arXiv subjects

Andrzej Staszczak

Publications and source records attributed to Andrzej Staszczak.

7 recordsLinked to original sources

arXiv2019

States of the $^{12}$C Nucleus in the Toroidal Configuration

The $^{12}$C nucleus with $N$=6 and $Z$=6 is a doubly closed-shell nucleus in a toroidal potential. In the description of the ground state and the Hoyle state of $^{12}$C in the resonating group method or the generator coordinate method, a superposition of the orientations of Wheeler's triangular cluster on the cluster plane would naturally generate an intrinsic toroidal density. A toroidal state also has a probability amplitude to overlap with a 3-alpha cluster, which is the dominant decay mode for the Hoyle state. For these reasons, we study a toroidal description of the states of $^{12}$C in the toroidal configuration both phenomenologically and microscopically. A toroidal $^{12}$C nucleus distinguishes itself by toroidal particle-hole multiplet excitations between one toroidal single-particle shell to another. From such a signature and experimental data, we find phenomenologically that the Hoyle state and many of its higher excited states may be tentatively attributed to those of the $^{12}$C nucleus in a toroidal configuration. We then study the $^{12}$C system from a microscopic mean-field approximation using variational wave functions. We find that the equidensity surfaces of the $^{12}$C ground state exhibit a dense toroidal core immersed in lower-density oblate spheroids in the surface region. Furthermore, there are prominent toroidal features of the equidensity surfaces for the state at the Hoyle excitation energy, at which previous cluster model calculations indicate the presence of a 3-alpha cluster state. A toroidal coexistence model therefore may emerge to suggest the possibility that the physical Hoyle state may have probability amplitudes to be in the toroidal configuration and the 3-alpha cluster configuration.

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arXiv2018

Shells in a Toroidal Nucleus in the Intermediate Mass Region

Attention is fixed on shells in toroidal nuclei in the intermediate mass region using a toroidal single-particle potential. We find that there are toroidal shells in the intermediate mass region with large single-particle energy gaps at various nucleon numbers located at different toroidal deformations characterized by the aspect ratios of toroidal major to minor radius. These toroidal shells provide extra stability at various toroidal deformations. Relative to a toroidal core, Bohr-Mottelson spin-aligning particle-hole excitations may be constructed to occupy the lowest single-particle Routhian energies to lead to toroidal high-spin isomers with different spins. Furthermore, as a nucleon in a toroidal nucleus possesses a vorticity quantum number, toroidal vortex nuclei may be constructed by making particle-hole excitations in which nucleons of one type of vorticity are promoted to populate un-occupied single-particle orbitals of the opposite vorticity. Methods for producing toroidal high-spin isomers and toroidal vortex nuclei are discussed.

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arXiv2015

Theoretical studies of possible toroidal high-spin isomers in the light-mass region

We review our theoretical knowledge of possible toroidal high-spin isomers in the light mass region in 28$\le$$A$$\le$52 obtained previously in cranked Skyrme-Hartree-Fock calculations. We report additional toroidal high-spin isomers in $^{56}$Ni with $I$=114$\hbar$ and 140$\hbar$, which follow the same (multi-particle)--(multi-hole) systematics as other toroidal high-spin isomers. We examine the production of these exotic nuclei by fusion of various projectiles on $^{20}$Ne or $^{28}$Si as an active target in time-projection-chamber (TCP) experiments.

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arXiv2015

Toroidal high-spin isomers in light nuclei with N not equal to Z

The combined considerations of both the bulk liquid-drop-type behavior and the quantized aligned rotation with cranked Skyrme-Hartree-Fock approach revealed previously [Phys. Lett. B 738 (2014) 401] that even-even, N=Z, toroidal high-spin isomeric states have general occurrences for light nuclei with A between 28 and 52. We find that in this mass region there are in addition N not equal to Z toroidal high-spin isomers when the single-particle shells for neutrons and protons occur at the same cranked frequency $\hbar ω$. Examples of N not equal to Z toroidal high-spin isomers, $^{36}_{16}$S$_{20}$($I$=74$\hbar$) and $^{40}_{18}$Ar$_{22}$($I$=80,102$\hbar$), are located and examined. The systematic properties of these N not equal to Z toroidal high-spin isomers fall into the same regular (muti-particle)-(muti-hole) patterns as other N=Z toroidal high-spin isomers.

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arXiv2014

A region of high-spin toroidal isomers

The combined considerations of both the bulk liquid-drop-type behawior and the quantized angular momentum reveal that high-spin toroidal isomeric states may have general occurrences for light nuclei with 28 <= A <= 48. High-spin N=Z toroidal isomers in this mass region have been located theoretically using cranked self-consistent constraint Skyrme-Hartree-Fock model calculations.

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arXiv2009

Chirally symmetric effective field theory for nuclei

The Lorentz-invariant nuclear lagrangian of Furnstahl, Serot and Tang (FST) is discussed. The FST lagrangian is derived in terms of an effective field theory and exhibits a nonlinear realization of chiral symmetry $SU(2)_L\times SU(2)_R$. The relevant degrees of freedom are nucleons, pions and the low-lying non-Goldstone bosons: isoscalar scalar ($σ$) and vector ($ω$) mesons, and isovector vector ($ρ$) mesons. The terms in the lagrangian are organized by applying Georgi's naive dimensional analysis and naturalness condition. As a consequence all coupling constants in theory are dimensionless and of order unity.

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arXiv2008

Toroidal Super-Heavy Nuclei in Skyrme-Hartree-Fock Approach

Within the self-consistent constraint Skyrme-Hartree-Fock+BCS model (SHF+BCS), we found equilibrium toroidal nuclear density distributions in the region of super-heavy elements. For nuclei with a sufficient oblate deformation ($Q_{20}\leq$ -200 b), it becomes energetically favourable to change the genus of nuclear surface from 0 to 1, i.e., to switch the shape from a biconcave disc to a torus. The energy of the toroidal (genus=1) SHF+BCS solution relative to the compact (genus=0) ground state energy is strongly dependent both on the atomic number Z and the mass number A. We discuss the region of Z and A where the toroidal SHF+BCS total energy begins to be a global minimum.

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