No Arabic abstract
Angular momentum projection is used to obtain eigen states of angular momentum from general wave functions. Multi-configuration mixing calculation with angular momentum projection is an important microscopic method in nuclear physics. For accurate multi-configuration mixing calculation with angular momentum projection, concentrated distribution of $z$ components $K$ of angular momentum in the body-fixed frame ($K$-distribution) is favored. Orientation of wave functions strongly affects $K$-distribution. Minimization of variance of $hat{J}_z$ is proposed as an alignment method to obtain wave functions that have concentrated $K$-distribution. Benchmark calculations are performed for $alpha$-$^{24}$Mg cluster structure, triaxially superdeformed states in $^{40}$Ar, and Hartree-Fock states of some nuclei. The proposed alignment method is useful and works well for various wave functions to obtain concentrated $K$-distribution.
Rotation of triaxially deformed nucleus has been an interesting subject in the study of nuclear structure. In the present series of work, we investigate wobbling motion and chiral rotation by employing the microscopic framework of angular-momentum projection from cranked triaxially deformed mean-field states. In this first part the wobbling motion is studied in detail. The consequences of the three dimensional cranking are investigated. It is demonstrated that the multiple wobbling rotational bands naturally appear as a result of fully microscopic calculation. They have the characteristic properties, that are expected from the macroscopic triaxial-rotor model or the phenomenological particle-triaxial-rotor model, although quantitative agreement with the existing data is not achieved. It is also found that the excitation spectrum reflects dynamics of the angular-momentum vector in the intrinsic frame of the mean-field (transverse vs. longitudinal wobbling). The results obtained by using the Woods-Saxon potential and the schematic separable interaction are mainly discussed, while some results with the Gogny D1S interaction are also presented.
In the sequel of the present study, we have investigated the rotational motion of triaxially deformed nucleus by using the microscopic framework of angular-momentum projection. The Woods-Saxon potential and the schematic separable-type interaction are employed as a microscopic Hamiltonian. As the first example nuclear wobbling motion was studied in detail in the part~I of the series. This second part reports on another interesting rotational mode, chiral doublet bands: two prototype examples, $^{128}$Cs and $^{104}$Rh, are investigated. It is demonstrated that the doublet bands naturally appear as a result of the calculation in this fully microscopic framework without any kind of core, and they have the characteristic properties of the $B(E2)$ and $B(M1)$ transition probabilities, which are expected from the phenomenological triaxial particle-rotor coupling model.
The adiabatic projection method is a general framework for studying scattering and reactions on the lattice. It provides a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time. Previous studies have used the adiabatic projection method to extract scattering phase shifts from finite periodic-box energy levels using Luschers method. In this paper we demonstrate that scattering observables can be computed directly from asymptotic cluster wave functions. For a variety of examples in one and three spatial dimensions, we extract elastic phase shifts from asymptotic cluster standing waves corresponding to spherical wall boundary conditions. We find that this approach of extracting scattering wave functions from the adiabatic Hamiltonian to be less sensitive to small stochastic and systematic errors as compared with using periodic-box energy levels.
Background: The role of angular momentum in fission has long been discussed but the observable effects are difficult to quantify. Purpose: We discuss a variety of effects associated with angular momentum in fission and present quantitative illustrations. Methods: We employ the fission simulation model $mathtt{FREYA}$ which is well suited for this purpose because it obeys all conservation laws, including linear and angular momentum conservation at each step of the process. We first discuss the implementation of angular momentum in $mathtt{FREYA}$ and then assess particular observables, including various correlated observables. We also study potential effects of neutron-induced fission of the low-lying isomeric state of $^{235}$U relative to the ground state. Results: The fluctuations inherent in the fission process ensure that the spin of the initial compound nucleus has only a small influence on the fragment spins which are therefore nearly uncorrelated. There is a marked correlation between the spin magnitude of the fission fragments and the photon multiplicity. We also consider the dynamical anisotropy caused by the rotation of an evaporating fragment and study especially the distribution of the projected neutron-neutron opening angles, showing that while it is dominated by the effect of the evaporation recoils, it is possible to extract the signal of the dynamical anisotropy by means of a Fourier decomposition. Finally, we note that the use of an isomeric target, $^{235 {rm m}}$U($n_{rm th}$,f), may enhance the symmetric yields and can thus result in higher neutron multiplicities for low total fragment kinetic energy.
A recent analysis of experimental data [J. Wilson $et. al$, Nature $mathbf 590$, 566 (2021)] found that the angular momenta of nuclear fission fragments are uncorrelated. Based on this finding, the authors concluded that the spins are therefore determined only $after$ scission has occurred. We show here that the nucleon-exchange mechanism, as implemented in the well-established event-by-event fission model $mathtt{FREYA}$, while agitating collective rotational modes in which the two spins are highly correlated, nevertheless leads to fragment spins that are largely uncorrelated. This fact invalidates the reasoning of those authors. Furthermore, it was reported [J. Wilson $et. al$, Nature $mathbf 590$, 566 (2021)] that the mass dependence of the average fragment spin has a sawtooth structure. We demonstrate that such a behavior naturally emerges when shell and deformation effects are included in the moments of inertia of the fragments at scission.