Relativistic energy density functional description of shape transitions in superheavy nuclei

Relativistic energy density functionals (REDF) provide a complete and accurate global description of nuclear structure phenomena. A modern semiempirical functional, adjusted to the nuclear matter equation of state and to empirical masses of deformed nuclei, is applied to studies of shapes of superheavy nuclei. The theoretical framework is tested in a comparison of calculated masses, quadrupole deformations, and potential energy barriers to available data on actinide isotopes. Self-consistent mean-field calculations predict a variety of spherical, axial, and triaxial shapes of long-lived superheavy nuclei, and their $\alpha$-decay energies and half-lives are compared to data. A microscopic, REDF-based, quadrupole collective Hamiltonian model is used to study the effect of explicit treatment of collective correlations in the calculation of $Q_{\alpha }$ values and half-lives.

Figure 1

Absolute deviations of the self-consistent RHB ground-state binding energies from the experimental values [40], for the isotopic chains of Th, U, Pu, Cm, Cf, Fm, and No (upper panel). In the lower panel the calculated ground-state axial quadrupole moments are shown in comparison to data [41] (open symbols).

Figure 2

Constrained energy curves of ${}^{236,238}$U, ${}^{240}$Pu, and ${}^{242}$Cm, as functions of the axial quadrupole deformation parameter. Results of self-consistent axially and reflection-symmetric, triaxial, and axially reflection-asymmetric RMF+BCS calculations are denoted by solid (black), dot-dashed (blue), and dashed (green) curves, respectively. The red squares, lines, and circles denote the experimental values for the inner barrier height, the excitation energy of the fission isomer, and the height of the outer barrier, respectively. The data are from Ref. [49].

Figure 3

$Q_{\alpha }$ values for even-even actinide chains obtained in a self-consistent axially symmetric RHB calculations using the functional DD-PC1 and the separable pairing interaction Eq. (1). The theoretical values (filled symbols) are connected by lines and compared to data (open symbols) [40].

Figure 4

Self-consistent RHB axially symmetric energy curves of isotopes in the $\alpha$-decay chains of ${}^{298}$120 and ${}^{300}$120, as functions of the quadrupole deformation parameter.

Figure 5

Self-consistent RHB triaxial energy maps of the even-even isotopes in the $\alpha$-decay chain of ${}^{298}$120 in the $\beta$-$\gamma$ plane ($0⩽\gamma ⩽{60}^{\circ }$). Energies are normalized with respect to the binding energy of the absolute minimum.

Figure 6

Same as described in the caption to Fig. 5 but for the the $\alpha$-decay chain of ${}^{300}$120.

Figure 7

$Q_{\alpha }$ values for the $\alpha$-decay chains of ${}^{298}$120 (a) and ${}^{300}$120 (b). The theoretical values are calculated as the difference between the mean-field minima of the parent and daughter nuclei (blue diamonds) and as the difference between the energies of the $0^{+}$ ground states of the quadrupole collective Hamiltonian (red circles). The data (squares) are from Ref. [24].

Figure 8

Half-lives for the $\alpha$-decay chains of ${}^{298}$120 (a) and ${}^{300}$120 (b). The theoretical values are calculated from a phenomenological Viola-Seaborg-type formula [5, 54], using the $Q_{\alpha }$ values from Fig. 7. Diamonds correspond to values of $Q_{\alpha }$ calculated from mean-field RHB solutions, whereas circles denote half-lives computed using $Q_{\alpha }$ values determined by the $0^{+}$ ground states of the quadrupole collective Hamiltonian. The data (squares) are from Ref. [24].

Figure 9

$Q_{\alpha }$ values (a) and half-lives (b) for the $\alpha$-decay chain of ${}^{287}$115 and for the nucleus ${}^{293}$117.

Figure 10

Same as described in the caption to Fig. 9 but for the $\alpha$-decay chain of ${}^{288}$115 and for the nucleus ${}^{294}$117.

Figure 11

Calculated proton (left) and neutron (right) density distributions of ${}^{284}$112, ${}^{292}$116, and ${}^{300}$120, as functions of the distance from the center of the nucleus. The dot-dashed and dashed curves correspond to the distribution profiles $\rho (z,0)$ along the $z$ axis and $\rho (0,r_{\perp })$ along the $r_{\perp }$ axis, respectively. The solid curves denote the corresponding density distributions $\rho \left(r\right)$ calculated assuming spherical shapes.