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Register a new userSpin-flip doublets of $^9$Be spectrum within a cluster model
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The structure of the $^9$Be low-lying spectrum is studied within the cluster model $alpha+alpha+n$. In the model the total orbital momentum is fixed for each energy level. Thus each level is determined as a member of the spin-flip doublet corresponding to the total orbital momentum ($L^pi=0^+, 2^+,4^+, 1^-, 2^-,3^-, 4^-$) of the system. The Ali-Bodmer potential (model E) is applied for the $alphaalpha$ interaction. We employ a local $alpha n$ potential which was constructed to reproduce the $alpha-n$ scattering data. The Pauli blocking is simulated by the repulsive core of the $s$-wave components of these potentials. Configuration space Faddeev equations are used to calculate the energy of the bound state ($E_{cal.}$=-1.493 MeV v.s. $E_{exp.}$=-1.5735 MeV) and resonances. A variant of the method of analytical continuation in the coupling constant is applied to calculate the energies of low-lying levels. Available $^9$Be spectral data are satisfactorily reproduced by the proposed model.
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The structure of the Borromean nucleus $^9$Be ($alpha+alpha+n$) is addressed within a three-body approach using the analytical transformed harmonic oscillator method. The three-body formalism provides an accurate description of the radiative capture reaction rate for the entire temperature range relevant in Astrophysics. At high temperatures, results match the calculations based on two-step sequential processes. At low temperatures, where the particles have no access to intermediate two-body resonances, the three-body direct capture leads to reaction rates larger than the sequential processes. These results support the reliability of the method for systems with several charged particles.
The study of inelastic scattering and multi-nucleon transfer reactions was performed by bombarding a $^{9}$Be target with a $^3$He beam at an incident energy of 30 MeV. Angular distributions for $^9$Be($^3$He,$^3$He)$^{9}$Be, $^9$Be($^3$He,$^4$He)$^{8}$Be, $^9$Be($^3$He,$^5$He)$^{7}$Be, $^9$Be($^3$He,$^6$Li)$^6$Li and $^9$Be($^3$He,$^5$Li)$^7$Li reaction channels were measured. Experimental angular distributions for the corresponding ground states (g.s.) were analysed within the framework of the optical model, the coupled-channel approach and the distorted-wave Born approximation. Cross sections for channels leading to unbound $^5$He$_{g.s.}$, $^5$Li$_{g.s.}$ and $^8$Be systems were obtained from singles measurements where the relationship between the energy and the scattering angle of the observed stable ejectile is constrained by two-body kinematics. Information on the cluster structure of $^{9}$Be was obtained from the transfer channels. It was concluded that cluster transfer is an important mechanism in the investigated nuclear reactions. In the present work an attempt was made to estimate the relative strengths of the interesting $^8$Be+$n$ and $^5$He+$alpha$ cluster configurations in $^9$Be. The branching ratios have been determined confirming that the $^5$He+$alpha$ configuration plays an important role. The configuration of $^9$Be consisting of two bound helium clusters $^3$He+$^6$He is significantly suppressed, whereas the two-body configurations ${}^{8}$Be+$n$ and ${}^{5}$He+$alpha$ including unbound $^8$Be and $^5$He are found more probable.
The spatial structure of $^{14}$N nucleus is studied within a five-particle model (three $alpha$-particles plus two nucleons). Using the variational approach with Gaussian bases, the ground-state energy and wave function are calculated for this five-particle system. Two spatial configurations in the ground-state wave function are revealed. The density distributions, pair correlation functions, and the momentum distributions of particles are analyzed and compared with those of the mirror nuclei $^{14}$C and $^{14}$O.
The previous Faddeev calculation of the two-alpha plus Lambda system for 9 Lambda Be is extended to incorporate the spin-orbit components of the SU_6 quark-model baryon-baryon interactions. We employ the Born kernel of the quark-model Lambda N LS interaction, and generate the spin-orbit component of the Lambda alpha potential by the alpha-cluster folding. The Faddeev calculation in the jj-coupling scheme implies that the direct use of the quark-model Born kernel for the Lambda N LS component is not good enough to reproduce the small experimental value Delta E^exp_{ls}=43 +- 5 keV for the 5/2^+ - 3/2^+ splitting. This procedure predicts three to five times larger values in the model FSS and fss2. The spin-orbit contribution from the effective meson-exchange potentials in fss2 is argued to be unfavorable to the small ls splitting, through the analysis of the Scheerbaum factors for the single-particle spin-orbit potentials calculated in the G-matrix formalism.
The cross section of the $^{9}$Be(n,$gamma$)$^{10}$Be reaction was calculated in the direct capture model. All parameters of the calculations were adjusted to properties of the $^{9}$Be + n system at thermal energies. The calculated cross section at thermonuclear energies shows the expected $1/v$ behavior of $s$-wave capture at low energies, but increases towards higher energies as typical $p$-wave capture. Excellent agreement between new experimental data in the astrophysically relevant energy region and the present calculation is found.
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