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Register a new userOne-dimensional $alpha$ condensation of $alpha$-linear-chain states in ${^{12}{rm C}}$ and ${^{16}{rm O}}$
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We present a new picture that the $alpha$-linear-chain structure for ${^{12}{rm C}}$ and ${^{16}{rm O}}$ has one-dimensional $alpha$ condensate character. The wave functions of linear-chain states which are described by superposing a large number of Brink wave functions have extremely large overlaps of nearly $100%$ with single Tohsaki-Horiuchi-Schuck-Ropke (THSR) wave functions, which were proposed to describe the $alpha$ condensed gas-like states. Although this new picture is different from the conventional idea of the spatial localization of $alpha$ clusters, the density distributions are shown to have localized $alpha$-clusters which is due to the inter-$alpha$ Pauli repulsion.
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We investigate the linear-chain configurations of four-$alpha$ clusters in $^{16}$O using a Skyrme cranked Hartree-Fock method and discuss the relationship between the stability of such states and angular momentum. We show the existence of a region of angular momentum (13-18 $hbar$) where the linear chain configuration is stabilized. For the first time we demonstrate that stable exotic states with a large moment of inertia ($hbar^2/2Theta$ $sim$ 0.06-0.08 MeV) can exist.
The molecular algebraic model based on three and four alpha clusters is used to describe the inelastic scattering of alpha particles populating low-lying states in $^{12}$C and $^{16}$O. Optical potentials and inelastic formfactors are obtained by folding densities and transition densities obtained within the molecular model. One-step and multi-step processes can be included in the reaction mechanism calculation. In spite of the simplicity of the approach the molecular model with rotations and vibrations provides a reliable description of reactions where $alpha$-cluster degrees of freedom are involved and good results are obtained for the excitation of several low-lying states. Within the same model we briefly discuss the expected selection rules for the $alpha$-transfer reactions from $^{12}$C and $^{16}$O.
We investigate structure of $^{13}_Lambda{rm C}$ and discuss the difference and similarity between the structures of $^{12}{rm C}$ and $^{13}_Lambda{rm C}$ by answering the questions if the linear-chain and gaslike cluster states, which are proposed to appear in $^{12}{rm C}$, survives, or new structure states appear or not. We introduce a microscopic cluster model called, Hyper-Tohsaki-Horiuchi-Schuck-Ropke (H-THSR) wave function, which is an extended version of the THSR wave function so as to describe $Lambda$ hypernuclei. We obtained two bound states and two resonance (quasi-bound) states for $J^pi=0^+$ in $^{13}_Lambda{rm C}$, corresponding to the four $0^+$ states in $^{12}{rm C}$. However, the inversion of level ordering between the spectra of $^{12}{rm C}$ and $^{13}_Lambda{rm C}$, i.e. that the $0_3^+$ and $0_4^+$ states in $^{13}_Lambda{rm C}$ correspond to the $0_4^+$ and $0_3^+$ states in $^{12}{rm C}$, respectively, is shown to occur. The additional $Lambda$ particle reduces sizes of the $0_2^+$ and $0_3^+$ states in $^{13}_Lambda{rm C}$ very much, but the shrinkage of the $0_4^+$ state is only a half of the other states. In conclusion, the Hoyle state becomes quite a compact object with ${^{9}_Lambda{rm Be}}+alpha$ configuration in $^{13}_Lambda{rm C}$ and is no more gaslike state composed of the $3alpha$ clusters. Instead, the $0_4^+$ state in $^{13}_Lambda{rm C}$, coming from the $^{12}{rm C}(0_3^+)$ state, appears as a gaslike state composed of $alpha+alpha+^{5}_Lambda{rm He}$ configuration, i.e. the Hoyle analog state. A linear-chain state in a $Lambda$ hypernucleus is for the first time predicted to exist as the $0_3^+$ state in $^{13}_Lambda{rm C}$ with more shrunk arrangement of the $3alpha$ clusters along $z$-axis than the $3alpha$ linear-chain configuration realized in the $^{12}{rm C}(0_4^+)$ state.
The astrophysical $^{3}{rm He}(alpha, gamma)^{7}{rm Be}$ and $^{3}{rm H}(alpha, gamma)^{7}{rm Li}$ direct capture processes are studied in the framework of the two-body model with the potentials of a simple Gaussian form, which describe correctly the phase-shifts in the s-, p-, d-, and f-waves, as well as the binding energy and the asymptotic normalization constant of the ground $p_{3/2}$ and the first excited $p_{1/2}$ bound states. It is shown that the E1-transition from the initial s-wave to the final p-waves is strongly dominant in both capture reactions. On this basis the s-wave potential parameters are adjusted to reproduce the new data of the LUNA collaboration around 100 keV and the newest data at the Gamov peak estimated with the help of the observed neutrino fluxes from the Sun, $S_{34}$(23$^{+6}_{-5}$ keV)=0.548$pm$0.054 keV b for the astrophysical S-factor of the capture process $^{3}{rm He}(alpha, gamma)^{7}{rm Be}$. The resulting model describes well the astrophysical S-factor in low-energy Big Bang nucleosynthesis region of 180-400 keV, however has a tendency to underestimate the data above 0.5 MeV. Two-body potentials, adjusted on the properties of the $^7$Be nucleus, $^3{rm He}+alpha$ elastic scattering data and the astrophysical S-factor of the $^{3}{rm He}(alpha, gamma)^{7}{rm Be}$ direct capture reaction, are able to reproduce the properties of the $^7$Li nucleus, the binding energies of the ground 3/2$^-$ and first excited 1/2$^-$ states, and phase shifts of the $^3 {rm H}+alpha$ elastic scattering in partial waves. Most importantly, these potential models can successfully describe both absolute value and energy dependence of the existing experimental data for the mirror astrophysical $^{3}{rm H}(alpha, gamma)^{7}{rm Li}$ capture reaction without any additional adjustment of the parameters.
The parity-transfer $({}^{16}{rm O},{}^{16}{rm F}(0^-,{rm g.s.}))$ reaction is presented as a new probe for investigating isovector $0^-$ states in nuclei. The properties of $0^-$ states provide a stringent test of the threshold density for pion condensation in nuclear matter. Utilizing a $0^+ rightarrow 0^-$ transition in the projectile, the parity-transfer reaction transfers an internal parity to a target nucleus, resulting in a unique sensitivity to unnatural-parity states. Consequently, the selectivity for $0^-$ states is higher than in other reactions employed to date. The probe was applied to a study of the $0^-$ states in ${}^{12}{rm B}$ via the ${}^{12}{rm C}({}^{16}{rm O},{}^{16}{rm F}(0^-,{rm g.s.}))$ reaction at $247~{rm MeV/u}$. The excitation energy spectra were deduced by detecting the ${}^{15}{rm O}+p$ pair produced in the decay of the ${}^{16}{rm F}$ ejectile. A known $0^-$ state at $E_x = 9.3~{rm MeV}$ was observed with an unprecedentedly high signal-to-noise ratio. The data also revealed new candidates of $0^-$ states at $E_x=6.6 pm 0.4$ and $14.8 pm 0.3~{rm MeV}$. The results demonstrate the high efficiency of $0^-$ state detection by the parity-transfer reaction.
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