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Register a new userCurvature Correction in the Strutinskys Method
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Mass calculations carried out by Strutinskys shell correction method are based on the notion of smooth single particle level density. The smoothing procedure is always performed using curvature correction. In the presence of curvature correction a smooth function remains unchanged if smoothing is applied. Two new curvature correction methods are introduced. The performance of the standard and new methods are investigated using harmonic oscillator and realistic potentials.
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This paper is dedicated to the memory of Vilen Mitrofanovich Strutinsky who would have been 80 this year. His achievements in theoretical nuclear physics are briefly summarized. I discuss in more detail the most successful and far-reaching of them, namely (1) the shell-correction method and (2) the extension of Gutzwillers semiclassical theory of shell structure and its application to finite fermionic systems, and mention some applications in other domains of physics.
For the Riemannian space, built from the collective coordinates used within nuclear models, an additional interaction with the metric is investigated, using the collective equivalent to Einsteins curvature scalar. The coupling strength is determined using a fit with the AME2003 ground state masses. An extended finite-range droplet model including curvature is introduced, which generates significant improvements for light nuclei and nuclei in the trans-fermium region.
The effect of correlations between the slope and the curvature of the symmetry energy on ground state nuclear observables is studied within the extended Thomas-Fermi approximation. We consider different isovector probes of the symmetry energy, with a special focus on the skin of $^{208}{rm Pb}$. We use a recently proposed meta-modelling technique to generate a large number of equation of state models, where the empirical parameters are independently varied. The results are compared to a set of calculations using 17 different Skyrme interactions. We show that the curvature parameter plays a non-negligible role on the neutron skin, while the effect is reduced in Skyrme functionals because of the correlation with the slope parameter.
It is shown that the continuum level density (CLD) at unbound energies can be calculated with the complex scaling method (CSM), in which the energy spectra of bound states, resonances and continuum states are obtained in terms of $L^2$ basis functions. In this method, the extended completeness relation is applied to the calculation of the Green functions, and the continuum-state part is approximately expressed in terms of discretized complex scaled continuum solutions. The obtained result is compared with the CLD calculated exactly from the scattering phase shift. The discretization in the CSM is shown to give a very good description of continuum states. We discuss how the scattering phase shifts can inversely be calculated from the discretized CLD using a basis function technique in the CSM.
The triple alpha reaction is a key to $^{12}$C production and is expected to occur in weakly-coupled, thermal plasmas as encountered in normal stars. We investigate how Coulomb screening affects the structure of a system of three alpha particles in such a plasma environment by precise three-body calculations within the Debye-Huckel approximation. A three-alpha model that has the Coulomb interaction modified in the Yukawa form is employed. Precise three-body wave functions are obtained by a superposition of correlated Gaussian bases with the aid of the stochastic variational method. The energy shifts of the Hoyle state due to the Coulomb screening are obtained as a function of the Debye screening length. The results, which automatically incorporate the finite size effect of the Hoyle state, are consistent with the conventional result based on the Coulomb correction to the chemical potentials of ions that are regarded as point charges in a weakly-coupled, thermal plasma. We have given a theoretical basis to the conventional point-charge approach to the Coulomb screening problem relevant for nuclear reactions in normal stars by providing the first evaluation of the Coulomb corrections to the $Q$ value of the triple alpha process that produces a finite size Hoyle state.
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