Mass splittings of nuclear isotopes in chiral solition approach
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ELEMENTARY PARTICLES AND FIELDS Theory
Mass Splittings of Nuclear Isotopes in Chiral Soliton Approach* V. B. Kopeliovich**, A. M. Shunderuk*** , and G. K. Matushko Institute for Nuclear Research, Russian Academy of Sciences, pr. Shestidesyatiletiya Oktyabrya 7a, Moscow, 117312 Russia Received April 4, 2005
Abstract—The differences in the masses of isotopes with atomic numbers between ∼10 and ∼30 can be described within the chiral soliton model in satisfactory agreement with data. The rescaling of the model is necessary for this purpose—a decrease in the Skyrme constant by ∼30%, providing the “nuclear variant” ¨ of the model. The asymmetric term in the Weizsacker–Bethe–Bacher mass formula for nuclei can be obtained as the isospin-dependent quantum correction to the nucleus energy. Some predictions of the binding energies of neutron-rich isotopes are made in this way from, e.g., 16 Be, 19 B to 31 Ne or 32 Na. The neutron-rich nuclides with high values of isospin are unstable relative to decay owing to strong interactions. The SK4 (Skyrme) variant of the model, as well as the SK6 variant (sixth-order term in the derivatives of the chiral field in the Lagrangian as soliton stabilizer), is considered; the rational-map approximation is used to describe multi-Skyrmions. PACS numbers : 11.30.Rd, 12.39.Fe DOI: 10.1134/S1063778806010169
1. INTRODUCTION In the absence of a complete theory of strong interactions and nuclear forces, the checking of fundamental principles, which are believed to hold in any theoretical model, can be useful and of great importance. The description of some well-established and rather general properties of nuclei, as well as searches for and studies of unusual forms of matter, in particular, neutron-rich nuclides, may provide an important source of lacking information and impact for the development of new concepts and ideas. The effective field theories are a powerful tool for the study of not only mesons, baryons, and their interactions at low energy [1–3], but also baryonic systems (nuclei) which appear as quantized bound states of Skyrmions with baryon number B ≥ 2. The properties of the deuteron and 3 He, 3 H, and 4 He were explained semiquantitatively [4, 5] starting from few basic principles and ingredients contained in the effective chiral Lagrangian of the Skyrme model [1] or its modifications (a brief review of early results can be found, e.g., in [6]). For the B = 2 system, the quantization of the bound state of Skyrmions possessing originally characteristic torus-like form [7] allows one to obtain the ∗
The text was submitted by the authors in English. E-mail: [email protected],kopelio@cpc. inr.ac.ru *** E-mail: [email protected] **
deuteron and the singlet N N -scattering state with isospin I = 1 [8]. The binding energy of the deuteron is about 30 MeV when zero-mode quantum corrections are taken into account. It decreases to ∼6 MeV when some nonzero-mode quantum corrections are included [9]. Some states with positive parity and unusual connection between isospin and angular mom
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