Antiproton is the antiparticle of proton. The existence of the antiproton with -1 electric charge, opposite to the +1 electric charge of the proton, was predicted by Paul Dirac in his 1933 Nobel Prize lecture [1]. Dirac received the Nobel Prize for his previous 1928 publication of his Dirac Equation that predicted the existence of positive and negative solutions to the Energy Equation ( ) of Einstein and the existence of the positron, the antimatter analog to the electron, with positive charge and opposite spin. The antiproton was
experimentally discovered in 1955 by Emilio Segrè and Owen Chamberlain at University of California, Berkeley physicists, for which they were awarded the 1959 Nobel Prize in Physics.
An antiproton consists of two up antiquark and one down antiquark ( ). The properties of the antiproton that have been measured all match the corresponding properties of the proton, with the exception that the antiproton has opposite electric charge and magnetic moment than the proton. The question of how matter is different from antimatter remains an open problem, in order to explain how our universe survived the Big Bang and why so little antimatter exists today [2]. The study of the interaction between antiprotons and ordinary matters is of special importance to test fundamental physical principles such as charge-parity-time (CPT)
invariance and the gravitational weak equivalence principle. Various projects for such
experimental studies have been proposed such as the collaborations of ASACUSA, ATHENA, and ATRAP [3, 4, 5].
According to the standard model, the lifetime of antiproton is infinite in the vacuum, and some grand unification theories require the decay of antiproton having the half lime time of about 1036 years. Recent experiments estimate a half life time of no shorter than 6.6 x1033 years [6]. When an antiproton is in a media, on the other hand, its life time is shortened since any collision with a proton will cause both particles to be annihilated in a burst of energy. Pair
annihilation of proton and antiproton makes it difficult to perform experiment using
antiproton. This is one of the reasons why the trap technique of antiproton has attracted much attention.
The stopping, capture and annihilation of antiprotons in liquids and gases has been intensively studied experimentally (Yamazaki et al 1989 [7], 1993 [8], Iwasaki et al 1991 [9], Morita et al 1994 [10], Widmann et al 1995 [11], Hori et al 1998 [12]) [13]. One noteworthy feature of these experiments has been the observation that, although most stopped antiprotons annihilate promptly (within ~ s), about 3% of all antiprotons ( ) annihilated with ~μ overall lifetime after being brought to rest in helium (see Figure 1-1), if the stopping medium is solid, liquid, or gaseous helium. In neon or argon, however, these long-lived states are not observed. This extremely long lifetime is explained by the idea of formation of antiprotonic helium atom ( ), which has consequently come to assume a role beyond its intrinsic interest as a metastable member of the exotic atom (atoms with antiproton bound) family, by providing us with a test-bench at which the antiproton itself can be studied in great detail. For example, the mass of antiproton is measured by the laser spectroscopy of with 10 digits of accuracy [14]
Figure 1-1 The Setup Schematic diagram of the antiproton injecting liquid helium experiment (left). The experiment result from Ref. [9]
The dynamical processes of antiproton from the injection to annihilation are considered as follows. After injection of the antiprotons, the kinetic energy of the antiproton is slowed down in any physico-chemical state of He, and eventually falls below the first ionization energy of He ( = 24.6 eV), at which point antiproton replaces one of the two electrons in the He atom; i.e., formation of antiprotonic helium . The new atom thus formed has recoil kinetic energy around 5 eV and continues its journey surrounded by the helium medium until it reaches thermal equilibrium after a time shorter than a nanosecond without suffering destruction. Whereas the remaining is in the 1sσ ground orbital, the captured is in a highly excited state with a large- state: , where is the reduced mass of the -He system. The antiproton is considered to be captured into
near-circular state, namely . As shown in Figure 1-2, the orbits the helium nucleus in a well localized semi-classical trajectory, while the is distributed as a fully quantum mechanical cloud. These features are the consequence of the small de Broglie wavelength of the antiproton compared to that of the electron, and of the Born-Oppenheimer approximation.
Metastability of occurs only within a limited zone of around (38, 37). Long before the discovery of the longevity, this was predicted by Condo [15] and Russell [16] to be the joint result of:
(1) Suppressed Stark decay
Since the is a neutral system retains one electron, antiproton is protected from intruding He atoms by the Pauli exclusion principle. Furthermore, it is resistant to collisional Stark effect with surrounding helium atoms, because the l degeneracy for the same n is broken by the presence of , strongly reducing the corresponding Stark mixing amplitudes.
Antiprotonic helium atoms can thus survive many collisions during and after thermalization.
(2) Suppressed Auger decay
Normally, the newly formed neutral antiprotonic atom will rapidly proceed to the ionized state by Auger transition of the electron into the continuum. However, because of
the large ionization energy ( 25 eV) of electron emission compared with the
level spacings (typically, 2 eV), the Auger process from near-circular states is associated with a large angular momentum jump, and thus is drastically hindered.
(3) Slow radiative decay
The remaining decay process is radiative decay, which is considered to be slow because of the small level spacings and of the retardation mechanism due to the correlation.
The main cascade is and the typical level lifetime is 1.5 for metastable states around n~38 and l~37.
The level scheme of antiprotonic helium is also shown in Figure 1-2. The red solid bars represent metastable states, whereas the blue broken lines show Auger dominated short-lived states. The energy levels of ionized states ( ) are shown by green dotted lines [18].
The long lifetime is attributed to the capture of antiproton by an atom, and the capture cross section of antiproton by atom has been turned out to be an important subject in the field of antiprotonic science. Cross section is defined as the effective area which governs the
Figure 1-2 The structure of the , in which the p with large (n, l) quantum numbers circulates in a localized orbit around the He2+ nucleus, while the electron occupies the distributed 1s state. (b) The level scheme of large (n, l) states of the . From Ref. [17]
probability of some scattering or absorption event [19]. In nuclear and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles. In experiment, deriving the cross sections of atom-antiproton collision is really difficult. Thus, the theoretical studies on capture/ionization cross section are required.
The capture of antiprotons by helium is a typical Coulomb four-body rearrangement problem. The full quantal and nonperturbative solution of this problem is still out of the reach of the current high-power supercomputers. Thus, several groups have studied the capture of antiprotons by hydrogen atoms, which is a Coulomb three-body rearrangement problem, by various approaches such as the classical trajectory Monte Carlo (CTMC) method [20], the time-dependent wave packet (TDWP) method [5], and other quantum methods [21, 22]. The state-specified capture cross sections of antiprotons by hydrogen atoms have been obtained recently by a time-dependent method [23, 24]. The advantage of this method is that by
rewriting the time independent scattering equation into a time-dependent one, the complicated boundary condition is converted into an initial condition which can be easily imposed.
Time-dependent approach has been used to problems with larger atomic targets. The capture cross sections of antiprotons by neutral helium (it is thus a Coulomb four-body rearrangement problem) were calculated by Tong [25], and recently Sakimoto [26] calculated the capture cross section of antiproton by neutral lithium atom (five-body problem).
Time-dependent approach can provide a reliable result, but it requires huge computational resources. This approach may be hard to be applied to atoms larger than Lithium, and a simple approximation is expected. Fermi and Teller proposed a simple model to discuss the problem of electron emission from atoms by the collision with a negatively charged particle, for example, the capture process of antiproton with atom. Fermi and Teller model is applicable to various elements, including heavy atoms without difficulty. The result of Fermi and Teller model, however, does not agree well with other reliable results (for example, CTMC or TDPW). In this thesis, we propose a simple and yet reliable model to calculate the capture
cross section in antiproton-atom collisions. Our model can provide not only reliable cross sections, but also a clear physical picture of antiproton capture. In this thesis the validity of our model is checked by comparing to other reliable results.
The rest of this thesis is organized as follows. In chapter II, the physical picture of the capture process is discussed by following the idea of Fermi and Teller to develop our new model to obtain the capture/ionization cross section. The calculation method is being introduced in Chapter III. The result and discussion is given in Chapter IV. The chapter V concludes this thesis.