Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userEffective theory for the non-rigid rotor in an electromagnetic field: Toward accurate and precise calculations of E2 transitions in deformed nuclei
155
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present a model-independent approach to electric quadrupole transitions of deformed nuclei. Based on an effective theory for axially symmetric systems, the leading interactions with electromagnetic fields enter as minimal couplings to gauge potentials, while subleading corrections employ gauge-invariant non-minimal couplings. This approach yields transition operators that are consistent with the Hamiltonian, and the power counting of the effective theory provides us with theoretical uncertainty estimates. We successfully test the effective theory in homonuclear molecules that exhibit a large separation of scales. For ground-state band transitions of rotational nuclei, the effective theory describes data well within theoretical uncertainties at leading order. In order to probe the theory at subleading order, data with higher precision would be valuable. For transitional nuclei, next-to-leading order calculations and the high-precision data are consistent within the theoretical uncertainty estimates. We also study the faint inter-band transitions within the effective theory and focus on the $E2$ transitions from the $0^+_2$ band (the $beta$ band) to the ground-state band. Here, the predictions from the effective theory are consistent with data for several nuclei, thereby proposing a solution to a long-standing challenge.
rate research
Read More
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband $E2$ transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
We develop an effective field theory (EFT) for deformed odd-mass nuclei. These are described as an axially symmetric core to which a nucleon is coupled. In the coordinate system fixed to the core the nucleon is subject to an axially symmetric potential. Power counting is based on the separation of scales between low-lying rotations and higher-lying states of the core. In leading order, core and nucleon are coupled by universal derivative terms. These comprise a covariant derivative and gauge potentials which account for Coriolis forces and relate to Berry-phase phenomena. At leading order, the EFT combines the particle-rotor and Nilsson models. We work out the EFT up to next-to-leading order and illustrate the results in $^{239}$Pu and $^{187}$Os. At leading order, odd-mass nuclei with rotational band heads that are close in energy and differ by one unit of angular momentum are triaxially deformed. For band heads that are well separated in energy, triaxiality becomes a subleading effect. The EFT developed in this paper presents a model-independent approach to the particle-rotor system that is capable of systematic improvement.
The effective field theory for collective rotations of triaxially deformed nuclei is generalized to odd-mass nuclei by including the angular momentum of the valence nucleon as an additional degree of freedom. The Hamiltonian is constructed up to next-to-leading order within the effective field theory formalism. The applicability of this Hamiltonian is examined by describing the wobbling bands observed in the lutetium isotopes $^{161,163,165,167}$Lu. It is found that by taking into account the next-to-leading order corrections, quartic in the rotor angular momentum, the wobbling energies $E_{textrm{wob}}$ and spin-rotational frequency relations $omega(I)$ are better described than with the leading order Hamiltonian.
Nuclear halos emerge as new degrees of freedom near the neutron and proton driplines. They consist of a core and one or a few nucleons which spend most of their time in the classically-forbidden region outside the range of the interaction. Individual nucleons inside the core are thus unresolved in the halo configuration, and the low-energy effective interactions are short-range forces between the core and the valence nucleons. Similar phenomena occur in clusters of $^4$He atoms, cold atomic gases near a Feshbach resonance, and some exotic hadrons. In these weakly-bound quantum systems universal scaling laws for s-wave binding emerge that are independent of the details of the interaction. Effective field theory (EFT) exposes these correlations and permits the calculation of non-universal corrections to them due to short-distance effects, as well as the extension of these ideas to systems involving the Coulomb interaction and/or binding in higher angular-momentum channels. Halo nuclei exhibit all these features. Halo EFT, the EFT for halo nuclei, has been used to compute the properties of single-neutron, two-neutron, and single-proton halos of s-wave and p-wave type. This review summarizes these results for halo binding energies, radii, Coulomb dissociation, and radiative capture, as well as the connection of these properties to scattering parameters, thereby elucidating the universal correlations between all these observables. We also discuss how Halo EFTs encoding of the long-distance physics of halo nuclei can be used to check and extend ab initio calculations that include detailed modeling of their short-distance dynamics.
Energy levels of the four lowest bands in 160,162,164Dy and 168Er, B(E2) transition strengths between the levels, and the B(M1) strength distribution of the ground state, all calculated within the framework of pseudo-SU(3) model, are presented. Realistic single-particle energies and quadrupole-quadrupole and pairing interaction strengths fixed from systematics were used in the calculations. The strengths of four rotor-like terms, all small relative to the other terms in the interaction, were adjusted to give an overall best fit to the energy spectra. The procedure yielded consistent parameter sets for the four nuclei.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
