Title: A hermetic semi-spherical electron-positron pair spectromter for high
energy nuclear transitions.
Author_list:
Athanasios Hatzikoutelis, Indranil Mazumdar, Istvan Diosezgi, Peter Paul
Stony Brook University
The Internal pair Conversion (IPC) is a well-understood channel of nuclear
decay since the early `40s when Oppenheimer introduced it. The
distributions of pair angular correlations from these channels have been used
to differentiate between the multipolarities of electric and magnetic Illustration 1Angular
transitions in nuclei. Rose [M.E. Rose Phys. Rev. 76(1949) 678; 78(1951)distributions of the IPC
184 ; 131(1963) 1260] was the first to calculate the angular distribution of pairs from E1,M1 and E0
the pairs from dipole transitions in nuclei using the Born and point nucleus transitions.
approximations. The most extensive description to-date of the theory of the
IPC is offered in [P. Schluter, et. al. Phys.Rep. (Rev. sec. of Phys. Lett.) 75 No.6 (1981) 327-392.].
In these references it is shown that the approximations are accurate for high-energy transitions and
light nuclei, which is the case for the present transitions of interest. The calculations of the
theoretical curves for the method described here are based on these approximations.
The essential characteristic of the IPC is the shape of the angular correlation distributions of the
pair members’ trajectories (i.e. their momentum vectors). The correlations strongly favor small
angular separation of the pairs, and relatively independent of multi-polarity (compare the E1 and
M1 for angles < 50o) but vary drastically at large separations (compare E0 to E1 and M1 at angles
> 50o).
The main purpose of the detector is the measurement of the angular correlation of e+-e- pairs. From
the set of discrete solutions of covering a sphere hermetically with
polyhedra (regular and irregular hexagons and pentagons) where each
element presents the same solid angle to the center, the one with 122
segments was chosen. This solution results in a 18o opening-angle for the
elements, which provids adequate angle resolution. The center of the
sphere, which is also the target center, is 9.6 cm from the front faces of
the detectors. This distance allows for adequate discrimination, by time of
flight (TOF), between slow and relativistic particles.
A phoswich design of fast and slow scintillators is adopted to measure the
Illustration 2An “open
signature energy loss and total energy in the same
arrangement of the
element. The front detector is a thin (4 mm) slice of a fast flower’
array’s back view.
scintillator that can stop slow particles while the second is
a long (15 cm) scintillator designed to stop minimum-ionizing particles of energy
as high as 30 MeV. The signal from each phoswich arrangement is a superposition
of two very different waveforms distinguished by their different rise and decay
times.
Illustration 3A
bare and a
wrapped element.
Understanding the detector response requires knowledge of the response function
of the array to the pair correlation angle (PCA) variable. This function is neither
uniform (because only half a sphere is covered) nor continuous (because of the finite size of the
segments) for all angle separations. The total number of possible combinations of two detector
elements that can register a pair in a reaction event are 2080 for the 65 elements. The possible
values of the separation angle with which the pairs are registered, are identified by the separation of
the centerlines of the detector elements that registered them. These values are clustered in discrete
groups that depend on the shape, size characteristics and separations of the centerlines of individual
elements. The distribution of permutations of PCA values provides a theoretical equivalent to the
detection-probability of two minimum-ionizing particles that have been emitted with a constant
probability of angle separation between them over all possible angle separations (much like two
electrons from the decay of 12B).
For the practical purposes in the analysis the permutations of
detector responses is usually binned in 18deg-bin of PCA
values. The bin-size is chosen from the angular separation of two
neighboring detector elements (minimum separation 18.5o). In
the resulting distribution the multiplicity of each bin is
normalized to the total number of permutations. It is interesting
to notice that, the combinations of elements that can detect
4Detector response
values of PCA larger than 60o (which were of interests for GMR Illustration
function to the PCA variable.
experiments) are 1317 or 63% of the total combinations. This
translates to high statistics in measurements of pairs with large angle separation. This is the real
advantage and uniqueness of this pair-detector array.
The calibration of detectors was done with the E1 decay of the 22.6MeV GDR state to the ground
state of 12C integrated in 18o bins. The theory, (shaded histogram), is
the angular correlations distribution of the IPC pairs from an E1
transition plotted at the center of each bin, folded with the detector
response to PCA and normalized to the total number of events with
angle separations above 36o. There are no other pair-production
channels for this reaction (background pair events, 12B was not
produced) in the energy range of the 0 transition. Therefore, the
correlation distribution corresponds to the one for the IPC of the E1
transition for all angles.
A further validation of the performance of the spectrometer was a
search for excess pair events in the IPC of the M1 transition of the
15.1-MeV state of 12C. There were tantalizing reports that this might
Illustration 5Angular
be the evidence of the existence of a massive short-lived Axion, an
correlations of the detected
elusive neutral pseudo-scalar boson first postulated 30 years ago by
events from the reaction 11Peccei-Quinn-Weinberg-Wilczek. Our spectrometer was very well
B(p,pair)12-C
suited for testing this with high statistics. In the experiment the pairs
from the decay of the Axion were expected to have large angular separations similar to those of the
E0 distribution. The Axion decays with a correlation angle of 180o in its rest frame. The significant
momentum vector of the emitted Axion somewhat shortens the angular separation of the pair
partners in the lab frame. From this lab system the mass of the Axion can be obtained. This search
will also be presented.