Design of a positron beam for the study of the entanglement in three gamma-rays generated by positronium annihilation

The positron is the antiparticle of the electron. In general, for any particle there exists a corresponding antiparticle. The two are identical except for the charges, i.e. electric charge, leptonic number, muonic number, …, which are equal in module but opposite sign. Examples are the electron and the positron, the first has negative electric charge, while the second has positive charge. Similarly for proton, which is positive charged, and the antiproton, which is negative charged. In the case of photons, they are their own antiparticle. When a particle and its antiparticle interact, they are destroyed in a process called annihilation which converts all their mass into energy following Einstein’s equation E=mc2. The inverse is also possible, a high-energy event creates a particle-antiparticle couple, this is called pair production. Needless to say, the products have total mass less than the one corresponding to initial energy from Einstein’s equation. For this reason, from an annihilation event, a cascade of particle-antiparticle pairs is generated, the mass of the created particle and antiparticle is less than the sum of the mass of the original particles. Still, in the annihilation process, the momentum and angular momentum of the initial particle-antiparticle system is conserved. The annihilation of a stationary positron-electron pair generates two photons. Due to the conservation of momentum, the two photons are emitted in opposite direction both with 511keV energy. The direction of emission is random. Due to their light mass, few MeV gamma-rays are capable of producing positron with pair production. In fact, the positrons are the most available antiparticle in the universe, the characteristic 511keV annihilation photons have been observed in active galactic nuclei [1], in the sun [2], and even in thunderstorm clouds on Earth [3]. The antiparticles are not easily available, the observable universe is mainly composed of matter, so any interaction would result in the annihilation. From here one of the main unanswered questions of modern physics: given the big bang was a high energy event, it should have generated matter and antimatter in equal quantity, however this symmetry is not observed in the universe around us. High-energy photons capable to produce positron-electron pairs can be generated in a controlled environment here on Earth with the use of LINACs [4] or nuclear reactor [5]. Moreover, positrons can be generated by radioisotope decay. The β^+ decay transforms a proton in a neutron in the atom nucleus, the process frees a positron, other than an electronic neutrino. This makes positrons the easiest available antiparticle and the first to be discovered and studied.In the 1920s, special relativity and quantum mechanics were two of the pillars of modern physics. One of the first attempts to combine the two was Dirac’s equation [6]. Dirac tried to explain the behavior of spin one-half particles like the electron when moving at relativistic speed, however the resulting equation admits free-particle solutions with positive and negative energies. Obviously, negative energies are not physically possible. An explanation proposed by Dirac involved a sea of particle [7]. The positive energy solution of the equation represents a particle excited from the sea, the hole left by this process corresponds to the negative energy solution. Then for any particle there is a correspond hole, called antiparticle. In the 1930s, Anderson was studying the behavior of cosmic rays interacting with a cloud chamber in the presence of a magnetic field [8]. Between the photographed particles, he demonstrated for the first time the existence if a particle with mass and charge equal in absolute value to the electron but positively charged. He called this particle positron, following studies confirmed the positron is the antiparticle of the electron. Nowadays, the positrons have found two main applications: in the medical field and in material studies. In medicine, β^+ radioisotopes are used as tracer for the individuation of cancer in patient with Positron Emission Tomography (PET). By detecting the two counterpropagating annihilation gamma-rays, it is possible to reconstruct the annihilation spot, and so the distribution of the absorption of the molecules with the radioisotope in the body. Cancerous cells have a different metabolism with respect normal cell, so their absorption of particular molecules is amplified. By selecting the correct molecular vector and radioisotope, the area in the patient body affected by the cancer is highlighted by the PET. In the case of material science, positrons are implanted in the material with energies up to tens of kiloelectronvolts. Interacting with the material, the positrons lose energy and diffuse in the material surrounding few tens of nanometers until they annihilate with an electron in the material, or they escape from the material surface. This makes the positrons a good probe because the information on the electrons transmitted outside the material by the annihilation gammas. How much time the positrons live in the material depends on the electron density. The presence of defects in the atomic structures creates spaces with lower electron density where the positron can live longer. This is studied with the Positron Annihilation Lifetime Spectroscopy (PALS). Because the positrons are generally consider thermalized at the annihilation, they have much less energy than the electron in the material. Then we can obtain information on the electron from any deviation in the direction and energy of the two annihilation photons form the case of stationary particles. The deviation in direction of the two photons is studied with Angular Correlation Annihilation Radiation (ACAR), the annihilation gammas energy with Doppler Broadening Spectroscopy (DBS). From the study of positron interaction with the matter, the bound state of the positron and the electron was discovered for the first time in the 1950s [9]. This bound state is called positronium (Ps) and it is the lightest bound matter-antimatter system. It is a hydrogen-like atom, with the positron substituting for the proton, this gives it particular properties [10]. The Ps is not stable, and, in its ground level, it is divided based on the total spin S in para- (S=0) and ortho- (S=1) positronium (p- and o- Ps, respectively) with different behaviors. Para-positronium is in a singlet spin state S=0 and m=0, where m is the projection of the spin on the z-axis. It tends to annihilate in two counterpropagating photons with 511keV energy and it has a vacuum lifetime of 125ps. Ortho-positronium corresponds to the triplet of spin states S=1 and m=-1, 0, +1. It annihilates mainly into three gamma-rays with a lifetime of 142ns in vacuum. This longer lifetime makes it possible to manipulate the o-Ps level with laser excitation [10], bringing it in longer lived levels for the study of its properties. In both the case of p-Ps and o-Ps, the conservation of energy and momentum in the annihilation fixes the gamma-rays direction and energy. For p-Ps like for free positrons, the two photons have a fixed energy and direction of one respect to the other, however the emission direction is random. The three photons resulting from the annihilation of o-Ps are emitted on a plane, called annihilation plane, with a wide range of energies and direction, the inclination of the annihilation plane is randomly distributed. In this discussion, we did not consider the conservation of the angular momentum in the annihilation process. This brings a constrain in the direction of polarization of the annihilation gamma-rays. For positronium in the ground level, the total angular momentum is given by the spin. For para-positronium and free positrons, the spin conservation means the two photons are entangled in the polarization state: the polarization of a gamma-ray is orthogonal to the other [11,12]. For ortho-positronium, the three gamma polarizations are genuinely multiparticle entangled, however the exact entanglement state depends on the emission direction of the three [13]. The correlation in the annihilation radiation of the two annihilation gammas was first experimentally studied in the 1940s [14–16]. Only a decade later, the experimental results demonstrated for the first time the existence of entanglement [17]. The entanglement in the case of three gammas has not yet been experimentally demonstrated. This is due to the complexity in the realization of a detector capable of measuring the polarization of three high-energy photon at the same time and of a source of positronium in a spin selected state in a free-field environment. This work thesis is centered on the design and study of an apparatus with the objective of study the entanglement of gamma-rays polarization generated by the annihilation of ortho-positronium. This apparatus is called PSICO (Positronium Inertial and Correlation Observations) apparatus, and it is under construction at the Antimatter laboratory (AML) of the University of Trento.At the center of the PSICO apparatus is the realization of a dense bunched positron beam capable of implanting the positrons in a positron/positronium converter in a field-free region with energy up to tens of kiloelectronvolt. No other positron beamline in the literature satisfies all these requirements. The creation of the PSICO positron beamline is based on four steps: the creation of a monoenergetic continuous positron beam, the trapping of the positrons in a buffer-gas trap (BGT) [18,19] and the generation of a dense bunched beam, the extraction of the bunched beam from the magnetic field of the trap, the acceleration, time-compression, and focalization of the positron bunches into a target in a free field region. To each step corresponds a part of the PSICO positron beamline. During this thesis work all fours parts have been designed, the last three parts are now under construction, the first part has been completed and commissioned. The creation of the monoenergetic continuous positron beam in the first step of the PSICO apparatus requires a radioactive source, a moderator, and a magnetic transport system. The design of this part of the apparatus is based on a commercial solution from First Point Scientific [20]. The source generates continuously positrons, which are emitted with a wide energy distribution. So, a moderator is required for the creation of a monoenergetic beam. The transport system guides the beam to the next section while eliminating the non-moderated positrons that are anyway emitted from the moderator. In the implementation, a sodium-22 source is used for its long half-life of 2.6 years. A solid noble gas moderator is used for the moderation process due to its high efficiency [21]. The design of the magnetic transport is based on raytracing simulation in order to optimize the speed-selection and transport of the positrons from the moderator with the minimal number of magnets. Once constructed, the first part of the PSICO apparatus can generate a continuous positron beam with up to 50 000 positrons per second with a total efficiency from the source to the end of the magnetic transport higher than 0.15%. Three solid noble gas moderators were tested: Neon, Argon, and Krypton. The advantages and disadvantages of the moderator realized with the three gases have been studied. The commissioning of the continuous positron beam has been completed by measuring the dimension of the beam spot, energy distribution, and polarization at the end of the magnetic transport system for the three gases. The measured beam dimensions are compatible with the transport simulation at the same position. The second part of the PSICO apparatus consists of the buffer-gas trap. The BGT is a modified Penning trap, where a 700G magnetic field confines radially the positrons which are accumulated in an electrostatic potential well along the magnet axis. When the positrons enter the trap, they are cooled by inelastic scattering with gas introduced into the chamber until they fall to the bottom of the potential well. The design of the PSICO BGT is based on a commercial design from First Point Scientific with changes in the magnet and terminal electron for the optimal release of the positron bunches from the BGT and their extraction from the trap magnetic field in the third stage of the PSICO beamline. From the simulation with the new trap design, the positron bunches are formed in a region with a field homogeneity ΔB\/B better than 0.1%, and the bunches are released from the trap with a temporal width less than 5ns [22].The extraction of magnetic field is done in the third step of the PSICO apparatus immediately after the trap. In the literature, a few configurations for the magnetic field extraction of positrons from the BGT have been proposed and implemented [23–25]. However, the present design is the first one where the positron extraction from the magnetic field is performed directly at the exit of the BGT. According to the simulations of our design, 60% of the positron can be extracted from the magnetic field of the trap [22].In order to perform the fourth step, a buncher-elevator followed by four lenses has been designed. After the extraction from the BGT, the positrons enter the buncher-elevator whose potential is shaped in 5.5 ns [26]. The final potential is given by a constant value superimposed by a parabolic potential. The parabolic potential has a height of 1kV at the start of the buncher-elevator and the vertex at its end, it is required for the time compression of the bunch. The constant potential value gives, instead, the majority of the implantation energy to the positrons and it can reach up to 21kV [22]. The positron bunch is then focused by the last four lenses onto the target in a spot smaller than 5mm in diameter and temporal width lower than 2ns. This will be the first positron beam from a BGT capable to operate at high implantation energy with a target in a field-free region. These four parts complete the dense bunched positron beam. For the study of the entanglement in the polarization of the o-Ps annihilation photons, a good positron/positronium converter is needed. In the literature, there are example of good converters [27,28], however they work in reflection geometry, i.e. they emit Ps on the same side where positrons are implanted. This presents some limitation in the manipulation and study of positronium in vacuum. Positron/positron converter capable of emitting Ps on the other side of the implantation can be found in the literature, however their efficiency is low [29]. So, a new kind of converter has been studied for the production of positronium in transmission [30]. It consists of silicon membranes of few microns of thickness where pass through nanochannels have been electrochemically etched. This kind of converters have shown a conversion efficiency of at least 16%. The last element needed for the entanglement measurement is the detector. This needs to be capable of measuring the polarization of the gamma-rays at the same time. The only way of measuring the polarization of hundreds of kiloelectronvolt photons is by applying the Compton scattering. For each annihilation gamma, the detector records the electron scattered from the Compton scattering and the scattered photons. The direction of the scattered photon depends on the polarization of the annihilation gammas. To reconstruct the three polarizations, the detector records six events, this requires a complex detection system. After an extensive study of literature, we are oriented into the use of modules of plastic scintillators originally developed for PET measurements by a group of the Jagiellonian University (Krakow, Poland) [31]. Two modules have been tested with the continuous positron beam from the first part of the apparatus. Just two modules were enough to reconstruct the beam spot with an uncertainty of few centimeters [31]. Using more modules, a higher precision can be obtained. Thanks to all the work done in the design, testing, and implementation of the different components of the PSICO apparatus it makes possible in the near future the realization of the first test of entanglement in the polarization of the three gamma-rays generated by annihilation of ortho-positronium.