Homepage Time Reversal Invariance Collaboration

Helmholtz-Institut für Strahlen- und Kernphysik

Time - Reversal Invariance Test at COSY

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TRIC for Pedestrians :

This page wants to give brief explanations of basic items that are necessary for an understanding of the TRIC-experiment. Click on a topic to get the referring informations :

– Polarization

– Measurement of total cross-sections with an external or internal Target

Polarization (to page-begin)

Proton Beam :

For the proton beam there are two substates with spin up or spin down
(parallel or antiparallel to the quantization axis, defined by a magnetic field).

Polarization :

Any unequal population of magnetic substates (number of particles in a beam with spin up or spin down) represents a polarization.

-> A proton beam with equal population of spin up and spin down states is unpolarized.
-> A proton beam in only one substate (spin up or spin down) has a maximal (vector-)polarization.

Deuteron Beam :

For the deuteron beam there are three substates with spin:
"up" ,   "down" and in addition "zero " (spin lies in the plane perpendicular to the quantization axis)

Assume all particles in a deuteron beam with spin "zero " are eliminated. According to the general definition of polarization given above we know this beam is polarized. On the other hand from the special definition of vector polarized protons we are lead to assume this beam is unpolarized.

-> This polarization is therefore called tensor polarization.

On the same token assume a deuteron beam in only the "zero" substate:

-> Again the special definition of vector polarization gives 0-polarization. On the other hand we know that this beam has to be polarized. It is the tensor polarization with the opposite sign.

Definitions :

In the formulas below the following symbols are used:
"+" means "spin up" ,     "-" means "spin down" ,     "0" means "spin zero"

P_vector = ( N⁺ - N^- ) / ( N⁺ + N^- + N^o )
(Relative ratio of the difference between N⁺ and N^-    or more precise: The difference of N⁺ and N^-
normalized to the total number of particles in the beam)

P_tensor = ( [N⁺ - N^o] - [N^- - N^o] )   /   ( N⁺ + N^- + N^o )
(Relative ratio of the difference between the differences to the third state N^o )

Remark :

Rotation of a tensor polarized particle by 180^o leaves the tensor polarization unchanged.
This is in general not true for the vector polarization.

Measurement of total cross-sections with an external or internal Target (to page-begin)

The Terms :

In the following explanations the term "External Target experiment" means a setup with a target mounted outside the accelerator ring. For this kind of experiment the accelerated particles are periodically extracted out of the ring and guided to the external target.

On the other hand an "Internal Target experiment" uses a target that is mounted inside the ring. In this case the proton beam is enabled to interact with the target each turn around the ring.

The TRIC-experiment is an "Internal Target experiment".

External Target :

Usually there are three ways to measure the total cross-section:

i) Measure all different particles at all energies these particles leave the target with.
    -> The detector has to be calibrated with respect to each of these conditions.

ii) Utilize the optical theorem and determine the total cross-section from the forward amplitude.
     Then there are two options: a) A measurement with infinitesimal solid angle around 0^o (forward direction)
    -> This requires a very small detector acceptance and the experiment will suffer from low countrates.

b) The solid angle is opened which allows for better statistics. But then the differential cross-section
     in the neighborhood of 0^o has to be measured very carefully, so that the forward scattering amplitude
     can be determined by analytical continuation.

    -> Special effort is required for the measurement and a lot of mathematics is involved, which requires in
        general high statistics in order to keep the resulting errors small.

Remark :

In case spin is involved, the countrates are not rotational symmetric (around 0^o) any more.
-> The detector-response has to be known for every solid angle element !

External versus Internal Target:

External (solid state) targets in usual have to be comparatively thick; because of the low limited beam-extraction frequency an appreciable luminosity for the experiment can not be obtained with very thin targets.

-> A thick target bears the difficulty of an energy degradation of scattered und unscattered particles. Further the probability of second- and even multiscattering increases with the target thickness, what may cause systematic errors in measurement

On the other hand an internal target experiment can afford to use a very thin target (e.g. TRIC even uses an atomic beam target) because the high revolution frequency of the beam (e.g. about 1 MHz at COSY) effects a sufficient luminosity.

-> A beam particle suffers only one interaction in such a target, what allows a high accuracy in the detection of scattering angles and energy loss

Further external targets provide only "one chance" experiments (after the extracted beam has interacted with the target the "event" is over), whereas internal experiments can check for the lost particles on every revolution of the beam (for days, if necessary). In addition for internal experiments no special calibration is required, since the total cross-section is calculated from the remaining protons circulating in the ring, as they interacted with the internal target.

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