Structure and decay of the pygmy dipole resonance in ${}^{26}\mathrm{Ne}$

The low-lying spectra of ${}^{24,25,26}\mathrm{Ne}$ and the structure of the pygmy dipole resonance (PDR) in ${}^{26}\mathrm{Ne}$ have been theoretically studied by the antisymmetrized molecular dynamics (AMD) and its extended version called shifted-basis AMD. The calculated energy and strength of the PDR reasonably agree with the observation, and the analysis of the wave function shows that the PDR is dominated by neutron excitation coupled to the quadrupole excited core nucleus ${}^{25}\mathrm{Ne}$, which explains the observed unexpected decay of PDR to the excited states of ${}^{25}\mathrm{Ne}$. The large isoscalar component of PDR is also shown and the enhancement of the core excitation in neutron-rich Ne isotopes is conjectured.

Figure 1

The energy curves as functions of quadrupole deformation parameter $\beta$ for ${}^{24}\mathrm{Ne}$, ${}^{25}\mathrm{Ne}$, and ${}^{26}\mathrm{Ne}$. Symbols denoted by “positive” or “negative” show the results of the energy variation after the parity projection, while others show those after the angular momentum projection. For the negative-parity states of ${}^{26}\mathrm{Ne}$, two different single-particle configurations were obtained, which are shown by open and filled symbols.

Figure 2

Intrinsic density distributions of ${}^{26}\mathrm{Ne}$ at energy minima of positive- and negative-parity states. Upper (lower) panels show proton (neutron) distributions. $\beta$, ${\beta }_p$, and ${\beta }_n$, respectively, denote the quadrupole deformation of matter (proton+neutron), proton, and neutron density distributions at each minima.

Figure 3

Observed [39, 40, 41, 42] and calculated spectrum of ${}^{24}\mathrm{Ne}$, ${}^{25}\mathrm{Ne}$, and ${}^{26}\mathrm{Ne}$. The results of the HFB-based theoretical calculations [43, 44] which also use Gogny D1S interaction are also shown.

Figure 4

(a) The electric dipole strength functions of ${}^{26}\mathrm{Ne}$. The histograms show the results calculated by $\beta$ GCM, shifted-basis GCM and full GCM summed in the energy bin of 0.5 MeV width. The solid line shows the result of full GCM smeared by the Lorentzian with 1-MeV width. (b) Comparison of the results of full GCM calculations in which the magnitude of the shift is changed from 0.20 to 0.40 fm.

Figure 5

The electric dipole strength functions of ${}^{26}\mathrm{Ne}$ obtained by the GCM calculations with the limited model spaces. (a) and (b) The $K$ quantum numbers are limited to $K=0$ or $K=\pm 1$. (c) and (d) The directions of the shift is limited to only $z$ or $x,y$ directions.

Figure 6

Distributions of the low-lying $E1$ strengths calculated by full GCM and $\beta$ GCM. Arrow shows the neutron threshold.

Figure 7

Schematic figure for the internal coordinates ${\mathbf{\xi }}_i$ and the relative coordinate $\mathit{r}$.

Figure 8

(a) Calculated IS dipole strength distribution. (b) Calculated electric dipole strength distribution which is the same as Fig. 4. (c) Calculated IS dipole strengths of the states having sizable magnitude of $E1$ strengths $[B\left(E1\right)>0.05e^2{\mathrm{fm}}^2]$.