On the correlation between the deuteron quadrupole moment, the deuteron asymptotic D/S ratio, and the S -wave normalizat
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CLEI Theory
On the Correlation between the Deuteron Quadrupole Moment, the Deuteron Asymptotic D/S Ratio, and the S -Wave Normalization Constant V. A. Babenko* and N. M. Petrov Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Metrologicheskaya ul. 14b, 03680 Kyiv, Ukraine Received March 31, 2010; in final form, September 3, 2010
Abstract—The correlation between the deuteron quadrupole moment Q, the deuteron asymptotic D/S ratio η, and the deuteron asymptotic normalization constant AS is studied. For local nucleon–nucleon potentials, it was found that the quantities Q/η and A2S are related by a linear equation. Owing to this, the deuteron quadrupole moment Q can be determined from known values of AS and η with an absolute precision of about 0.0003 fm2 . The inclusion of the correction for meson-exchange currents and the use of the experimental neutron–proton phase shifts from the GWU partial-wave analysis made it possible to estimate the deuteron quadrupole moment at Q = 0.2852 fm2 , which is in good agreement with experimental data. DOI: 10.1134/S1063778811030069
1. INTRODUCTION The quadrupole moment Q of the deuteron is one of its fundamental features; its investigation permits deriving important information about nuclear nucleon–nucleon (N N ) interaction. The presence of a quadrupole moment in the ground state of the deuteron indicates that the deuteron is not a pure S-wave state but contains states of nonzero orbital angular momenta l. The simplest explanation for the existence of the deuteron quadrupole moment is that the 3 S1 + 3 D1 triplet state is the deuteron ground state [1]. This state is described by central forces with an admixture of tensor forces, which depend not only on the spacing between nucleons but also on the orientation of their spins. The presence of a D wave in the deuteron ground state violates spherical symmetry in the charge distribution, and this leads to the appearance of an electric quadrupole moment. Much attention has always been given to studying the deuteron quadrupole moment, both experimentally and theoretically [1–15]. Since the deuteron quadrupole moment is expressed in terms of the deuteron wave function, this moment can readily be determined for any N N potential. Values calculated by using many potentials for deuteron features, such as the binding energy εd , the quadrupole moment Q, the root-mean-square *
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matter radius rm , the asymptotic normalization constants AS and AD for the S and D waves, and the corresponding deuteron asymptotic D/S ratio η = AD /AS , make it possible to establish simple empirical correlations between these quantities. In particular, a linear dependence between Q/A2S and η calculated for a number of N N potentials was considered in [8–10]. Concurrently, the quantities Q and η were renormalized in such a way as to take into account the possible values of the pion–nucleon coupling constant f 2 that correspond to various potential models. It is noteworthy that the results obtained in [10] sug
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