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Register a new userContinued fraction representation of the Coulomb Greens operator and unified description of bound, resonant and scattering states
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If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Greens operator can be constructed in terms of a continued fraction. As an illustrative example we discuss the Coulomb Greens operator in Coulomb-Sturmian basis representation. Based on this representation, a quantum mechanical approximation method for solving Lippmann-Schwinger integral equations can be established, which is equally applicable for bound-, resonant- and scattering-state problems with free and Coulombic asymptotics as well. The performance of this technique is illustrated with a detailed investigation of a nuclear potential describing the interaction of two $alpha$ particles.
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The electromagnetic interactions of a relativistic two-body bound state are formulated in three dimensions using an equal-time (ET) formalism. This involves a systematic reduction of four-dimensional dynamics to a three-dimensional form by integrating out the time components of relative momenta. A conserved electromagnetic current is developed for the ET formalism. It is shown that consistent truncations of the electromagnetic current and the $NN$ interaction kernel may be made, order-by-order in the coupling constants, such that appropriate Ward-Takahashi identities are satisfied. A meson-exchange model of the $NN$ interaction is used to calculate deuteron vertex functions. Calculations of electromagnetic form factors for elastic scattering of electrons by deuterium are performed using an impulse-approximation current. Negative-energy components of the deuterons vertex function and retardation effects in the meson-exchange interaction are found to have only minor effects on the deuteron form factors.
The relativistic mean field theory with the Greens function method is taken to study the single-particle resonant states. Different from our previous work [Phys.Rev.C 90,054321(2014)], the resonant states are identified by searching for the poles of Greens function or the extremes of the density of states. This new approach is very effective for all kinds of resonant states, no matter it is broad or narrow. The dependence on the space size for the resonant energies, widths, and the density distributions in the coordinate space has been checked and it is found very stable. Taking $^{120}$Sn as an example, four new broad resonant states $2g_{7/2}$, $2g_{9/2}$, $2h_{11/2}$ and $1j_{13/2}$ are observed, and also the accuracy for the width of the very narrow resonant state $1h_{9/2}$ is highly improved to be $1times 10^{-8}$ MeV. Besides, our results are very close to those by the complex momentum representation method and the complex scaling method.
We developed a novel approach based on a generalization of factorization and nuclear spectral functions, allowing for a consistent treatment of the amplitudes involving one- and two-nucleon currents, whose contribution to the nuclear electromagnetic response in the transverse channel is known to be significant. We report the results of calculations of the inclusive electron-carbon cross section, showing that the inclusion of processes involving two-nucleon currents appreciably improves the agreement between theory and data in the dip region, between the quasi elastic and $Delta$-production peaks. The implications for the analysis of neutrino-nucleus cross sections are discussed.
We describe bound states, resonances and elastic scattering of light ions using a $delta$-shell potential. Focusing on low-energy data such as energies of bound states and resonances, charge radii, asymptotic normalization coefficients, effective-range parameters, and phase shifts, we adjust the two parameters of the potential to some of these observables and make predictions for the nuclear systems $d+alpha$, $mbox{$^3$He}+alpha$, $mbox{$^3$He}+alpha$, $alpha+alpha$, and $p+mbox{$^{16}$O}$. We identify relevant momentum scales for Coulomb halo nuclei and propose how to apply systematic corrections to the potentials. This allows us to quantify statistical and systematic uncertainties. We present a constructive criticism of Coulomb halo effective field theory and compute the unknown charge radius of $^{17}$F.
We propose a new type of Monte-Carlo method which enables us to study the excited state of many-body systems.
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