Preamble

We present ab initio calculations of the highest-multipole electromagnetic transition ever observed in nuclei. High multipole electromagnetic transitions are rare in nature, and the highest multipole transition observed in atomic nuclei is the electric hexacontatetrapole (E6) transition from the $T_{1/2} = 2.54(2)$-min $J^\pi = 19/2^-$ isomer to the $7/2^-$ ground state in $^{53}$Fe, involving an angular momentum change of six units. In this work, we perform ab initio calculations for this unique case using chiral effective field theory (EFT) forces. The in-medium similarity renormalization group is employed to derive the valence-space effective Hamiltonian and multipolar transition operators, with bare nucleon charges used in all multipolar transition rate calculations, yielding good agreement with experimental data. The valence space encompasses the full $fp$ shell, where low-lying states in $^{53}$Fe are dominated by the $0f_{7/2}$ component. We test the dependence on the interaction using two different versions of the chiral EFT two- plus three-nucleon interaction, and we examine the convergence of the transition rate calculations with respect to the harmonic oscillator parameter $\hbar\Omega$ and basis truncations $e_{\text{max}}$ and $E_{3\text{max}}$ for two- and three-nucleon forces, respectively.

Keywords: Isomerism, Highest-multipole electromagnetic transitions, Ab initio calculations, Chiral two- plus three-nucleon forces, Valence-space in-medium similarity renormalization group

Introduction

The $T_{1/2} = 2.54$-min $J^\pi = 19/2^-$ isomer at 3.0 MeV in $^{53}$Fe is unique in atomic nuclei in that it has a direct decay branch to the $J^\pi = 7/2^-$ ground state, requiring a hexacontatetrapole electric transition (E6) \cite{1,2,3}. This transition was recently confirmed experimentally with improved precision \cite{4}, providing a sensitive probe for nuclear structure \cite{5,6}. More broadly, this scenario offers unique insights into the highest-order shapes and correlations in nuclei and tests the applicability of nuclear models under extreme conditions. In the present work, we focus on ab initio calculations with bare nucleon charges that can simultaneously explain both $^{53}$Fe excited-state energies and electromagnetic decay transition rates.

In nature, a free photon carries angular momentum of $1\hbar$, whereas in a high multipole transition, a single photon carries away large angular momentum. Naively, the probability of emitting a high-spin photon should be very small. In $^{53}$Fe, a single E6 photon mediates a spin change as large as $6\hbar$. No other isolated physical system is known to exhibit such high multipole or single-photon emission. By comparison, infrared spectra have revealed $6\hbar$ absorption in solid hydrogen \cite{7}, and magneto-optical studies of atomic $^{85}$Rb have reported $6\hbar$ spontaneous emissions \cite{8}. Thus, a small group of physical environments exists where high multipole radiation provides access to novel and exceptional physics.

In a recent experimental study by Palazzo et al. \cite{4}, the existence of E6 decay in $^{53}$Fe was firmly established using empirical shell model calculations. However, Ref. \cite{4} does not provide calculations of high multipole electromagnetic transition probabilities because empirical calculations require both proton and neutron effective charges that cannot be determined from the single available set of experimental E6 transition rate data. In empirical models, different effective charges are used for different multipolarities of transitions. To improve upon such ad hoc features, ab initio calculations using realistic interactions and bare nucleon charges are required, offering the prospect of gaining insight into rare high-multipole transitions and testing the ab initio method itself. Ab initio nuclear theory stands at the forefront of current nuclear structure studies, and over the past two decades, significant progress has been made in ab initio many-body methods \cite{9,10,11,12,13} using nuclear forces based on chiral effective field theory \cite{14}.

In this study, we employ the ab initio valence-space in-medium similarity renormalization group (VS-IMSRG) \cite{15,16,17,18} to derive the valence-space effective Hamiltonian and effective multipole transition operators for subsequent shell model calculations of the observed excited states and their electromagnetic transitions in $^{53}$Fe. Unique bare nucleon charges are used in the calculation of all multipolar transitions. We aim to provide solid calculations that explain the experimental observations and offer deep insight into the structure of the $J^\pi = 19/2^-$ isomer.

II. Theoretical Framework

Our calculations begin from the intrinsic Hamiltonian of the $A$-nucleon system \cite{19,20}:

$$
H = \sum_i \frac{p_i^2}{2m} + \sum_{i