Algebraic fermion models and nuclear structure physics

Troltenier, D.; Blokhin, A. L.; Draayer, J. P.; Rompf, D.; Hirsch, Jorge G.

doi:10.1063/1.50225

Cited by 4 publications

(4 citation statements)

References 2 publications

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“…Further, it has been shown that there exists an inverse correlation between the Gamow-Teller strength and the quadrupole moment [34,35]. It is well known that the pairing degree of freedom accounts for the preference of nuclei to have a spherical form, whereas the quadrupole-quadrupole (QQ) interaction increases the collectivity in the nuclear intrinsic wave functions and makes the nucleus deformed.…”

Section: Introductionmentioning

confidence: 99%

Two-neutrino positron double-beta decay of 106Cd for the 0+ → 0+ transition

et al. 2004

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The two neutrino positron double beta decay of 106 Cd for 0 + → 0 + transition has been studied in the Hartree-Fock-Bogoliubov model in conjunction with the summation method. In the first step, the reliability of the intrinsic wave functions of 106 Cd and 106 Pd nuclei has been tested by comparing the theoretically calculated results for yrast spectra, reduced B(E2:0 + → 2 + ) transition probabilities, quadrupole moments Q(2 + ) and gyromagnetic factors g(2 + ) with the available experimental data. In the second step, the nuclear transition matrix element M 2ν and the half-life1/2 for 0 + → 0 + transition have been calculated with these wave functions. Moreover, we have studied the effect of deformation on nuclear transition matrix element M 2ν .

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Section: Introductionmentioning

confidence: 99%

Two-neutrino positron double-beta decay of 106Cd for the 0+ → 0+ transition

et al. 2004

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“…In the HO scheme the proton ( ) and the neutron irrep (ν) irreps for 16 O are (λ , ν ) HO =(0, 0), (λ ν , µ ν ) HO =(0, 0) (see Table I). The result of the outer product (λ, µ) ⊗ (λ, µ) ν [46,[85][86][87] is:…”

Section: Harmonic Oscillator (Ho) Magic Numbersmentioning

confidence: 99%

“…[125]. The fact, that the irreps of a proton or neutron configuration in a SO-like and in a HO shell have to be coupled by their outer product [46,[85][86][87] is further reinforced by the experimentally observed monopole transition probabilities B(E0) among the two bands of shape coexistence [23,112]. If the irreps of the two bands of shape coexistence were irrelevant, then the strong B(E0)s would not have been justified in the SU(3) symmetry.…”

Section: The Islands Of Shape Coexistencementioning

confidence: 99%

“…[126][127][128], the finite barrier among the two minima of the potential guarantees, that B(E0)s are allowed to occur among the coexisting shapes, while an infinite barrier in the double well potential would not allow tunneling among the two shapes. The shell merging is accomplished within the SU(3) symmetry, by the outer product (coupling) of two irreps [46,[85][86][87], which derives numerous irreps as a result. A physical criterion, based on the first principles of nuclear physics, has to be applied, in order to pick the right irrep, which describes the coexisting bands of a heavy nucleus with shape coexistence.…”

Section: The Islands Of Shape Coexistencementioning

confidence: 99%

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The islands of shape coexistence within the Elliott and the proxy-SU(3) Models

Martinou,

Bonatsos,

Mertzimekis

et al. 2021

Preprint

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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 unificaton of the HO shell with the SO-like shell.

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