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Register a new userCompeting shell effect of protons and neutrons for superdeformation in $^{60}$Zn, $^{62}$Zn, and $^{64}$Ge
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Kenichi Yoshida
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Background: The observation of the superdeformed (SD) bands in $^{60,62}$Zn indicates a strong SD-shell effect at the particle numbers 30 and 32, where two and four neutron single-particles are considered to be promoted to the intruder $1g_{9/2}$ shell. However, the SD-yrast band in $^{62}$Zn is assigned negative parity. Purpose: I investigate various SD configurations in the rapidly rotating $^{60,62}$Zn isotopes, and attempt elucidating the different roles of the SD magic numbers 30 and 32. Method: I employ a nuclear energy-density functional (EDF) method: the configuration-constrained cranked Skyrme-Kohn-Sham approach is used to describe the rotational bands near the yrast line. Results: I find that the neutron number 32 favors stronger deformation than 30; a competing shell effect of protons and neutrons makes the SD-yrast structures of $^{62}$Zn unique. Due to the coherent shell effect, the positive-parity band emerges in $^{64}$Ge as an SD-yrast band with greater deformation than that in $^{60,62}$Zn. Furthermore, the present calculation predicts the occurrence of the hyperdeformed (HD) magic numbers 30 and 32 at a high rotational frequency $sim 2.0$ MeV$/hbar$. Conclusions: The negative-parity SD bands appear higher in energy than the positive-parity SD-yrast band in $^{60}$Zn and $^{64}$Ge, indicating that both the particle numbers 30 and 32 are SD magic numbers. The positive-parity HD states appear as the yrast band at $I sim 50hbar$ in $^{60}$Zn and $^{64}$Ge. The particle numbers 30 and 32 are magic numbers of SD and HD.
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Background $alpha$-nucleus potentials play an essential role for the calculation of $alpha$-induced reaction cross sections at low energies in the statistical model. Uncertainties of these calculations are related to ambiguities in the adjustment of the potential parameters to experimental elastic scattering angular distributions (typically at higher energies) and to the energy dependence of the effective $alpha$-nucleus potentials. Purpose The present work studies cross sections of $alpha$-induced reactions for $^{64}$Zn at low energies and their dependence on the chosen input parameters of the statistical model calculations. The new experimental data from the recent Atomki experiments allow for a $chi^2$-based estimate of the uncertainties of calculated cross sections at very low energies. Method The recent data for the ($alpha$,$gamma$), ($alpha$,$n$), and ($alpha$,$p$) reactions on $^{64}$Zn are compared to calculations in the statistical model. A survey of the parameter space of the widely used computer code TALYS is given, and the properties of the obtained $chi^2$ landscape are discussed. Results The best fit to the experimental data at low energies shows $chi^2/F approx 7.7$ per data point which corresponds to an average deviation of about 30% between the best fit and the experimental data. Several combinations of the various ingredients of the statistical model are able to reach a reasonably small $chi^2/F$, not exceeding the best-fit result by more than a factor of 2. Conclusions The present experimental data for $^{64}$Zn in combination with the statistical model calculations allow to constrain the astrophysical reaction rate within about a factor of 2. However, the significant excess of $chi^2/F$ of the best-fit from unity asks for further improvement of the statistical model calculations and in particular the $alpha$-nucleus potential.
In the present work we have reported comprehensive analysis of recently available experimental data [H.M. David et al., Phys. Lett. B {bf 726}, 665 (2013)] for high-spin states up to $17^+$ with $T=0$ in the odd-odd $N=Z$ nucleus $^{62}$Ga using shell model calculations within the full $f_{5/2}pg_{9/2}$ model space and deformed shell model based on Hartee-Fock intrinsic states in the same space. The calculations have been performed using jj44b effective interaction developed recently by B.A. Brown and A.F. Lisetskiy for this model space. The results obtained with the two models are similar and they are in reasonable agreement with experimental data. In addition to the $T=0$ and $T=1$ energy bands, band crossings and electromagnetic transition probabilities, we have also calculated the pairing energy in shell model and all these compare well with the available theoretical results.
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CUPID-0 is the first pilot experiment of CUPID, a next-generation project searching for neutrino-less double beta decay. In its first scientific run, CUPID-0 operated 26 ZnSe cryogenic calorimeters coupled to light detectors in the underground Laboratori Nazionali del Gran Sasso. In this work, we analyzed a ZnSe exposure of 11.34 kg$times$yr to search for the neutrino-less double beta decay of $^{70}$Zn and for the neutrino-less positron-emitting electron capture of $^{64}$Zn. We found no evidence for these decays and set 90$%$ credible interval limits of ${rm T}_{1/2}^{0 ubetabeta}(^{70}{rm Zn}) > 1.6 times 10^{21}$ yr and ${rm T}_{1/2}^{0 u EC beta+}(^{64}{rm Zn}) > 1.2 times 10^{22}$ yr, surpassing by almost two orders of magnitude the previous experimental results
We study the behavior of the fusion, break-up, reaction and elastic scattering of different projectiles on $^{64}$Zn, at near and above barrier energies. We present fusion and elastic scattering data with the tightly bound $^{16}$O and the stable weakly bound $^{6}$Li, $^{7}$Li and $^{9}$Be projectiles. The data were analyzed by coupled channel calculations. The total fusion cross sections for these systems are not affected by the break-up process at energies above the barrier. The elastic (non-capture) break-up cross section is important at energies close and above the Coulomb barrier and increases the reaction cross sections. In addition we also show that the break-up process at near and sub-barrier energies is responsible for the vanishing of the usual threshold anomaly of the optical potential and give rise to a new type of anomaly.
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