Neutron and Proton Asymptotic Coefficients for Symmetric and Mirror Nuclei

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Neutron and Proton Asymptotic Coefficients for Symmetric and Mirror Nuclei

$$$ The Sixth International Conference "Modern Problems of Nuclear Physics", September 19-22,2006 MPNP'2006 , DVp.50 NEUTRON AND PROTON ASYMPTOTIC COEFFICIENTS FOR SYMMETRIC AND MIRROR NUCLEI Nie G.K., Artemov S.V. Institute of Nuclear Physics, Tashkent, Uzbekistan UZ0603023 2 The asymptotic normalization coefficient (ANC) Cn/P of overlap function of nuclei A and B where A—»B+n/p is calculated with using the spectroscopic factor Sn/P as follows [1] Cn/p ~Sn/pbn/p , where bn/p stands for the asymptotic coefficient of the normalized to unit bound state wave function of the nucleon. The spectroscopic factors of the last neutron and proton in the 2 symmetric and mirror nuclei are equal. Therefore C ICp-b^lbp. It was shown in [2] that the requirement of equivalence of the nuclear bound state potentials of the neutron and the proton belonging to one pair for the nuclei with N=Z and the mirror nuclei together with the well-depth procedure for Woods-Saxon potential in numerical calculations of 2 m the Shrodinger equation makes bp and the root mean square radius <r p> of the square wave function distribution dependent on each other. The requirement of equivalence of the nuclear bound state potentials for neutron and proton is a consequence of the isospin independence of the nuclear force. The representation allows one to estimate the radius of the last proton position Rp in the nucleus on the value of the difference of the experimental binding energies of the neutron and the proton [3,4]. On the assumption that <r p> =RP the bound state potential parameters and the values of bnip have been obtained for a set of the nuclei of \p and \d shells. That allows one to calculate the theoretical values of C^p for the known values of theoretical 5n/p, as well as to obtain the empirical values of the spectroscopic factors in the framework of the standard DWBA analysis of one nucleon transfer reactions. It is also possible to O O O*7 **}*! *^o calculate the proton ANC Cp , if Cn is known and in reverse, as it was done for AI, Si H Si [5]. The work has been supported by the international grant STCU 3081. References: 1. L.D. Blokhintsev, I. Borbey, E.I. Dolinsky//EPAN. 1977. v.8. p. 1189 2. G.K. Nie, Proceedings of Russian Academy of Sciences, physics series, T69, 1 (2005) 95 3. G.K.Nie, Radii and binding energies in the alpha-cluster model, arXiv:nucl-th/0603054vl 22Mar2006 4. G.K.Nie, Charge radii for P-stable nuclei, MPLA 2006, to be published. 5. G.K. Nie, S.V.Artemov, E.A.Zaparov, Frontiers in the Physics of Nucleus, LV National Conference on Nuclear Physics, June 28-July 1, 2005, Saint-Petersburg, Russia, Book of Abstracts, P. 269 91 Section I. Physics of Particles and Nuclei.

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