Electric dipole response of low-lying excitations in the two-neutron halo nucleus <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">F</mml:mi><mml:mprescripts/><mml:none/><mml:mn>29</mml:mn></mml:mmultiscripts></mml:math>
J. Casal, Jagjit Singh, L. Fortunato, W. Horiuchi, A. Vitturi
Abstract
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 $(E1)$ 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 $B(E1)$ 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 ${({p}_{3/2})}^{2}$ intruder components, a strong dineutron configuration, and an increase of the matter radius with respect to the core radius of $\mathrm{\ensuremath{\Delta}}R=0.20$ 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. $B(E1)$ 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 $\ensuremath{\approx}0.85$ MeV. Results using a standard shell-model order for $^{28}\mathrm{F}$ lead to a considerable reduction of the $B(E1)$ 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.