Interacting Boson Model Research Articles

Role of Single-Particle Energies in Microscopic Interacting Boson Model Double Beta Decay Calculations

Single-particle level energies form a significant input in nuclear physics calculations where single-particle degrees of freedom are taken into account, including microscopic interacting boson model investigations. The single-particle energies may be treated as input parameters that are fitted to reach an optimal fit to the data. Alternatively, they can be calculated using a mean field potential, or they can be extracted from available experimental data, as is done in the current study. The role of single-particle level energies in the microscopic interacting boson model calculations is discussed with special emphasis on recent double beta decay calculations.

Calculation of nuclear structure in N = 90 isotones

The behavior of nuclear structures with an increase in atomic number from $${}^{150}$$ Nd to $${}^{158}$$ Er was investigated in this study. $${}^{152}$$ Sm and $${}^{154}$$ Gd are typical nuclei lying between the rotational and vibrational states, which can be explained by a slight breaking of the SU(3) symmetry in the U(5)-direction via the interacting boson model (IBM). Furthermore, $$N=90$$ isotones lie in the path of this symmetry-breaking phase transition. Moreover, the nuclear structure of $${}^{150}$$ Nd can be explained using X(5) symmetry. However, because the $${}^{156}$$ Dy and $${}^{158}$$ Er nuclei are not fully symmetrical, they can be represented by adding a perturbed term to express symmetry breaking. We identified the tendency of change in the nuclear structure using the following three calculation steps. First, the structures of $${}^{152}$$ Sm and $${}^{154}$$ Gd were described using the matrix elements of the Hamiltonian and the electric quadrupole operator between the basis states of the SU(3) limit in the IBM. Second, the low-lying energy levels and E2 transition ratios corresponding to the observable physical values were calculated by adding a perturbed term with the first-order Casimir operator of the U(5) limit to the SU(3) Hamiltonian in the IBM. We compared the calculation results with the experimental data of $$N=90$$ isotones. Finally, the potential of the Bohr Hamiltonian was represented by a harmonic oscillator; consequently, the structure of $$N=90$$ isotones could be expressed in the closed form by an approximate separation of variables. These nuclear structure prediction results were applied to elucidate the low-lying energy and E2 transitions in isotones.

Low-lying mixed symmetry states in the N=84 isotones 140Ba and 142Ce within interacting boson model-2

The characteristics of the low-lying mixed-symmetry states for 140Ba and 142Ce in the even-even N=84 isotones are investigated within the framework of the IBM-2 model. Electromagnetic transitions, B(E2) and B(M1) were calculated. Results showed that the lowest mixed-symmetry state is for 140Ba and 142Ce nuclei. A good agreement is found between experiment and predictions made using the U (5) limit of IBM-2.

Spectral features of nuclear structure of $$^{114-122}\hbox {Xe}$$

The light $$Z=54$$ Xe isotopes in the $$A=130$$ region, have been studied in the last 4 decades, in experiment and in theory. For ( $$N < 82$$ ) region, the evolution of the nuclear structure between the analytical symmetries U(5) and O(6) with neutron number N, is shown to be different for $$N=60\hbox {--}68$$ and $$N=70\hbox {--}78$$ . Here we focus on the lighter mass group. The shape transition between U(5) and O(6) symmetry is studied in terms of the variation in quadrupole deformation with N, the variation of the $$\upgamma $$ -band and the growth of the $$K^{{\uppi }} \quad =0_{\mathrm {2}}^{\mathrm {+}}$$ band and $$0_{\mathrm {3}}^{\mathrm {+}}$$ state. The effect of increasing triaxiality varying with N is illustrated. This variation is also reflected in the B(E2) values and the interband E2 transitions. Also, the role of neutrons filling the Nilsson single particle orbits in changing the spectra is studied. The sd interacting boson model IBM-1 is used to reproduce this spectral evolution. The study of the shape change between the analytical symmetries leads to the underlying basic physics.

Studying the Nuclear Structure of the () Deformed Nucleus using (IBM-1) and (GVMI) Models

In this research, some properties of the nuclear structure of even-even deformed nucleus were studied with dynamic symmetry SU (3). The energy levels E (L), excited energy levels (Eγ ), and electric quadrupole moment(QL ) were calculated using a set of parameters in the calculation to obtain a match with the practical values available using the first interacting boson model. IBM-1 and generalized variable moment of inertia (GVMI) model, The calculated results are in good agreement with the available practical values, especially, the values calculated according to the GVMI program. The phenomenon of band intersection, and back bending were also studied, the results showed no effect of the moment of inertia on the shape of the nucleus under consideration, because the back bending phenomenon was not occur.

Octupole correlations in light actinides from the interacting boson model based on the Gogny energy density functional

The quadrupole-octupole coupling and the related spectroscopic properties have been studied for the even-even light actinides $^{218-238}$Ra and $^{220-240}$Th. The Hartree-Fock-Bogoliubov approximation, based on the Gogny-D1M energy density functional, has been employed as a microscopic input, i.e., to obtain (axially symmetric) mean-field potential energy surfaces as functions of the quadrupole and octupole deformation parameters. The mean-field potential energy surfaces have been mapped onto the corresponding bosonic potential energy surfaces using the expectation value of the $sdf$ Interacting Boson Model (IBM) Hamiltonian in the boson condensate state. The strength parameters of the $sdf$-IBM Hamiltonian have been determined via this mapping procedure. The diagonalization of the mapped IBM Hamiltonian provides energies for positive- and negative-parity states as well as wave functions which are employed to obtain transitional strengths. The results of the calculations compare well with available data from Coulomb excitation experiments and point towards a pronounced octupole collectivity around $^{224}$Ra and $^{226}$Th.

Evolution of collectivity in Xe118

A recoil-distance Doppler shift experiment has been performed using the $^{102}\mathrm{Pd}(^{19}\mathrm{F},p2n$) reaction at a beam energy of 73 MeV to measure the lifetime of excited states in $^{118}\mathrm{Xe}$. The differential decay-curve method using $\ensuremath{\gamma}\ensuremath{\gamma}$ coincidences and a gating procedure that allows to extract the lifetime without feeding assumptions has been employed. The lifetimes obtained for the yrast states up to spin-parity ${8}^{+}$ are compared with interacting boson model calculations and $^{118}\mathrm{Xe}$ can be classified as a transitional nucleus between the spherical and a deformed shape. Systematics of the $B(E2)$ values for the ${2}^{+}\ensuremath{\rightarrow}{0}^{+}$ and ${4}^{+}\ensuremath{\rightarrow}{2}^{+}$ transitions in the isotopic chains of tin, tellurium and xenon are presented. It is proposed that a ``critical point'' exists at which the $B(E2;{4}^{+}\ensuremath{\rightarrow}{2}^{+})/B(E2;{2}^{+}\ensuremath{\rightarrow}{0}^{+})$ ratio drops to unity for lower neutron numbers within the isotopic chain. The position of the ``critical point'' varies with proton number, i.e., it is presumed to be located at the same mass number $A=114$ in the Sn, Te, and Xe isotopes.

Tests of collectivity in Zr98 by absolute transition rates

Lifetimes of low-spin excited states in $^{98}$Zr were measured using the recoil-distance Doppler-shift technique and the Doppler-shift attenuation method. The nucleus of interest was populated in a $^{96}$Zr($^{18}$O,$^{16}$O)$^{98}$Zr two-neutron transfer reaction at the Cologne FN Tandem accelerator. Lifetimes of six low-spin excited states, of which four are unknown, were measured. The deduced $B(E2)$ values were compared with Monte Carlo shell model and interacting boson model with configuration mixing calculations. Both approaches reproduce well most of the data but leave challenging questions regarding the structure of some low lying states.

Theoretical study of nuclear collective phenomena and broken SU(3) symmetry of even-even 238−244Pu isotopes

Theoretical nuclear study of the even-even Plutonium Isotopes Pu238−244 was carried out. The positive-parity rotational state band was calculated in the framework of the interacting Boson model-1 (IBM-1) and modified soft rotor formula (MSRF), while the negative-parity band was calculated in the framework of the new modified negative-parity formula (NMF). Furthermore, the energy levels for the β- and γ-vibrational energy bands were calculated. The odd-even staggering effect between the ground and octupole bands, which is a function of spin, was analyzed. The intrinsic coherent state was used to find the potential energy surfaces (PES). In addition, electric transition probabilities B(E1), B(E2), and B(E3) for these isotopes were calculated. The results obtained by applying the IBM-1, MSRF, and the NMF were inferred to be in good agreement with the corresponding experimental data for most of the nuclear states.

Electric Monopole Transitions in Nd Nuclei within IBM-2

The monopole transitions of 144-154Nd isotopes have been investigated in this work within the interacting boson model-2 (IBM-2) framework. The low-lying energy levels, electric quadrupole transition probability rates B(E2), electric quadrupole moments for first excited states monopole transition matrix elements and the intensity ratio were calculated in this work. The results of IBM-2 have been compared with the available experimental data; we have obtained a reasonable agreement. Unfortunately, the experimental data available on E0 transitions are very rare.The electric transition probability rates of beta and gamma bands to ground state band were calculated are fairly good agreement with available experimental values. Concerning the electric transition rates properties in IBM-2, we find that all calculations trends is reproduced well reasonably. The effective charges for neutron bosons and proton bosons calculated within IBM-2 are depending on the IBM-2 symmetries, we get suitable values for which is a constant for all 144-154Nd isotopes because the number of proton bosons is constant. The effective charge for neutron bosons varies from isotope to another

A note on Jacobi-type transitions in finite nuclei

The Jacobi-type transitions (JTTs) in nuclei and their connections with excite-state quantum phase transitions (ESQPTs) have been investigated within the framework of the interacting boson model (IBM) by both the semiclassical analysis and quantal calculations. The results indicate that the quadrupole deformation of a transitional system may change from γ rigid to γ soft as the angular momentum increases. This change may in turn drive the JTTs to occur around the saddle point of the corresponding classical potential, where the precursors of ESQPT can be also identified even for a realistic boson number. A further comparison between the experimental data and the model predictions confirms that the JTT phenomena may widely occur in the rare-earth isotopes associated with the 1st-order quantum phase transitions.

Energy Levels and Electromagnetic Transition of 90-94mo Nuclei Using Ibm-1

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

Band mixing in 96,98Mo isotopes * *Supported by the National Natural Science Foundation of China (11875171, 11675071, 11747318), the U. S. National Science Foundation (OIA-1738287, ACI -1713690), U. S. Department of Energy (DE-SC0005248), the Southeastern Universities Research Association, the China-U. S. Theory Institute for Physics with Exotic Nuclei (CUSTIPEN) (DE-SC0009971), and the LSU–LNNU joint research program (9961)

We use the two lowest weight states to fit E2 strengths connecting the and transitions in Mo. Our results confirm that the and states are maximally mixed, and that the states are weakly mixed in both nuclei. An appropriate Hamiltonian to represent the band mixing is found to be exactly solvable, and its eigenstates can be expressed as the basis vectors in the configuration mixing scheme and interacting boson model. The interacting boson model and coexistence mixing configuration under the solvable methods are suitable models for analyzing the band mixing with high accuracy.

Double beta decay and the quest for Majorana neutrinos

The observation of neutrinoless double beta (0νββ) decay remains crucial for understanding lepton number violation. The inverse half-life for 0νββ-decay is given by the product of a phase space factor (PSF), a nuclear matrix element (NME), which both rely on theoretical description, and a function f containing the physics beyond the standard model. Phase space factors and nuclear matrix elements have been evaluated, or are under evaluation, systematically for all processes of interest. The nuclear matrix elements have been calculated within the framework of the microscopic interacting boson model (IBM-2), and phase space factors have been evaluated using exact Dirac electron wave functions. The current situation is then discussed by combining the theoretical results with experimental limits on the half-life of neutrinoless double beta decay. The extracted limits on the average light neutrino mass are addressed, complemented with a discussion of other possible 0νββ-decay mechanisms and scenarios.

Subtle connection between shape coexistence and quantum phase transition: The Zr case

Background: Zr region is characterized by very rapid changes in the ground state structure of the nuclei. In particular, the onset of deformation when passing from $^{98}$Zr to $^{100}$Zr is one of the fastest ever observed in the nuclear chart. It has been probed both experimental and theoretically that certain low-lying excited states of Zr isotopes own different shapes than the ground state. Purpose: We intend to disentangle the interplay between the sudden changes in the ground state shape, i.e., the existence of a quantum phase transition, and the presence in the spectra of coexisting states with very different deformation, i.e., the presence of shape coexistence. Method: We rely on a previous calculation using the Interacting Boson Model with Configuration Mixing (IBM-CM) which reproduces in detail the spectroscopic properties of $^{96-110}$Zr. This IBM-CM calculation allows to compute mean-field energy surfaces, wave functions and any other observable related with the presence of shape coexistence or with a quantum phase transition. Results: We obtain energy surfaces and the equilibrium value of the deformation parameter $\beta$, the U(5) decomposition of the wave functions and the density of states. Conclusions: We confirm that Zr is a clear example of quantum phase transition that originates from the crossing of two configurations with a very different degree of deformation. Moreover, we observe how the intruder configuration exhibits its own evolution which resembles a quantum phase transition too.

Analysis of light neutrino exchange and short-range mechanisms in0νββdecay

Neutrinoless double beta decay ($0\nu\beta\beta$) is a crucial test for lepton number violation. Observation of this process would have fundamental implications for neutrino physics, theories beyond the Standard Model and cosmology. Focussing on so called short-range operators of $0\nu\beta\beta$ and their potential interplay with the standard light Majorana neutrino exchange, we present the first complete calculation of the relevant nuclear matrix elements, performed within the interacting boson model (IBM-2). Furthermore, we calculate the relevant phase space factors using exact Dirac electron wavefunctions, taking into account the finite nuclear size and screening by the electron cloud. The obtained numerical results are presented together with up-to-date limits on the standard mass mechanism and effective $0\nu\beta\beta$ short-range operators in the IBM-2 framework. Finally, we interpret the limits in the particle physics scenarios incorporating heavy sterile neutrinos, Left-Right symmetry and R-parity violating supersymmetry.

Pairing vibrations in the interacting boson model based on density functional theory

We propose a method to incorporate the coupling between shape and pairing collective degrees of freedom in the framework of the interacting boson model (IBM), based on the nuclear density functional theory. To account for pairing vibrations, a boson-number non-conserving IBM Hamiltonian is introduced. The Hamiltonian is constructed by using solutions of self-consistent mean-field calculations based on a universal energy density functional and pairing force, with constraints on the axially-symmetric quadrupole and pairing intrinsic deformations. By mapping the resulting quadrupole-pairing potential energy surface onto the expectation value of the bosonic Hamiltonian in the boson condensate state, the strength parameters of the boson Hamiltonian are determined. An illustrative calculation is performed for $^{122}$Xe, and the method is further explored in a more systematic study of rare-earth $N=92$ isotones. The inclusion of the dynamical pairing degree of freedom significantly lowers the energies of bands based on excited $0^+$ states. The results are in quantitative agreement with spectroscopic data, and are consistent with those obtained using the collective Hamiltonian approach.

Nuclear Structure and Energy Levels of 158Er, 160Yb and 162Hf Isotones

The properties of even-even158Er, 160Yb and 162Hf isotones are studied and its energy states calculated. To identify the properties of each isotone, the values of the first excited states and the ratio of the second to the first excited states were adopted. The phenomenon of back-bending, the E-GOS curve and the odd-even staggering were studied. Examining the algebraic structure of the Bohr model (BM) clarified the relationship with the interacting vector boson model (IVBM) and the interacting boson model (IBM) which it has related solvable limits and corresponding dynamical symmetries. BM, IVBM and IBM were used to calculate the energy states for each isotone and compared with the experimental data. The results showed that the BM and IVBM are more comfort than the calculation of IBM-1. The contour plots of the potential energy surface (PES) to the IBM Hamiltonian for Er–Hf with N = 90 have been obtained using the intrinsic coherent state and evolve from deformed shapes to γ- unstable with decreasing the boson number.

Properties of O(6)-U(5) transition symmetry for 122-124Cd isotopes in IBM

The some properties, Energy levels, B(E2) values and potential energy surface, for even-even 122,124Cd isotopes have been studied using the interacting boson model. The predicted levels (energies, spins and parities) and B(E2) values results were reasonably consistent with the experimental data. The contour plot of the potential energy surfaces shows all interest nuclei were deformed and have O(6)-U(5) transition symmetry.

Nuclear structure features in 72-80Se isotopes

Interacting boson model (IBM – 1 and IBM – 2) have been used to perform a whole studying for isotopes. The low lying positive party states, dynamic symmetries, mixed symmetry states MSS, reducing electric quadruple transition probabilities B(E2), branching ratio, quadruple momentum , reducing magnetic dipole transition probability B(M1), mixing ratio δ(E2/M1), reducing electric monopole transition probability B(E0), and X(E0/E2) ratio have been investigated. U(5) features are the dominant in with addition of a 2 small effect of parameter started from to isotopes, energy ratios show that isotopes as the nearest isotopes to typical vibrational limit while isotopes tend towards the rotational region that lied on U(5) - SU(3), leg of “Casten’s triangle”. Spin and party for many energy levels and electromagnetic transition probability are confirmed. The mixing symmetry states in isotopes are slowly increased with ζ2 while there is no clear effected in isotope. The calculated branching ratios B(E2), B(M1) mixing ratios δ(E2/M1), B(E0), and X(E0/E2) depend in comparisons with fewer available experimental data. The results are in acceptable agreement; to completed a perfect comparison, more experimental investigations are still needed to these nuclei. isotopes have small values of electric quadruple moment of state.