The two-neutron separation energy of 6 He has been reproduced for the first time in a realistic parameter-free microscopic multicluster model comprising the α + n + n and t + t clusterizations, with α cluster breathing excitations included. The contribution of the t + t channel is substantial. A very thick (0.85 fm) neutron halo has been found in full agreement with the results of the latest phenomenological analysis.Recently nuclei far from stability attract much interest in nuclear physics. Prominent representatives of these nuclei are e.g. 6 He, 8 He, 8 Li, 8 B, 11 Li. There are several calculations for their description in macroscopic [1,2,3,4], semimicroscopic  and microscopic  models. In this paper we use our dynamical microscopic multiconfiguration multicluster model, developed and applied recently to the ground state of 6 Li , to study the neutron halo structure of the ground state of 6 He. All realistic macroscopic three-body models underbind 6 He by about 0.6-0.3 MeV. The situation is similar for 11 Li, which is predicted to be unbound by the most realistic parameter-free variational calculation . Our first aim is to check the validity of these models by comparing them with our microscopic model, and to understand the physics of this underbinding. Secondly, we calculate the thickness of the neutron halo of 6 He. For this quantity there are two contradicting experimental predictions, both of them are based on Glauber-type analyses of certain reaction cross section data. A simpler analysis gives ∼ 0.4 fm , while the other one, which comes from more realistic model assumptions, results in ∼ 0.9 fm . The latter result is well reproduced in a relativistic mean field model . As we shall see, our model strongly supports the second prediction, too.As the α particle is an inert cluster, it is natural to assume that an α + n + n model is a most adequate one for the description of 6 He. This nucleus is said to be borromean , which means that after the removal of any of the three clusters, the remaining nucleus decays into two fragments. This indicates that 6 He has a genuine three-body nature and explains why the macroscopic three-body models are so successful in describing its ground state structure and reactions . Although several physical quantities have been calculated, and a good overall agreement with experiment has been reached in these models, it is neccessary to investigate the validity of their foundation starting from microscopic grounds, because nucleon exchange and cluster rearrangement effects are expected to be important in this mass range. II. MODELThe microscopic dynamical multiconfiguration three-cluster model starts from the following trial function for the six-body problem: Ψ = S,l1,l2,L Ψ α(nn) S,(l1l2)L + S,l1,l2,L Ψ n(αn) S,(l1l2)L =
Abstract:The bulk of the carbon in our universe is produced in the triple-alpha process in helium-burning red giant stars. We calculated the change of the triple-alpha reaction rate in a microscopic 12-nucleon model of the 12 C nucleus and looked for the effects of minimal variations of the strengths of the underlying interactions. Stellar model calculations were performed with the alternative reaction rates. Here, we show that outside a narrow window of 0.5 and 4 % of the values of the strong and Coulomb forces, respectively, the stellar production of carbon or oxygen is reduced by factors of 30 to 1000. The formation of12 C through the triple-alpha process takes place in two sequential steps in the He-burning phase of red giants. In the first step, the unstable 8 Be with a lifetime of only about 10 −16 s is formed in a reaction equilibrium with the two alpha particles, α + α ⇀ ↽ 8 Be. In the second step, an additional alpha particle is captured, 8 Be(α, γ) 12 C. Without a suitable resonance in 12 C, the triple-alpha rate would be much too small to account for the 12 C abundance in our universe. Hoyle (1) suggested that a resonance level in 12 C, at about 300-400 keV above the three-alpha threshold, would enhance the triple-alpha reaction rate and would explain the abundance of 12 C in our universe. Such a level was subsequently found experimentally when a resonance that possessed the required properties was discovered (2, 3). It is the second 0 + state in 12 C, denoted by 0 + 2 . Its modern parameters (4) are ε = (379.47 ± 0.18) keV, Γ = (8.3 ± 1) eV, and Γ γ = (3.7 ± 0.5) meV, where ε is the resonance energy in the center-of-mass frame relative to the three-alpha threshold, and Γ and Γ γ are the total width and radiative width, respectively.The isotope 12 C is synthesized further in the He burning in red giants by alpha capture to the O isotope 16 O, leading to an abundance ratio in the universe of 12 C : 16 O ≈ 1 : 2 (5). If the carbon abundance in the universe were suppressed by orders of magnitude, no carbon-based life could have developed in the universe. But the production of O is also necessary because no spontaneous development of carbon-based life is possible without the existence of water.Here, we investigated the abundance ratios of C and O by starting from slight variations of the strength of the nucleon-nucleon (N-N) interaction with a microscopic 12-nucleon model. In previous studies, only hypothetical ad hoc shifts of the resonance energy of the 0 + 2 state were considered (6). Some preliminary results of our cal-1
The relationship between the Coulomb displacement energy for the A=8, J=2 + , T=1 state and the low-energy astrophysical S 17 factor for the 7 Be(p,γ) 8 B reaction is discussed. The displacement energy is interpreted in a particle-hole model. The dependence of the particle displacement energy on the potential well geometry is investigated and is used to relate the particle displacement energy to the rms radius and the asymptotic normalization of the valence proton wave function in 8 B. The asymptotic normalization is used to calculate the astrophysical S 17 factor for the 7 Be(p,γ) reaction. The relationship to the 7 Li(n,γ) reaction, the 8 B quadrupole moment, radial density, and break-up momentum distribution are also discussed.
We study the nonresonant part of the 7 Be(p, γ) 8 B reaction using a threecluster resonating group model that is variationally converged and virtually complete in the 4 He+ 3 He+p model space. The importance of using adequate nucleon-nucleon interaction is demonstrated. We find that the low-energy astrophysical S-factor is linearly correlated with the quadrupole moment of 7 Be. A range of parameters is found where the most important 7 Be and 7 Li properties are reproduced simultaneously; the corresponding S-factor at E cm = 20 keV is 24.6 − 26.1 eV·b.PACS numbers: 25.40. Lw, 21.60.Gx, 27.20.+n, 95.30.Cq Typeset using REVT E X
Using the complex scaling method, the low-lying three-body resonances of 6 He, 6 Li, and 6 Be are investigated in a parameter-free microscopic threecluster model. In 6 He a 2 + , in 6 Li a 2 + and a 1 + , and in 6 Be the 0 + ground state and a 2 + excited state is found. The other experimentally known 2 + state of 6 Li cannot be localized by our present method. We have found no indication for the existence of the predicted 1 − soft dipole state in 6 He. We argue that the sequential decay mode of 6 He through the resonant states of its two-body subsystem can lead to peaks in the excitation function. This process can explain the experimental results in the case of 11 Li, too. We propose an experimental analysis, which can decide between the soft dipole mode and the sequential decay mode.
We investigate the dependence of the carbon and oxygen production in stars on the 3α rate by varying the energy of the 0 + 2 -state of 12 C and determine the resulting yields for a selection of low-mass, intermediate-mass, and massive stars. The yields are obtained using modern stellar evolution codes that follow the entire evolution of massive stars, including the supernova explosion, and consider in detail the 3 rd dredge-up process during the thermally pulsating asymptotic giant branch of low-mass and intermediate-mass stars. Our results show that the C and O production in massive stars depends strongly on the initial mass, and that it is crucial to follow the entire evolution. A rather strong C production during the Heshell flashes compared to quiescent He burning leads to a lower sensitivity of the C and O production in low-mass and intermediate-mass stars on the 3α-rate than predicted in our previous work. In particular, the C production of intermediate-mass stars seems to have a maximum close to the actual value of the 0 + 2 energy level of 12 C.
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