In this paper, we have applied a simple interacting boson model (IBM) to Cadmium (Cd) isotopic ch... more In this paper, we have applied a simple interacting boson model (IBM) to Cadmium (Cd) isotopic chain to obtain the quadrupole transition rates and effective deformation. To this aim, we use the U(5) and O(6) dynamical symmetry limits of this model to classify the considered states. Also, the energy spectra of some levels are determined which their experimental counterparts are available. The results describe the regular states with high accuracy but suggest notable deviation in the prediction of intruder energy levels. Also, our results show the advantages of this formalism in the description of quadrupole transition rates and indicate a significant relationship between the values of effective quadrupole deformations and effective boson charge. Also, for the [Formula: see text]Cd, [Formula: see text]Cd and [Formula: see text]Cd isotopes, we have the largest variation of the quadrupole shape constants which are located in the region of shape coexistence. The study of the ratios of di...
In this paper, we have considered the evolution of the local part of two neutron separation energ... more In this paper, we have considered the evolution of the local part of two neutron separation energies in the Zr, Gd, Sm, Ba, Xe, Os and Pt isotopic chain. We have used the interacting boson model as the most widely used approach to study the quantum phase transitions in nuclei to determine the global and local parts of two neutron separation energies. The constants of relations are extracted in comparison with the experimental counterparts. Theoretical predictions reproduce the experimental counterparts with high accuracy. Also, the signals of phase transition in some nuclei that show sudden changes in local part of two neutron separation energies are greatly enhanced and show the ability of the interacting boson model calculations to reproduce this picture.
Introduction: Ultraviolet index (UVI) is a dimensionless scale, which describes the maximum inten... more Introduction: Ultraviolet index (UVI) is a dimensionless scale, which describes the maximum intensity and biologic effects of UV during a specific time, on surface of the earth. The UVI is an international standard measurement of the strength of sunburn producing ultraviolet radiation at a particular place and time. This index is an easy and understandable concept for protection and application for people, which can be described: 2 or less means low exposure, 3-5 means average, 6-7 means high, 8-10 means very high and more than that means dangerous. The major approach is to calculate UVI by measuring the intensity of UV exposure on the surface of earth. In this study we calculated the UVI at Tabriz, based on the measurement of UV intensity. Materials and Methods: First, the amounts of UV type A and B by handheld lux UV-IR meter, for a whole year from sunrise to sunset were measured in Tabriz during 2016-2017. We use the following formula to calculate UVI: UVI k er o E l ....
Introduction: Normal exposure to sunlight results in the production of vitamin D in human body, w... more Introduction: Normal exposure to sunlight results in the production of vitamin D in human body, which happens because of the interaction between ultraviolet radiation and cholesterol in skin. Exposure to sunlight is responsible for 90 percent of vitamin D needed for the body. Studies show that Iran is a country with high percentage of lack of vitamin D (83 percent). Based on previous studies, it has been estimated that if 25 percent of human skin get exposed to sunlight (head, neck, hands and arms), enough vitamin D can be synthesized. In a new definition this amount of vitamin D is called Standard Vitamin D Dose (SDD). In this study the SDD has been calculated and predicted for people who live in Tabriz. Materials and Methods: First, the amounts of UV type A and B by handheld lux UV-IR meter, for a whole year from sunrise to sunset were measured in Tabriz during 2016-2017. UV indexes were calculated. Skin type of people in Tabriz can be classified in type five (which is specific ...
Statistical analyses of the spectral distributions of rotational bands in 51 deformed prolate eve... more Statistical analyses of the spectral distributions of rotational bands in 51 deformed prolate even–even nuclei in the 152 ≤ A ≤ 250 mass region $$R_{{4_{1}^{ + } /2_{1}^{ + } }} \ge 3.00$$ R 4 1 + / 2 1 + ≥ 3.00 are examined in terms of nearest neighbor spacing distributions. Specifically, the focus is on data for 0+, 2+, and 4+ energy levels of the ground, gamma, and beta bands. The chaotic behavior of the gamma band, especially the position of the $$2_{\gamma }^{ + }$$ 2 γ + band-head compared to other levels and bands, is clear. The levels are analyzed within the framework of two models, namely, a SU(3)-partial dynamical symmetry Hamiltonian and a SU(3) two-coupled quasi-dynamical symmetry Hamiltonian, with results that are further analyzed using random matrix theory. The partial and quasi dynamics both yield outcomes that are in reasonable agreement with the known experimental results. However, due to the degeneracy of the beta and gamma bands within the simplest SU(3) picture, ...
It is interesting that a change of nuclear shape may be described in terms of a phase transition.... more It is interesting that a change of nuclear shape may be described in terms of a phase transition. This paper studies the quantum phase transition of the U(5) to SO(6) in the interacting boson model (IBM) on the finite number N of bosons. This paper explores the well-known distinctive signatures of transition from spherical vibrational to γ-soft shape phase in the IBM with the variation of a control parameter. Quantum phase transitions occur as a result of properties of ground and excited states levels. We apply an affine SU (1, 1) approach to numerically solve non-linear Bethe Ansatz equation and point out what observables are particularly sensitive to the transition. The main aim of this work is to describe the most prominent observables of QPT by using IBM in shape coexistence configuration. We calculate energies of excited states and signatures of QPT as energy surface, energy ratio, energy differences, quadrupole electric transition rates and expectation values of boson number operators and show their behavior in QPT. These observables are calculated and examined for 98−102 Mo isotopes. Keywords Quantum phase transition (QPT) • Signatures of quantum phase transition • Interacting boson model (IBM) • Shape coexistence configuration • Affine SU (1, 1) approach
Level statistics for given spin and parity below 10 MeV within A ≤ 71, 71 ≤ A ≤ 151, and 151 ≤ A ... more Level statistics for given spin and parity below 10 MeV within A ≤ 71, 71 ≤ A ≤ 151, and 151 ≤ A ≤ 221 mass regions are systematically analyzed. We have taken 5316 level spacings from 266 odd-A nuclei in the light mass region, 6897 level spacings from 478 ones in the medium mass region, and 2768 level spacings from 143 ones in the heavy mass region for the statistics. In the analysis, the chaoticity parameter in the Berry-Robnik distribution is determined based on the method of maximum likelihood estimation. The results show a mass number A-dependence in the level statistics. The larger the mass number, the relatively stronger in chaoticity. In addition, with the level statistics in using data sequences classified according to the order of magnitude of halflives, it is shown that the level energies to be more chaotic for longer lived light and heavy mass odd-A nuclei, and intermediate between regular and chaotic in medium mass odd-A nuclei. The level statistical analysis in concerning E2 transition strengths of E2 or mixed E2+M1 transitions in odd-A nuclei is also made, which shows chaos in level energies likely occurring in those with weaker E2 transition strengths. Therefore, it can be concluded that odd-A nuclei are, more often than not, chaotic. Chaos is likely emergent in level energies of stable light mass nuclei with weaker E2 transition strengths, while it is definitely emergent in level energies of heavy mass nuclei, and even stronger in comparatively stable ones and those with weaker E2 transition strengths.
In this paper, we have considered the energy spectra, quadrupole transition probabilities, energy... more In this paper, we have considered the energy spectra, quadrupole transition probabilities, energy surface, charge radii, and quadrupole moment of the 190 Hg nucleus to describe the interplay between phase transitions and configuration mixing of intruder excitations. To this aim, we have used four different formalisms: (i) interacting boson model including configuration mixing, (ii) Z(5) critical symmetry, (iii) U(6)-based transitional Hamiltonian, and (iv) a transitional interacting boson model Hamiltonian in both interacting boson model (IBM)-1 and IBM-2 versions which are based on affineŜU 1; 1 ð Þ Lie algebra. Results show the advantages of configuration mixing and transitional Hamiltonians, in particular IBM-2 formalism, to reproduce the experimental counterparts when the weight of spherical symmetry increased.
In this study, we tried to get significant relations between the spectral statistics of atomic nu... more In this study, we tried to get significant relations between the spectral statistics of atomic nuclei and their different degrees of deformations. To this aim, the empirical energy levels of 109 eveneven nuclei in the 22 A 196 mass region are classified as their experimental and calculated quadrupole, octupole, hexadecapole and hexacontatetrapole deformations values and analyzed by random matrix theory. Our results show an obvious relation between the regularity of nuclei and strong quadrupole, hexadecapole and hexacontatetrapole deformations and but for nuclei that their octupole deformations are nonzero, we have observed a GOE-like statistics.
Exactly solvable model in quadrupole-octupole coupled (QOC) states is an interesting nuclear stru... more Exactly solvable model in quadrupole-octupole coupled (QOC) states is an interesting nuclear structure phenomenon. For example, several transitions of the electric dipole and quadrupole (E1 and E2) values are indicative of QOC states. Various collective models as three-level and four-level pairing models were employed in order to account for the observed properties of the QOC states. We suggest a simultaneous description of low-lying collective positive and negative-parity states to use the spdf and sdf interacting boson model to reproduce the general characteristics of the QOC states. Also, quantum phase transitions are investigated based on dual algebraic structures for the sd, sdf and spdf-IBM. The low lying positive and negative parity states and the QOC properties of the stable even-even Cd isotopes are calculated in solvable extended transitional Hamiltonian of the IBM-spdf and IBM-sdf models based on the affine SU (1, 1) Lie algebra. Some observables such as energy levels, transition rates, expectation value of boson number operators, energy differences and staggering pattern are calculated and examined for Cd isotopes. The IBM calculations indicate a nuclear structure of the electric E1, E2 and E3 strength and energy spectra in the low-lying, thus confirming the experimental results for transition region. The calculations confirm a good agreement for the energy spectra, quantum phase transitions and fragmentation of the E1, E2 and E3 strengths.
In this paper, the spectral statistics of 482 stable and radioactive nuclei in the 10 A 250 mass ... more In this paper, the spectral statistics of 482 stable and radioactive nuclei in the 10 A 250 mass region are considered with emphasis on nearest neighbor spacing statistics. The sequences are constructed by using all the available empirical data for considered nuclei in different categories and analyzed via Maximum Likelihood estimation technique in the framework of Abul-Magd distribution. The results offer more regular dynamic for stable nuclei in comparison with unstable nuclei and there are suggestions of the effects due to the radioactivity types, mass, quadrupole deformation and also the on more chaotic dynamics of unstable nuclei.
The critical behavior of 100-106 Ru isotopes is investigated in the U(5) SO(9) transitional regio... more The critical behavior of 100-106 Ru isotopes is investigated in the U(5) SO(9) transitional region of the spd-interacting boson model. We have developed a solvable extended transitional Hamiltonian based on affine SU(1,1) Lie algebra within the framework of the spd-interacting boson model. Also, we have used the Catastrophe theory in combination with coherent state formalism to generate the energy surfaces of considered isotopes. The parameters of the transitional Hamiltonian are determined via Least-Square Fitting (LSF) to the experimental data of Ru isotopes to describe both positive and negative parity states and also E(1) and E(2) transition probabilities. Results describe experimental counterparts with satisfactory degrees of agreement and also suggest 100 Ru as the best candidate for the critical point of this transitional region.
We have used kernel density estimation (KDE) technique to analyze the spectral statistics of nucl... more We have used kernel density estimation (KDE) technique to analyze the spectral statistics of nuclear systems with emphasis on the nearest neighbor spacing distribution. The deviations to regular and chaotic dynamics are described by closer distances to Poisson and Wigner limits, respectively which have calculated via Kullback-Leibler divergence measure. The level statistics of nuclei provide empirical evidences for three dynamical symmetry limits of interacting boson model, considering oblate and prolate nuclei. The predictions of KDE technique suggest a considerable reduction in the uncertainties of chaocity degrees and also more regular dynamics in comparison with other estimation methods for considered systems.
In this paper, Brody distribution is generalized to explore the Poisson, Gaussian Orthogonal Ense... more In this paper, Brody distribution is generalized to explore the Poisson, Gaussian Orthogonal Ensemble and Gaussian Unitary Ensemble limits of Random Matrix Theory in the nearest neighbor spacing statistic framework. Parameters of new distribution are extracted via Maximum Likelihood Estimation technique for different sequences. This general distribution suggests more exact results in comparison with the results of other estimation methods and distribution functions.
We consider the possibility of identifying nuclei exhibiting the partial dynamical SU(3) symmetry... more We consider the possibility of identifying nuclei exhibiting the partial dynamical SU(3) symmetry (SU(3)-PDS) as those having excitation energy ratio 4/2 3.00 R . For this purpose, the level energy spectra of a set of 51 nuclei in the rare earth and actinide regions which presenting an axially deformed prolate rotational structure were analyzed via nuclear partial dynamical SU(3) symmetry in the framework of interacting boson model, to see if the SU(3)-PDS is broadly applicable, and where, how, and in which nuclei it breaks down. Overall, the PDS works very well, the predictions of such intermediate symmetry structure for energy spectrum were compared with the most recent experimental data and an acceptable degree of agreement is achieved. We conclude that PDS predictions have a more regular behavior in description of axially deformed prolate rotational nuclei than DS, which may lead to accurate predictions of such nuclei, and hence play a significant role in understanding the regular behavior of complex nuclei.
In this paper, we have analyzed the critical behavior of even–even Ru and Pd isotopes between U(5... more In this paper, we have analyzed the critical behavior of even–even Ru and Pd isotopes between U(5) and SO(6) limits of interacting boson model via Catastrophe Theory in combination with a coherent state formalism to generate energy surfaces. The parameters of the Hamiltonian are determined via least-square fitting to the experimental data for different Ru and Pd isotopes. Our results suggest a second-order phase transition in these isotopic chains and propose the best candidates for E(5) critical symmetry. Also, the analogy between the critical exponents of ground state quantum phase transition and Landau values for the critical exponents of thermodynamic phase transitions are described.
Fluctuation properties of a SU (1, 1)-based transitional Hamiltonian in the U (5) ↔ SO(6) transit... more Fluctuation properties of a SU (1, 1)-based transitional Hamiltonian in the U (5) ↔ SO(6) transitional region are considered in the nearest-neighbor spacing statistics. Energy spectra are determined via the Bethe-Ansatz method, which contains an extraction of Hamiltonian parameters from the experimental data of nuclei-provided empirical evidences for the considered region. Our results suggest an approach to chaotic dynamics for the transitional region in comparison with both dynamical symmetry limits in sequences prepared by theoretical and experimental data. Also, nuclei which are known as the best candidates for the E(5) critical symmetry exhibit more regularity compared to other nuclei in the transitional region.
In this paper, Kernel Density Estimation (KDE) as a non-parametric estimation method is used to i... more In this paper, Kernel Density Estimation (KDE) as a non-parametric estimation method is used to investigate statistical properties of nuclear spectra. The deviation to regular or chaotic dynamics, is exhibited by closer distances to Poisson or Wigner limits respectively which evaluated by Kullback-Leibler Divergence (KLD) measure. Spectral statistics of different sequences prepared by nuclei corresponds to three dynamical symmetry limits of Interaction Boson Model(IBM), oblate and prolate nuclei and also the pairing effect on nuclear level statistics are analyzed (with pure experimental data). KD-based estimated density function, confirm previous predictions with minimum uncertainty (evaluated with Integrate Absolute Error (IAE)) in compare to Maximum Likelihood (ML)-based method. Also, the increasing of regularity degrees of spectra due to pairing effect is reveal.
The Nearest Neighbor Spacing Distribution (NNSD) is one of the commonly used methods in statistic... more The Nearest Neighbor Spacing Distribution (NNSD) is one of the commonly used methods in statistical analysis of regular and chaotic behaviors of nuclear spectra. In this paper, Maximum Likelihood Estimation (MLE) method is proposed to evaluate the parameter of (NNSD)s. We estimate the parameter of (NNSD)s for different mass groups, nuclei with special values of deformation parameter () and also for nuclear spectra correspond to three dynamical symmetry limits and transition regions in the framework of the Interacting Boson Model (IBM) (with pure experimental data). The obtained results confirm theoretical predictions even in cases where the small size of data does not allow definite conclusions with the other methods. Also the ML estimated parameters have minimum uncertainty with variations very close (much closer than those obtained by other methods) to the so called Cramer-Rao Lower Bound (CRLB). ML estimated values predict more regular dynamics in compare to what other estimation methods indicate. We have also evaluated CRLB for all distributions (Brody, Berry-Robnik and Abul-Magd) with both values obtained from MLE and in different sequences where Brody distribution has the least CRLB.
In this paper, we have applied a simple interacting boson model (IBM) to Cadmium (Cd) isotopic ch... more In this paper, we have applied a simple interacting boson model (IBM) to Cadmium (Cd) isotopic chain to obtain the quadrupole transition rates and effective deformation. To this aim, we use the U(5) and O(6) dynamical symmetry limits of this model to classify the considered states. Also, the energy spectra of some levels are determined which their experimental counterparts are available. The results describe the regular states with high accuracy but suggest notable deviation in the prediction of intruder energy levels. Also, our results show the advantages of this formalism in the description of quadrupole transition rates and indicate a significant relationship between the values of effective quadrupole deformations and effective boson charge. Also, for the [Formula: see text]Cd, [Formula: see text]Cd and [Formula: see text]Cd isotopes, we have the largest variation of the quadrupole shape constants which are located in the region of shape coexistence. The study of the ratios of di...
In this paper, we have considered the evolution of the local part of two neutron separation energ... more In this paper, we have considered the evolution of the local part of two neutron separation energies in the Zr, Gd, Sm, Ba, Xe, Os and Pt isotopic chain. We have used the interacting boson model as the most widely used approach to study the quantum phase transitions in nuclei to determine the global and local parts of two neutron separation energies. The constants of relations are extracted in comparison with the experimental counterparts. Theoretical predictions reproduce the experimental counterparts with high accuracy. Also, the signals of phase transition in some nuclei that show sudden changes in local part of two neutron separation energies are greatly enhanced and show the ability of the interacting boson model calculations to reproduce this picture.
Introduction: Ultraviolet index (UVI) is a dimensionless scale, which describes the maximum inten... more Introduction: Ultraviolet index (UVI) is a dimensionless scale, which describes the maximum intensity and biologic effects of UV during a specific time, on surface of the earth. The UVI is an international standard measurement of the strength of sunburn producing ultraviolet radiation at a particular place and time. This index is an easy and understandable concept for protection and application for people, which can be described: 2 or less means low exposure, 3-5 means average, 6-7 means high, 8-10 means very high and more than that means dangerous. The major approach is to calculate UVI by measuring the intensity of UV exposure on the surface of earth. In this study we calculated the UVI at Tabriz, based on the measurement of UV intensity. Materials and Methods: First, the amounts of UV type A and B by handheld lux UV-IR meter, for a whole year from sunrise to sunset were measured in Tabriz during 2016-2017. We use the following formula to calculate UVI: UVI k er o E l ....
Introduction: Normal exposure to sunlight results in the production of vitamin D in human body, w... more Introduction: Normal exposure to sunlight results in the production of vitamin D in human body, which happens because of the interaction between ultraviolet radiation and cholesterol in skin. Exposure to sunlight is responsible for 90 percent of vitamin D needed for the body. Studies show that Iran is a country with high percentage of lack of vitamin D (83 percent). Based on previous studies, it has been estimated that if 25 percent of human skin get exposed to sunlight (head, neck, hands and arms), enough vitamin D can be synthesized. In a new definition this amount of vitamin D is called Standard Vitamin D Dose (SDD). In this study the SDD has been calculated and predicted for people who live in Tabriz. Materials and Methods: First, the amounts of UV type A and B by handheld lux UV-IR meter, for a whole year from sunrise to sunset were measured in Tabriz during 2016-2017. UV indexes were calculated. Skin type of people in Tabriz can be classified in type five (which is specific ...
Statistical analyses of the spectral distributions of rotational bands in 51 deformed prolate eve... more Statistical analyses of the spectral distributions of rotational bands in 51 deformed prolate even–even nuclei in the 152 ≤ A ≤ 250 mass region $$R_{{4_{1}^{ + } /2_{1}^{ + } }} \ge 3.00$$ R 4 1 + / 2 1 + ≥ 3.00 are examined in terms of nearest neighbor spacing distributions. Specifically, the focus is on data for 0+, 2+, and 4+ energy levels of the ground, gamma, and beta bands. The chaotic behavior of the gamma band, especially the position of the $$2_{\gamma }^{ + }$$ 2 γ + band-head compared to other levels and bands, is clear. The levels are analyzed within the framework of two models, namely, a SU(3)-partial dynamical symmetry Hamiltonian and a SU(3) two-coupled quasi-dynamical symmetry Hamiltonian, with results that are further analyzed using random matrix theory. The partial and quasi dynamics both yield outcomes that are in reasonable agreement with the known experimental results. However, due to the degeneracy of the beta and gamma bands within the simplest SU(3) picture, ...
It is interesting that a change of nuclear shape may be described in terms of a phase transition.... more It is interesting that a change of nuclear shape may be described in terms of a phase transition. This paper studies the quantum phase transition of the U(5) to SO(6) in the interacting boson model (IBM) on the finite number N of bosons. This paper explores the well-known distinctive signatures of transition from spherical vibrational to γ-soft shape phase in the IBM with the variation of a control parameter. Quantum phase transitions occur as a result of properties of ground and excited states levels. We apply an affine SU (1, 1) approach to numerically solve non-linear Bethe Ansatz equation and point out what observables are particularly sensitive to the transition. The main aim of this work is to describe the most prominent observables of QPT by using IBM in shape coexistence configuration. We calculate energies of excited states and signatures of QPT as energy surface, energy ratio, energy differences, quadrupole electric transition rates and expectation values of boson number operators and show their behavior in QPT. These observables are calculated and examined for 98−102 Mo isotopes. Keywords Quantum phase transition (QPT) • Signatures of quantum phase transition • Interacting boson model (IBM) • Shape coexistence configuration • Affine SU (1, 1) approach
Level statistics for given spin and parity below 10 MeV within A ≤ 71, 71 ≤ A ≤ 151, and 151 ≤ A ... more Level statistics for given spin and parity below 10 MeV within A ≤ 71, 71 ≤ A ≤ 151, and 151 ≤ A ≤ 221 mass regions are systematically analyzed. We have taken 5316 level spacings from 266 odd-A nuclei in the light mass region, 6897 level spacings from 478 ones in the medium mass region, and 2768 level spacings from 143 ones in the heavy mass region for the statistics. In the analysis, the chaoticity parameter in the Berry-Robnik distribution is determined based on the method of maximum likelihood estimation. The results show a mass number A-dependence in the level statistics. The larger the mass number, the relatively stronger in chaoticity. In addition, with the level statistics in using data sequences classified according to the order of magnitude of halflives, it is shown that the level energies to be more chaotic for longer lived light and heavy mass odd-A nuclei, and intermediate between regular and chaotic in medium mass odd-A nuclei. The level statistical analysis in concerning E2 transition strengths of E2 or mixed E2+M1 transitions in odd-A nuclei is also made, which shows chaos in level energies likely occurring in those with weaker E2 transition strengths. Therefore, it can be concluded that odd-A nuclei are, more often than not, chaotic. Chaos is likely emergent in level energies of stable light mass nuclei with weaker E2 transition strengths, while it is definitely emergent in level energies of heavy mass nuclei, and even stronger in comparatively stable ones and those with weaker E2 transition strengths.
In this paper, we have considered the energy spectra, quadrupole transition probabilities, energy... more In this paper, we have considered the energy spectra, quadrupole transition probabilities, energy surface, charge radii, and quadrupole moment of the 190 Hg nucleus to describe the interplay between phase transitions and configuration mixing of intruder excitations. To this aim, we have used four different formalisms: (i) interacting boson model including configuration mixing, (ii) Z(5) critical symmetry, (iii) U(6)-based transitional Hamiltonian, and (iv) a transitional interacting boson model Hamiltonian in both interacting boson model (IBM)-1 and IBM-2 versions which are based on affineŜU 1; 1 ð Þ Lie algebra. Results show the advantages of configuration mixing and transitional Hamiltonians, in particular IBM-2 formalism, to reproduce the experimental counterparts when the weight of spherical symmetry increased.
In this study, we tried to get significant relations between the spectral statistics of atomic nu... more In this study, we tried to get significant relations between the spectral statistics of atomic nuclei and their different degrees of deformations. To this aim, the empirical energy levels of 109 eveneven nuclei in the 22 A 196 mass region are classified as their experimental and calculated quadrupole, octupole, hexadecapole and hexacontatetrapole deformations values and analyzed by random matrix theory. Our results show an obvious relation between the regularity of nuclei and strong quadrupole, hexadecapole and hexacontatetrapole deformations and but for nuclei that their octupole deformations are nonzero, we have observed a GOE-like statistics.
Exactly solvable model in quadrupole-octupole coupled (QOC) states is an interesting nuclear stru... more Exactly solvable model in quadrupole-octupole coupled (QOC) states is an interesting nuclear structure phenomenon. For example, several transitions of the electric dipole and quadrupole (E1 and E2) values are indicative of QOC states. Various collective models as three-level and four-level pairing models were employed in order to account for the observed properties of the QOC states. We suggest a simultaneous description of low-lying collective positive and negative-parity states to use the spdf and sdf interacting boson model to reproduce the general characteristics of the QOC states. Also, quantum phase transitions are investigated based on dual algebraic structures for the sd, sdf and spdf-IBM. The low lying positive and negative parity states and the QOC properties of the stable even-even Cd isotopes are calculated in solvable extended transitional Hamiltonian of the IBM-spdf and IBM-sdf models based on the affine SU (1, 1) Lie algebra. Some observables such as energy levels, transition rates, expectation value of boson number operators, energy differences and staggering pattern are calculated and examined for Cd isotopes. The IBM calculations indicate a nuclear structure of the electric E1, E2 and E3 strength and energy spectra in the low-lying, thus confirming the experimental results for transition region. The calculations confirm a good agreement for the energy spectra, quantum phase transitions and fragmentation of the E1, E2 and E3 strengths.
In this paper, the spectral statistics of 482 stable and radioactive nuclei in the 10 A 250 mass ... more In this paper, the spectral statistics of 482 stable and radioactive nuclei in the 10 A 250 mass region are considered with emphasis on nearest neighbor spacing statistics. The sequences are constructed by using all the available empirical data for considered nuclei in different categories and analyzed via Maximum Likelihood estimation technique in the framework of Abul-Magd distribution. The results offer more regular dynamic for stable nuclei in comparison with unstable nuclei and there are suggestions of the effects due to the radioactivity types, mass, quadrupole deformation and also the on more chaotic dynamics of unstable nuclei.
The critical behavior of 100-106 Ru isotopes is investigated in the U(5) SO(9) transitional regio... more The critical behavior of 100-106 Ru isotopes is investigated in the U(5) SO(9) transitional region of the spd-interacting boson model. We have developed a solvable extended transitional Hamiltonian based on affine SU(1,1) Lie algebra within the framework of the spd-interacting boson model. Also, we have used the Catastrophe theory in combination with coherent state formalism to generate the energy surfaces of considered isotopes. The parameters of the transitional Hamiltonian are determined via Least-Square Fitting (LSF) to the experimental data of Ru isotopes to describe both positive and negative parity states and also E(1) and E(2) transition probabilities. Results describe experimental counterparts with satisfactory degrees of agreement and also suggest 100 Ru as the best candidate for the critical point of this transitional region.
We have used kernel density estimation (KDE) technique to analyze the spectral statistics of nucl... more We have used kernel density estimation (KDE) technique to analyze the spectral statistics of nuclear systems with emphasis on the nearest neighbor spacing distribution. The deviations to regular and chaotic dynamics are described by closer distances to Poisson and Wigner limits, respectively which have calculated via Kullback-Leibler divergence measure. The level statistics of nuclei provide empirical evidences for three dynamical symmetry limits of interacting boson model, considering oblate and prolate nuclei. The predictions of KDE technique suggest a considerable reduction in the uncertainties of chaocity degrees and also more regular dynamics in comparison with other estimation methods for considered systems.
In this paper, Brody distribution is generalized to explore the Poisson, Gaussian Orthogonal Ense... more In this paper, Brody distribution is generalized to explore the Poisson, Gaussian Orthogonal Ensemble and Gaussian Unitary Ensemble limits of Random Matrix Theory in the nearest neighbor spacing statistic framework. Parameters of new distribution are extracted via Maximum Likelihood Estimation technique for different sequences. This general distribution suggests more exact results in comparison with the results of other estimation methods and distribution functions.
We consider the possibility of identifying nuclei exhibiting the partial dynamical SU(3) symmetry... more We consider the possibility of identifying nuclei exhibiting the partial dynamical SU(3) symmetry (SU(3)-PDS) as those having excitation energy ratio 4/2 3.00 R . For this purpose, the level energy spectra of a set of 51 nuclei in the rare earth and actinide regions which presenting an axially deformed prolate rotational structure were analyzed via nuclear partial dynamical SU(3) symmetry in the framework of interacting boson model, to see if the SU(3)-PDS is broadly applicable, and where, how, and in which nuclei it breaks down. Overall, the PDS works very well, the predictions of such intermediate symmetry structure for energy spectrum were compared with the most recent experimental data and an acceptable degree of agreement is achieved. We conclude that PDS predictions have a more regular behavior in description of axially deformed prolate rotational nuclei than DS, which may lead to accurate predictions of such nuclei, and hence play a significant role in understanding the regular behavior of complex nuclei.
In this paper, we have analyzed the critical behavior of even–even Ru and Pd isotopes between U(5... more In this paper, we have analyzed the critical behavior of even–even Ru and Pd isotopes between U(5) and SO(6) limits of interacting boson model via Catastrophe Theory in combination with a coherent state formalism to generate energy surfaces. The parameters of the Hamiltonian are determined via least-square fitting to the experimental data for different Ru and Pd isotopes. Our results suggest a second-order phase transition in these isotopic chains and propose the best candidates for E(5) critical symmetry. Also, the analogy between the critical exponents of ground state quantum phase transition and Landau values for the critical exponents of thermodynamic phase transitions are described.
Fluctuation properties of a SU (1, 1)-based transitional Hamiltonian in the U (5) ↔ SO(6) transit... more Fluctuation properties of a SU (1, 1)-based transitional Hamiltonian in the U (5) ↔ SO(6) transitional region are considered in the nearest-neighbor spacing statistics. Energy spectra are determined via the Bethe-Ansatz method, which contains an extraction of Hamiltonian parameters from the experimental data of nuclei-provided empirical evidences for the considered region. Our results suggest an approach to chaotic dynamics for the transitional region in comparison with both dynamical symmetry limits in sequences prepared by theoretical and experimental data. Also, nuclei which are known as the best candidates for the E(5) critical symmetry exhibit more regularity compared to other nuclei in the transitional region.
In this paper, Kernel Density Estimation (KDE) as a non-parametric estimation method is used to i... more In this paper, Kernel Density Estimation (KDE) as a non-parametric estimation method is used to investigate statistical properties of nuclear spectra. The deviation to regular or chaotic dynamics, is exhibited by closer distances to Poisson or Wigner limits respectively which evaluated by Kullback-Leibler Divergence (KLD) measure. Spectral statistics of different sequences prepared by nuclei corresponds to three dynamical symmetry limits of Interaction Boson Model(IBM), oblate and prolate nuclei and also the pairing effect on nuclear level statistics are analyzed (with pure experimental data). KD-based estimated density function, confirm previous predictions with minimum uncertainty (evaluated with Integrate Absolute Error (IAE)) in compare to Maximum Likelihood (ML)-based method. Also, the increasing of regularity degrees of spectra due to pairing effect is reveal.
The Nearest Neighbor Spacing Distribution (NNSD) is one of the commonly used methods in statistic... more The Nearest Neighbor Spacing Distribution (NNSD) is one of the commonly used methods in statistical analysis of regular and chaotic behaviors of nuclear spectra. In this paper, Maximum Likelihood Estimation (MLE) method is proposed to evaluate the parameter of (NNSD)s. We estimate the parameter of (NNSD)s for different mass groups, nuclei with special values of deformation parameter () and also for nuclear spectra correspond to three dynamical symmetry limits and transition regions in the framework of the Interacting Boson Model (IBM) (with pure experimental data). The obtained results confirm theoretical predictions even in cases where the small size of data does not allow definite conclusions with the other methods. Also the ML estimated parameters have minimum uncertainty with variations very close (much closer than those obtained by other methods) to the so called Cramer-Rao Lower Bound (CRLB). ML estimated values predict more regular dynamics in compare to what other estimation methods indicate. We have also evaluated CRLB for all distributions (Brody, Berry-Robnik and Abul-Magd) with both values obtained from MLE and in different sequences where Brody distribution has the least CRLB.
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