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Register a new userMulti-cluster dynamics in $^{13}_Lambda{rm C}$ and analogy to clustering in $^{12}{rm C}$
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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.
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The lithium abundances in a few percent of giants exceed the value predicted by the standard stellar evolution models, and the mechanisms of Li enhancement are still under debate. The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) survey has obtained over six million spectra in the past five years, and thus provides a great opportunity to search these rare objects and to more clearly understand the mechanisms of Li enhancement. Based on the high-resolution spectrum we obtained the stellar parameters ($T_mathrm{eff}$, $log g$, [Fe/H]), and determined the elemental abundances of Li, C, N, $alpha$, Fe-peak, r-process, s-process elements, and the projected rotational velocity. For a better understanding of the effect of mixing processes, we also derived the $^{12}rm{C}$ to $^{13}rm{C}$ ratio, and constrained the evolutionary status of TYC,3251-581-1 based on the BaSTI stellar isochrones. The super Li-rich giant TYC,3251-581-1 has $rm{A(Li)} = 3.51$, the average abundance of two lithium lines at $lambda = 6708$ AA and 6104 AA based on the non-local thermodynamic equilibrium (NLTE) analysis. The atmospheric parameters show that our target locates on the luminosity function bump. The low carbon isotopic ratio ($^{12}rm{C}/^{13}rm{C} = 9.0 $), a slow rotational velocity $vsin i = 2.2 rm{km,s}^{-1}$, and no sign of IR excess suggest that additional mixing after first dredge up (FDU) should occur to bring internal synthesized Li to the surface. The low carbon ($[rm{C}/rm{Fe}] sim -0.34$ ) and enhanced nitrogen ($[rm{N}/rm{Fe}] sim 0.33$) are also consistent with the sign of mixing. Given the evolutionary stage of TYC,3251-581-1 with the relatively low $^{12}rm{C}/^{13}rm{C}$, the internal production which replenishes Li in the outer layer is the most likely origin of Li enhancement for this star.
The secondary $gamma$ rays emitted following a nuclear reaction are often relatively straightforward to detect experimentally. Despite the large volume of such data, a practical formalism for describing these $gamma$ rays in terms of partial-wave $T$-matrix elements has never been given. The partial-wave formalism is applicable when $R$-matrix methods are used to describe the reaction in question. This paper supplies the needed framework, and it is demonstrated by the application to the ${}^{15}{rm N}(p,alpha_1gamma){}^{12}{rm C}$ reaction.
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.
The neutron yield in $^{12}$C(d,n)$^{13}$N and the proton yield in $^{12}C(d,p)^{13}$C have been measured by deuteron beam from 0.6 MeV to 3 MeV which is delivered from a 4-MeV electro static accelerator bombarding on the thick carbon target. The neutrons are detected at $0degree$, $24degree$, $48degree$ and the protons at $135degree$ in the lab frame. The ratios of the neutron yield to the proton one have been calculated and can be used as an effective probe to pin down the resonances. The resonances are found at 1.4 MeV, 1.7 MeV, 2.5 MeV in $^{12}C(d,p)^{13}$C and at 1.6 MeV, 2.7 MeV in $^{12}$C(d,n)$^{13}$N. This method provides a way to reduce the systematic uncertainty and helps to confirm more resonances in compound nuclei.
We use an underground counting lab with an extremely low background to perform an activity measurement for the $^{12}$C+$^{13}$C system with energies down to $Erm_{c.m.}$=2.323 MeV, at which the $^{12}$C($^{13}$C,$p$)$^{24}$Na cross section is found to be 0.22(7) nb. The $^{12}$C+$^{13}$C fusion cross section is derived with a statistical model calibrated using experimental data. Our new result of the $^{12}$C+$^{13}$C fusion cross section is the first decisive evidence in the carbon isotope systems which rules out the existence of the astrophysical S-factor maximum predicted by the phenomenological hindrance model, while confirming the rising trend of the S-factor towards lower energies predicted by other models, such as CC-M3Y+Rep, DC-TDHF, KNS, SPP and ESW. After normalizing the model predictions with our data, a more reliable upper limit is established for the $^{12}$C+$^{12}$C fusion cross sections at stellar energies.
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