Nuclear molecule of heavy nuclei

TL;DR

The paper develops a self-consistent Hamiltonian for a dinuclear, heavy-nucleus system with one axially deformed and one spherical fragment, using Euler angles and a Born–Oppenheimer separation to treat slow angular motion and fast radial dynamics. It diagonalizes the Hamiltonian in a bipolar spherical-function basis, yielding analytic solutions in pole-to-pole and equatorial regimes and quantifying roto-vibrational couplings through second-order perturbation theory. The authors validate the approach by comparing with full numerical results for $^{240}$Pu, predict HD-state spectra for $^{232}$Th modeled as $^{132}$Sn+$^{100}$Zr, and explain angular anisotropies in neutron-induced fission of $^{239}$Pu. The work provides a unified framework to interpret HD states, fission-fragment angular distributions, and clusterization phenomena in heavy nuclei, with implications for spectroscopic predictions and reaction observables. All key results are expressed with explicit angular-move and energy formulas, linking structural and reaction aspects of nuclear molecules through a consistent dynamical model.

Abstract

The model of a nuclear molecule that composed of two heavy nuclei is proposed. To this aim the Hamiltonian of a dinuclear system is derived and diagonalized in the basis of bipolar spherical functions. Analytical expressions, describing excitations of highly deformed states of a nuclear molecule, are obtained. A remarkable agreement between numerical and analytical results is demonstrated at the description of roto-vibrational excitations in $^{240}$Pu at low energies. We provide the prediction for the spectrum of hyperdeformed states of the nucleus $^{232}$Th, considering it as a nuclear molecule that consists of $^{132}$Sn+$^{100}$Zr nuclei. The angular distribution of fission fragments for the nucleus $^{240}$Pu have been analyzed as well and compared with available experimental data.

Figures (13)

• Figure 1: (Color online) Left panel: a sketch of the molecular system. The vector ${\bf R}$ connects the centers of a quadrupole-deformed fragment and a spherical fragment. For the sake of illustration the magnitude of the vector ${\bf R}$ is much enhanced. The vector ${\bf l}$ coincides with the symmetry axis of a quadrupole-deformed fragment. The center of the laboratory system Oxyz coincides with the center of mass of the molecule. Right panel: The orientation of the vector ${\bf R}$ is defined by the angles $\Omega_R=(\theta_R, \phi_R)$ with respect to the laboratory system $Oxyz$. The orientation of the intrinsic coordinate system $O'x'y'z'$ of the quadrupole-deformed fragment with respect to the laboratory system is described by the angles $\Omega_H=(\phi_H, \theta_H, 0).$ The axes of the intrinsic coordinate system $O"x"y"z"$ of the spherical fragment are chosen to be parallel with those of the laboratory system.
• Figure 2: Left panel: The coordinates of the body-fixed system $O\tilde{x}\tilde{y} \tilde{z}$ with respect to the coordinates of the laboratory system $Oxyz$. The axis $O\tilde{z}$ coincides with the symmetry axis (the vector ${\bf l}$) of a deformed nucleus. The vector ${\bf R}$ lies in the plane $O\tilde{x}\tilde{z}$. Right panel: The coordinates of the body-fixed system and a deformed nucleus with the axial symmetry. Both the vector ${\bf R}$ and the symmetry axis of the deformed nucleus lie in $O'{\tilde{x}}'{\tilde{z}}'$ plane.
• Figure 3: A sketch of the effective interaction potential between fragments as a function of a relative distance $x$. Here $U_C$ is the Coulomb potential, $U_N$ is a nuclear interaction potential.
• Figure 4: Scetch of the binary system at the touching configuration.
• Figure 5: Sketch of the pole-to-pole vibrations.