The role of neutron pairs in nuclear collective properties

Abstract

Abstract. The role of surface neutrons in nuclear properties was examined by comparing rigidities of nuclear collective vibrations and charge radii of even-even nuclei. Correlations of peaks in rigidities and minimal values of r 0 = R ch · A −1/3 parameters were revealed.Eighty years of nuclear investigations have revealed a large variety in nuclear characteristics, their consistent theoretical interpretation is up to now only partly successful. For example, the theory of multipole giant resonances (MGR) observed experimentally in the cross sections of different reactions on even-even nuclei cannot explain in full extent a great variety of their forms and widths. E.g., in the region of middle-mass nuclei the giant E1 resonance has a complicated structure. It is a well-known phenomenon and many more or less successful attempts were made to describe the GR structure in magic and semimagic nuclei. However, as one can see from experimental data, sometimes addition of a couple of neutrons drastically changes the envelope of resonance peak.One may assume that one of the sources of diversity in the resonance shape is a variety of rigidities of nuclear surface. This characteristic of nuclei was discussed already at the dawn of nuclear physics when liquid drop model of nuclei was created [1,2].In the collective coordinate representation the Hamiltonian of the nuclear surface vibrations reads [1]where the momenta b λμ conjugate to collective coordinates a λμ which describe the deformation of nuclear surface. The coefficient B λ is the vibrational mass parameter. The rigidity C λ which determines the potential energy of nuclear deformation is connected with the nuclear surface tension. For the quadrupole surface vibrations (λ = 2) the connection of rigidity with the surface tension σ of a nucleus having the charge and radius Ze and R, respectively, has the formIt was already mentioned in [1] that the nuclear rigidity (deformability) may considerably vary from nucleus to a e-mail: n.g.goncharova@gmail.com nucleus and is strongly influenced by its shell structure. Nuclear rigidity as regards to quadrupole vibrations is connected with the energy of the first collective 2 + 1 state and the mean squared deformation of a nucleus βThe values of β were estimated and listed in [3] for all at that time available even-even nuclei. The estimations were based on the measured probabilities of quadrupole transitions to the ground states B(2). Certainly, the results are model dependent and the variations in the root-mean-square deformation estimations is less than 20%.In this work, we present the results of comparison of the calculated rigidities with the charge radii parameters for several isotopic chains of even-even nuclei. The data on the nuclear charge radii are taken from [4]. The dependence of nuclear charge radii on the neutron number is shown in [5].