Figure 1

The $m_{\omega }$ and $g_{\omega }$ parameters of different modern parametrizations of the RMF Lagrangian. They are combined into four groups, dependent on how self- and mixed couplings are introduced. Group A represents parametrizations that include nonlinear self-couplings only for the $\sigma$ meson. Group B contains parametrizations that include self-couplings for $\sigma$ and $\omega$ mesons (and $\rho$ mesons in the case of PK1R). Group C represents parametrizations that include density-dependent meson-nucleon couplings for $\sigma$, $\omega$, and $\rho$ mesons. The other parametrizations are included in group D. SVI and SVI-2 parametrizations neglect nonlinear self-couplings for the $\sigma$ meson but include isoscalar-isovector couplings. The other parametrizations in group D include mixed interaction terms (such as isoscalar-isovector couplings [52]) in addition to nonlinear self-couplings for the $\sigma$ meson. Parameters are taken from Refs. [40] (NL1), [42] (NL3), [43] (NL$3^{*}$), [44] (NLZ), [45] (NLZ2), [47] (NLSH), [46] (NLRA-1), [48] (PK1,PK1R), [49] (TMA), [50] (TM1), [51] (SVI1,SVI-2), [52] (FSUGold), [53] (FSUGZ00,FSUGZ03,FSUGZ06), [54] (TW99), [55] (DDME1), [56] (DDME2), and [48] (PKDD). Note that we omitted mass-dependent terms for $g_{\omega }$ in the TMA parametrization, which is a good approximation for heavy nuclei, as $g_{\omega }=12.842+3.191A^{-0.4}$ [49].Reuse & Permissions

Figure 2

Impact of NM on binding energies of light odd-mass nuclei. Calculations were performed with the NL3 parametrization of the RMF Lagrangian. They cover nuclei from the proton drip line up to the neutron drip line.Reuse & Permissions

Figure 3

The same as Fig. 2 but for results obtained with the indicated parametrizations of the RMF Lagrangian in Ar isotopes. The structure of the ground states is shown by the Nilsson labels. Only when the structure of the ground state is the same as in the NL3 parametrization the results obtained with other parametrizations are shown.Reuse & Permissions

Figure 4

Impact of NM on the binding energies of positive-parity configurations in odd-mass Ce ($Z=58$) nuclei. The upper panel shows additional binding $E^{\mathrm{NM}}-E^{\mathrm{WNM}}$ owing to NM and its configuration dependence. Configurations are labeled with the Nilsson labels of the blocked states; configurations at and to the right of the Nilsson label up to the next Nilsson label have the same blocked state. The bottom panel shows the corresponding deformations of the configurations. Calculations were performed with the NL3 parametrization of the RMF Lagrangian. They cover nuclei from the proton drip line up to the neutron drip line.Reuse & Permissions

Figure 5

The same as Fig. 4 but for negative-parity configurations.Reuse & Permissions

Figure 6

Total neutron current distributions ${\mathit{j}}^n$($\mathit{r}$) in the intrinsic frame in the $y$–$z$ plane at $x=0.48$ fm for several configurations with signature $(r=+i)$ in Ce nuclei. The only exceptions are the $[413]5/2^{\pm }$ configurations in ${}^{119}\mathrm{Ce}$, for which both signatures are shown in (d) and (e). Nilsson quantum numbers $[{\mathit{Nn}}_z\Lambda ]\Omega$ indicate the blocked state. Currents in (d) and (e) are plotted at arbitrary units for better visualization. Currents in other panels are normalized to the currents in (d) and (e) by using factor F. This factor was chosen in such a way that the current distribution for every nucleus is clearly shown. The shape and size of the nucleus are indicated by density lines, which are plotted in the range 0.01–0.06 fm${}^{-3}$ in steps of 0.01 fm${}^{-3}$. The panels are arranged so that the $\Omega$ value of the Nilsson label of the blocked state increases on going from (a) to (h).Reuse & Permissions

Figure 7

The same as Fig. 6 but for neutron current distributions ${\mathit{j}}^n$($\mathit{r}$) in the $z$–$x$ plane (at $y=0.48$ fm) and in the $y$–$x$ plane (at $z=0.53$ fm) for the $\nu [413]5/2^{+}$ configuration of ${}^{119}\mathrm{Ce}$.Reuse & Permissions

Figure 8

Current distributions ${\mathit{j}}^n$($\mathit{r}$) produced by single neutron in indicated single-particle states with signature $(r=+i)$ of the $\nu [660]1/2$ configuration in ${}^{171}\mathrm{Ce}$. The shape and size of the nucleus are indicated by the density line, which is plotted at $\rho =0.01$ fm${}^{-3}$ [$\rho =0.0005$ fm${}^{-3}$ in (b)]. The single-neutron density distribution owing to the occupation of the indicated Nilsson state is plotted starting with $\rho =0.0005$ fm${}^{-3}$ in steps of 0.0005 fm${}^{-3}$ [$0.0003$ fm${}^{-3}$ in (d)–(f)]. Currents in (d) are plotted at arbitrary units for better visualization. Currents in other panels are normalized to the currents in (d) by using factor F. Currents and densities are shown in the intrinsic frame in the $y$–$z$ plane at $x=0.48$ fm.Reuse & Permissions

Figure 9

Neutron (a) and proton (b) dependences of additional binding owing to NM. Open and filled circles are used for odd-proton and odd-neutron nuclei, respectively.Reuse & Permissions

Figure 10

Columns (1) and (3): energy splittings $\Delta E_{\mathrm{split}}$ between different signatures of single-particle states in the presence of NM. Results of the calculations are shown for configurations of ${}^{119}\mathrm{Ce}$ in which either the $\nu [413]5/2^{-}$ [column (1)] or the $\nu [413]5/2^{+}$ [column (3)] states are blocked. These signatures are degenerated in energy in calculations without NM [column (2)]. Note that the single-particle states of interest are shown at arbitrary absolute energy in column (2). Filled and open circles indicate occupied and unoccupied states, respectively. Solid and dotted lines are used for the $r=+i$ and ($r=-i$) states, respectively.Reuse & Permissions

Figure 11

The ratio $\Delta E_{\mathrm{split}}/(E^{\mathrm{NM}}-E^{\mathrm{WNM}})$ in Ce isotopes. The structure of blocked states is shown by the Nilsson labels; the states at and to the right of the Nilsson label up to the next Nilsson label have the same blocked state.Reuse & Permissions

Figure 12

The $\Delta E_{\mathrm{tot}}^{\mathrm{self}-\mathrm{const}}-\Delta E_{\mathrm{tot}}^{\mathrm{pert}}$ and $E^{\mathrm{NM}}-E^{\mathrm{WNM}}$ quantities for odd-neutron Fe and Ce nuclei.Reuse & Permissions

Figure 13

The same as Fig. 12, but for odd-proton $N=94$ nuclei.Reuse & Permissions

Figure 14

Schematic illustration of the impact of time-odd mean fields on the properties of odd-proton nuclei in the vicinity of the proton drip line. The single-proton states, involved in the mechanisms discussed in the text, and proton nucleonic potential (which also includes the Coulomb potential) are shown.Reuse & Permissions

Figure 15

Neutron single-particle energies (Routhians) as a function of the rotational frequency ${\Omega }_x$. They are given along the deformation path of the doubly magic SD configuration $\pi 3^2\nu 3^2$ in ${}^{32}\mathrm{S}$. Solid, short-dashed, dot-dashed, and dotted lines indicate $(\pi =+,r=-i)$, $(\pi =+,r=+i)$, $(\pi =-,r=+i)$, and $(\pi =-,r=-i)$ orbitals, respectively. At ${\Omega }_x=0.0$ MeV, single-particle orbitals are labeled by means of the asymptotic quantum numbers $[{\mathit{Nn}}_z\Lambda ]\Omega$ (Nilsson quantum numbers) of the dominant component of the wave function.Reuse & Permissions

Figure 16

Impact of NM on binding energies of different configurations under study. Energies of configurations calculated without NM are normalized to zero. To guide the eye the dotted line is used for the zero value of the $E^{\mathrm{NM}}-E^{\mathrm{WNM}}$ quantity. Short lines show the magnitude of additional gain (negative $E^{\mathrm{NM}}-E^{\mathrm{WNM}}$ values) or loss (positive $E^{\mathrm{NM}}-E^{\mathrm{WNM}}$ values) in binding energies in the presence of NM. Short-dashed, solid, and long-dashed lines are used for total signatures $r=-1$, $r=+1$, and $r=\pm i$ of the configuration, respectively. Configurations are labeled by the particle (p) and/or hole (h) states with respect to the ${}^{32}\mathrm{S}$ SD core: configurations with holes (particles) are shown to the left (right) of ${}^{32}\mathrm{S}$.Reuse & Permissions

Figure 17

Impact of NM on binding energies of the lowest configurations in odd-odd Al nuclei. (a) The $E^{\mathrm{NM}}-E^{\mathrm{WNM}}$ quantity for different signatures. Structures of the blocked states are shown by the Nilsson labels only in cases where the configurations are near-prolate. The same state is blocked in the proton subsystem of all nuclei. (b) The ${\beta }_2$ and $\gamma$ deformations of the configurations under study.Reuse & Permissions

Figure 18

The same as Fig. 17 but for the lowest configurations in odd-odd Cl nuclei.Reuse & Permissions

Figure 19

Impact of NM on binding energies of the configurations in odd-odd nuclei in the vicinity of the $N=Z$ line as a function of proton number $Z$. (a) Results for configurations with different blocked proton and neutron states; (b) results for configurations with the same blocked proton and neutron states. Structures of the blocked states are shown by the Nilsson labels only in cases where the configurations are near-prolate. Note that in (b), only one Nilsson label is shown, as the blocked proton and neutron states have the same structure. Results are shown only in cases where convergence has been achieved for both $N=Z$ and $N=Z-2$ (or $N=Z+2$) nuclei.Reuse & Permissions