Homework 10 1 the born approximation for the yukawa potential 2. The libretexts libraries are powered by mindtouch and are supported by the department of education open textbook pilot project, the uc davis office of the provost, the uc davis library, the california state university affordable learning solutions program, and merlot. In metals, the coulomb potential of a charged point scatterer is. Born approximation for a yukawa potential 0 er vrv r. Scattering theory is essentially timeindependent perturbation theory applied to the case of a continuous spectrum. Applications of quantum mechanics damtp university of.
Physics 216 problem set 4 spring 2012 welcome to scipp. Consider the problem of scattering by the yukawa potential that is defined by v. Yukawa potential november 11, 2014 1 the yukawa potential weconsiderpropertiesoftheyukawapotential, vr k r e r a thispotentialisthestatic. In this limit, the born differential crosssection becomes 1276 recall that is equivalent to, so the above equation can be rewritten 1277. We also acknowledge previous national science foundation support under grant numbers 1246120, 1525057, and 14739. When is the born approximation a good approximation. Coulomb potential, because this is the relevant one for the rutherford scat.
Using three different approaches perturbation theory pt, the lagrange mesh method lmm, and the variational method, we study the lowlying states of the yukawa potential. The born approximation for the yukawa potential gives rutherfords formula as a a 0. However, you may assume that the potential is hermitian. Calculation of the cross section for the yukawa potential. Within the born approximation, calculate the scattering amplitude fk. To leave a comment or report an error, please use the. Physics 722, spring 2019 problem set 1 born approximation. Scattering from the yukawa potential physics pages. It is of great interest on its own apart from the limit 0. The yukawa potential in its general form is vr e r r 1 where and are constants. In tokamak plasma condition, it can be assumed that the kinetic energy of electron is much greater than the perceived potential energy of electron due to the ions debye sphere potential thus born.
That means that we know there is an eigenstate of the full hamiltonian for every possible energy, e. Instead, asymptotically, far from the potential, scattering states take the form of plane. Weve looked at the yukawa potential as an example of the variational principle, so here well look at scattering by a yukawa potential, using the. Show that the first born approximation of the scattering amplitude eq. Since the potential is spherically symmetric, we can use the born approximation in.
Dark matter selfinteractions and light force carriers. These same bound states will also lead to a large enhancement in the scattering crosssection. The approximation is that the scattering potential can be treated as a perturbation, allowing us to use the fermi golden rule, from which we get the formula above. The first born approximation consists then of approximating the scattered wave function. Physics 722, spring 2019 problem set 1, due thursday, jan 31. Institute for advanced simulation forschungszentrum julich gmbh. Hideki yukawa formemrs frse, yukawa hideki, 23 january 1907 8 september 1981 was a japanese theoretical physicist and the first japanese nobel laureate for his prediction of the pi meson. Pdf the effect of debye sphere potential on electron. Born approximation and the yukawa potential a consider the theory of a spinor eld x coupled to a scalar eld. This approximation corresponds to the first iteration in the born series of 1. What is the characteristic range of the interaction. The yukawa potential reduces to the familiar coulomb potential as, provided that. Do not assume that the potential is spherically symmetric. Homework 10 1 the born approximation for the yukawa potential.