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): Parity nonconcervation effects in atoms....

The probability of the transition The coefficient R 1 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.

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 level equals the time of 40 cycles and. 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 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.

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, are the 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: Methods for ion polarization measurement in storage rings. 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:..

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 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 Eu 61+ 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 Assuming also the statistical distribution of the population of all L 12 subshell levels we will have the factor ~ Finally, the branching ratio for the HFQ M1 decay compared to the main decay 2E1 channel is about In total, we have a statistical loss of The total number of the ions in the GSI storage ring is approximately 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 R 2 ≈10 -4 we should have at least N e =R -2 2 ≈10 8 events to observe the effect. Then from the equality n f · = R -2 2 we find the number of fillings n f ≈10 5. To compete with the Cs experiment, where the accuracy of the order of 0.3% is already reached, we should register at least N e ≈10 12 events, i.e. the number of fillings should be n f ≈10 9. Since each filling takes about 10 2 s, the total observation time becomes too large, about s.

denotes the direction of the ion polarization, denotes the nuclear polarization. Conclusions. An estimation the feasibility of experiment with Eu 61+ with the reference to the characteristics of the existing storage ring in GSI. A scheme of the PNC experiment: Spin rotator Longitudinal magnet, Siberian snake Spin rotator Dressing target Stripping target X-ray detectors Bending magnet

Conclusions. An estimation the feasibility of experiment with Eu 61+ 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 3·10 4 s≈10 hours, the “leakage” coefficient should be diminished up to 3·10 -7.

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