 sin sin ,
( ) sin 2 cos sin ,
( ) 0,
1.
2
z
T T z
P t t bt
P t t bt
P t
b B
B A
When t ~ 1000 s, P║ ~ 1 %. This polarization is measurable.
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Measurement of tensor electric and magnetic polarizabilities of the deuteron by the frozen spin
method
2
1.
1 1a
e aa a
m
ω B β β B β E
2
2 2
2, 0, .
2 1 z
aga E B
a
β B
The spin orientation relatively the momentum direction remains unchanged!
F. J. M. Farley, K. Jungmann, J. P. Miller, W. M. Morse, Y. F. Orlov, B. L. Roberts, Y. K. Semertzidis, A. Silenko, and E. J. Stephenson, Phys. Rev. Lett. 93, 052001 (2004).
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dd
23
2 2
2 2.z
T
zT
zV B E S
B E S
22 2 2 2
22 21 .
1T Tz zV B a S S
a
2 22
22 2
222 2
1,
2 1
.1
z
T
T
z
aB
a
Ba
A
B=
Correction to the Hamilton
operator
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When the direction of the initial tensor polarization is defined by the spherical angles θ and ψ,
0 00
0 00
20 0
0
22 222 2
( ) sin 2 sin sin sin ,
( ) sin 2 cos sin cos ,
2( ) sin sin sin 2 ,
11 .
21T T
z
z
P t bt t t
P t bt t t
P t t t
b B aa
A
A
A
B A
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The frozen spin method provide a less experimental sensitivity of measurement of the
tensor electric polarizability of the deuteron than the resonance method
Nevertheless, well-controlled dynamics of the horizontal spin components can improve the
experimental conditions of measurement of tensor magnetic polarizability of the deuteron by the frozen
spin method as compared with other methods
The frozen spin method provides a weaker magnetic field than other methods
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V.G. Baryshevsky, A.A. Gurinovich, Nucl. Instrum. Meth. B 252, 136 (2006).
Particle motion in bent and straight crystals is accompanied by a rotation and an oscillation of the particle spin that allows to measure the tensor electric and magnetic polarizabilities of nuclei and elementary particles
When 1<g<2 and γ=g/(g-2), the electric field of a bent crystal does not influence the spin and the effect of the tensor polarizabilities can be measured with a vector-polarized beam
If one uses an initial tensor-polarized beam, the effect of the tensor polarizabilities can be measured for arbitrary g and γ in both bent and straight crystals
However, the effects are very small: an additional vector polarization of the beam is of order of 10-4 or less
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Summary Spin dynamics caused by the tensor electric and
magnetic polarizabilities of the deuteron and other nuclei in storage rings is calculated
Potential for the measurement of the tensor polarizabilities of the deuteron and other nuclei in experiments with polarized beams is investigated
For the tensor electric polarizability of the deuteron, the resonance method provides the experimental sensitivity of the order of 10−45 ÷ 10−44 cm3
Both a purely magnetic ring and the frozen spin method can be used for the measurement of the tensor magnetic polarizability of the deuteron
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Thank you for attention