Japanese is here
Teacher
Experiments: Ken'ichi Imai (Professor), Tetsuya Murakami (Assistant
Professor)
Theory: Ken'ichi Matsuyanagi (Associate Professor)
Teaching Assistant: Katsuro Nakamura (M1)
As well known, each nucleus consists of protons and neutrons (which are both called nucleons). In general, however, the knowledge about what the components are does not give us any other information about the aggregate. In fact, we can hardly construct the theory of verifying existence of nuclei and their shapes by considering interaction between nucleons. This is because we do not completely understand about attractive force between nucleons, i.e. strong interaction. Furthermore, it is difficult to analyze by the fact that a nucleus is few-body system, that is, the number of particles constructing a nucleus is number from several to the order of 100. If we understand all about that interaction, it is difficult to analyze because the number of particles constructing a nucleus is too much large to analyze and is too much small to consider statistically. This is why many theorists and experimentalists all over the world study nuclei, although it has passed about one century since discovered.
In resent days, we can create unnatural nuclei e.g. neutron rich nuclei or unstable nuclei with particle accelerators developed, and can get more opportunity to study the interaction or the structures, as shown more information for their density distributions and excited states, while many theorists approach the structure by studying QCD (Quantum Chromo Dynamics).
In this year, we try to measure the shapes of some stable nuclei by following experiment. Because each nucleus consists of protons and neutrons, it is efficient to measure the density distributions of both protons and neutrons when we try to determine the shape of the nuclei. We can easily measure the proton density distribution by using electron scattering because only protons interact with electrons for their charge. On the other hand, it is much more difficult to measure the neutron density distribution than the proton one. This is because neutrons interact with only nuclei, but, as mentioned above, the interaction between nuclei is still unknown in detail.
However, it is known by a lot of previous experiments that the proton density distribution in a nucleus is approximately equal to the neutron one. It is particularly shown by many experiments that, in massive nucleus, density is spherically symmetric and distributed like Fermi distribution function, furthermore, density of central part is saturated.
In our experiment, considering these fact, we will measure some nuclei density and to determine the shape of those. By experiments, neutron rich nuclei have more broad neutron density distribution than proton one, but stable nuclei do not have the property.
To be concretely, first, we apply electron beam to target(nuclei) and measure the number of scattered electron with respect to angles to the beam line, and then calculate the differential cross section and 'form factor', which is needed in determining the shape of nuclei.
We do experiment in Institute for Chemical Research in Kyoto University and utilize electron beam (LINAC) whose energy is 100MeV, so the movement of electron must be considered relatively. So we calculate the differential cross section by using not the Rutherford scatterign formula but the Mott scattering formula, which get by using QED. The Mott scattering formula is intended for point charge, and so, considering the finite extent of nuclei, we have to multiply 'form factor' to the differential cross section. 'Form factor' signifies the shape of nuclear, and this is derived by three-dimensional Fourier transform of proton density distribution. So, for calculating the proton density distribution, we have to decide model of some density distribution, and then fit what the distribution Fourier transformed into 'form factor'. Then, what kind of models we use in fitting? To use the Fermi function is easiest, but we want to fit more theoretically.
Determining a potential, we will calculate the wave function by using Schrodinger equation, and then, probability of existence, i.e. density distribution is decided. So, in this situation, most important thing is how we determine the potential in which a nucleon moves. It is simplest to do numerical calculation by applying simple potential, for example, Wood-Saxon potential. However, we do not use such potential. We will try to think one model as not contradictory to the idea that a nucleus consists of many components (nucleons), and to make a potential based on that model. In addition to this, we think it is better to make a potential for self-consistent by the use of Hartree-Fock approximation.
In this section, we write information about our experiment. We apply accelerated electron beam (100MeV by LINAC) to target (nuclei), and detect the scattered electrons by plastic scintillator and photomultiplier. In fact, not only elastic scattering but also inelastic will occur, and then the nuclei are excited. Therefore, we bend the scattered electrons by magnet and distinguish elastic scattering electrons from inelastic, for the radii of electrons in magnetic field are proportional to their own momenta.
In this process, resolution of measured momenta is about 2MeV. So, using the target whose lowest excited energy is lower energy than 2MeV, we cannot that distinct. As considering above, we decide to measure the shape of 12C, 208Pb, 40Ca, and 16O. A little thinking practically enables us to notice that Ca has hydroscopy and that O is gas in room temperature. So, both simple substances are not suitable for targets in air. Consequently, we will use C, Pb, CaO, and H2O for targets. In addition, natural Pb contains comparatively some isotopes and is not suitable too, but we get pure Pb and use it for target.
Seminar about experiments
Techniques for Nuclear and Particle Physics Experiments
W.R.Leo, Springer-Verlag
Seminar about theory
1st semester
Shapes and Shells in Nuclear Structure
Sven Goesta Nilsson and Ingemar Ragnarsson, Cambridge
university press
2nd semester
Computational Physics (FORTRAN version)
Steven E. Koonin,
Dawn C. Meredith, ABP