133 research outputs found
Islands of shape coexistence in proxy-SU(3) symmetry and in covariant density functional theory
Shape coexistence in even-even nuclei is observed when the ground state band
of a nucleus is accompanied by another K=0 band at similar energy but with
radically different structure. We attempt to predict regions of shape
coexistence throughout the nuclear chart using the parameter-free proxy-SU(3)
symmetry and standard covariant density functional theory. Within the
proxy-SU(3) symmetry the interplay of shell model magic numbers, formed by the
spin-orbit interaction, and the 3-dimensional isotropic harmonic oscillator
magic numbers, leads to the prediction of specific horizontal and vertical
stripes on the nuclear chart in which shape coexistence should be possible.
Within covariant density functional theory, specific islands on the nuclear
chart are found, in which particle-hole excitations leading to shape
coexistence are observed. The role played by particle-hole excitations across
magic numbers as well as the collapse of magic numbers as deformation sets in
is clarified.Comment: 12 pages, 2 figures, to appear in the Proceedings of the 39th
International Workshop on Nuclear Theory (Rila 2022), ed. M. Gaidarov and N.
Minkov (Heron Press, Sofia, 2022
Microscopic origin of shape coexistence in the N=90, Z=64 region
A microscopic explanation of the nature of shape coexistence in the N=90,
Z=64 region is suggested, based on calculations of single particle energies
through standard covariant density functional theory. It is suggested that
shape coexistence in the N=90 region is caused by the protons, which create
neutron particle-hole (p-h) excitations across the N=112 3-dimensional
isotropic harmonic oscillator (3D-HO) magic number, signaling the start of the
occupation of the 1i13/2 intruder orbital, which triggers stronger
proton-neutron interaction, causing the onset of the deformation and resulting
in the shape/phase transition from spherical to deformed nuclei described by
the X(5) critical point symmetry. A similar effect is seen in the N=60, Z=40
region, in which p-h excitations across the N=70 3D-HO magic number occur,
signaling the start of the occupation of the 1h11/2 intruder orbital.Comment: 6 pages, 7 figure
Islands of shape coexistence from single-particle spectra in covariant density functional theory
Using covariant density functional theory with the DDME2 functional and
labeling single-particle energy orbitals by Nilsson quantum numbers, a search
for particle-hole (p-h) excitations connected to the appearance of shape
coexistence is performed for Z=38 to 84. Islands of shape coexistence are found
near the magic numbers Z=82 and Z=50, restricted in regions around the relevant
neutron midshells N=104 and N=66 respectively, in accordance to the well
accepted p-h interpretation of shape coexistence in these regions, which we
call neutron-induced shape coexistence, since the neutrons act as elevators
creating holes in the proton orbitals. Similar but smaller islands of shape
coexistence are found near N=90 and N=60, restricted in regions around the
relevant proton midshells Z=66 and Z=39 respectively, related to p-h
excitations across the 3-dimensional isotropic harmonic oscillator (3D-HO)
magic numbers N=112 and N=70, which correspond to the beginning of the
participation of the opposite parity orbitals 1i13/2 and 1h11/2 respectively to
the onset of deformation. We call this case proton-induced shape coexistence,
since the protons act as elevators creating holes in the neutron orbitals, thus
offering a possible microscopic mechanism for the appearance of shape
coexistence in these regions. In the region around N=40, Z=40, an island is
located on which both neutron p-h excitations and proton p-h excitations are
present.Comment: 21 pages, 17 figure
Islands of shape coexistence: theoretical predictions and experimental evidence
Parameter-free theoretical predictions based on a dual shell mechanism within
the proxy-SU(3) symmetry of atomic nuclei, as well as covariant density
functional theory calculations using the DDME2 functional indicate that shape
coexistence (SC) based on the particle-hole excitation mechanism cannot occur
everywhere on the nuclear chart, but is restricted on islands lying within
regions of 7-8, 17-20, 34-40, 59-70, 96-112, 146-168 protons or neutrons.
Systematics of data for even-even nuclei possessing K=0 (beta) and K=2 (gamma)
bands support the existence of these islands, on which shape coexistence
appears whenever the K=0 bandhead 0_2^+ and the first excited state of the
ground state band 2_1^+ lie close in energy, with nuclei characterized by 0_2^+
lying below the 2_1^+ found in the center of these islands. In addition a
simple theoretical mechanism leading to multiple shape coexistence is briefly
discussed.Comment: 14 pages, 3 tables, 5 figure
Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry
The consequences of the attractive, short-range nucleon-nucleon (NN)
interaction on the wave functions of the Elliott SU(3) and the proxy-SU(3)
symmetry are discussed. The NN interaction favors the most symmetric spatial
SU(3) irreducible representation, which corresponds to the maximal spatial
overlap among the fermions. The percentage of the symmetric components out of
the total in an SU(3) wave function is introduced, through which it is found,
that no SU(3) irrep is more symmetric than the highest weight irrep for a
certain number of valence particles in a three dimensional, isotropic, harmonic
oscillator shell. The consideration of the highest weight irreps in nuclei and
in alkali metal clusters, leads to the prediction of a prolate to oblate shape
transition beyond the mid-shell region.Comment: 16 pages, 1 figure, 10 table
The islands of shape coexistence within the Elliott and the proxy-SU(3) Models
A novel dual-shell mechanism for the phenomenon of shape coexistence in
nuclei within the Elliott SU(3) and the proxy-SU(3) symmetry is proposed for
all mass regions. It is supposed, that shape coexistence is activated by large
quadrupole-quadrupole interaction and involves the interchange among the
spin-orbit (SO) like shells within nucleon numbers 6-14, 14-28, 28-50, 50-82,
82-126, 126-184, which are being described by the proxy-SU(3) symmetry, and the
harmonic oscillator (HO) shells within nucleon numbers 2-8, 8-20, 20-40, 40-70,
70-112, 112-168 of the Elliott SU(3) symmetry. The outcome is, that shape
coexistence may occur in certain islands on the nuclear map. The dual-shell
mechanism predicts without any free parameters, that nuclei with proton number
(Z) or neutron number (N) between 7-8, 17-20, 34-40, 59-70, 96-112, 146-168 are
possible candidates for shape coexistence. In the light nuclei the nucleons
flip from the HO shell to the neighboring SO-like shell, which means, that
particle excitations occur. For this mass region, the predicted islands of
shape coexistence, coincide with the islands of inversion. But in medium mass
and heavy nuclei, in which the nucleons inhabit the SO-like shells, shape
coexistence is accompanied by a merging of the SO-like shell with the open HO
shell. The shell merging can be accomplished by the outer product of the SU(3)
irreps of the two shells and represents the unification of the HO shell with
the SO-like shell.Comment: 31 pages, 25 figures, 4 table
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