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Register a new userSignature dependent triaxiality for shape evolution from superdeformation in rapidly rotating $^{40}$Ca and $^{41}$Ca
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We investigate the possible occurrence of the highly-elongated shapes near the yrast line in $^{40}$Ca and $^{41}$Ca at high spins on the basis of the nuclear energy-density functional method. Not only the superdeformed (SD) yrast configuration but the yrare configurations on top of the SD band are described by solving the cranked Skyme-Kohn-Sham equation in the three-dimensional coordinate-space representation. It is suggested that some of the excited SD bands undergo band crossings and develop to the hyperdeformation (HD) beyond $J simeq 25 hbar$ in $^{40}$Ca. We find that the change of triaxiality in response to rotation plays a decisive role for the shape evolution towards HD, and that this is governed by the signature quantum number of the last occupied orbital at low spins. This mechanism can be verified in an experimental observation of the positive-parity SD yrast signature-partner bands in $^{41}$Ca, one of which ($alpha=+1/2$) undergoes crossings with the HD band while the other ($alpha=-1/2$) shows the smooth evolution from the collective rotation at low spins to the non-collective rotation with oblate shape at the termination.
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For $^{48}$Ca, we determined $r_{m}$fm and $r_{rm skin}$fm from the central values of $sigma_{rm R}({rm EXP})$ of p+$^{48}$Ca scattering, using the chiral (Kyushu) $g$-matrix folding model with the GHFB+AMP densities. For $^{40}$Ca, Zenihiro {it et al.} determined $r_n({rm RCNP})=3.375$~fm and $r_{rm skin}({rm RCNP})=-0.01 pm 0.023$fm from the differential cross section and the analyzing powers for p+$^{40}$Ca scattering. For $^{40}$Ca, $sigma_{rm R}({rm EXP})$ are available with high accuracy. Our aim is to determine matter radius $r_{m}^{40}$ and skin $r_{rm skin}^{40}$ from $sigma_{rm R}({rm EXP})$ by using the Kyushu $g$-matrix folding model with the GHFB+AMP densities. We first determine $r_m({rm RCNP})=3.380$fm from the central value -0.01~fm of $r_{rm skin}({rm RCNP})$ and $r_p({rm RCNP})=3.385$fm. The folding model with the GHFB+AMP densities reproduces $sigma_{rm R}({rm EXP})$ in $30 leq E_{rm in} leq 180$MeV, in 2-$sigma$ level. We scale the GHFB+AMP densities so as to $r_p({rm AMP})=r_p({rm RCNP})$ and $r_n({rm AMP})=r_n({rm RCNP})$. The $sigma_{rm R}({rm RCNP})$ thus obtained agrees with the original one $sigma_{rm R}({rm AMP})$ for each $E_{rm in}$. For $E_{rm in}=180$MeV, we define $F$ as $F=sigma_{rm R}({rm EXP})/sigma_{rm R}({rm AMP})=0.929$. The $Fsigma_{rm R}({rm AMP})$ be much the same as the center values of $sigma_{rm R}({rm EXP})$ in $30 leq E_{rm in} leq 180$MeV. We then determine $r_{rm m}^{40}({rm EXP})$ from the center values of $sigma_{rm R}({rm EXP})$, using $sigma_{rm R}({rm EXP})=C r_{m}^{2}({rm EXP})$ with $C=r_{m}^{2}({rm AMP})/(Fsigma_{rm R}({rm AMP}))$. The $r_{m}({rm EXP})$ are averaged over $E_{rm in}$. The averaged value is $r_{m}({rm EXP})=3.380$fm. Eventually, we obtain $r_{rm skin}({rm EXP})=-0.01$fm from the averaged $r_{rm m}({rm EXP})$~fm and $r_p({rm PCNP})=3.385$fm.
Superdeformed (SD) states in $^{40}$Ar have been studied using the deformed-basis antisymmetrized molecular dynamics. Low energy states were calculated by the parity and angular momentum projection (AMP) and the generator coordinate method (GCM). Basis wave functions were obtained by the energy variation with a constraint on the quadrupole deformation parameter $beta$, while other quantities such as triaxiality $gamma$ were optimized by the energy variation. By the GCM calculation, an SD band was obtained just above the ground state (GS) band. The SD band involves a $K^pi = 2^+$ side band due to the triaxiality. The calculated electric quadrupole transition strengths of the SD band reproduce the experimental values appropriately. Triaxiality is significant for understanding low-lying states.
We present a consistent emph{ab initio} computation of the longitudinal response function $R_L$ in $^{40}$Ca using the coupled-cluster and Lorentz integral transform methods starting from chiral nucleon-nucleon and three-nucleon interactions. We validate our approach by comparing our results for $R_L$ in $^4$He and the Coulomb sum rule in $^{40}$Ca against experimental data and other calculations. For $R_L$ in $^{40}$Ca we obtain a very good agreement with experiment in the quasi-elastic peak up to intermediate momentum transfers, and we find that final state interactions are essential for an accurate description of the data. This work presents a milestone towards emph{ab initio} computations of neutrino-nucleus cross sections relevant for experimental long-baseline neutrino programs.
The superdeformed band, recently discovered in Ca-40 is analysed in an spherical shell model context. Two major oscillator shells, sd and pf are necessary to describe it. The yrast band of the fixed 8p-8h configuration fits extremely well with the experimental energies and transition rates of the superdeformed band. The 4p-4h configuration generates a normally deformed band plus a gamma-band pattern, both are also present in the experimental data.
Anisotropic flows ($v_1$, $v_2$, $v_3$ and $v_4$) of light fragments up till the mass number 4 as a function of rapidity have been studied for 25 MeV/nucleon $^{40}$Ca + $^{40}$Ca at large impact parameters by Quantum Molecular Dynamics model. A phenomenological scaling behavior of rapidity dependent flow parameters $v_n$ (n = 1, 2, 3 and 4) has been found as a function of mass number plus a constant term, which may arise from the interplay of collective and random motions. In addition, $v_4/{v_2}^2$ keeps almost independent of rapidity and remains a rough constant of 1/2 for all light fragments.
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