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]
We present the first application of the Basis Light-Front Quantization method to a simple chiral model of the nucleon-pion system as a relativistic bound state for the physical proton. The light-front mass-squared matrix of the nucleon-pion system is obtained within a truncated basis. The mass and the corresponding light-front wave function (LFWF) of the proton are computed by numerical diagonalization of the resulting mass-squared matrix. With the boost invariant LFWF, we calculate the probability density distribution of the pion's longitudinal momentum fraction and the Dirac form factor of the proton. * BLFQ employs the LF formalism [18,19], where physical systems are quantized at fixed LF time x + = t+z [8,20]. The structure and dynamics of the systems are characterized by the Hamiltonian formalism. The LF vacuum has a simple structure since the Fock vacuum is an exact eigenstate of the full normal-ordered Hamiltonian [21,22]. This provides access to the Fock-space expansion of the physical states in the LF field theory and thereby generates physical intuition for their underlying structures [21,22].BLFQ also takes the advantage of the developments in ab initio non-relativistic quantum many-body theories, such as the No-Core Shell Model (NCSM) [23][24][25], and the rapidly developing supercomputing techniques (algorithms and hardwares) (see, e.g., [26] and references therein). In BLFQ, the LF mass-squared operator of a hadron system in the basis representation becomes a sparse matrix whose dimensions are controlled by truncations that respect the relativistic symmetries. By matrix diagonalization, the eigenvalues produce the mass sprectum, while the resulting eigenfunctions are the light-front wave functions (LFWFs) that encode the hadronic properties. The LFWFs can be boosted to a general Lorentz frame for calculating, e.g., form factors and scattering processes [21].The LF quantization approach to treat a chiral model of the nucleon-pion (N π) system was first proposed by Miller [27,28] in investigating the N π scattering and the nucleon-nucleon scattering via perturbation theory. In this work, we will present the first non-perturbative treatment of the same chiral model via the BLFQ method. In particular, we consider a physical proton as the relativistic bound state of the N π system. Via the BLFQ approach, we obtain the LF mass-squared matrix of the N π system within a truncated basis. We compute the proton's mass and the corresponding LFWF by numerical diagonalization of the mass-squared matrix. Based on the LFWF, we evaluate the probability density distribution of the pion's longitudinal momentum fraction and the Dirac form factor of the proton.The outline of this paper is the following. We begin by introducing our adopted Lagrangian density in Sec. 2. Then, in Sec. 3, we introduce the elements of BLFQ, such as the derivation of the LF Hamiltonian density, our choice of the basis construction and truncation schemes, the derivation of the mass-squared matrix element in the basis representation, and the fo...
Based on the multi-configuration Dirac–Hartree–Fock method and using the GRASPVU package, a theoretical investigation was performed to study the lifetimes of hyperfine levels of the first excited level 3d94s 3D3 in Ni-like ions (Z = 72–79) for all stable isotopes with nuclear spin. Comparisons between hyperfine-induced electric quadrupole transition rates and the pure magnetic octupole transition rates show that the extra electric quadrupole transition channel caused by the nuclear magnetic dipole and electric quadrupole hyperfine interaction is important for most hyperfine levels in each individual ion. Lifetimes of most hyperfine levels are sensitive to this extra decay channel. Extreme cases are found in 181Ta, 185Re and 187Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.
We present the first application of the Basis Light-Front Quantization method to study a simple chiral model of the nucleon-pion system via an ab initio, nonperturbative, Hamiltonian approach. As a test problem, we consider the physical proton as the relativistic bound state of the nucleon-pion system. Based on the chiral model of the nucleon-pion system, we construct the mass-squared matrix of the system within our light-front basis representation. We obtain the proton's mass and the corresponding light-front wave function by solving the eigenvalue problem of the mass-squared matrix. With the resulting boost-invariant lightfront wave function, we also compute the proton's parton distribution function.
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