Alternative similarity renormalization group generators in nuclear structure calculations

Abstract

The similarity renormalization group (SRG) has been successfully applied to soften interactions for ab initio nuclear calculations. In almost all practical applications in nuclear physics, an SRG generator with the kinetic energy operator is used. With this choice, a fast convergence of manybody calculations can be achieved, but at the same time substantial three-body interactions are induced even if one starts from a purely two-nucleon (N N ) Hamiltonian. Three-nucleon (3N ) interactions can be handled by modern many-body methods. However, it has been observed that when including initial chiral 3N forces in the Hamiltonian, the SRG transformations induce a nonnegligible four-nucleon interaction that cannot be currently included in the calculations for technical reasons. Consequently, it is essential to investigate alternative SRG generators that might suppress the induction of many-body forces while at the same time might preserve the good convergence. In this work we test two alternative generators with operators of block structure in the harmonic oscillator basis. In the no-core shell model calculations for 3 H, 4 He and 6 Li with chiral N N force, we demonstrate that their performances appear quite promising.

Operator evolution forab initioelectric dipole transitions ofHe4

“…The residual dependence on λ displayed by these rescaled results comes then from four-body induced SRG terms but also from missing three-body induced dipole operator terms in the calculation of the Green's function, G(E 0 ), of Eq. (15). This latter contribution is expected to be small if the Hamiltonian is evolved up to the three-body level.…”

“…Since this is a transition between different initial and final states, the representation in HO space is not symmetric. Snapshots of this kind are useful for examining the behavior of the matrix elements during evolution and have been shown previously for operators evolved in momentum space [25] and for the Hamiltonian evolved in HO [15,51] and momentum space [12,52]. Here, the discretized axes, n and n ′ , are the radial quantum numbers of the HO wavefuntion and directly correspond to the energy is HO space.…”

“…As for the electric polarizability, the present results represent an upper bound due to the missing effect of three-body induced dipole operator terms in the calculation of the Green's function of Eq. (15). The photodisintegration of 4 He has been the subject of many experiments (see, e.g.…”

“…Although other generators have been used [42,43], a common choice for this operator is the commutator of the evolved Hamiltonian with the kinetic energy,η s = [T ,Ĥ s ]. This drives the Hamiltonian towards diagonal form in momentum space, thus decoupling high-and low-momentum states.…”

“…The SRG transformation (or, evolution) of the Hamiltonian has been carried out up to the three-body level both on a harmonic oscillator (HO) basis [8,[13][14][15] and, more recently, in momentum representation [16], and the resulting interactions have been successfully applied to compute properties of a variety of nuclei [8,9,11,13,14,[17][18][19].…”