Fission dynamics of excited nuclei within the liquid-drop model

We evaluate the temperature T_scis at the scission point and the saddle-to-scission time τ_scis for the fission of heated nuclei. We use classical Lagrange-like equations of motion within the liquid-drop model. The nuclear surface is parameterized by a two-parameter family of the Lawrence shapes. Conservative forces are defined through the free energy of the nucleus at finite temperatures. We use the friction tensor that is derived from the Navier-Stokes momentum-flux tensor and which takes into account the boundary conditions at the nuclear surface. The scission line is determined from the instability condition of the nuclear shape with respect to variations of the neck radius. A numerical solution to the dynamical equations is obtained for the ²³⁶U nucleus. The viscosity coefficient μ is deduced from a comparison of experimental data on the kinetic energy of fission fragments with the computed one. It is found that μ obtained by using our approach deviates significantly from μ of the standard hydrodynamic model.     

New formula for calculating coulomb energies in the liquid-drop model

A new transformation of double volume integrals into double surface integrals is presented. A simple regular method for deriving integrands in a surface integral is proposed. This method is used to calculate the Coulomb energy of a nucleus within the model of a liquid drop with a sharp boundary. Numerical results obtained on the basis of the new formula are compared with those calculated by one of the formulas employed previously.     

An analytical folding potential for deformed nuclei

Concentrating on nucleon- andα-nucleus interactions the folding approach is applied to light deformed target nuclei. The analytically evaluated potentials depend onl. Forl=0, 2 and 4 the formulae for the elastic and inelastic interactions are given discussing also the effect of different forces and charge distributions on the formfactors.     

Heavy deformed nuclei in the shell model Monte Carlo method

We extend the shell model Monte Carlo approach to heavy deformed nuclei using a new proton-neutron formalism. The low excitation energies of such nuclei necessitate low-temperature calculations, for which a stabilization method is implemented in the canonical ensemble. We apply the method to study a well-deformed rare-earth nucleus, 162Dy. The single-particle model space includes the 50-82 shell plus 1f_{7/2} orbital for protons and the 82-126 shell plus 0h_{11/2}, 1g_{9/2} orbitals for neutrons. We show that the spherical shell model reproduces well the rotational character of 162Dy within this model space. We also calculate the level density of 162Dy and find it to be in excellent agreement with the experimental level density, which we extract from several experiments.     

Released energy formula for proton radioactivity based on the liquid-drop model

In this work, based on the liquid-drop model and considering the shell correction, we propose a simple formula to calculate the released energy of proton radioactivity(Q_p). The parameters of this formula are obtained by fitting the experimental data of 29 nuclei with proton radioactivity from ground state. The standard deviation between the theoretical values and experimental ones is only 0.157 Me V. In addition, we extend this formula to calculate 51 proton radioactivity candidates in region 51≤Z≤83 taken from the latest evaluated atomic mass table AME2016 and compared with the Q_p calculated by WS4 and HFB-29. The calculated results indicate that the evaluation ability of this formula for Q_p is inferior to WS4 while better than HFB-29.     

Similarities and differences between nuclei and metallic clusters in the liquid-drop model

The gross features of potential-energy surfaces of metallic, liquid clusters are compared with the corresponding properties of nuclei and their influence on the decay modes of excited systems is discussed. The interaction of two spherical, surface-charged droplets is compared with heavy-ion interaction potentials. Presented at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1998.     

Shell model calculations for heavy deformed nuclei

The pseudo SU(3) model is shown to be a powerful scheme for describing the excitation spectra as well asB(E2) andB(M1) transition strengths in heavy deformed nuclei. It is also useful for describing double beta decay amplitudes for transitions from the ground state of an even-even nucleus to the ground and excited states of the daughter nucleus, both for the two and zero neutrino emitting modes. The existence of selection rules which strongly restricts the decays is discussed. Anti-correlations between the quadrupole deformation and the Gamow-Teller (GT⁺) strength are found in an extension of the pseudo SU(3) model which explicitly includes pairing, which is also able to describe the fragmentation of the scissors mode. The projected shell model is introduced and proposed as an alternate means for studying single and double beta decay processes. Presented by J.G. Hirsch at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. This work was supported in part by CONACyT (México), CONICET (Argentina), NSF and DOE (U.S.A.).     

Investigation of deformed nuclei with a new potential combination

We investigate the alpha-decay half-lives of non-spherical nuclei with the Yukawa potential as the prox- imity potential and an angle-dependent term that accounts for the deformation effects and apply the results to Ho, Tb, Lu, Tin, Ta, Hf, Yb, Re, Ir, Pt, Au, Po, etc. as examples. The comparison with the existing data is encouraging.     

Confrontation between the quasiparticle-phonon nuclear model and the interacting boson model for deformed nuclei

TheK ^π=0⁺, 2⁺ and 4⁺ states are considered in doubly even deformed nuclei. It is shown that in the quasiparticle-phonon nuclear model (QPNM) and in the interacting boson model (IBM) a vibrational state has one dominating component. The states withK _n ^π =0 ₃ ⁺ , 0 ₄ ⁺ 0 ₅ ⁺ 2 ₂ ⁺ , 2 ₃ ⁺ , 4 ₁ ⁺ and 4 ₂ ⁺ have a dominating one-phonon component within the QPNM and a two- or three-boson component within the IBM. According to the QPNM the contribution of two-phonon components to the wave functions of these states is less than 10%, i.e. there is a qualitative discrepancy in describing the structure of these states within the QPNM and the IBM. The experimental data indicate the existence in these states of one-phonon or two-quasiparticle components. They are rather well described within the QPNM. These states cannot be described within the IBM. This is due to the fact that the IBM takes into account only a small part of the space of two-quasiparticle states, just the one entering intoΒ- andγ-vibrational states.     

A method for calculating the ground-state properties of light closed-shell nuclei

The He⁴ nucleus ground state is studied by means of the Goldstone perturbation theory. Explicit expressions for the binding energy up to the second order in the t-interaction and for expectation values of single-particle operators (mean square radius, mass and charge distribution) up to the first order are derived. The effects of the centre-of-mass motion of the whole nucleus are considered in detail, especially with respect to mass and charge distribution. The numerical results for the charge form factor and distribution confirm the deviation from the Gaussian model measured recently.The author thanks Professor I. Úlehla for interesting discussions and M. Plchová for technical assistance.     

A new model for calculating the binding energy of the lithium nucleus under the generalized Yukawa potential and Hellmann potential

In this paper, the Schrodinger equation for a 6-body system is studied. We solve this equation for the lithium nucleus by using a supersymmetry method with several specific potentials. These potentials are the Yukawa potential, the generalized Yukawa potential and the Hellmann potential. The results of our model for all calculations show that the ground state binding energy of the lithium nucleus with these potentials is very close to that obtained experimentally.     

Extension of the multiphonon method to odd mass deformed nuclei

The multiphonon method based on one type of phonon is extended to odd mass nuclei. The formulas for the matrix elements of one and two body operators are given.     

Algebraic solutions of an extended pairing model for well deformed nuclei

A Nilsson mean-field plus extended pairing interaction Hamiltonian with many-pair interaction terms is proposed. Eigenvalues of the extended pairing model are easy to obtain. Our investigation shows that one- and two-body interactions continue to dominate the dynamics for relatively small values of the pairing strength. As the strength of the pairing interaction grows, however, the three- and higher many-body interaction terms grow in importance. A numerical study of even-odd mass differences in the (154-171)Yb isotopes shows that the extended pairing model is applicable to well deformed nuclei.     

Effective theory for deformed nuclei

Techniques from effective field theory are applied to nuclear rotation. This approach exploits the spontaneous breaking of rotational symmetry and the separation of scale between low-energy Nambu–Goldstone rotational modes and high-energy vibrational and nucleonic degrees of freedom. A power counting is established and the Hamiltonian is constructed at next-to-leading order.     

A method for calculating the ground state properties of light closed-shell nuclei

A method for solving the reaction matrix equation in closed-shell nuclei using a spherical harmonic-oscillator representation is presented. The equation is transformed to an infinite algebraic system for the matrix elements, the exclusion operator being treated exactly. The system can be solved with arbitrary accuracy which depends only on the chosen truncation.