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تسجيل مستخدم جديدLarge collection of astrophysical S-factors and its compact representation
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Numerous nuclear reactions in the crust of accreting neutron stars are strongly affected by dense plasma environment. Simulations of superbursts, deep crustal heating and other nuclear burning phenomena in neutron stars require astrophysical S-factors for these reactions (as a function of center-of-mass energy E of colliding nuclei). A large database of S-factors is created for about 5000 non-resonant fusion reactions involving stable and unstable isotopes of Be, B, C, N, O, F, Ne, Na, Mg, and Si. It extends the previous database of about 1000 reactions involving isotopes of C, O, Ne, and Mg. The calculations are performed using the Sao Paulo potential and the barrier penetration formalism. All calculated S-data are parameterized by an analytic model for S(E) proposed before [Phys. Rev. C 82, 044609 (2010)] and further elaborated here. For a given reaction, the present S(E)-model contains three parameters. These parameters are easily interpolated along reactions involving isotopes of the same elements with only seven input parameters, giving an ultracompact, accurate, simple, and uniform database. The S(E) approximation can also be used to estimate theoretical uncertainties of S(E) and nuclear reaction rates in dense matter, as illustrated for the case of the 34Ne+34Ne reaction in the inner crust of an accreting neutron star.
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Using the Sao Paulo potential and the barrier penetration formalism we have calculated the astrophysical factor S(E) for 946 fusion reactions involving stable and neutron-rich isotopes of C, O, Ne, and Mg for center-of-mass energies E varying from 2
MeV to 18-30 MeV (covering the range below and above the Coulomb barrier). We have parameterized the energy dependence S(E) by an accurate universal 9-parameter analytic expression and present tables of fit parameters for all the reactions. We also discuss the reduced 3-parameter version of our fit which is highly accurate at energies below the Coulomb barrier, and outline the procedure for calculating the reaction rates. The results can be easily converted to thermonuclear or pycnonuclear reaction rates to simulate various nuclear burning phenomena, in particular, stellar burning at high temperatures and nucleosynthesis in high density environments.
We propose a physically transparent analytic model of astrophysical S-factors as a function of a center-of-mass energy E of colliding nuclei (below and above the Coulomb barrier) for non-resonant fusion reactions. For any given reaction, the S(E)-mod
el contains four parameters [two of which approximate the barrier potential, U(r)]. They are easily interpolated along many reactions involving isotopes of the same elements; they give accurate practical expressions for S(E) with only several input parameters for many reactions. The model reproduces the suppression of S(E) at low energies (of astrophysical importance) due to the shape of the low-r wing of U(r). The model can be used to reconstruct U(r) from computed or measured S(E). For illustration, we parameterize our recent calculations of S(E) (using the Sao Paulo potential and the barrier penetration formalism) for 946 reactions involving stable and unstable isotopes of C, O, Ne, and Mg (with 9 parameters for all reactions involving many isotopes of the same elements, e.g., C+O). In addition, we analyze astrophysically important 12C+12C reaction, compare theoretical models with experimental data, and discuss the problem of interpolating reliably known S(E) values to low energies (E <= 2-3 MeV).
Low energy capture cross sections are calculated within a microscopic many-body approach using an effective Hamiltonian derived from the Argonne V18 potential. The dynamics is treated within Fermionic Molecular Dynamics (FMD) which uses a Gaussian wa
ve-packet basis to represent the many-body states. A phase-shift equivalent effective interaction derived within the Unitary Correlation Operator Method (UCOM) that treats explicitly short-range central and tensor correlations is employed. As a first application the 3He(alpha,gamma)7Be reaction is presented. Within the FMD approach the microscopic many-body wave functions of the 3/2- and 1/2- bound states in 7Be as well as the many-body scattering states in the 1/2+, 3/2+ and 5/2+ channels are calculated as eigenstates of the same microscopic effective Hamiltonian. Finally the S-factor is calculated from E1 transition matrix elements between the many-body scattering and bound states. For 3He(alpha,gamma)7Be the S-factor agrees very well, both in absolute normalization and energy dependence, with the recent experimental data from the Weizmann, LUNA, Seattle and ERNA experiments. For the 3H(alpha,gamma)7Li reaction the calculated S-factor is about 15% above the data.
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