Electric dipole response of low-lying excitations in the two-neutron halo nucleus ${}^{29}\mathrm{F}$

Background: The neutron-rich ${}^{28,29}\mathrm{F}$ isotopes have been recently studied via knockout and interaction cross-section measurements. The two-neutron halo in ${}^{29}\mathrm{F}$ has been linked to the occupancy of $pf$ intruder configurations.

Purpose: We investigate the bound spectrum and continuum states in ${}^{29}\mathrm{F}$, focusing on the electric dipole $\left(E1\right)$ response of low-lying excitations and the effect of dipole couplings on nuclear reactions.

Method: ${}^{29}\mathrm{F}$ $({}^{27}\mathrm{F}+n+n)$ wave functions are built within the hyperspherical harmonics expansion formalism, and total reaction cross sections are calculated using the Glauber theory. Continuum states and $B\left(E1\right)$ transition probabilities are described in a pseudostate approach using the analytical transformed harmonic oscillator basis. The corresponding structure form factors are used in continuum-discretized coupled-channels (CDCC) calculations to describe low-energy scattering.

Results: Parity inversion in ${}^{28}\mathrm{F}$ leads to a ${}^{29}\mathrm{F}$ ground state characterized by 57.5% of ${\left(p_{3/2}\right)}^2$ intruder components, a strong dineutron configuration, and an increase of the matter radius with respect to the core radius of $\mathrm{\Delta }R=0.20$ fm. Glauber-model calculations for a carbon target at 240 MeV/nucleon provide a total reaction cross section of 1370 mb, in agreement with recent data. The model produces also a barely bound excited state corresponding to a quadrupole excitation. $B\left(E1\right)$ calculations into the continuum yield a total strength of 1.59 $e^2$ ${\mathrm{fm}}^2$ up to 6 MeV, and the $E1$ distribution exhibits a resonance at $\approx 0.85$ MeV. Results using a standard shell-model order for ${}^{28}\mathrm{F}$ lead to a considerable reduction of the $B\left(E1\right)$ distribution. The four-body CDCC calculations for ${}^{29}\mathrm{F}+{}^{120}\mathrm{Sn}$ around the Coulomb barrier are dominated by dipole couplings, which totally cancel the Fresnel peak in the elastic-scattering cross section.

Conclusions: Our three-body calculations for ${}^{29}\mathrm{F}$, using the most recent experimental information on ${}^{28}\mathrm{F}$, are consistent with a two-neutron halo. Our predictions show the low-lying enhancement of the $E1$ response expected for halo nuclei and the relevance of dipole couplings for low-energy reactions on heavy targets. These findings may guide future experimental campaigns.

Figure 1

Jacobi-$T$ (left) and -$Y$ (right) coordinates for the ${}^{29}\mathrm{F}$ nucleus described as ${}^{27}\mathrm{F}+n+n$.

Figure 2

Phase shifts for the ${}^{27}\mathrm{F}+n$ system in the present paper. The dotted line corresponds to $\delta =\pi /2$.

Figure 3

Convergence of the ground-state energy with (a) $K_{\text{max}}$ and (b) $N$, keeping the other parameter fixed. Vertical dotted lines represent the adopted values at which the three-body force has been adjusted to reproduce $S_{2n}=1.44$ MeV.

Figure 4

Convergence of the ground-state density $P\left(\rho \right)$ with $K_{\text{max}}$. Calculations correspond to $N=16$.

Figure 5

Ground-state probability density (in ${\mathrm{fm}}^{-2}$) of ${}^{29}\mathrm{F}$ using the present three-body model, as a function of $r_x\equiv r_{nn}$ and $r_y\equiv r_{c\text{−}nn}$.

Figure 6

As Fig. 5 but for the $2^{+}$ excited bound state predicted in this paper. Note that, for a proper comparison, the probability scale is the same in both figures.

Figure 7

Convergence of the $B\left(E1\right)$ distribution for ${}^{29}\mathrm{F}$ with respect to $K_{\text{max}}$.

Figure 8

$B\left(E1\right)$ distribution for ${}^{29}\mathrm{F}$ as a function of the continuum energy. The inset shows the cumulative integral up to $\varepsilon$. The dashed blue line corresponds to the RCE cross section of ${}^{29}\mathrm{F}$ at 235 MeV/u on a lead target. Note the different scales.

Figure 9

$B\left(E1\right)$ distribution compared with the results setting the potential for dipole states to zero (dashed red line). The inset shows this unrealistic calculation with a more appropriate scale and up to 10 MeV in the continuum.

Figure 10

$B\left(E1\right)$ distribution obtained in the present paper (solid black line) compared with the results using the potential set A of Ref. [42] (dashed red line), which corresponds to a standard shell-model order.

Figure 11

Coordinates in the four-body CDCC framework, considering a three-body projectile impinging on a structureless target.

Figure 12

Energies of the $0^{+}$, $1{}^{-}$, and $2^{+}$ states of ${}^{29}\mathrm{F}$ included in the present four-body coupled-channels calculations. Note there are two bound states (thick red lines).

Figure 13

Diagonal real form factors (nuclear monopole) for the ground state (solid black line) and the only excited bound state (dashed blue line) considered in the ${}^{29}\mathrm{F}+{}^{120}\mathrm{Sn}$ reaction at $E_{\mathrm{lab}}=84$ MeV. The thin dashed and dotted lines correspond to the imaginary parts. The inset shows the real part (absolute value) in logarithmic scale.

Figure 14

Form factors (real part only) for the ${}^{29}\mathrm{F}+{}^{120}\mathrm{Sn}$ reaction at $E_{\mathrm{lab}}=84$ MeV. (a) Quadrupole couplings involving the bound states, i.e., $0^{+}\iff 2^{+}$ (solid black line) and $2^{+}\iff 2^{+}$ (dashed blue line). (b) Monopole (solid black line), dipole (dashed blue line), and quadrupole (dot-dashed red line) couplings connecting the ground state with continuum pseudostates at $\varepsilon \approx 1$ MeV.

Figure 15

Angular distribution of the elastic-scattering cross section (relative to Rutherford) for the ${}^{29}\mathrm{F}+{}^{120}\mathrm{Sn}$ reaction at $E_{\mathrm{lab}}=84$ MeV. The thick solid line corresponds to the full CDCC calculations, while the others contain a restricted set of ${}^{29}\mathrm{F}$ states. See the text for details.