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Alpha-Cluster Model of Nuclear Structure <$ The Sixth International Conference "Modern Problems of Nuclear Physics", September 19-22, 2006 MPNP'ZOOa INP-SO behavior, respectively. If /r, < K , then the second (anomalous) term dominates at r -> oo. Examples of the anomalous asymptotic behavior of the 011{f) (*;, <K) have been found. The normal asymptotic term corresponds to the configuration when the distance between d and / fragments is finite at r -»oo, whereas the anomalous term originates from the configuration when the distance between c and/is finite at r —>• co . The anomalous asymptotic terms of the 01 corresponding to the 'generalized' triangle diagram containing an arbitrary number n of inner lines in place of lines d, e, and/have also been found. References: 1. A.M. Mukhamedzhanov and R.E. Tribble, Phys. Rev. C, V. 59, P. 3418 (1999). 2. L.D. Blokhintsev, Yad. Fiz. V. 34, P. 944(1981). UZ0603021 ALPHA-CLUSTER MODEL OF NUCLEAR STRUCTURE NieG.K. Institute of Nuclear Physics, Tashkent, Uzbekistan The approach based on the a-cluster model proposes some formulas to calculate the binding energies and the charge radii of the nuclei of the ^-stability valley and around it [1]. The formulas have been derived on the basis of the idea of isospin independence of inter-nucleon interactions. The approach implies that the nucleus is a dense package of alpha-clusters. The inter-cluster distances are determined by the charge radii of the clusters, so the radius of the nucleus R is defined by their number. Some amount of excess neutrons fill in the gap between the matter bodies of the a-clusters of the core [2]. Then the radius Rm of a p - stable isotope can be estimated by the volume occupied by the matter of the core and the volume of the charge of a few peripheral clusters. It has been shown that the condition Rm = R determines the amount of excess neutrons. The energy of these excess neutrons is described by a smooth function on the number of the neutron pairs. The formula to calculate the binding energy proper for the nucleus with five a-clusters turned out to be good for the other nuclei up to the most heavy ones. The formula to calculate the nuclear binding energy is evidently different from the well known Weizsacker formula. These two approaches give different estimations of the total Coulomb energy and the energy due to all inter-nucleon interactions, but the values of the total binding energies of these approaches are close. To calculate the charge radii both the approaches propose successful but different formulas, one is R ~A1/3 and the other R~ZI/S. A few useful phenomenological formulas have been found in the approach. These are the formulas to calculate the root mean square charge radius, the Coulomb radius and the radius of the last proton's position in dependence on the number of a-clusters. Besides, the empirical values of the Coulomb energy and the surface tension energy with a good accuracy have been obtained for the nuclei with N=Z. The values of the Coulomb repulsion energy and the nuclear force energy of the inter- cluster interaction, which are 1.925 MeV and 4.350 MeV, correspondingly, could be a good test in a microscopic description of the light nuclei 12C and 16O in the framework of the few-body approach. 89 Section I. Physics of Particles and Nuclei <^> The Sixth International Conference "Modern Problems of Nuclear Physics", September 19-22, 2006 MPW'2006 'NP-SO References: 1. G. K. Nie, arXiv:nucl-th/0512023vl 07Dec2005, accepted for publication in Modern Physics Letters A. 2. G. K. Nie, arXiv:nucl-th/0603054vl 22Mar2006, accepted for publication in Modern Physics Letters A UZ0603022 ASYMPTOTIC NORMALIZATION COEFFICIENTS OF BINDINGS 3t^ d + n AND 3He -+ d + p Nie G.K., Artemov S.V. Institute of Nuclear Physics, Tashkent, Uzbekistan One nucleon transfer reactions (d,t) and (3He,d) are important tools for obtaining spectroscopic information about nuclei [1,2]. For analysis of these reactions the values of neutron 2 2 and proton asymptotic normalization coefficients C and Cp of overlapping integrals of the nuclei t H d for the vertex t-^d+n and the nuclei 3He and d for the vertex 3He-»d+p are needed. 2 In [3] the value of the vertex constant for t->d+n: |Gt^d+J = 1.34 ± 0.02 fm, which 2 corresponds to Cn = 4.29 fm, was obtained from analysis of the experimental data on the reaction 2 2 d+d->t+p made in the framework of Dispersion Theory of nuclear reactions. Since Cn = Snbn 2 2 and Cp =Spbp [4], where ill/p is the asymptotic coefficient of the normalized to unit bound state wave function, Sn/P is the spectroscopic factor for the neutron and proton bindings, which are 2 2 2 2 equal in the case, the value of Cp can be obtained from equation Cn/Cp - bn /bp . In [5] the values bn/? have been obtained for the symmetric and mirror nuclei of lp shell by means of the Shrodinger equation where the equivalent neutron and proton nuclear bound state potentials are used. The equivalence of the single particle potentials is a consequence of isospin independence of nuclear force. For the nucleus 4He and the mirror nuclei 3t H He the radius of the last proton position is less than Coulomb radius, therefore the method is not proper for the nuclei. 2 2 In the work the values of Cn /Cv for the symmetric and mirror nuclei of lp shell in dependence on the difference between the proton and neutron binding energies AEnp are 2 2 extrapolated into AEnp=0 with Cn /Cp =l for neutron and proton bindings in deutron. The value of C/=4.37 fm for 3He-*d+p has been obtained. The work has been supported by Grant CST of Uzbekistan F-2.1.27. References: 1. I.R. Gulamov, A. M. Mukhamedzhanov and G.K. Nie// Phys. At. Nucl., V. 58. (1995)1689. 2. S.V. Artemov, I.R. Gulamov, E.A. Zaparov, I.Yu. Zotov, G.K. Nie. Phys. At. Nucl. V. 59. 3 (1996)428. 3. I. Borbei, A.M. Mukhamedzhanov, Intern. Conf. "Nuclear Spectroscopy and Structure of Nuclei" Almaty, 17-20 April, 1984, Nauka, p. 413. 4. L.D. Blokhintsev, I. Borbei, E.I. Dolinskii //EPAN 1977. T.8. p. 1189 5. G.K. Nie, Proceedings of Russian Academy of Sciences, physics series, V69, 1 (2005) 95. 90 Section I. Physics of Particles and Nuclei.
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