Shape transition in some rare-earth nuclei in relativistic mean field theory

Agrawal, B. K.; Sil, Tapas; Samaddar, S. K.; De, J. N.

doi:10.1103/physrevc.63.024002

Cited by 27 publications

(3 citation statements)

References 26 publications

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“…The finite-temperature relativistic Hartree-Bogoliubov theory citeNiu2013 and relativistic Hartree-Fock-Bogoliubov theory [39] for spherical nuclei have been formulated, and used to study pairing transitions in hot nuclei. The relativistic Hartree-BCS theory has been applied to study the temperature dependence of shapes and pairing gaps for 166,170 Er and rare-earth nuclei [40,41]. A shape transition from prolate to spherical shapes is found at temperatures ranging from 1.0∼2.7 MeV.…”

Section: Introductionmentioning

confidence: 99%

Shape evolution of ^72,74 Kr with temperature in covariant density functional theory

Zhang¹,

Niu²

2017

Chinese Phys. C

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The rich phenomena of deformations in neutron-deficient krypton isotopes such as the shape evolution with neutron number and the shape coexistence attract the interests of nuclear physicists for decades. It will be interesting to study such shape phenomena using a novel way, i.e., by thermally exciting the nucleus. So in this work, we develop the finite temperature covariant density functional theory for axially deformed nuclei with the treatment of pairing correlations by BCS approach, and apply this approach for the study of shape evolutions in 72,74 Kr with increasing temperatures. For 72 Kr, with temperature increasing, the nucleus firstly experiences a relatively quick weakening in oblate deformation at temperature T ∼ 0.9 MeV, and then changes from oblate to spherical at T ∼ 2.1 MeV. For 74 Kr, its global minimum locates at quadroupole deformation β2 ∼ −0.14 and abruptly changes to spherical at T ∼ 1.7 MeV. The proton pairing transition occurs at critical temperature 0.6 MeV following the rule Tc = 0.6∆p(0) where ∆p(0) is the proton pairing gap at zero temperature. The signatures of the above pairing transition and shape changes can be found in the curve of the specific heat. The single-particle level evolutions with the temperature are presented.

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Section: Introductionmentioning

confidence: 99%

Shape evolution of ^72,74 Kr with temperature in covariant density functional theory

Zhang¹,

Niu²

2017

Chinese Phys. C

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“…However, this kind of transition frequently occurs at high temperatures, e.g. 1.7 − 2.1 MeV for 72,74 Kr [58] and 1.0 − 2.7 MeV for 166,170 Er [59,60], which is above the temperature region considered in the present work. Despite that, we still calculate theoretical critical temperature due to shape phase transition (T C def ) using the formula T 6.6…”

Section: Resultsmentioning

confidence: 72%

Systematic investigation on semi-empirical thermodynamic quantities of excited nuclei using canonical ensemble

Tran,

Phan,

Nguyen

et al. 2024

J. Phys. G: Nucl. Part. Phys.

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Semi-empirical thermodynamic quantities (TQs) of 78 nuclei ranging from $^{43}$Sc to $^{243}$Pu have been systematically investigated in the temperature region below 1 MeV using the thermodynamic canonical ensemble. The latter is carried out by taking into account the experimental nuclear level density (NLD) data measured using the Oslo method for the low-excitation region below the neutron binding energy $B_n$ combining with the back-shifted Fermi gas NLD model for the excitation energy from $B_n$ to about 250 MeV. In particular, the uncertainty of the TQs propagating from the fluctuation of the experimental NLD data has been, for the first time, calculated. The results obtained indicate that the uncertainty of TQs due to the experimental NLD is incomparable with the changes caused by the nuclear structure effects. The free energy of even-even nuclei behave differently from that of odd-$A$ ones. The total energy in the \rev{low-temperature region below $T_E \simeq 0.4-0.6$ MeV for medium-mass nuclei and $T_E \simeq 0.2-0.4$ MeV for heavy-mass ones slowly varies. When temperature is from $T_E$ to 1 MeV, the total energy} increases extremely faster than the increase of temperature, exhibiting the constant-temperature behavior. The entropy exhibits an abrupt change in their slope at \rev{$T_S \simeq 0.2-0.4$ MeV} in medium-mass nuclei and \rev{$T_S \simeq 0.5-0.6$ MeV} in heavy-mass ones. \rev{The existence of $T_E$ and $T_S$ has been interpreted due to the breaking of the first Cooper pair.} Finally, the heat capacity shows strongly pronounced $S$-shape in nuclei belong to rare-earth region. \rev{The temperatures defined at the center of the $S-$shaped heat capacities, which are known to closely relate to the critical temperature of the pairing phase transition $T_C$, are quite close to those theoretically predicted, namely $T_C \approx 0.5\Delta-0.6\Delta$ with $\Delta = 12A^{-1/2}$ being the empirical pairing gap at zero temperature.} The semi-empirical TQs obtained in the present work can be, therefore, a reliable data source to test and/or validate many nuclear thermodynamical models and to examine some nuclear structure properties such as pairing and deformation.

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“…The basic thermal theory was developed in a period as early as the 1950s [38]. Later, the finite temperature Hartree-Fock approximation [39][40][41] and the finite temperature Hartree-Fock-Bogoliubov theory [42] Er and rare-earth nuclei using the relativistic Hartree-BCS theory [43,44]. In recent years, the finite temperature relativistic Hartree-Bogoliubov theory [45] and relativistic Hartree-Fock-Bogoliubov theory [46] for spherical nuclei were developed and employed in studies in which the relations between the critical temperature for the pairing transition and pairing gap at zero temperature are explored.…”

Section: Introductionmentioning

confidence: 99%

Shell corrections with finite temperature covariant density functional theory *

Zhang¹,

Lv²,

Sun³

2021

Chinese Phys. C

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The temperature dependence of the shell corrections to the energy , entropy , and free energy is studied by employing the covariant density functional theory for closed-shell nuclei. Taking Sm as an example, studies have shown that, unlike the widely-used exponential dependence , exhibits a non-monotonous behavior, i.e., first decreasing 20% approaching a temperature of MeV, and then fading away exponentially. Shell corrections to both free energy and entropy can be approximated well using the Bohr-Mottelson forms and , respectively, in which . Further studies on the shell corrections in other closed-shell nuclei, Sn and Pb, are conducted, and the same temperature dependencies are obtained.

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Shape transition in some rare-earth nuclei in relativistic mean field theory

Cited by 27 publications

References 26 publications

Shape evolution of ^72,74 Kr with temperature in covariant density functional theory

Shape evolution of ^72,74 Kr with temperature in covariant density functional theory

Systematic investigation on semi-empirical thermodynamic quantities of excited nuclei using canonical ensemble

Shell corrections with finite temperature covariant density functional theory *

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Shape transition in some rare-earth nuclei in relativistic mean field theory

Cited by 27 publications

References 26 publications

Shape evolution of 72,74 Kr with temperature in covariant density functional theory

Shape evolution of 72,74 Kr with temperature in covariant density functional theory

Systematic investigation on semi-empirical thermodynamic quantities of excited nuclei using canonical ensemble

Shell corrections with finite temperature covariant density functional theory *

Contact Info

Product

Resources

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Shape evolution of ^72,74 Kr with temperature in covariant density functional theory

Shape evolution of ^72,74 Kr with temperature in covariant density functional theory