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Register a new userHigh-spin structures of the near-spherical nuclei $^{91,92}$Zr
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Praveen Chandra Srivastava Dr.
Publication date
2015
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English
Authors
P.C. Srivastava
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In the present work, we have interpreted recently available experimental data for high-spin states of the near-spherical nuclei $^{91,92}$Zr, using the shell-model calculations within the full $f_{5/2}$, $p_{3/2}$, $p_{1/2}$, $g_{9/2}$ model space for protons and valence neutrons in $g_{9/2}$, $g_{7/2}$, $d_{5/2}$ orbits. We have employed a truncation for the neutrons due to huge matrix dimensions, by allowing one neutron excitation from $g_{9/2}$ orbital to $d_{5/2}$ and $g_{7/2}$ orbitals. Results are in good agreement with the available experimental data. Thus, theoretically, we have identified the structure of many high-spin states, which were tentatively assigned in the recent experimental work. The $^{91}$Zr $21/2^+$ isomer lies at low-energy region due to fully aligned spins of two $g_{9/2}$ protons and one $d_{5/2}$ neutron.
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In the present work we report comprehensive set of shell model calculations for arsenic isotopes. We performed shell model calculations with two recent effective interactions JUN45 and jj44b. The overall results for the energy levels and magnetic moments are in rather good agreement with the available experimental data. We have also reported competition of proton- and neutron-pair breakings analysis to identify which nucleon pairs are broken to obtain the total angular momentum of the calculated states. Further theoretical development is needed by enlarging model space by including $pi 0f_{7/2}$ and $ u 1d_{5/2}$ orbitals.
Shape evolution of Zr nuclei are investigated by the axial Hartree-Fock (HF) calculations using the semi-realistic interaction M3Y-P6, with focusing on roles of the tensor force. Deformation at $Napprox 40$ is reproduced, which has not been easy to describe within the self-consistent mean-field calculations. The spherical shape is obtained in $46leq Nleq 56$, and the prolate deformation is predicted in $58leq Nleq 72$, while the shape switches to oblate at $N=74$. The sphericity returns at $N=80$ and $82$. The deformation in $60lesssim Nlesssim 70$ resolves the discrepancy in the previous magic-number prediction based on the spherical mean-field calculations [Prog. Theor. Exp. Phys. textbf{2014}, 033D02]. It is found that the deformation at $Napprox 40$ takes place owing to the tensor force with a good balance. The tensor-force effects significantly depend on the configurations, and are pointed out to be conspicuous when the unique-parity orbit (e.g. $n0h_{11/2}$) is present near the Fermi energy, delaying deformation. These effects are crucial for the magicity at $N=56$ and for the predicted shape change at $N=74$ and $80$.
Nuclear level densities (NLDs) and $gamma$-ray strength functions ($gamma$SFs) have been extracted from particle-$gamma$ coincidences of the $^{92}$Zr($p,p gamma$)$^{92}$Zr and $^{92}$Zr($p,d gamma$)$^{91}$Zr reactions using the Oslo method. The new $^{91,92}$Zr $gamma$SF data, combined with photonuclear cross sections, cover the whole energy range from $E_{gamma} approx 1.5$~MeV up to the giant dipole resonance at $E_{gamma} approx 17$~MeV. The wide-range $gamma$SF data display structures at $E_{gamma} approx 9.5$~MeV, compatible with a superposition of the spin-flip $M1$ resonance and a pygmy $E1$ resonance. Furthermore, the $gamma$SF shows a minimum at $E_{gamma} approx 2-3$~MeV and an increase at lower $gamma$-ray energies. The experimentally constrained NLDs and $gamma$SFs are shown to reproduce known ($n, gamma$) and Maxwellian-averaged cross sections for $^{91,92}$Zr using the {sf TALYS} reaction code, thus serving as a benchmark for this indirect method of estimating ($n, gamma$) cross sections for Zr isotopes.
The properties of toroidal hyperheavy even-even nuclei and the role of toroidal shell structure are extensively studied within covariant density functional theory. The general trends in the evolution of toroidal shapes in the $Zapprox 130-180$ region of nuclear chart are established for the first time. These nuclei are stable with respect of breathing deformations. The most compact fat toroidal nuclei are located in the $Zapprox 136, Napprox 206$ region of nuclear chart, but thin toroidal nuclei become dominant with increasing proton number and on moving towards proton and neutron drip lines. The role of toroidal shell structure, its regularity, supershell structure, shell gaps as well as the role of different groups of the pairs of the orbitals in its formation are investigated in detail. The lowest in energy solutions at axial symmetry are characterized either by large shell gaps or low density of the single-particle states in the vicinity of the Fermi level in at least one of the subsystems (proton or neutron). Related quantum shell effects are expected to act against the instabilities in breathing and sausage deformations for these subsystems. The investigation with large set of covariant energy density functionals reveals that substantial proton $Z=154$ and 186 and neutron $N=228$, 308 and 406 spherical shell gaps exist in all functionals. The nuclei in the vicinity of the combination of these particle numbers form the islands of stability of spherical hyperheavy nuclei. The study suggests that the $N=210$ toroidal shell gap plays a substantial role in the stabilization of fat toroidal nuclei.
The recently observed two and four-quasiparticle high-spin rotational bands in the odd-odd nuclei $^{166, 168, 170, 172}$Re are investigated using the cranked shell model with pairing correlations treated by a particle-number conserving method. The experimental moments of inertia and alignments can be reproduced well by the present calculation if appropriate bandhead spins and configurations are assigned for these bands, which in turn confirms their spin and configuration assignments. It is found that the bandhead spins of those two rotational bands observed in $^{166}$Re~[Li {it et al.}, Phys. Rev. C 92 014310 (2015)] should be both increased by $2hbar$ to get in consistent with the systematics of the experimental and calculated moments of inertia for the same configurations in $^{168, 170, 172}$Re. The variations of the backbendings/upbendings with increasing neutron number in these nuclei are investigated. The level crossing mechanism is well understood by analysing the variations of the occupation probabilities of the single-particle states close to the Fermi surface and their contributions to the angular momentum alignment with rotational frequency. In addition, the influence of the deformation driving effects of the proton $1/2^-[541]$ ($h_{9/2}$) orbtial on the level crossing in $^{172}$Re is also discussed.
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