Deuterons display surprising spin gymnastics

Just before the Cooler Ring at the Indiana University Cyclotron Facility (IUCF) passed into history, it produced another impressive result using the ring’s unique accelerator physics capabilities. A team of accelerator spin physicists from Michigan and Indiana, led by Alan Krisch, used their RF-solenoid once again to spin-flip a beam of stored polarized particles. However, in this case the particles were not spin-1/2 Fermi-Dirac protons or electrons, but instead were spin-1 Bose-Einstein deuterons, and the results were quite surprising.

Manipulating a deuteron’s spin is much harder than manipulating a proton’s spin because the deuteron’s anomalous magnetic moment is more than 12 times smaller. However, Vassili Morozov, a graduate student, found ways to strengthen the RF-solenoid’s strength to its limit, so allowing a first glance at the behaviour of spin-1 particles when their spin is manipulated.

Polarized beams of spin-1/2 protons and electrons are not only easier to spin-manipulate, they are also easier to understand, since their classical spin motion in a ring’s magnetic field can only be either counter-clockwise (up) or clockwise (down). The well known polarization of a beam of protons or electrons is simply the difference between the fractions of the beam spinning in these two directions. The vector polarization of a beam of spin-1 deuterons is defined in the same way; however, the vector polarization alone does not fully describe spin-1 particles. There is also a tensor polarization, which involves the fraction of deuterons spinning (classically) in any and all sideways directions perpendicular to the ring’s magnetic field. This part of the classical picture for spin-1 particles seems paradoxical.

While the quantum mechanics of spin-1 particles has been known for decades, the behaviour of spin-1 deuterons undergoing spin-manipulation has apparently never been studied experimentally. The upper part of the figure above shows that the deuterons’ vector polarization behaviour can be fit to the classical Froissart-Stora equation, as can the polarization of spin-1/2 protons. The deuterons’ vector polarization appeared to be spin-flipped, although with less efficiency due to the smaller anomalous magnetic moment.

By contrast, the behaviour of the tensor polarization was quite striking, and at first surprising. When the spin-manipulating solenoid was activated for a longer time (Δt), both tensor states (P_zz = +1 and -2) first reversed their signs as their magnitudes dropped by about 50%. Then, as the spin-manipulation time was further increased, the P_zz signs again reversed to their original signs and approached their original values. Notice also that the tensor polarization reached its minimum value at exactly the same place where the vector polarization passed through zero.

It turned out that this striking behaviour of the tensor polarization could be directly related to the vector polarization behaviour by using the known rotational properties of the vector and tensor polarizations of spin-1 particles (see the curves drawn in the figure). This confirmed that polarized spin-1 Bose-Einstein particles were indeed being spin-manipulated. Taken together, the two-part figure shows how all the vector and tensor polarizations of the spin-1 polarized deuteron beam in the Cooler Ring were spin-manipulated and flipped.

Now that the venerable IUCF Cooler Ring has been decommissioned, the Michigan team is continuing deuteron spin-manipulation studies at the 3 GeV COSY Cooler Ring in Jülich, Germany, along with new colleagues from COSY, Bonn and Hamburg, and long-term colleagues from KEK and Brookhaven. In February 2003, the new SPIN@COSY collaboration flipped the first polarized deuteron beam at COSY with about 50% efficiency using a prototype air-core RF-dipole. A new stronger ferrite RF-dipole has recently been successfully tested for use in COSY’s polarized deuteron run in December.