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Nucleons, which are the building blocks of nuclei, are now known to be complicated systems of quarks and gluons. The strong forces between these particles are, in principle, described by the underlying theory of Quantum Chromodynamics (QCD) but so far it has not been possible to calculate these forces from first principles. Only the longest range part of the potential energy between two nucleons is well understood: it arises from the exchange of virtual pions [1]. The form of this potential is determined by the symmetries of QCD and it can be calculated from a quantum field theory of nucleons and pions [2,3]. More recently this simpler "effective" theory has also been used to calculate the potential due to exchange of two virtual pions [4]. The quantum mechanical amplitudes for scattering of two particles can be found by solving the Schrödinger equation with the appropriate potential [1,5]. These can be expressed as shifts in the phase of the waves describing the scattered particles. By comparing the phase shifts for scattering of two nucleons calculated from one-pion (or two-pion) exchange with those deduced from experimental data [6], we can learn about the remaining scattering produced by other physics at shorter distances. This project will require solving the Schrödinger equation for the nucleon-nucleon wave function and extracting the phase shift as a function of energy for each value of the angular momentum. This will involve writing a program (in C or FORTRAN) to solve a second-order ODE. Information on the strength and energy dependence of the scattering produced by short-range physics will then be obtained by subtracting these phase-shifts from the empirical ones. This project may be done either on its own or in combination with the one on "Quantum scattering" to form a full-year project. In a full-year project, it should be possible to study the channels where the singular, spin-dependent forces are important. References
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25th September 2007