[en] In the nucleon-pair shell model truncated to the S-D subspace with single-particle level splitting fully taken into account, the effects on the collectivity due to the pair structure are studied for ¹³⁴Ba. It is found that the yrast states are not sensitive, but the others, especially the 0₂⁺ and 2₂⁺ states, are very sensitive to the D-pair structure. Among the four pair structures studied in the paper, only the SD pairs taken from the 0₁⁺, 2₁⁺ states of two-valence-nucleon systems with surface delta interaction can describe the spectra, and the B(E2) and B(M1) values of ¹³⁴Ba. (orig.)

[en] Random matrix theory (RMT) is used to provide a measure of the chaoticity (q) of calculated results for the spectra for various Cd isotopes. The goal is to gain a better understanding of the internal dynamics in play; namely, whether it tracks with regular or irregular (chaotic) behavior as determined through an RMT analyses of calculated spectra. The basis-state configurations used to determine the spectra includes all positive, negative, natural (J ^π = 1⁻, 2⁺, …), and unnatural parity configurations (J ^π = 0⁻, 1⁺, 2⁻, …), unless suppressed for comparative purposes. The results show that when intruder-state configurations are in play, regular behavior emerges, but when not in play, chaotic behavior seems to dominate the dynamics. (paper)

[en] In this study, we considered the fluctuation properties of some energy levels of even and odd mass radionuclides, which are used in complex phenomena. Different sequences are prepared by using all the available experimental data and analyzed by using the maximum likelihood estimation technique to get the chaoticity parameter of Abul-magd distribution. The dependence of chaoticity degrees of different radionuclides to their mass regions, their decay modes, and also their physical half-lives are studied. Our results show more chaotic behavior of odd-mass radionuclides in comparison with even–even mass and also the most Poisson-like behavior for even–even mass in the A > 150 mass region. The results offer the most regular behavior for long-lived, even mass radionuclides in comparison to other categories of half-lives. Also, we got an obvious difference between the chaoticity degrees for nuclei which undergo β ⁺ decay in comparison with radionuclides which show electron capture mode. (paper)

[en] Influences of some important residual interactions considered in the shell model on nuclear dynamics and the shape phase evolution have been investigated in the SD-pair shell model for an identical nucleon system. The results indicate that the collective modes including the spherical vibration, prolate rotation, and X(5)-like critical dynamics are mainly driven by the competition between the monopole-pairing interaction and the quadrupole-quadrupole interaction, and the main features of the U(5)-SU(3) phase transition can be well reproduced within the SD-pair model. In addition, it is also shown that the quadrupole-pairing interaction cannot be ignored in reproducing an ideal rotational spectrum with a realistic single-particle configuration.

[en] The spectral fluctuations and transition intensity fluctuations in the excited-state quantum phase transitions (ESQPTs) have been investigated within the framework of the interacting boson model (IBM) by adopting three statistical measures, including the nearest neighbor level spacing distribution P(S) measuring the chaoticity (regularity) in energy spectra, the Δ₃(L) statistics of Dyson and Mehta measuring the spectral rigidity and the intensity distribution P(y) measuring the chaoticity (regularity) in B(E0) transitions. The results indicate that that the ESQPT as a function of the excitation energy may occur as a transition from regular (or semiregular) to highly chaotic if only the associated whole spectrum is chaotic, which fits most of the deformed situations in the IBM including those in the U(5)–SU(3) and SU(3)–O(6) transitional regions. Otherwise, the ESQPT will appear as a transition from regular (or semiregular) to regular such as the cases in the U(5)–O(6) transitional region or those on the ‘Alhassid–Whelan arc’, which represents a nearly regular parameter region connecting the U(5) and SU(3) limits in the IBM. (paper)

[en] A novel approach is introduced for obtaining precise solutions of the pairing Hamiltonian for tetraquarks, which utilizes an algebraic technique in infinite dimensions. The parameters involved in the transition phase are calibrated based on potential tetraquark candidates derived from phenomenology. Our investigation shows that the rotation and vibration transitional theory delivers a reasonable agreement with other works for heavy tetraquarks compared to other methods. To illustrate the concept, we compute the spectra of several tetraquarks, namely charm, bottom, bottom–charm and open charm and bottom systems, and contrast them with those of other particles. (author)

[en] The angular momentum projection for the axially deformed Nilsson mean-field plus a modified standard pairing (MSP) or the nearest-level pairing (NLP) model is proposed. Both the exact projection, in which all intrinsic states are taken into consideration, and the approximate projection, in which only intrinsic states with $K=0$ are taken in the projection, are considered. The analysis shows that the approximate projection with only $K=0$ intrinsic states seems reasonable, of which the configuration subspace considered is greatly reduced. As simple examples for the model application, low-lying spectra and electromagnetic properties of ¹⁸O and ¹⁸Ne are described by using both the exact and approximate angular momentum projection of the MSP or the NLP, while those of ²⁰Ne and ²⁴Mg are described by using the approximate angular momentum projection of the MSP or NLP.