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Register a new userMicroscopic coupled-channel calculation of proton and alpha inelastic scattering to the $4^+_1$ and $4^+_2$ states of $^{24}$Mg
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Background: The triaxial and hexadecapole deformations of the K=0+ and K=2+ bands of 24Mg have been investigated by the inelastic scatterings of various probes, including electrons, protons, and alpha particles, for a prolonged time. However, it has been challenging to explain the unique properties of the scatterings observed for the $4^+_1$ state through reaction calculations. Purpose: To investigate the structure and transition properties of the K=0+ and K=2+ bands of 24Mg employing the microscopic structure and reaction calculations via inelastic proton and alpha-scattering. Particularly, the E4 transitions to the $4^+_1$ and $4^+_2$ states were reexamined. Method: The structure of 24Mg was calculated employing the variation after the parity and total-angular momentum projections in the framework of the antisymmetrized molecular dynamics(AMD). The inelastic proton and alpha reactions were calculated by the microscopic coupled-channel (MCC) approach by folding the Melbourne g-matrix NN interaction with the AMD densities of 24Mg. Results: Reasonable results were obtained on the properties of the structure, including the energy spectra and E2 and E4 transitions of the K=0+ and K=2+ bands owing to the enhanced collectivity of triaxial deformation. The MCC+AMD calculation successfully reproduced the angular distributions of the $4^+_1$ and $4^+_2$ cross sections of proton scattering at incident energies of $E_p$=40--100MeV and alpha-scattering at $E_alpha$=100--400MeV. Conclusions: This is the first microscopic calculation that described the unique properties of the $0^+_1to 4^+_1$ transition. In the inelastic scattering to the $4^+_1$ state, the dominant two-step process of the $0^+_1to 2^+_1to 4^+_1$ transitions and the deconstructive interference is the weak one-step process were essential.
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[Background:] The band structure of the negative-parity states of $^{24}$Mg has not yet been clarified. The $K^pi=0^-$, $K^pi=1^-$, and $K^pi=3^-$ bands have been suggested, but the assignments have been inconsistent between experiments and theories. [Purpose:] Negative-parity states of $^{24}$Mg are investigated by microscopic structure and reaction calculations via proton and alpha inelastic scattering to clarify the band assignment for the observed negative-parity spectra. [Method:] The structure of $^{24}$Mg was calculated using the antisymmetrized molecular dynamics~(AMD). Proton and alpha inelastic reactions were calculated using microscopic coupled-channel (MCC) calculations by folding the Melbourne $g$-matrix $NN$ interaction with the AMD densities of $^{24}$Mg. [Results:] The member states of the $K^pi=0^+$, $K^pi=2^+$, $K^pi=0^-$, $K^pi=1^-$, and $K^pi=3^-$ bands of $^{24}$Mg were obtained through the AMD result. In the MCC+AMD results for proton and alpha elastic and inelastic cross sections, reasonable agreements were obtained with existing data, except in the case of the $4^+_1$ state. [Conclusions:] The $3^-$ state of the $K^pi=3^-$ band and the $1^-$ and $3^-$ states of the $K^pi=0^-$ bands were assigned to the $3^-_1$(7.62 MeV), $1^-_1$(7.56 MeV), and $3^-_2$(8.36 MeV) states, respectively. The present AMD calculation is the first microscopic structure calculation to reproduce the energy ordering of the $K^pi=0^-$, $K^pi=1^-$, and $K^pi=3^-$ bands of $^{24}$Mg.
The proton inelastic scattering of $^{24}$O($p,p$) at 62 MeV/nucleon is described by a self-consistent microscopic calculation with the continuum particle-vibration coupling (cPVC) method. The SLy5, SkM*, and SGII parameters are adopted as an effective nucleon-nucleon interaction. For all the parameters, the cPVC calculation reproduces very well the first peak at 4.65 MeV in the $^{24}$O excitation energy spectrum as well as its angular distribution. The role of the cPVC self-energy strongly depends on the effective interactions. The higher-lying strength around 7.3 MeV is suggested to be a superposition of the $3^-$ and $4^+$ states by the results with SLy5 and SGII, whereas the SkM* calculation indicates it is a pure $3^-$ state. This difference gives a rather strong interaction dependence of the angular distribution corresponding to the higher-lying strength.
Information on the equation of state (EOS) of neutron matter may be gained from studies of 208Pb. Descriptions of 208Pb require credible models of structure, taking particular note also of the spectrum. Such may be tested by analyses of scattering data. Herein, we report on such analyses using an RPA model for 208Pb in a folding model of the scattering. No a posteriori adjustment of parameters are needed to obtain excellent agreement with data. From those analyses, the skin thickness of 208Pb is constrained to lie in the range 0.13-0.17 fm.
The correspondence between the isoscalar monopole (IS0) transition strengths and $alpha$ inelastic cross sections, the $B({rm IS0})$-$(alpha,alpha)$ correspondence, is investigated for $^{24}$Mg($alpha,alpha$) at 130 and 386 MeV. We adopt a microscopic coupled-channel reaction framework to link structural inputs, diagonal and transition densities, for $^{24}$Mg obtained with antisymmetrized molecular dynamics to the ($alpha,alpha$) cross sections. We aim at clarifying how the $B({rm IS0})$-$(alpha,alpha)$ correspondence is affected by the nuclear distortion, the in-medium modification to the nucleon-nucleon effective interaction in the scattering process, and the coupled-channels effect. It is found that these effects are significant and the explanation of the $B({rm IS0})$-$(alpha,alpha)$ correspondence in the plane wave limit with the long-wavelength approximation, which is often used, makes no sense. Nevertheless, the $B({rm IS0})$-$(alpha,alpha)$ correspondence tends to remain because of a strong constraint on the transition densities between the ground state and the $0^+$ excited states. The correspondence is found to hold at 386 MeV with an error of about 20%-30%, while it is seriously stained at 130 MeV mainly by the strong nuclear distortion. It is also found that when a $0^+$ state that has a different structure from a simple $alpha$ cluster state is considered, the $B({rm IS0})$-$(alpha,alpha)$ correspondence becomes less valid. For a quantitative discussion on the $alpha$ clustering in $0^+$ excited states of nuclei, a microscopic description of both the structure and reaction parts will be necessary.
We present a reliable double-folding (DF) model for $^{4}$He-nucleus scattering, using the Melbourne $g$-matrix nucleon-nucleon interaction that explains nucleon-nucleus scattering with no adjustable parameter. In the DF model, only the target density is taken as the local density in the Melbourne $g$-matrix. For $^{4}$He elastic scattering from $^{58}$Ni and $^{208}$Pb targets in a wide range of incident energies from 20~MeV/nucleon to 200~MeV/nucleon, the DF model with the target-density approximation (TDA) yields much better agreement with the experimental data than the usual DF model with the frozen-density approximation in which the sum of projectile and target densities is taken as the local density. We also discuss the relation between the DF model with the TDA and the conventional folding model in which the nucleon-nucleus potential is folded with the $^{4}$He density.
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