Quasiparticle-phonon Nuclear Model Research Articles

Understanding the Relationship Between Electric Dipole Polarizability and Photonuclear (-2) Moment in Odd-A Actinide Nuclei

Abstract The nuclear electric dipole (E1) polarizability (αE1) is mainly dominated by the dynamics of the giant dipole resonance (GDR). αE1 is proportional to the (-2) moment of the total photo nuclear cross-section (σ-2). This research investigates the relationship between αE1 and σ-2, along with the effects of the Pygmy Dipole Resonance (PDR) and GDR in odd-mass actinide nuclei. For the first time, αE1 and σ-2 values have been calculated using the Translational and Galilean Invariant Quasiparticle Phonon Nuclear Model (TGI-QPNM) approach for odd-A actinide nuclei. According to TGI-QPNM results, E1 dipole transitions in the GDR region significantly contribute to σ-2 due to the energy weighting factor. Below the neutron separation threshold, the PDR in neutron-rich nuclei shows a contribution of about 5% to σ-2 values. In this region, E1 polarizability can reach values of 20-25%. The αE1 values indicate the presence of PDR in these nuclei. Additionally, the Adaptive Neuro-Fuzzy Inference System (ANFIS), a new machine learning method, has been performed to analyze the relationship between αE1 and σ-2. The ANFIS results have been compared with those from the TGI-QPNM and experimental data. The TGI-QPNM model achieves an R² of 0.85-0.95, while the ANFIS model achieves an R² of 0.99. Moreover, the study suggests that the ANFIS model, consistent with TGI-QPNM results, could be an effective tool for estimating σ-2 in odd-A actinide nuclei.

The electric dipole characteristics of well-deformed 171,173Yb

The electric dipole response of well-deformed 171,173Yb in the giant dipole resonance (GDR) and pygmy dipole resonance (PDR) range has been theoretically analyzed using the translation and Galileo invariant quasiparticle phonon nuclear model (TGI-QPNM). The TGI-QPNM consists of an axially symmetric Woods-Saxon Potential, monopole pairing, dipole-dipole residual interaction, and the restoration terms for broken translation and Galilean symmetries. Numerical calculations show the existence of considerable E1 excitations around the neutron separation threshold (S n ) in both isotopes. The TGI-QPNM results of the photoabsorption cross-section give a double-humped shape in both nuclei, consistent with the available experimental data. The integrated moments (σ 0, σ −1) and the centroid energies in the GDR region are also reproduced well.

Integrated photonuclear cross sections in the giant dipole resonance of odd-mass actinide nuclei

This study explores the integrated total photonuclear cross section (σ0) within the context of the giant dipole resonance (GDR) in odd-mass actinide nuclei. Using artificial neural networks (ANNs) and adaptive neuro-fuzzy ınference system (ANFIS) machine learning algorithms, we analyze the GDR behaviors associated with the σ0 values in these nuclei. The modeling results obtained from ANFIS and ANN are compared among themselves and with the Translational Galilean Invariant Quasiparticle Phonon Nuclear Model (TGI-QPNM) and experimental data. Machine learning analysis and TGI-QPNM results provide valuable insights into the GDR characteristics of odd-mass actinides, shedding light on their photonuclear properties. The ANFIS model has achieved an R2 value of 0.98 and an RMSE of 0.19, while the ANN model (LM) has yielded an R2 value of 0.95 and an RMSE of 0.24. These findings deepen our understanding of nuclear physics, underscoring the role of artificial intelligence techniques in deciphering complex phenomena within nuclear structures. In conclusion, our study suggests that the ANFIS model, in agreement with TGI-QPNM results, generally outperforms the ANN (LM) method and could be a more effective tool for estimating the energy-weighted sum rule for GDR.

Polarization factors and their effects on the rotational gyromagnetic ratio

The effect of the polarizations on the collective gyromagnetic ratio (g R ) has been investigated in detail using the Rotational Invariant Quasiparticle Phonon Nuclear Model (RI-QPNM). The model includes an axially symmetric mean-field potential, monopole pairing, spin-dependent residual interactions, and the restoration forces determined according to Pyatov’s prescription for rotational invariance. The restoration of the rotational symmetry gives a solution at the zero energy associated with the rotational branch of nucleonic motion, allowing us to obtain the g R -factors of the core. The remaining solutions lead to the appearance of configuration mixing in the excitation spectrum of the odd-mass deformed nucleus. The configuration mixing quenches both spin and angular momentum matrix elements and affects the contribution of the odd particle to the g R . It has been demonstrated that the polarization factors associated with the ΔK = 1 matrix elements are essential to achieve quantitative agreement with the experimental data. It has also been shown that the general assumption for core polarization, i.e., is insufficient to explain the experimental data.

Microscopic calculation of the electromagnetic dipole strength for 239,243Pu isotopes

This work investigates the electric and magnetic dipole (E1 and M1) responses for 239,243Pu isotopes based on the quasiparticle phonon nuclear model, which was complemented by adding, for the first time, residual interactions for addressing the violations of rotational, translational, and Galilean symmetries caused by the mean-field approach. We focus on the E1 and M1 dipole strengths and photoabsorption cross sections up to 20 MeV, with the results revealing that the giant dipole resonance best describes the experimental trend with a ratio of 95%. It appears that most of the E1 strength is found at Ex = 8–20 MeV, but the total B(E1)↑ strength for the pygmy dipole resonance at Ex = 4–8 MeV accounts for some 1.83 e2fm2, which in turn corresponds to 2% of the Thomas–Reiche–Kuhn sum rule. Furthermore, the resultant total B(M1)↑ value for the scissors mode strength below 4 MeV is 5.65 which is below that of the Oslo data (10.1(15) ). However, the theoretically predicted scissors resonance structure has two peaks in the 1–3.5 MeV energy range, so it exhibits a similar trend to that found in the Oslo data.

First Theoretical Identification of the Magnetic Dipole Moment of the 97.43 keV State in 153Eu

Two alternative values, +3.21±0.22 μ_N and-0.52±0.22 μ_N, for the magnetic dipole (M1) moment of the excited [532] 5/2- state at 97.43 keV in 153Eu were reported in the Mossbauer-effect study. The Quasiparticle Phonon Nuclear Model (QPNM) has been used to determine the correct value of the magnetic moment of this state. According to the QPNM calculations, the experimental 97.43 keV level is the [532] 5/2- Nilsson state occurring at 79 keV. The QPNM predicted the magnetic moment of this state to be +3.2162 μ_N, which agrees well with one of the experimental values, i.e., +3.21±0.22 μ_N. Therefore, the correct value for the magnetic moment of the 97.43 keV level of 153Eu is most probably +3.21±0.22 μ_N. The measured value (+3.4717±0.006 μ_N) of the magnetic moment of 5/2- ground-state, which is probably a [532] Nilsson state according to our QPNM calculations, supports our prediction.

Spin-isospin structure of the nuclear scissors mode

The fine structure of the scissors mode is investigated within the time dependent Hartree-Fock-Bogoliubov (TDHFB) approach. The solution of TDHFB equations by the Wigner function moments (WFM) method predicts a splitting of the scissors mode into three intermingled branches. Together with the conventional scissors mode two new modes arise due to spin degrees of freedom. They generate significant $M1$ strength below the conventional energy range. The results of calculations of scissors resonances in rare earths and actinides by WFM and quasiparticle-phonon nuclear model methods are compared with experimental data. A remarkable coherence of both methods together with experimental data is observed.

Theoretical description of pygmy and giant dipole resonances in 237Np

This study presents the descriptive characteristics of the electric dipole (E1) excitations for the first time in the 237Np nucleus, such as the reduced transition probability, the photo-absorption cross-section, the energy-weighted sum rule, and so on, as calculated by the Translational and Galilean Invariant Quasiparticle Phonon Nuclear Model (TGI-QPNM). To accurately determine the dipole properties of the collective pygmy and giant resonances, it was necessary to eliminate the spurious states mixed into the dipole spectrum because the mean-field Hamiltonian breaks the translational invariance symmetry. We therefore also investigated the effect of spurious states on the PDR and GDR spectra using the TGI-QPNM method. In addition, we consulted the available knowledge for the energy-weighted sum rule to test the TGI-QPNM model, and this resulted in 97% accuracy for E1 dipole excitations. Furthermore, the theoretical results were compared with experimental data for the photo-absorption cross-sections in the 5–20 MeV energy range for the 237Np nucleus, with a satisfactory agreement being found.

Electromagnetic dipole transitions below 4 MeV in odd-neutron 161,163Dy

Low-lying dipole excitations in 161,163Dy isotopes have been investigated within the Quasiparticle Phonon Nuclear Model (QPNM), including effective restoration forces for broken Rotational, Translational, and Galilean symmetries due to the mean-field approach. The fine structure of the experimental spectra has been agreeably produced by theory. Besides, a good agreement with the existing experimental data for the gross properties of the low-lying dipole strength has been obtained. It has been demonstrated that although most of the dipole strength in the low-lying part of the dipole spectrum is due to the magnetic dipole (M1) transitions, the contribution of the electric dipole (E1) strength to the fragmentation as well as the summed radiation widths cannot be ruled out in 161,163Dy.

Study of the high lying electric dipole excitations in Odd-A 153–159Eu isotopes

In this paper, we have studied the electric dipole (E1) transitions in odd-mass 153–159Eu nuclei within Translational+Galilean Invariant Quasiparticle Phonon Nuclear Model (TGI-QPNM). Within the scope, the Giant and Pygmy Dipole Resonances (GDR and PDR) have been investigated in the energy range of 5–20 MeV. The numerical results show that the contribution of PDR and GDR to the total E1 strength is 2% and 98%, respectively. It has been found that the TGI-QPNM predicts the double hump structure and that the agreement between theoretical results and the existing experimental data is perfect, especially near the neutron binding energy Sn and the first hump of the GDR. Also the comparison of the theoretical results and the existing experimental data shows reasonable agreement for the integrated moments of the cross-sections in the GDR region. We can also deduce from the structure analysis of excited states the studied isotopes, that the GDR states can be considered to be more collective than the PDR states.

A comparison of calculated β-decay half-lives with photonuclear reaction data and other experiments

We try to give a comparison of the calculated Gamow–Teller [Formula: see text]-decay half-lives for [Formula: see text], [Formula: see text] and [Formula: see text] nuclei with the experimental ones obtained from ([Formula: see text],p), ([Formula: see text],n) and (n,[Formula: see text]) reactions, respectively. The calculations are performed within the framework of quasi-particle phonon nuclear model. The nucleon–nucleon interaction potential is included according to Pyatov’s restoration method. The calculated decay half-lives are also compared with available experimental data in the literature.

ΔK=0 M1 Excitation Strength of the Well-Deformed Nucleus Dy164 from K Mixing

The size of a ΔK=0 M1 excitation strength has been determined for the first time in a predominantly axially deformed even-even nucleus. It has been obtained from the observation of a rare K-mixing situation between two close-lying J^{π}=1^{+} states of the nucleus ^{164}Dy with components characterized by intrinsic projection quantum numbers K=0 and K=1. Nuclear resonance fluorescence induced by quasimonochromatic linearly polarized γ-ray beams provided evidence for K mixing of the 1^{+} states at 3159.1(3) and 3173.6(3)keV in excitation energy from their γ-decay branching ratios into the ground-state band. The ΔK=0 transition strength of B(M1;0_{1}^{+}→1_{K=0}^{+})=0.008(1)μ_{N}^{2} was inferred from a mixing analysis of their M1 transition rates into the ground-state band. It is in agreement with predictions from the quasiparticle phonon nuclear model. This determination represents first experimental information on the M1 excitation strength of a nuclear quantum state with a negative R-symmetry quantum number.

Translational and Galilean Invariant Quasiparticle Phonon Nuclear Model (TGI-QPNM) for electric dipole (E1) transitions in odd-mass deformed nuclei

The method of Pyatov, proposed for the exclusion of the spurious states associated with the spontaneous symmetry breaking due to the mean field approximation, is applied to restore broken translation and Galilean invariance of the Quasiparticle Phonon Nuclear Model (QPNM) Hamiltonian of deformed odd-mass nuclei for the first time. The point of the formulated translation and Galilean invariant (TGI-) QPNM is to study electric dipole (E1) response of odd-mass deformed nuclei. The proposed TGI-QPNM is tested by the calculations for fine and gross features of E1 resonance in 165Ho, 169Tm, and 235U in a wide range of excitation energy from 2 to 20 MeV. Predictions of the TGI-QPNM are shown to be in good agreement with the corresponding experimental data.

Numerical Analysis of the Ground-State Magnetic Moments of ${}^{143,145,147}{\rm{Sm}}$ Isotopes

The explanation of the ground state magnetic properties of odd-mass nuclei is very informative in understanding of the complex structure of the deformed nuclei. The ground-state magnetic moments of most of the odd-A deformed nuclei have been measured by various experimental studies and there are numerous studies in the literature. However, many of the theoretical studies on magnetic moments and spin polarization effects affecting them are far from explaining these measured values. In this paper, the magnetic moments and effective spin g factors of 143,145,147Sm isotopes in the lanthanides region of the periodic table were investigated within the framework of the Quasiparticle-Phonon Nuclear Model (QPNM) for the first time. Spin-spin interaction parameters (χ) were determined by comparing theoretical and experimental values of magnetic moments of the related isotopes and it was determined that these interactions were found to have an isovector character (q = -1). It has been observed that the ground-state structures of the studied isotopes are weakly affected by quasiparticlephonon interactions and the contribution of these interactions ( values) to the ground-state wave functions is quite small (around 0.01%). Theoretical explanation of the renormalization of spin gyromagnetic factor is one of the most important problems of nuclear structure physics. The results obtained in this study for the effective spin gyromagnetic factor also agree with the phenological value .

Comparission of E1 Response of 154Sm and 155Sm in the Pygmy Dipole Resonance (PDR) Region

The dipole response associated with the pygmy dipole resonance (PDR) in 154 Sm and 155 Sm has been studied. In the 154 Sm nucleus 1 - phonons with K =0 and K =1 branches have been calculated using the Translation and Galilean Invariant Quasiparticle Random Phase Approximation (TGI-QRPA). The structure of the more pronounced electric dipole ( E 1) peaks in PDR region in 154 Sm is composed of predominantly two-quasiproton or two-quasineutron states. The calculations in 155 Sm has been performed in the framework of the Translation and Galilean Invariant Quasiparticle Phonon Nuclear Model (TGI- QPNM) based on the TGI-QRPA 1 - phonons calculated for 154 Sm. When going from 154 Sm to neighbouring 155 Sm, the fragmentation of the E 1 strength is dramatically enhanced. The results emphasize the role of the quasiparticle ⨂ phonon interactions in enhancing the fragmentation of the strength in the PDR region in 155 Sm. Even though the strong fragmentation of the E 1 strength obtained for 155 Sm, in 5-8 MeV energy region the summed E 1 strength is comparable to that in 154 Sm. The results indicate that one quasiparticle behaves solely as a spectator in 155 Sm.

Effects of the isoscalar and isovector interaction on the ground-state magnetic moments of odd-mass 137–145Ce nuclei

A systematic study of the magnetic properties of deformed odd-neutron 137–145Ce isotopes using the microscopic quasiparticle phonon nuclear model (QPNM) has been presented. The QPNM includes residual spin–spin interaction in both isoscalar and isovector channels. The analysis shows that in the isoscalar channel contributions to the magnetic moment coming from the neutron and proton systems practically cancel out each other. On the other hand, in the isovector channel, the coherent contribution coming from the quasiparticle–phonon interactions leads to a spin polarization (core polarization), which is important for determination of the quenched spin gyromagnetic factors (gs). The quenched spin gyromagnetic factors so called [Formula: see text] have been found to range from [Formula: see text] to [Formula: see text] in the odd-mass 137–145Ce isotopic chain, which is similar to its phenomenological value ([Formula: see text] between [Formula: see text] and [Formula: see text]). By taking into consideration the core polarization effects, the available experimental data are satisfactorily reproduced with an accuracy of 0.01μN–0.1μN.

A theoretical investigation of the magnetic dipole moment of the ground- and excited-states below 600keV in well-deformed 183,185W, 185,187Re and 187,189Os

Magnetic dipole moments of the ground- and excited-states below 600[Formula: see text]keV in [Formula: see text]W, [Formula: see text]Re and [Formula: see text]Os nuclei have been systematically studied in the framework of a microscopic Quasiparticle Phonon Nuclear Model (QPNM) including an axially symmetric Wood–Saxon potential as a mean field and the residual spin–spin interaction. The obtained results of the magnetic moment, intrinsic [Formula: see text] factor and the effective spin gyromagnetic factor have been compared with the available experimental data and also with the calculations based on different approaches. It has been demonstrated that the QPNM reproduces reasonably well the recent experimental value of the ground-state magnetic moment and satisfactorily describes the measured magnetic moment of low-lying states below 600[Formula: see text]keV in these nuclei.

A theoretical study on the ground and low-energy magnetic dipole characteristics of 239Pu nucleus

A microscopic model analysis of the magnetic dipole (M1) properties of 239Pu nucleus, which is a fissile material not only used in nuclear weapons but also used in some nuclear reactors as a source of energy, has been performed. The microscopic formalism used in the study is based on the Quasiparticle Phonon Nuclear Model (QPNM) and includes an axially symmetric Woods-Saxon potential as a mean field, a spin-spin residual interaction as well as the symmetry-restoring forces for the rotational invariance of the Hamiltonian. The investigations have been carried out in two steps. Firstly, the theoretical value of the ground-state magnetic moment and quenching spin gyromagnetic factor have been determined and it has been found that the predicted magnetic moment show a good agreement with the experimental data. Secondly, the calculations of M1 transitions from ground- to excited-states have been carried out in the energy range 2-4 MeV. A satisfactorily good agreement is obtained from the comparison of the theoretical results with the experimental data for 2-2.5 MeV.

Magnetic properties of K = 1/2 states in deformed odd-mass nuclei

A method for calculation of the ground-state magnetic moment, effective spin gyromagnetic factors and rotational decoupling parameter of the K=1/2 states in deformed odd-mass nuclei has been described by using the concept of the Quasiparticle Phonon Nuclear Model (QPNM). The model includes a Woods-Saxon potential as a mean field with pairing correlations and the residual separable spin-spin force in both isovector and isoscalar channels. The method has been employed to investigate K=1/2 ground-state magnetic properties of 169Er, 167,169Tm, and 171Yb nuclei, as an example. It has been shown that two different quenched spin gyromagnetic factors, i.e., gsz(eff.) and gs+(eff.) have a significant effect on the magnetic properties of K=1/2 states in odd-mass nuclei. Whereas the first one is occurred due to the interaction between the valence nucleon and IπK=1+0 excitations of the core, second one is associated with the coupling of the valence nucleon to IπK=1+1 excitations of the core. The observed magnetic moments and the phenomenological value of gsz(eff.) for considered odd-mass nuclei have been reproduced very well by the calculations. The role of the isoscalar and isovector interactions on the magnetic properties of K=1/2 states in these nuclei has been also discussed.

Magnetic dipole response of the 169Tm nucleus

The magnetic dipole (M1) response of the 169Tm nucleus is investigated from a theoretical point of view. The theoretical tool used in this study is the Rotational Invariant Quasiparticle Phonon Nuclear Model (RI-QPNM) which gives a possibility to eliminate spurious contributions in the M1 spectrum. In the framework of this model, both the low-lying and high-lying parts of the M1 excitation spectrum of 169Tm are calculated. The result shows that the low-lying excitations have almost pure orbital character and can be interpreted as scissors mode, whereas the high-lying transitions can be read as spin-flip mode because of its spin nature. The reduced transition probability summed up in the energy range 2–4 MeV is found to be B(M1↑)=3.040μN2 which agrees with the available experimental data. The fragmentation of the low-energy M1 strength is also well reproduced. This is also the first study in which both the low-lying and high-lying M1 spectrum of the 169Tm nucleus is theoretically investigated.