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Register a new userResearch on the halo in $^{31}$Ne with complex momentum representation method
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Halo is one of the most interesting phenomena in exotic nuclei especially for $^{31}$Ne, which is deemed to be a halo nucleus formed by a $p-$wave resonance. However, the theoretical calculations dont suggest a $p-$wave resonance using the scattering phase shift approach or complex scaling method. Here, we apply the complex momentum representation method to explore resonances in $^{31}$Ne. We have calculated the single-particle energies for bound and resonant states together with their evolutions with deformation. The results show that the $p-$wave resonances appear clearly in the complex momentum plane accompanied with the $p-f$ inversion in the single-particle levels. As it happens the $p-f$ inversion, the calculated energy, width, and occupation probabilities of major components in the level occupied by valance neutron support a $p-$wave halo for $^{31}$Ne.
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Lying at the lower edge of the `island of inversion, neutron-rich Fluorine isotopes ($^{29-31}$F) provide a curious case to study the configuration mixing in this part of the nuclear landscape. Recent studies have suggested that a prospective two-neutron halo in the dripline nucleus $^{31}$F could be linked to the occupancy of the $pf$ intruder configurations. Focusing on configuration mixing, matter radii and neutron-neutron ($nn$) correlations in the ground-state of $^{31}$F, we explore various scenarios to analyze its possible halo nature as well as the low-lying electric dipole ($E$1) response within a three-body approach. We use an analytical, transformed harmonic oscillator basis under the aegis of a hyperspherical formalism to construct the ground state three-body wave function of $^{31}$F. The $^{31}$F ground-state configuration mixing and its matter radius are computed for different choices of the $^{30}$F structure coupled to the valence neutron. The admixture of {$p_{3/2}$, $d_{3/2}$, and $f_{7/2}$} components is found to play an important role, favouring the dominance of inverted configurations with dineutron spreads for two-neutron halo formation. The increase in matter radius with respect to the core radius, $Delta r geqslant$ 0.30 fm and the dipole distributions along with the integrated $B(E1)$ strengths of $geqslant$ 2.6 $e^2$fm$^2$ are large enough to be compatible with other two-neutron halo nuclei. Three-body results for $^{31}$F indicate a large spatial extension in its ground state due to the inversion of the energy levels of the normal shell model scheme. The increase is augmented by and is proportional to the extent of the $p_{3/2}$ component in the wave function. Additionally, the enhanced dipole distributions and large $B(E1)$ strengths all point to the two-neutron halo character of $^{31}$F.
Resonance plays critical roles in the formation of many physical phenomena, and many techniques have been developed for the exploration of resonance. In a recent letter [Phys. Rev. Lett. 117, 062502 (2016)], we proposed a new method for probing single-particle resonances by solving the Dirac equation in complex momentum representation for spherical nuclei. Here, we extend this method to deformed nuclei with theoretical formalism presented. We elaborate numerical details, and calculate the bound and resonant states in $^{37}$Mg. The results are compared with those from the coordinate representation calculations with a satisfactory agreement. In particular, the present method can expose clearly the resonant states in complex momentum plane and determine precisely the resonance parameters for not only narrow resonances but also broad resonances that were difficult to obtain before.
We present a new observable to study halo nuclei. This new observable is a particular ratio of angular distributions for elastic breakup and scattering. For one-neutron halo nuclei, it is shown to be independent of the reaction mechanism and to provide significant information about the structure of the projectile, including binding energy, partial-wave configuration, and radial wave function of the halo. This observable offers new capabilities for the study of nuclear structure far from stability.
We develop a complex scaling method for describing the resonances of deformed nuclei and present a theoretical formalism for the bound and resonant states on the same footing. With $^{31}$Ne as an illustrated example, we have demonstrated the utility and applicability of the extended method and have calculated the energies and widths of low-lying neutron resonances in $^{31}$Ne. The bound and resonant levels in the deformed potential are in full agreement with those from the multichannel scattering approach. The width of the two lowest-lying resonant states shows a novel evolution with deformation and supports an explanation of the deformed halo for $^{31}$Ne.
We study the resonance spectroscopy of the proton-rich nucleus 7B in the 4He+p+p+p cluster model. Many-body resonances are treated on the correct boundary condition as the Gamow states using the complex scaling method. We predict five resonances of 7B and evaluate the spectroscopic factors of the 6Be-p components. The importance of the 6Be(2+)-p component is shown in several states of 7B, which is a common feature of 7He, a mirror nucleus of 7B. For only the ground state of 7B, the mixing of 6Be(2+) state is larger than that of 6He(2+) in 7He, which indicates the breaking of the mirror symmetry. This is caused by the small energy difference between 7B and the excited 6Be(2+) state, whose origin is the Coulomb repulsion.
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