A. Bondarevskaya Highly charged ion beam polarization and its application to the search for the parity nonconservation effects in ions. 2009

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.

The effective relativistic Hamiltonian of the interaction between the atomic electron and the nucleus:

Here is the Fermi constant, is the proton mass, is the so called “weak charge” of the nucleus:

are the numbers of neutrons and protons in the nucleus, is the Wigner angle (a free parameter of the Standard Model):


.

.

.



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:



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


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 level equals the time of

40 cycles and .

And one could obtain:

Degree of polarization is conserved in the process of spontaneous decay.


Nuclear polarization in HCI.

The states of interest for the search of PNC effects in He-like HCI are .

The ion polarization nuclear polarization

For H-like ions in the ground hyperfine state with the maximum possible

value of the nuclear degree of polarization appears to be

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.


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:

,

.


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, arethe vector potentials for the magnetic field, is the electron charge.

The final expression for the decay rates of the polarized ions in the presence of magnetic field:


HFQ transitions for the polarized ions in the presence of an external 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:

.

.


Linear polarization of the X-ray photons in the HFQ transitions of polarized ions.

The photon density matrix


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 ion nucleus with the proposed method:

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 X-

ray spectra due to the closeness of their frequencies.

PNC effect in He-like Gd and Eu.

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.

denotes the direction of the ion polarization, denotes the nuclear polarization.

Conclusions.


A scheme of the PNC experiment:

Spin rotatorLongitudinal magnet,

Siberian snake

Spin rotator

Dressingtarget

StrippingtargetX-ray

detectors

Bending magnet

Conclusions.


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!

Documents

A. Bondarevskaya Highly charged ion beam polarization and its application to the search for the parity nonconservation effects in ions. 2009