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arXiv:2408.00423

Pairing phase transition in the odd-A nuclei: identification and classification

Yumeng Wang, Yuhang Gao, Lang Liu

Published Aug 1, 2024• 0 citations
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Abstract

The investigation into the pairing phase transition in the odd-A nucleus 161Dy utilizes a sophisticated blend of covariant density functional theory and the shell-model-like approach. It is discerned that variations in thermodynamic quantities at the critical temperature do not exclusively align with pairing phase transitions. The presence of an S-shaped heat capacity curve, often interpreted as an indication of such transitions, does not offer a definitive confirmation. Additional factors, including the blocking effect, can modify the heat capacity curve and impede the transition process. The pairing phase transition in 161Dy, occurring around 0.7 to 1.0 MeV, is unequivocally characterized as a first-order transition. Furthermore, an exploration into the impact of varying strengths of pairing correlations on these transitions reveals a nonlinear relationship, adding complexity to the transition dynamics.

DOI
10.48550/arxiv.2408.00423

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The investigation into the pairing phase transition in the odd-A nucleus 161Dy utilizes a sophisticated blend of covariant density functional theory and the shell-model-like approach. It is discerned that variations in thermodynamic quantities at the critical temperature do not exclusively align with pairing phase transitions. The presence of an S-shaped heat capacity curve, often interpreted as an indication of such transitions, does not offer a definitive confirmation. Additional factors, including the blocking effect, can modify the heat capacity curve and impede the transition process. The pairing phase transition in 161Dy, occurring around 0.7 to 1.0 MeV, is unequivocally characterized as a first-order transition. Furthermore, an exploration into the impact of varying strengths of pairing correlations on these transitions reveals a nonlinear relationship, adding complexity to the transition dynamics.
The hot nucleus [Formula: see text] is investigated using covariant density functional theory, where the shell-model-like approach treats the pairing correlation. Lee–Yang’s theorem is applied to classify the pairing phase transition by analyzing the distribution of zeros of the partition function in the complex temperature plane. The distribution of zeros of the partition function converges with increasing particle numbers and illustrates the characteristics of the phase transition. In our calculations, we determine the first-order of the phase transition near the critical temperature. Different seniority states show the pairing phase transition from a superfluid to a normal phase, ranging from fully paired states to completely unpaired states.
Abstract. The mean-field approximation predicts pairing and shape phase transitions in nuclei as a function of temperature or excitation energy. However, in the finite nucleus the singularities of these phase transitions are smoothed out by quantal and thermal fluctuations. An interesting question is whether signatures of these transitions survive despite the large fluctuations. The shell model Monte Carlo (SMMC) approach enables us to calculate the statistical properties of nuclei beyond the mean-field approximation in model spaces that are many orders of magnitude larger than spaces that can be treated by conventional diagonalization methods. We have extended the SMMC method to heavy nuclei and used it to study the transition from vibrational (spherical) to rotational (deformed) nuclei in families of rare-earth isotopes. We have calculated collective enhancement factors of level densities as a function of excitation energy and found that the decay of the vibrational and rotational enhancements is well correlated with the pairing and shape phase transitions, respectively.
The mean-field approximation predicts pairing and shape phase transitions in nuclei as a function of temperature or excitation energy. However, in the finite nucleus the singularities of these phase transitions are smoothed out by quantal and thermal fluctuations. An interesting question is whether signatures of these transitions survive despite the large fluctuations. The shell model Monte Carlo (SMMC) approach enables us to calculate the statistical properties of nuclei beyond the mean-field approximation in model spaces that are many orders of magnitude larger than spaces that can be treated by conventional diagonalization methods. We have extended the SMMC method to heavy nuclei and used it to study the transition from vibrational (spherical) to rotational (deformed) nuclei in families of rare-earth isotopes. We have calculated collective enhancement factors of level densities as a function of excitation energy and found that the decay of the vibrational and rotational enhancements is well correlated with the pairing and shape phase transitions, respectively.
We study quantum phase transitions between spherical, prolate, and oblate nuclear ground-state shapes using the interacting sd\mathrm{sd}sd-boson model (sd(sd(sd-IBM) and demonstrate the analogy between the IBM results (also results of any axially symmetric quadrupole collective model) and predictions of the Landau theory of phase transitions in classical thermodynamics. A detailed comparison of the two frameworks is performed exploiting the concept of ``specific heat,'' introduced in four alternative ways in the quantum case. All these definitions (two of them based on spectroscopic features of the ground state, the others on a randomized version of the model) lead to similar peaked forms of the ``specific heat'' at the point of the quantum phase transition. We analyze the effect of an increasing boson number on these curves and observe convergence to the singular phase-transitional behavior in the classical limit. Other observable signatures of the IBM structural phase transitions are also discussed with the aim to facilitate the location of a particular nucleus in the parameter space (extended Casten triangle) near the transitions.
The heat capacity of iron isotopes is calculated within the interacting shell model using the complete (pf+0g9/2)({pf+0g}_{9/2})(pf+0g9/2​) shell. We identify a signature of the pairing transition in the heat capacity that is correlated with the suppression of the number of spin-zero neutron pairs as the temperature increases. Our results are obtained by a novel method that significantly reduces the statistical errors in the heat capacity calculated by the shell model Monte Carlo approach. The Monte Carlo results are compared with finite-temperature Fermi gas and BCS calculations.
Quantum shape-phase transitions in odd-nuclei are investigated within the framework of the interacting boson-fermion model (IBFM). We consider the case of a single-j fermion coupled to an even-even boson core that performs a transition from spherical to oblate shapes varying a control parameter in the boson Hamiltonian. The aim of this work is to see the effect of the coupling of the unpaired fermion on the transition, to understand how the coupled single particle modifies the geometric shape of the system and how each of the odd states behaves when the boson core shifts along the transitional path.