Similarity Renormalization Group Approach Research Articles

Prediction of novel effects in rotational nuclei at high speed

The study of high-speed rotating matter is a crucial research topic in physics due to the emergence of novel phenomena. In this letter, we combined cranking covariant density functional theory (CDFT) with a similarity renormalization group approach to decompose the Hamiltonian from the cranking CDFT into different Hermite components, including the non-relativistic term, the dynamical term, the spin-orbit coupling, and the Darwin term. Especially, we obtained the rotational term, the term relating to Zeeman-like effect, and the spin-rotation coupling due to consideration of rotation and spatial component of vector potential. By exploring these operators, we aim to identify novel phenomena that may occur in rotating nuclei. Signature splitting, Zeeman-like effect, and spin-rotation coupling are among the potential novelties that may arise in rotating nuclei. Additionally, we investigated the observability of these phenomena and their dependence on various factors such as nuclear deformation, rotational angular velocity, and magnetic field-like strength.

Ab initio calculations of mirror energy difference in sd-shell nuclei* *Supported by the National Natural Science Foundation of China (12205340, 11975282); the Gansu Natural Science Foundation (22JR5RA123); the Special Research Assistant Project of the Chinese Academy of Sciences; the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000); the Key Research Program of the Chinese Academy of Sciences (XDPB15);

Mirror energy difference is a key observable in isospin symmetry breaking, containing rich information about nuclear structure. Understanding the mechanisms underlying mirror energy difference is important in nuclear physics. In the present work, we extensively investigated mirror energy difference using ab initio valence-space in-medium similarity renormalization group approach, focusing specifically on -shell nuclei. The low-lying spectra of Al isotopes and isotones, together with their mirror nuclei, were calculated, followed by a systematic analysis of the evolution of the mirror energy difference. The results suggest that the large mirror energy difference is mainly caused by the weakly-bound effects and large average occupations of the orbit. Lastly, we compare the results of our ab initio calculations with shell model results, elucidating the relationship and coherence between these two models.

A Similarity Renormalization Group Approach to Green's Function Methods.

The family of Green's function methods based on the GW approximation has gained popularity in the electronic structure theory thanks to its accuracy in weakly correlated systems combined with its cost-effectiveness. Despite this, self-consistent versions still pose challenges in terms of convergence. A recent study [Monino and Loos J. Chem. Phys. 2022, 156, 231101.] has linked these convergence issues to the intruder-state problem. In this work, a perturbative analysis of the similarity renormalization group (SRG) approach is performed on Green's function methods. The SRG formalism enables us to derive, from first-principles, the expression of a naturally static and Hermitian form of the self-energy that can be employed in quasiparticle self-consistent GW (qsGW) calculations. The resulting SRG-based regularized self-energy significantly accelerates the convergence of qsGW calculations, slightly improves the overall accuracy, and is straightforward to implement in existing code.

Investigation of isospin-symmetry breaking in mirror energy difference and nuclear mass with ab initio calculations

Isospin-symmetry breaking is responsible for the energy difference of excited states in mirror nuclei. It also influences the coefficient of the isobaric multiplet mass equation. In the present work, we extensively investigate isospin-symmetry breaking in medium-mass nuclei within ab initio frameworks. For this, we employ the ab initio valence-space in-medium similarity renormalization group approach, in which charge-symmetry and charge-independence breakings are included in the adopted nuclear force. The mirror energies of $sd$- and $pf$-shell nuclei are computed for that matter. The effects of single-particle states on weakly bound and unbound nuclear states, especially those of the $s$ wave, are discussed. Predictions are also made concerning proton drip-line nuclei bearing large mirror energy difference. Finally, the coefficient of the isobaric multiplet mass equation in $T=1/2$ and $T=1$ isospin multiplets for $A=18$ to $A=76$ is calculated.

Investigation of pseudospin and spin symmetries in relativistic mean field theory combined with a similarity renormalization group approach

Similarity renormalization group (SRG) is combined with the relativistic mean-field (RMF) theory, the Schr\"odinger-like Hamiltonian describing the motion of nucleon is obtained. The Hamiltonian with the scalar and vector potential from the self-consistent RMF calculations is used to explore the pseudospin and spin symmetries and their evolution with mass number for Sn isotopes. The contribution of every term to the pseudospin (spin) energy splitting is extracted. The spin energy splitting comes almost entirely from spin-orbit coupling, whereas the pseudospin energy splitting is also dominated by nonrelativistic and dynamical terms. The magnitude of the splitting is related to the radial, angular, and isospin quantum numbers of the doublet. The isospin dependence of pseudospin (spin) symmetry comes from the nonrelativistic term (the spin-orbit coupling). The pseudospin symmetry of neutron is superior to that of proton from the weakening of nonrelativistic and dynamical breaking. These results are helpful to understand the origin and breaking mechanism of pseudospin and spin symmetries.

Natural orbitals for many-body expansion methods

The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While various options for the computational basis are available, perturbatively constructed natural orbitals recently have been shown to lead to significant improvement in many-body applications yielding faster model-space convergence and lower sensitivity to basis set parameters in large-scale no-core shell model diagonalizations. This work provides a detailed comparison of single-particle basis sets and a systematic benchmark of natural orbitals in nonperturbative many-body calculations using the in-medium similarity renormalization group approach. As a key outcome we find that the construction of natural orbitals in a large single-particle basis enables for performing the many-body calculation in a reduced space of much lower dimension, thus offering significant computational savings in practice that help extend the reach of ab initio methods towards heavier masses and higher accuracy.

Nonempirical Interactions for the Nuclear Shell Model: An Update

The nuclear shell model has perhaps been the most important conceptual and computational paradigm for the understanding of the structure of atomic nuclei. While the shell model has been used predominantly in a phenomenological context, there have been efforts stretching back more than half a century to derive shell model parameters based on a realistic interaction between nucleons. More recently, several ab initio many-body methods—in particular, many-body perturbation theory, the no-core shell model, the in-medium similarity renormalization group, and coupled-cluster theory—have developed the capability to provide effective shell model Hamiltonians. We provide an update on the status of these methods and investigate the connections between them and their potential strengths and weaknesses, with a particular focus on the in-medium similarity renormalization group approach. Three-body forces are demonstrated to be important for understanding the modifications needed in phenomenological treatments. We then review some applications of these methods to comparisons with recent experimental measurements, and conclude with some remaining challenges in ab initio shell model theory.

Precision mass measurements of neutron-rich Co isotopes beyond N=40

The region near Z=28, N=40 is a subject of great interest for nuclear structure studies due to spectroscopic signatures in $^{68}$Ni suggesting a subshell closure at N=40. Trends in nuclear masses and their derivatives provide a complementary approach to shell structure investigations via separation energies. Penning trap mass spectrometry has provided precise measurements for a number of nuclei in this region, however a complete picture of the mass surfaces has so far been limited by the large uncertainty remaining for nuclei with N > 40 along the iron and cobalt chains. Here we present the first Penning trap measurements of $^{68,69}$Co, performed at the Low-Energy Beam and Ion Trap facility at the National Superconducting Cyclotron Laboratory. In addition, we perform ab initio calculations of ground state and two-neutron separation energies of cobalt isotopes with the valence-space in-medium similarity renormalization group approach based on a particular set of two- and three-nucleon forces which predict saturation in infinite matter. We discuss the importance of these measurements and calculations for understanding the evolution of nuclear structure near $^{68}$Ni.

Spectroscopy ofSc50andab initiocalculations ofB(M3)strengths

The GRIFFIN spectrometer at TRIUMF-ISAC has been used to study excited states and transitions in $^{50}$Sc following the $\beta$-decay of $^{50}$Ca. Branching ratios were determined from the measured $\gamma$-ray intensities, and angular correlations of $\gamma$ rays have been used to firmly assign the spins of excited states. The presence of an isomeric state that decays by an $M3$ transition with a $B(M3)$ strength of 13.6(7)\,W.u. has been confirmed. We compare with the first {\it ab initio} calculations of $B(M3$) strengths in light and medium-mass nuclei from the valence-space in-medium similarity renormalization group approach, using consistently derived effective Hamiltonians and $M3$ operator. The experimental data are well reproduced for isoscalar $M3$ transitions when using bare $g$-factors, but the strength of isovector $M3$ transitions are found to be underestimated by an order of magnitude.

A driven similarity renormalization group approach to quantum many-body problems.

Applications of the similarity renormalization group (SRG) approach [F. Wegner, Ann. Phys. 506, 77 (1994) and S. D. Głazek and K. G. Wilson, Phys. Rev. D 49, 4214 (1994)] to the formulation of useful many-body theories of electron correlation are considered. In addition to presenting a production-level implementation of the SRG based on a single-reference formalism, a novel integral version of the SRG is reported, in which the flow of the Hamiltonian is driven by a source operator. It is shown that this driven SRG (DSRG) produces a Hamiltonian flow that is analogous to that of the SRG. Compared to the SRG, which requires propagating a set of ordinary differential equations, the DSRG is computationally advantageous since it consists of a set of polynomial equations. The equilibrium distances, harmonic vibrational frequencies, and vibrational anharmonicities of a series of diatomic molecules computed with the SRG and DSRG approximated with one- and two-body normal ordered operators are in good agreement with benchmark values from coupled cluster with singles, doubles, and perturbative triples. Particularly surprising results are found when the SRG and DSRG methods are applied to C2 and F2. In the former case, both methods fail to converge, while in the latter case an unbound potential energy curve is obtained. A modified commutator approximation is shown to correct these problems in the case of the DSRG method.

Systematics of binding energies and radii based on realistic two-nucleon plus phenomenological three-nucleon interactions

We investigate the influence of phenomenological three-nucleon interactions on the systematics of ground-state energies and charge radii throughout the whole nuclear mass range from 4-He to 208-Pb. The three-nucleon interactions supplement unitarily transformed two-body interactions constructed within the Unitary Correlation Operator Method or the Similarity Renormalization Group approach. To be able to address heavy nuclei as well, we treat the many-body problem in Hartree-Fock plus many-body perturbation theory, which is sufficient to assess the systematics of energies and radii, and limit ourselves to regularized three-body contact interactions. We show that even with such a simplistic three-nucleon interaction a simultaneous reproduction of the experimental ground-state energies and charge radii can be achieved, which is not possible with unitarily transformed two-body interactions alone.

SMALL x DIVERGENCES IN THE SIMILARITY RG APPROACH TO LF QCD

We study small x divergences in boost invariant similarity renormalization group approach to light-front QCD in a heavy quark–antiquark state. With the boost invariance maintained, the infrared divergences do not cancel out in the physical states, contrary to previous studies where boost invariance was violated by a choice of a renormalization scale. This may be an indication that the zero mode, or nontrivial light-cone vacuum structure, might be important for recovering full Lorentz invariance.

Weak-coupling treatment of nonperturbative QCD dynamics to heavy hadrons

Based on the recently developed light-front similarity renormalization group approach and the light-front heavy quark effective theory, we derive analytically from first-principles QCD a heavy quark light-front Hamiltonian which contains explicitly a confinement interaction at long distances and a Coulomb-type interaction at short distances. With this light-front QCD Hamiltonian, we further demonstrate that the nonperturbative QCD dynamics of the strongly interacting heavy hadron bound states can be treated as a weak-coupling problem.