Effective operators in two-nucleon systems

Abstract

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]

Effective interactions in the sd shell

“…To gain insights into collectivity, we have also calculated E2-transition rates between the low-energy states and the quadrupole moment of the first 2 + state. Standard shell-model effective charges have been used, e π = 1.5 e and e ν = 0.5 e. In a more complete treatment in the future, we will derive effective E2 operators in the same framework as the associated valence effective interactions [63].…”

Ab initio nuclear structure via quantum adiabatic algorithm

“…We follow Ref. [2,9,10,43] and use the three-dimensional harmonic oscillator (3DHO) basis throughout this work. We set the oscillator energy ω = 5 MeV.…”

“…For the deuteron, we take the orbital angular momenta l = 0, 2, the total spin S = 1, the total angular momentum (coupled from the orbital angular momentum and the total spin) J = 1, and the magnetic projection M = 0. Together with the principle quantum number n, we have the complete set of quantum numbers for expressing the 3DHO basis for the deuteron structure calculation [2,9,10,43]. The matrix element for the kinetic energy reads [44]:…”

Sub Coulomb barrier d+$^{208}$Pb scattering in the time-dependent basis function approach

“…(3). The parameters of the 3DHO basis include the basis strength ω and the basis truncation parameter N max (defined as the maximum of twice the radial quantum number plus the orbital angular momentum) [21,22]. Once the basis size is sufficiently large (scaled by N max ), the lowest lying state coincides with the deuteron bound state, while all the other excited states are regarded as a discretized approximation of the continuum [23,24].…”