We develop an ab initio, non-perturbative, time-dependent Basis Function (tBF) method to solve the nuclear structure and scattering problems in a unified manner. We apply this method to a test problem: the Coulomb excitation of a trapped deuteron by an impinging heavy ion. The states of the deuteron system are obtained by the ab initio nuclear structure calculation implementing a realistic inter-nucleon interaction with a weak external trap to localize the center of mass and to discretize the continuum. The evolution of the internal state of the deuteron system is directly solved using the equation of motion for the scattering. We analyze the excitation mechanism of the deuteron system by investigating its internal transition probabilities and observables as functions of the exposure time and the incident speed. In this investigation, the dynamics of the Coulomb excitation are revealed by the time evolution of the system's internal charge distribution. * Corresponding author: yinpeng@impcas.ac.cn 1 arXiv:1804.01156v1 [nucl-th] 3 Apr 2018 method [23][24][25], the configuration interaction with resonating group method [26], the Green's function Monte Carlo method [27,28], and the nuclear lattice effective field theory [29,30]. However, these successful methods may be challenged to retain the full, non-perturbative quantum coherence of the scattering over all potentially relevant intermediate and final states which could be important for complex scattering processes involving exotic nuclei. For short-lived rare isotopes, where the low-lying states are either weakly bound or unbound, one will be challenged to include the relevant degrees of freedom for a complete description of the inelastic processes. In particular, a large number of intermediate states may be needed to provide accurate descriptions of the dynamical multi-step processes contributing to the final states.In order to address these complex processes and retain predictive power, we propose an ab initio, timedependent non-perturbative approach, which we call the time-dependent Basis Function (tBF) approach.The idea, which is based on a successful time-dependent approach in quantum field theory [31][32][33][34][35], is to solve the equation of motion (EOM) for the scattering of the system in the representation constructed from the energy eigenbases of the system before scattering. The state vector for the system hence reduces to a set of amplitudes with respect to the chosen eigenbases, in which the full coherence is retained, and the EOM becomes a set of first order differential equations in time.We demonstrate the tBF approach with a very simple problem, the internal excitation of a trapped deuteron in the time-varying external Coulomb field of a heavy ion, or deuteron Coulomb excitation [36,37]. Note in this initial application, the motion of the center of mass (COM) of the deuteron is constrained to the trap and the excitation in the COM degree of freedom is neglected. Future work will remove the trap and evolve the motion of the COM. Within the tBF f...

Effective Hamiltonians and effective electroweak operators are calculated with the Okubo-Lee-Suzuki formalism for two-nucleon systems. Working within a harmonic oscillator basis, first without and then with a confining harmonic oscillator trap, we demonstrate the effects of renormalization on observables calculated for truncated basis spaces. We illustrate the renormalization effects for the root-mean-square point-proton radius, electric quadrupole moment, magnetic dipole moment, Gamow-Teller transition and neutrinoless double-beta decay operator using nucleon-nucleon interactions from chiral Effective Field Theory. Renormalization effects tend to be larger in the weaker traps and smaller basis spaces suggesting applications to heavier nuclei with transitions dominated by weakly-bound nucleons would be subject to more significant renormalization effects within achievable basis spaces. IntroductionPrecision studies of electroweak properties of nuclei have become of great interest to complement major advances underway in experimental nuclear physics. As an example, significant experimental and theoretical efforts are aimed at searches for neutrinoless double-beta (0ν2β) decay which require significant investments in new experimental facilities and in theoretical advances. Our limited goal here is to use solvable two-nucleon systems within a configuration-interaction (CI) approach in order to explore the dependence of electroweak operators on the CI basis-space truncation when evaluating nuclear properties. Information on the size of these effects can help interpret previous studies and guide plans for calculations in larger nuclei.We select systems of two nucleons interacting via realistic nucleon-nucleon (N N ) interactions both in free space and in a harmonic oscillator (HO) trap for investigating renormalization effects on a suite of electroweak properties. These systems are numerically solvable in a large HO basis space providing high precision results for comparison with approximate results. This allows us to map out the effects arising from the correlations governed by different interactions, as well as the effects due to basis space truncation and the effects linked with the length scale of the environment, the trap. To accurately calculate these 1 arXiv:1809.00276v1 [nucl-th]

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