A. Bondarevskaya
Highly charged ion beam polarization
and its application to the search for the parity
nonconservation effects in ions.
2009
Contents
• Parity nonconcervation effects in atoms (recent status of a problem).
• PNC experiments with the highly charged ions.
• Production of ion beam polarization.
• Preservation of polarization in storage rings.
• Methods for ion polarization measurement in storage rings.
• PNC effect in He-like Gd and Eu.
• Conclusions.
Parity nonconcervation effects in atoms.
Neutral Weak Current Hypothesis.
The formulation of the Standard Model (SM):
The optical dichroism in Cs atom and the optical rotation in Bi atom vapor:
The history of the corrections:
The most accurate up-to-date calculation:
Measuring PNC effects in He-like HCI.
Parity nonconcervation effects in atoms.
The effective relativistic Hamiltonian of the interaction between the atomic electron and
the nucleus:
.
Here
is the Fermi constant,
is the proton mass,
the so called “weak charge” of the nucleus:
.
are the numbers of neutrons and protons in the nucleus,
angle (a free parameter of the Standard Model):
.
is the Wigner
is
Parity nonconcervation effects in atoms.
Parity nonconcervation effects in atoms.
The probability of the transition
The coefficient R1 is usually called the “degree of parity nonconcervation”.
PNC experiments with the highly charged ions.
Production of ion beam polarization.
Radiative polarization of the electrons due to spin-flip transitions in the magnetic field:
A comprehensive reviews on radiative and nonradiative polarization of electrons,
protons, muons and deuterons:
Radiative polarization of HCI in storage rings:
Production of ion beam polarization.
Production of ion beam polarization.
Description of the polarization.
The spin-polarized state of an ion is described by the density matrix
with the normalization condition
The degree of polarization
Production of ion beam polarization.
The dynamics of the polarization.
With the uniform initial population
the first cycle gives
.
After 40 cycles the polarization becomes
The build-up time for a degree of polarization at the
40 cycles and
level equals the time of
.
And one could obtain:
Degree of polarization is conserved in the process of spontaneous decay.
Production of ion beam polarization.
Nuclear polarization in HCI.
The states of interest for the search of PNC effects in He-like HCI are
The ion polarization
For H-like
.
nuclear polarization
ions in the ground hyperfine state with
value of the nuclear degree of polarization appears to be
the maximum possible
Preservation of polarization in storage rings.
The problem arises since the bending magnet rotates the beam trajectory by an angle of
about
This rotation occurs due to the Lorentz force.
The rotation angle for the IQA after passing only one bending magnet will be
the order of
The situation can be improved by the use of “Siberian snakes”, the special magnets
which rotate the direction of the polarization of the particles. These snakes were first
proposed in Novosibirsk for the rotation of the electron polarization. Practically they were
used later for the preservation of the beam polarization of electrons and protons in
accelerator rings.
Methods for ion polarization measurement in storage rings.
Hyperfine quenching of metastable level in an external magnetic field.
Energy level scheme of the first excites
states of He-like Gd.
Energy level scheme of the first excites
states of He-like Eu.
Methods for ion polarization measurement in storage rings.
The decay rate for the HFQ transition
with the admixture
state in the absence of external magnetic field:
Within the point-like nucleus approximation the hyperfine magnetic-dipole interaction
for the two-electron ions (in r.u.):
The two-electron wave function:
,
.
Methods for ion polarization measurement in storage rings.
In an external magnetic field
an additional contribution to the transition rate arises:
is the interaction of the magnetic moment of an ion
with an external magnetic
field. We will use for this interaction another equivalent expression:
where
are the Dirac matrices and radius-vectors for the two electrons,
the vector potentials for the magnetic field,
is the electron charge.
are
Methods for ion polarization measurement in storage rings.
HFQ transitions for the polarized ions in the presence of an external magnetic field.
The final expression for the decay rates of the polarized ions in the presence of
magnetic field:
Evaluation of the constant
for this transition in the field
:
.
This smallness is exactly of the PNC effect itself. Therefore, if the experiment for the
search of the PNC effect with He-like Eu ion will become feasible.
The polarization can be deduced from the difference between two signals corresponding
to the opposite directions of the magnetic field:
.
Methods for ion polarization measurement in storage rings.
Linear polarization of the X-ray photons in the HFQ transitions of polarized ions.
The photon density matrix
Methods for ion polarization measurement in storage rings.
Linear polarization of the X-ray photons in the HFQ transitions of polarized ions.
The photons are nonpolarized, if they are emmited by the nonpolarized ions:
For the maximum polarization which is available for the polarization of the
nucleus with the proposed method:
ion
PNC effect in He-like Gd and Eu.
The level crossing occurs very close to Z = 64, but we are considering the Eu ion, the
reason is that in Gd 62+ we have a strong background from the HFQ
transition: its transition rate is 5 order of magnitude larger than the basic HFQ
transition rate and both transitions cannot be distinguished in the Xray spectra due to the closeness of their frequencies.
Conclusions.
An estimation the feasibility of experiment with Eu61+ with the reference to the
characteristics of the existing storage ring in GSI.
The efficiency of the photon detector, limited only by the solid angle we assume to be of the order
10-2 . Assuming also the statistical distribution of the population of all L12 subshell levels we will
have the factor ~10-1 . Finally, the branching ratio for the HFQ M1 decay compared to the main
decay 2E1 channel is about 10-4 . In total, we have a statistical loss of 10-7. The total number of the
ions in the GSI storage ring is approximately 1010. From the beginning of the experiments, all these
ions should be H-like. Then, according to our argumentation, all these ions can be polarized within
0.44 second. After this the dressing target should be inserted in the ring, the ions become He-like
ones in the desired exited states, emit photons via HFQ transition and leave the ring. Two
detectors, positioned opposite each other with respect to the beam, should reflect the asymmetry of
the photon emission with respect to the polarization vector, oriented longitudinally.
With the degree of PNC R2 ≈10-4 we should have at least Ne =R-2 2≈108 events to observe the
effect. Then from the equality nf ·103 2= R-2 2 we find the number of fillings nf ≈105 . To compete
with the Cs experiment, where the accuracy of the order of 0.3% is already reached, we should
register at least Ne ≈1012 events, i.e. the number of fillings should be nf ≈109 . Since each filling
takes about 102 s, the total observation time becomes too large, about 1011 s.
Conclusions.
An estimation the feasibility of experiment with Eu61+ with the reference to the
characteristics of the existing storage ring in GSI.
A scheme of the PNC experiment:
Spin rotator
Spin rotator
Longitudinal magnet,
Dressing
Siberian snake
target
Bending
magnet
X-ray
detectors
denotes the direction of the ion polarization,
Stripping
target
denotes the nuclear polarization.
Conclusions.
An estimation the feasibility of experiment with Eu61+ with the reference to the
characteristics of the existing storage ring in GSI.
In case of the experiment with the stripping target a crucial importance has a “leakage”
of the ions from the ring, i.e. the number of ions which remain two-electron and hence
leave the ring.
To receive the realistic observation time about 3·104 s≈10 hours, the “leakage”
coefficient should be diminished up to 3·10-7 .
Thank you for your attention!