Average ground-state energy of finite Fermi systems

Centelles, M.; Lebœuf, P.; Monastra, Alejandro; Roccia, Jérôme; Schuck, Peter; Viñas, X.

doi:10.1103/physrevc.74.034332

Cited by 16 publications

(33 citation statements)

References 30 publications

(60 reference statements)

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“…In particular, the average is positive for a fixed shape, while it is negative in self-bound systems. Such a bias toward negative energies of the fluctuating part in self-bound systems is clearly observed in realistic calculations [5]. In the bottom part of Fig.…”

Section: Introductionsupporting

confidence: 52%

“…Recently, an explicit description for this effect was given. It was found that the contribution of the fluctuating part to the average of the energy is given by [5] …”

Section: General Settingmentioning

confidence: 99%

“…Moreover, the typical value of N is also small, and we find a correction to the mean value coming from the oscillatory part, calculated from Eq. (6), that vanishes as N −2/3 (cf [5] for further details of the method). Table II) using the first term in each sum in full line.…”

Section: External Potentialsmentioning

confidence: 99%

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Ground-state energy of finite Fermi systems

Roccia

Lebœuf

2007

Phys. Rev. C

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We study the ground-state shell correction energy of a fermionic gas in a mean-field approximation. Considering the particular case of 3D harmonic trapping potentials, we show the rich variety of different behaviors (erratic, regular, supershells) that appear when the number-theoretic properties of the frequency ratios are varied. For self-bound systems, where the shape of the trapping potential is determined by energy minimization, we obtain accurate analytic formulas for the deformation and the shell correction energy as a function of the particle number N . Special attention is devoted to the average of the shell correction energy. We explain why in self-bound systems it is a decreasing (and negative) function of N .

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Section: Introductionsupporting

confidence: 52%

“…Recently, an explicit description for this effect was given. It was found that the contribution of the fluctuating part to the average of the energy is given by [5] …”

Section: General Settingmentioning

confidence: 99%

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Ground-state energy of finite Fermi systems

Roccia

Lebœuf

2007

Phys. Rev. C

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“…The semiclassical Wigner-Kirkwood (WK) approach [18][19][20][21][22][23][24][25], on the other hand, makes no explicit reference to the single-particle spectrum, and achieves an accurate averaging of the given one-body Hamiltonian. Thus, the WK approach is a good alternative to the conventional Strutinsky smoothing scheme.…”

Section: Introductionmentioning

confidence: 99%

Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method

et al. 2010

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The semiclassical Wigner-Kirkwoodh expansion method is used to calculate shell corrections for spherical and deformed nuclei. The expansion is carried out up to fourth order inh. A systematic study of Wigner-Kirkwood averaged energies is presented as a function of the deformation degrees of freedom. The shell corrections, along with the pairing energies obtained by using the Lipkin-Nogami scheme, are used in the microscopic-macroscopic approach to calculate binding energies. The macroscopic part is obtained from a liquid drop formula with six adjustable parameters. Considering a set of 367 spherical nuclei, the liquid drop parameters are adjusted to reproduce the experimental binding energies, which yields a root mean square (rms) deviation of 630 keV. It is shown that the proposed approach is indeed promising for the prediction of nuclear masses.

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“…Using semiclassical POT arguments, the difference between energy and particle-number averaging was understood [41,42] as a symmetry correction which becomes especially significant for spherical nuclear shapes (particularly in the harmonic oscillator model). Smaller discrepancies for the deformed Fermi systems in the resulting shell-correction energies persist, however, as discussed in [41,42,43]. This point is thus still an object of current debate.…”

Section: 7)mentioning

confidence: 99%

Shell structure and orbit bifurcations in finite fermion systems

et al. 2011

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We first give an overview of the shell-correction method which was developed by V. M.Strutinsky as a practicable and efficient approximation to the general selfconsistent theory of finite fermion systems suggested by A. B. Migdal and collaborators. Then we present in more detail a semiclassical theory of shell effects, also developed by Strutinsky following original ideas of M. Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on shell structure. We first give a short overview of semiclassical trace formulae, which connect the shell oscillations of a quantum system with a sum over periodic orbits of the corresponding classical system, in what is usually called the "periodic orbit theory". We then present a case study in which the gross features of a typical double-humped nuclear fission barrier, including the effects of mass asymmetry, can be obtained in terms of the shortest periodic orbits of a cavity model with realistic deformations relevant for nuclear fission. Next we investigate shell structures in a spheroidal cavity model which is integrable and allows for fargoing analytical computation. We show, in particular, how period-doubling bifurcations are closely connected to the existence of the so-called "superdeformed" energy minimum which corresponds to the fission isomer of actinide nuclei. Finally, we present a general class of radial power-law potentials which approximate well the shape of a Woods-Saxon potential in the bound region, give analytical trace formulae for it and discuss various limits (including the harmonic oscillator and the spherical box potentials).

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Average ground-state energy of finite Fermi systems

Cited by 16 publications

References 30 publications

Ground-state energy of finite Fermi systems

Ground-state energy of finite Fermi systems

Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method

Shell structure and orbit bifurcations in finite fermion systems

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