Mixed-symmetry States Research Articles

Mixed symmetry states in 96Mo and 98Ru isotones in the framework of interacting boson model

The software package IBM code for interacting boson model-1 and Neutron Proton Boson NPBOS code for interacting boson model-2 have been used to calculate energy levels for, for by estimating a set of parameters which are used to predict the behavior of even-even isotones within the current scope of work there is clear competition between the two parameters (ε and a2) in isotones, as an inverse relationship. This means that vibrational qualities are continuous mixed with the rotational properties. In interacting boson model-2 parameters(ε, κ, χπ and χν) have been shown similarity with interacting boson model-1 expected. The Majorana parameter effect (ζ2) on the calculated excitation energy level for isotones has been accomplished by vary the ζ2 around the optimum-matches to practical data. The effect of increasing ζ2 on mixing symmetry states is the same in all isotones but different from state to another, we find the state J+ = 23+ was the lowest mixing symmetry states still approximately constant in the all. In that time,isotones have 1+, 3+1, 5+1 mixed symmetry states, rapidly increasing with increasing ζ2. The results of the calculated energy levels were in acceptable agreement with the experimental data. There is no pure vibrational property of these isotones

Structure of low-lying states in 158-168Hf nuclei

The characteristics of low-lying mixed-symmetry states in 158-168Hf isotopes have been investigated in the framework of the interacting boson model. The obtained results of the low energy spectra, B(E2) and mixing ratio δ(E2/M1) for all isotopes are compared with empirical values . The effect of the Majrona terms on the energy levels have been investigated. The 2ms+ and 1+ states are the lowest mixed-symmetry for vibrational 158-164Hf nuclei and for rotational 166,168Hf nuclei, respectively.

Coriolis mixing of the K = 1 and K = 0 mixed symmetry states in the well deformed even–even nuclei

The Coriolis matrix elements responsible for mixing of the $$1^+ K=1$$ and $$1^+ K=0$$ states are calculated in the framework of the Quasiparticle Phonon Model for several Gd and Dy isotopes. In many considered cases these matrix elements are equal to several tens of keV and are comparable with energy distances between the mixed levels. The results obtained indicates that Gd isotopes could be more suitable for finding deviations from Alaga rules in M1 transitions from $$1^+$$ state to the states of the ground band.

Description of Ba-Sm (N=84) Isotones in the Framework of IBM Model

The level structure of Ba-Sm (N=84) isotones is discussed in the interacting boson model (IBM). Energy levels, electromagnetic transition probabilities and mixing ratios are calculated. The experimental mixed symmetry identification for the lowest + 2 state in 140Ba, 142Ce and 144Nd supported, and a + 2 mixed symmetry state is proposed for 146Ba. Potential Energy Surface is examined and PES contours are plotted. The U(5) limit of the model is used to achieve agreement between theory and experiment.

Ising machines with strong bilinear coupling

Networks of coupled parametric resonators (parametrons) hold promise for parallel computing architectures. En route to realizing complex networks, we report an experimental and theoretical analysis of two coupled parametrons. In contrast to previous studies, we explore the case of strong bilinear coupling between the parametrons, as well as the role of detuning. We show that the system can still operate as an Ising machine in this regime, even though careful calibration is necessary to ensure that the correct solution space is available. Apart from the formation of split normal modes, new states of mixed symmetry are generated. Furthermore, we predict that systems with $N>2$ parametrons will undergo multiple phase transitions before arriving at a regime that can be equivalent to the Ising problem.

Mixed Symmetry States in 92Zr and 94Mo Nuclei

Mixed-symmetry states of 92Zr and 94Mo isotopes are investigated with the use of the collective models, Interacting Boson Model-2 (IBM-2) and Quasiparticle Phonon Model (QPM). The energy spectra and electromagnetic transition rates for these isotopes are calculated. The results of IBM-2 and QPM are compared with available experimental data. We have obtained a satisfactory agreement, and IBM-2 gives a better description. In these isotopes, we observe a few states having a mixed symmetry such as 2+2, 2+3, 3+1, and 1+s. It is found that these isotopes have a vibrational shape corresponding to the U(5) symmetry.

Symmetry and mixed-symmetry states in the transitional nuclei neodymium $$A = 144{-}154$$

Symmetry and mixed-symmetry states in the transitional nuclei neodymium $$A = 144{-}154$$

Stability of Mixed-Symmetry Superconducting States with Broken Time-Reversal Symmetry against Lattice Distortions

We examine the stability of mixed-symmetry superconducting states with broken time-reversal symmetry in spatial-symmetry-broken systems, including chiral states, on the basis of the free-energy functional derived in the weak-coupling theory. We consider a generic a_1 + i a_2 wave state, with a_1 and a_2 being different symmetry indices such as (a_1,a_2) = (d,s), (p_x,p_y), and (d,d').The time-reversal symmetry of the mixed-symmetry state with the a_1- and a_2-wave components is broken when the phases of these components differ, and such a state is called the time-reversal-symmetry breaking (TRSB) state. However, their phases are equated by Cooper-pair scattering between these components if it occurs; i.e., when the off-diagonal elements S_{a_1 a_2} = S_{a_2 a_1} of the scattering matrix are nonzero, they destabilize the TRSB state. Hence, it has often been believed that the TRSB state is stable only in systems with a spatial symmetry that guarantees S_{a_1 a_2}=0. We note that, contrary to this belief, the TRSB state can remain stable in systems without the spatial symmetry when the relative phase shifts so that S_{a_1 a_2} = 0 is restored, which results in a distorted TRSB (a_1 + a_2) + i a_2 wave state. Here, note that the restoration of S_{a_1 a_2} = 0 does not imply that the symmetry of the quasi-particle energy E_k is recovered. This study shows that such stabilization of the TRSB state occurs when the distortion is sufficiently small and \Delta_{a_1} \Delta_{a_2} is sufficiently large, where \Delta_a is the amplitude of the a-wave component in the TRSB state in the absence of the distortion. We clarify the manner in which the shift in the relative phase eliminates S_{a_1 a_2} and prove that such a state yields a free-energy minimum. We also propose a formula for the upper bound of the degree of lattice distortion, below which the TRSB state can be stable.

Revisiting higher-spin gyromagnetic couplings

We analyze Bosonic, Heterotic, and Type II string theories compactified on a generic torus having constant moduli. By computing the hamiltonian giving the interaction between massive string excitations and U(1) gauge fields arising from the graviton and Kalb-Ramond field upon compactification, we derive a general formula for such couplings that turns out to be universal in all these theories. We also confirm our result by explicitly evaluating the relevant string three-point amplitudes. From this expression, we determine the gyromagnetic ratio g of massive string states coupled to both gauge-fields. For a generic mixed symmetry state, there is one gyromagnetic coupling associated with each row of the corresponding Young Tableau diagram. For all the states having zero Kaluza Klein or Winding charges, the value of g turns out to be 1. We also explicitly consider totally symmetric and mixed symmetry states (having two rows in the Young diagram) associated with the first Regge-trajectory and obtain their corresponding g value.

E2 decay characteristics of the M1 scissors mode of Sm152

The $E2/M1$ multipole mixing ratio of the ${1}_{\text{sc}}^{+}\ensuremath{\rightarrow}{2}_{1}^{+}\phantom{\rule{4pt}{0ex}}\ensuremath{\gamma}$-ray transition and therefore the $F$-vector $E2$ decay of the scissors mode of the shape-phase transitional nucleus $^{152}\mathrm{Sm}$ have been measured with the nuclear resonance fluorescence method at the High-Intensity $\ensuremath{\gamma}$-ray Source ($\mathrm{HI}\ensuremath{\gamma}\mathrm{S}$). Furthermore, parity quantum numbers of several dipole-excited states have been remeasured, making use of the polarized $\ensuremath{\gamma}$-ray beam at $\mathrm{HI}\ensuremath{\gamma}\mathrm{S}$, and partially reassigned. The new data enable an unambiguous determination of the proton and neutron effective boson quadrupole charges within the proton-neutron interacting boson model. With the well-constrained parameter set, a new mixed-symmetry state is predicted.

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.

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.

Mixed Symmetry States for even-even 218-224 Ra Isotopes by using (IBM-2)

In present investigation we employ IBM-2 parameters in Hamiltonian operator and applying the NPBOS bundle to determine mixed symmetry states for even-even 218-224 Ra isotopes, in addition to extract some theoretical nuclear properties, one of which the excited energy levels, which gave best match between practical data and theoretical results specially for the ground state bands, and acceptable agreement for semi β bands and semi γ bands. The (MSS) property which gets a speedy reaction while changing majorana term δ2 due to mixture between wave function for protons and neutrons was diagnosed for levels Energy ratios were calculated between and which shows these isotopes have a varied dynamic stretch starting from their pure vibrational state at A = 218 transition state U (5) - O (6) at A = 220 and finally transition state O (6)-SU (3), when A = 222 And 224, respectively. Finally, determined the likelihood for electric quadruple transition B(E2), magnetic dipole B(M1), which All express a decent agreement with the practical data.

Restoring the valence-shell stabilization in Nd140

A projectile Coulomb-excitation experiment was performed at the radioactive-ion beam facility HIE-ISOLDE at CERN to obtain E2 and M1 transition matrix elements of Nd140 using the multistep Coulomb-excitation code gosia. The absolute M1 strengths, B(M1;22+→21+)=0.033(8)μN2,B(M1;23+→21+)=0.26-0.10+0.11μN2, and B(M1;24+→21+)<0.04μN2, identify the 23+ state as the main fragment of the one-quadrupole-phonon proton-neutron mixed-symmetry state of Nd140. The degree of F-spin mixing in Nd140 was quantified with the determination of the mixing matrix element VF-mix<7-7+13keV.

Experimental evidence for low-lying quadrupole isovector excitation of $$^{208}$$Po

We present the results from an experiment dedicated to measure the lifetime of the $$2^+_2$$ state, candidate for the one-phonon mixed-symmetry state, of $$^{208}$$ Po. This nucleus was studied in the $$\alpha $$ -transfer reaction $$^{204}$$ Pb( $$^{12}$$ C, $$^{8}$$ Be) $$^{208}$$ Po and the lifetime of the $$2^+_2$$ state was determined by utilizing the Doppler-shift attenuation method. The experimental data show that the $$2^+_2$$ state decays with a sizable M1 transition to the $$2^+_1$$ state revealing its isovector nature.

Investigation of Mixed Symmetry States in 170-178Yb isotopes

low-lying positive parity states, dynamic symmetries, mixed symmetry states (MSS), reducing electric quadrupole transition probabilities B(E2), branching ratio, reducing magnetic dipole transition probabilities B(M1), and mixing ratios δ(E2/M1) for 170-178Yb have been investigated by applied IBM-1 and IBM-2 program package. The software package IBM-1 and IBMT computer code for IBM-1 and Neutron Proton Boson NPBOS and Neutron Proton Boson Electromagnetic NPBEM software package have been used. The Ytterbium nuclei with the (170 − 178) mass number considered as rotational nuclei after applying the first and second interacting boson model with studying dynamic symmetry and energy ratios , and that approximated to (3.33,7 and 12). The reducing transition probability for electric quadruple B(E2) and branching ratios that state the small values of the ratios R′ and R″ as having rotational characteristics. A study of the mixed symmetry state of these nuclei shows that the lower energy mixing level is the first 1+ level, which distinguishes the rotational determination nuclei. The energy levels values for the states have a clear mixed symmetry state (MSS) directly proportional with Majorana parameters ζ2, while , and , tend to be approximately more conservative.

Coulomb Excitation of Proton-rich N = 80 Isotones at HIE-ISOLDE

A projectile Coulomb-excitation experiment was performed at the radioactive ion beam facility HIE-ISOLDE at CERN. The radioactive 140Nd and 142Sm ions were post accelerated to the energy of 4.62 MeV/A and impinged on a 1.45 mg/cm2-thin 208Pb target. The γ rays depopulating the Coulomb-excited states were recorded by the HPGe-array MINIBALL. The scattered charged particles were detected by a double-sided silicon strip detector in forward direction. Experimental γ-ray intensities were used for the determination of electromagnetic transition matrix elements. Preliminary results for the reduced transition strength of the of 140Nd and a first estimation for 142Sm have been deduced using the Coulomb-excitation calculation software GOSIA. The states of 140Nd and 142Sm show indications of being the main fragment of the proton-neutron mixed-symmetry state.

A unified description of shape coexistence and mixed-symmetry states in 98Mo using IBM-2**Supported by the National Natural Science Foundation of China under Grant Nos. 11947410, 11147148 and U1832139 and the Natural Science Foundation of Zhejiang Province under grant No. LY19A050002.

Level structure and electromagnetic transitions in 98Mo have been investigated on the basis of the proton-neutron interacting boson model (IBM-2) by considering the energy difference between neutron boson εν and proton boson επ. The results are compared with the recent experimental data and it is observed that they are in good agreement. In particular, the strongest M1 transition from state to can be well reproduced, from which one can determine the as an mixed-symmetry (MS) state. We have calculated the electric monopole strength , and our result agrees with the experimental one. The calculation indicates that shape coexistence and MS states are simultaneously well described using IBM-2.

Decoupling Parameter for Rotational Bands Based on Mixed-Symmetry States

The energy as determined experimentally for the first excited 2+ state of the 156Gd rotational band based on the mixed-symmetry state is extremely small in relation to characteristic values of this energy in deformed nuclei. The possibility of explaining this experimental fact by a large value of the decoupling parameter is explored. The result is that the decoupling-parameter values obtained under various assumptions on the structure of the mixed-symmetry state are too small for explaining the experimental excitation energy of the state in question.

Investigation of isospin excited and mixed-symmetry states in even–even N = Z nuclei

Mixed-symmetry and isospin excited states are typical of the interacting boson model with isospin (IBM-3). With a view to look for such states, levels scheme of the IBM-3 dynamical symmetry is discussed. A systematic investigation in the proton and neutron degrees of freedom of the energy levels has been carried out. A sequence of isospin excitation bands has been identified. We have analyzed the wave functions and given the symmetrical labeling of the states. The transition probabilities between the isospin excitation states of model limits are analyzed in terms of isoscalar and isovector decompositions. The present calculations suggest that a combination of isospin excitation and mixed-symmetry states can provide substantial information on the structure of nuclear states. Calculations for [Formula: see text] and [Formula: see text] nuclei are presented and compared with the results of the shell model and available experimental data.