Semiclassical shell-structure micro-macroscopic approach for the level density

Magner, A. G.; Sanzhur, A. I.; Fedotkin, S. N.; Levon, A. I.; Shlomo, S.

doi:10.1103/physrevc.104.044319

Cited by 9 publications

(44 citation statements)

References 59 publications

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“…But, in the following we will consider a critical point at the zero-excitation energy limit (β → ∞) where all high-order derivatives of the entropy over β are zeros, as suggested in Refs. [34][35][36][37]. This catastrophe point is similar to that in the zero-deformation limit for particles in a mean field for solving the symmetry breaking phenomenon within the semiclassical periodic-orbit theory (POT) [38][39][40][41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 53%

“…Following the development of Refs. [35,36] we will show below that the MMA has the same power expansion as the constant "temperature" model for low energy states at small excitation energies U .…”

Section: Introductionmentioning

confidence: 92%

“…Therefore, the integral over the Lagrange multiplier β in the inverse Laplace transformation of the partition function Z(β, α) should be carried out more accurately beyond the standard saddle-point method, see Refs. [34][35][36][37]. For other variables related to the neutron N and proton Z numbers, and projection M of the angular momentum I, one can apply the saddle point method assuming that N , Z, and I are large.…”

Section: Introductionmentioning

confidence: 99%

“…As shown in Refs. [34,36,37], the level density calculations for large particle numbers and angular momenta, and for a deeper understanding of the correspondence between the classical and the quantum approach, it is worthwhile to analyze the shell effects in the level density ρ (see Refs. [6,7]) and in the entropy, S, using the semiclassical POT [40,[43][44][45].…”

Section: Introductionmentioning

confidence: 99%

“…The MMA approach [34] was extended [35][36][37] for the description of shell, rotational, pairing and isotopic asymmetry effects on the level density itself for larger excitation energies U in nuclear systems. We will apply in the following this MMA for analytical level-density calculations for other nuclear systems with larger deformations and angular momenta.…”

Section: Introductionmentioning

confidence: 99%

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Microscopic-macroscopic level densities for low excitation energies

Magner,

Sanzhur,

Fedotkin

et al. 2022

Preprint

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Level density ρ(E, Q) is derived within the micro-macroscopic approximation (MMA) for a system of strongly interacting Fermi particles with the energy E and additional integrals of motion Q, in line with several topics of the universal and fruitful activity of A.S. Davydov. Within the extended Thomas Fermi and semiclassical periodic orbit theory beyond the Fermi-gas saddle-point method we obtain ρ ∝ Iν(S)/S ν , where Iν(S) is the modified Bessel function of the entropy S. For small shell-structure contribution one finds ν = κ/2 + 1, where κ is the number of additional integrals of motion. This integer number is a dimension of Q, Q = {N, Z, ...} for the case of two-component atomic nuclei, where N and Z are the numbers of neutron and protons, respectively. For much larger shell structure contributions, one obtains, ν = κ/2 + 2. The MMA level density ρ reaches the well-known Fermi gas asymptote for large excitation energies, and the finite micro-canonical combinatoric limit for low excitation energies. The additional integrals of motion can be also the projection of the angular momentum of a nuclear system for nuclear rotations of deformed nuclei, number of excitons for collective dynamics, and so on. Fitting the MMA total level density, ρ(E, Q), for a set of the integrals of motion Q = {N, Z}, to experimental data on a long nuclear isotope chain for low excitation energies, one obtains the results for the inverse level-density parameter K, which differs significantly from those of neutron resonances, due to shell, isotopic asymmetry, and pairing effects.

show abstract

Section: Introductionmentioning

confidence: 53%

Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Microscopic-macroscopic level densities for low excitation energies

Magner,

Sanzhur,

Fedotkin

et al. 2022

Preprint

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Level density within a micro-macroscopic approach

Magner¹,

Sanzhur²,

Fedotkin³

et al. 2022

Nuclear Physics A

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Microscopic-macroscopic level densities for low excitation energies

Magner

Sanzhur

Fedotkin

et al. 2022

Low Temperature Physics

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Level density [Formula: see text] is derived within the micro-macroscopic approximation (MMA) for a system of strongly interacting Fermi particles with the energy E and additional integrals of motion Q, in line with several topics of the universal and fruitful activity of A. S. Davydov. Within the extended Thomas Fermi and semiclassical periodic orbit theory beyond the Fermi-gas saddle-point method, we obtain [Formula: see text], where Iν ( S) is the modified Bessel function of the entropy S. For small shell-structure contribution, one finds ν = κ/2 + 1, where κ is the number of additional integrals of motion. This integer number is a dimension of Q, Q = { N, Z, …} for the case of two-component atomic nuclei, where N and Z are the numbers of neutrons and protons, respectively. For much larger shell structure contributions, one obtains ν = κ /2 + 2. The MMA level density ρ reaches the well-known Fermi gas asymptote for large excitation energies and the finite micro-canonical combinatoric limit for low excitation energies. The additional integrals of motion can also be the projection of the angular momentum of a nuclear system for nuclear rotations of deformed nuclei, number of excitons for collective dynamics, and so on. Fitting the MMA total level density ρ( E, Q) for a set of the integrals of motion Q = { N, Z}, to experimental data on a long nuclear isotope chain for low excitation energies, one obtains the results for the inverse level-density parameter K, which differs significantly from those of neutron resonances due to shell, isotopic asymmetry, and pairing effects.

show abstract

Semiclassical shell-structure micro-macroscopic approach for the level density

Cited by 9 publications

References 59 publications

Microscopic-macroscopic level densities for low excitation energies

Microscopic-macroscopic level densities for low excitation energies

Level density within a micro-macroscopic approach

Microscopic-macroscopic level densities for low excitation energies

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