Proton entropy excess and possible signature of pairing reentrance in hot nuclei

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The empirical heat capacities of some hot-rotating A ∼ 200 nuclei (184Re, 200Tl, 211Po, and 212At) have been investigated by combining the angular-momentum dependent back-shifted Fermi gas (BSFG) model of nuclear level density (NLD) with the experimental NLD data extracted from the neutron-evaporation spectra at the total angular momentum J = 12 hbar. The parameters of the BSFG are obtained by fitting its NLD to the corresponding measured data by using an advanced package of Program Modeling (CPM) provided by Python feature of IBM Decision Optimization CPLEX. The results obtained show that the shell correction plays an important role in the formation of empirical S-shaped heat capacity, which serves as a fingerprint for the pairing phase transition in finite nuclear systems. The 184Re nucleus, which is deformed and has small shell correction, exhibits a weaker S-shaped heat capacity than the remaining three spherical 200Tl, 211Po, and 212At nuclei that have large shell effect. This result contrasts with that recently predicted by the microscopic exact pairing plus independent-particle model at finite temperature (EP+IPM), in which the S-shaped heat capacity was predicted in 184Re only. This discrepancy between the heat capacities obtained within the BSFG and EP+IPM models suggests that an NLD model capable of well describing the experimental data while also having intrinsic and as complete as possible physical interpretations is still required in order to provide the exact description of nuclear thermodynamic quantities. In addition, more experimental NLD data in other mass and higher energy regions are also demanded.

supporting

confidence: 60%

Investigation of empirical heat capacity in hot-rotating A ∼ 200 nuclei

Xuan¹,

Hưng²,

Le³

et al. 2022

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“…Following our previous analyses in [24,27,34], a microscopic approach, based on the exact pairing plus independent-particle model at finite temperature (the so-called EP+IPM model), has been chosen to best describe the experimental NLD data. The formalism of EP+IPM has been widely presented in several studies, e.g.…”

Section: Resultsmentioning

confidence: 99%

“…It is also seen in figure 2(a) that the neutron pairing gap increases at low T, reaches a maximum at T ∼ 0.5 MeV, and strongly decreases after that. This is well-known as the pairing reentrance phenomenon, which is caused by the weakening of the thermal blocking effect due to the odd neutron in 69 Zn [24,34,41]. This phenomenon also results in a stronger variation of the neutron pairing gap with temperature at T > 0.5 MeV than that of the proton one as shown in figures 2(a) and (c).…”

Section: The Value Of Ementioning

confidence: 87%

Pairing phase transition in an odd–even hot ⁶⁹Zn nucleus

Senapati

Mondal

Bhattacharya³

et al. 2023

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The pairing phase transition in an odd-even hot-rotating 69Zn nucleus has been investigated by using the reported nuclear level density (NLD) data, which were experimentally extracted from the γ-gated particle spectra. The experimental NLDs have been compared with those obtained within the microscopic exact pairing plus independent-particle model at finite temperature (EP+IPM) along with the results of other microscopic calculations such as the Hartree-Fock BCS (HFBCS) and Hartree-Fock-Bogoliubov plus combinational (HFBC) methods. It is found that the experimental NLDs can be well described by the EP+IPM using the recommended quadrupole deformation parameter β2 = -0.164. Intriguingly, the heat capacity calculated using the EP+IPM NLD exhibits a sharp S-shape, which is not expected in such odd-even hot or hot-rotating system as reported earlier. Changing the deformation parameter β2 does not change much this S-shape. However, increasing or decreasing the pairing gaps could enhance or destroy the S-shaped heat capacity. Therefore, the S-shaped heat capacity in odd-even 69Zn nucleus is explained due to the deformation induced pairing correlation.

“…The entropy is also an interesting quantity as it represents the degree of disorder in a nuclear system, which is associated with the number of ways that nucleons can be arranged within a particular set of energy levels. For example, the entropy excess caused by one nucleon reveals the presence of pairing reentrance phenomenon [7], which has been predicted in both hot [8,9] and hot rotating nuclei [10][11][12][13].…”

Section: Introductionmentioning

confidence: 89%

“…[24][25][26]). For instance, Dey et al [7] indicated a possible signature of pairing reentrance at excitation energy below 1 MeV by studying the proton entropy excess of five pairs of nuclei, whose mass ranges from medium to heavy regions based on the entropy derived by using the MCE. Another example is the work of Guttormsen et al [28], in which the MCE is applied to extract empirical entropies of 231−233 Th and 237−239 U, revealing a constant entropy increase in even-odd nuclei as compared to their even-even neighbors.…”

Section: Introductionmentioning

confidence: 99%

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

Tran,

Phan,

Nguyen

et al. 2024

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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.