Band head spin assignment of Tl isotopes of superdeformed rotational bands

The Variable Moment of Inertia (VMI) model is proposed for the assignment of band head spin of super deformed (SD) rotational bands, which in turn is helpful in the spin prediction of SD bands. The moment of inertia and stiffness parameter (C), were calculated by fitting the proposed transition energies. The calculated transition energies are highly dependent on the prescribed spins. The calculated and observed transition energies agree well when an accurate band head spin (I ₀) is assigned. The results are in good agreement with other theoretical results reported in literature. In this paper, we have reported the band head spin value 16 rotational band of super deformed Tl isotopes.     

Band head spin assignment of superdeformed bands in Hg isotopes through power index formula

The power index formula has been used to obtain the band head spin(I_0) of all the superdeformed(SD) bands in Hg isotopes. A least squares fitting approach is used. The root mean square deviations between the determined and the observed transition energies are calculated by extracting the model parameters using the power index formula. Whenever definite spins are available, the determined and the observed transition energies are in accordance with each other. The computed values of dynamic moment of inertia J~((2)) obtained by using the power index formula and its deviation with the rotational frequency is also studied. Excellent agreement is shown between the calculated and the experimental results for J~((2)) versus the rotational frequency. Hence, the power index formula works very well for all the SD bands in Hg isotopes expect for ~(195)Hg(2, 3, 4).     

Systematic study of rotational energy formulae for superdeformed bands in La and Ce isotopes

The experimental rotational spectra of superdeformed(SD) bands of ~(130)La, ~(131)Ce(1,2), ~(132)Ce(1,2,3) and133 Ce(1,2,3) in the A～130 mass region are systematically analyzed with the four parameter formula, power index formula, nuclear softness formula, and VMI model. It is observed that out of all the formulae, the four parameter formula suits best for the study of the ~(130)La, ~(131)Ce(1,2), ~(132)Ce(2,3) and ~(133)Ce(1,2,3) SD bands. The four parameter formula works efficiently in determining the band head spin of the ~(130)La, ~(131)Ce(1,2) ~(132)Ce(2,3) and ~(133)Ce(1,2,3) SD bands. Good agreement is seen between the calculated and observed transition energies whenever the accurate spin is assigned. In ~(132)Ce(1), the power index formula is found to work better than the other three formulae. The dynamic moment of inertia is also calculated for all the formulae and its variation with the rotational frequency is investigated.     

Identification of Bandhead Spin and Identical Bands for Odd-A Nuclei in $A\sim190$ Superdeformed Mass Region

The dynamical moment of inertia is estimated with its even-power expansion of the rotational frequency and in accordance we determine the intermediate spins of the superdeformed (SD) rotational bands. Using Marquardt method of nonlinear least-squares routines, we determine the expansion coefficients by fitting the proposed dynamical moment of inertia with its recent experimental data of the SD nuclei in the A=190 mass region. The comparison between our theoretical and available experimental data for the dynamic moment of inertia and spin shows good agreements. Also, we have calculated the static moment of inertia at three alternative values of spin. The value of spin at which the two moments of inertia are nearly equals is to be regarded as a bandhead spin of the corresponding band. These studies are carried out for eighteen bands of odd-A nuclei of the superdeformed region 190, namely ¹⁸⁹Hg(b1), ¹⁹¹Hg(b1, b2, b3, b4), ¹⁹³Hg(b2, b3, b5), ¹⁹⁵Hg(b1, b2, b3, b4), ¹⁹³Tl(b1, b2, b3, b5), ¹⁸⁹Tl(b1), and ¹⁹⁷Bi(b1). We also notice the occurrence of identical SD bands with near identical transition energies among the considered SD bands.     

Properties of rotational excitations in odd mass Dy isotopes

The data on high-spin rotational states in¹⁵⁵Dy,¹⁵⁷Dy,¹⁵⁹Dy and¹⁶¹Dy are discussed within a model where a particle is coupled to a rotor with a variable moment of inertia. In this model there is often a definite improvement in the quality and stability of the fits to levels in the positive-parity band below spin 25/2 when the moment of inertia of the core exhibits a linear dependence on the square of the rotational angular velocity as compared to the situation where a linear dependence onI(I+1) is assumed. In the improved fits the empirical matrix elements of the Coriolis force exhibit a smooth and significant increase with decreasing moment of inertia. The rotational energies above spin 25/2 in the positive-parity band and above 19/2 in the 11/2^? [505] band are understood within the present theoretical model if the moment of inertia increases more rapidly than the linear trend established at lower spin. In the 11/2^? [505] band this increase follows rather closely the behaviour in the even nuclei whereas in the positive-parity band the curves are quite flat even beyond the point where the moment of inertia in the even nuclei exhibits a discontinuous or back-bending behaviour. The significance of this observation is discussed in the light of existing theories on nuclear moments of inertia.     

Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

The positive-parity yrast bands of ^{79, 81, 83, 85, 87, 89}Y isotopes have been studied using the projected shell model (PSM). Nuclear-structure properties like yrast spectra, transition energies, band diagrams, kinetic moment of inertia, rotational frequencies and reduced transition probabilities (B(M1) and B(E2) are calculated. The results obtained from the PSM calculations are also compared with the available experimental as well as theoretical data and, in general, a reasonable agreement is obtained between them. Calculations in the present work also predict that these isotopes have multi-quasiparticle structure.     

High-spin yrast and non-yrast bands in 176Os, 178Os and 180Os

High-spin yrast and non-yrast states have been identified in ¹⁷⁶Os, ¹⁷⁸Os and ¹⁸⁰Os using (¹⁶O, xn) reactions, and γ-ray techniques. Band crossing anomalies are observed in each of the positive-parity yrast bands. The magnitude of these anomalies decreases with decreasing neutron number, an effect attributed to the change in the moment of inertia of the ground state rotational bands. A 23 ns isomer, predominantly K^π = 7^?, is identified at 1930 keV in ¹⁸⁰Os. The configuration of this isomer is discussed on the basis of the properties of its rotational band. Negative parity, odd and even spin, sideband sequences are observed in each isotope. Their relationship to rotation-aligned octupole and 2-quasiparticle bands is discussed from their excitation energies, band spacings, and decay properties. Detailed calculations for Coriolis mixed bands are carried out for the likely 2-quasiproton and 2-quasineutron configurations. An anomaly observed at spin 17 in the odd-spin negative-parity sequence in ¹⁸⁰Os is attributed to a band crossing with a fourquasiparticle configuration.     

Microscopic study of electromagnetic properties and band spectra of neutron deficient ~(133,135,137)Sm

A microscopic high spin study of neutron deficient and normally deformed ~(133,135,137)Sm has been carried out in projected shell model framework.The theoretical results have been obtained for the spins,parities and energy values of yrast and excited bands.Besides this,the band spectra,band head energies,moment of inertia and electromagnetic transition strengths are also Predicted in these isotoPes.The calculations successfully give a deeper understanding of the mechanism of the formation of yrast and excited bands from the single and multi-quasi particle configurations.The results on moment of inertia predict an alignment of a pair of protons in the proton(1 h_(11/2))~2 orbitals in the yrast ground state bands of ~(133-137)Sm due to the crossing of one quasiparticle bands by multi-quasiparticle bands at higher spins.The discussion in the present work is based on the deformed single particle scheme.Any future experimental confirmation or refutation of our predictions will be a valuable information which can help to understand the deformed single particle structure in these odd mass neutron deficient ~(133-137)Sm.     

Study for Superdeformed Bands in A～190 Region with Quantum Group Uqp(u2) Model

superdeformed bands in the A～190 region are systematically analyzed by using the twoparameter expansion of quantum group U_qp(u₂) Model. The calculated results of E2 transition γ ray energies are in agreement with experimental data. According to three different methods for the spin assignment of rotational bands, the spin values of the band head I₀ of the yrast SD bands in ¹⁹⁴Hg(1) and ¹⁹⁴Pb(1) are assigned. Furthermore, the physical meaning of the nuclear softness is discussed, and these nuclear softness values of a signature partner are almost equal.     

Observation of superdeformed bands in194Hg

Two rotational bands, with energy spacings characteristic of superdeformed shapes, have been observed following bombardment of¹⁵⁰Nd with⁴⁸Ca. The more intensively populated band consists of 18 transitions and is assigned to¹⁹⁴Hg. The depopulation of this band occurs around spin 10. The second band, consisting of at least 16 transitions, was populated less strongly and is tentatively assigned to¹⁹⁴Hg also. The lowest level in this band is assigned spin 8. The energy differences between transitions for both bands decrease from ～40 keV at low rotational frequencies to ～30 keV at the highest observed frequencies. The moments of inertia of the bands are similar to those of the two previously observed superdeformed bands in^191,192Hg. The similarities and differences of the four known bands in the mercury region are discussed.     

Collective structures and smooth band termination in 109Sn

Six rotational bands up to energies E _x = 24.7 MeV and spins J^π=(79/2^?) have been identified in ¹⁰⁹Sn using the GAMMASPHERE γ-detector array. Four of the bands show smoothly decreasing dynamic moments of inertia at rotational frequencies ?ω > 0.6 MeV. The bands arise at medium spins from a coupling of a valence d_5/2, g_7/2 or h_11/2 neutron to the deformed 2p2h proton excitation of the Z=50 core ¹⁰⁸Sn. At very high ?ω these bands show the typical behaviour of smoothly terminating bands, i.e. a gradual alignment of the angular momenta of the valence particles and holes corresponding to a transition from high collectivity to noncollective states.     

Dynamic rotational characteristics of actinides on empirical approach

In the paper calculation of the moments of inertia for nuclei from the region 87 ≤ Z ≤ 100 and 130 ≤ N ≤ 156 was made in dependence on the angular momentum of their rotational states. The experimental values of the moments of inertia were calculated for rotational energy of the classic rotor in its quantum form, with the use of a simple formula. The moment of inertia term appearing in the formula was treated as a variable. The calculations were carried out on the basis of experimental data for the energies of the rotational levels for 51 bands built on ground states for even-even nuclei and for nuclei with odd mass number A. In addition, 30 rotational bands built on excited states were also analysed in the investigated region in case of even-even nuclei. For many bands and nuclei the considered dependence of the moment of inertia on angular momentum has been found in the analytical form by fitting polynomials to the experimental data. It turned out that obtained results for the moments of inertia made it possible to describe the energies of rotational levels with a relative deviation not greater or only slightly greater than 1%. In general, in the case of 12 bands of ground level the maximum relative deviation of obtained level energies is smaller than 1%.      

Collective structures and smooth band termination in109Sn

Six rotational bands up to energies E _x =24.7 MeV and spinsj ^π=(79/2^?) have been identified in¹⁰⁹Sn using the GAMMASPHEREγ-detector array. Four of the bands show smoothly decreasing dynamic moments of inertia at rotational frequencies?ω>0.6 MeV. The bands arise at medium spins from a coupling of a valence d_5/2, g_7/2 or h_11/2 neutron to the deformed 2p2h proton excitation of the Z=50 core¹⁰⁸Sn. At very high?ω these bands show the typical behaviour of smoothly terminating bands, i.e. a gradual alignment of the angular momenta of the valence particles and holes corresponding to a transition from high collectivity to noncollective states.     

Observation of back- and forwardbending in the182Os ground-state band

From a study of theγ-decay of high-spin states populated using the (α, 8n) reaction, the ground-state rotational band in¹⁸²Os has been established up to spin 20⁺. A plot of the moment of inertia as a function of the square of the rotational frequency for this ground-state band results in a back-and-forwardbending curve, indicating that an explanation in terms of pure Coriolis decoupling in thei _13/2 neutron orbital requires revision. The moment of inertia reaches a maximum of only 74% of the rigid rotor value.     

Elimination of the Fluctuation in the Observed Transition Energies and Spin Assignments of the Superdeformed Bands in A≈150 Region

The spins of superdeformed bands in A≈150 region are assigned by the ah fitting provided the fluctuation are removed from the observed transition energies. Some typical superdeformed bands are discussed. For some superdeformed bands, the precision of spin assignments by the ah fitting could be improved.     

转动谱的若干理论及其对超形变带的研究

简述了若干转动谱理论及其对超形变带的应用 ,并用 Bohr- Mottelson的 I(I+1 )展开公式分析了 A=1 90区超形变带的性质和指定了它们的能级自旋 ,用 Harris的ω2 展开公式 J(1) =2α+(4/3 )βω2 +(6 /5 )γω4分析了 A=1 5 0区 Tb和 Dy同位素 2 0条超形变带的性质 ,指定了它们的能级自旋 .对于首次发现的152 Dy(1 )超形变带 ,带首自旋指定为 2 6 h,与实验结果更加符合. The recent developments of rotational spectral theories and its application to superdeformed bands were briefly reviewed. The superdeformed bands in A ≈190 region were analyzed and the spins of energy level were determined by the least square fitting experimental transition energy with the formula of Bohr Mottelson’s I(I+1) expansions. The superdeformed bands in A ≈150 region were analyzed by using the kinematic moments of inertia formula J (1) =2α+(4/3)βω 2+(6/5)γω 4 in...     

Rotational properties of the odd-Z transfermium nucleus 255Lr by a particle-number-conserving method in the cranked shell model

Experimentally observed ground state band based on the 1/2-[521] Nilsson state and the first exited band based on the 7/2-[514]Nilsson state of the odd-Z nucleus ~(255)Lr are studied by the cranked shell model(CSM) with the paring correlations treated by the particle-number-conserving(PNC) method. This is the first time the detailed theoretical investigations are performed on these rotational bands. Both experimental kinematic and dynamic moments of inertia(J~(1)and J~(2)) versus rotational frequency are reproduced quite well by the PNC-CSM calculations. By comparing the theoretical kinematic moment of inertia J~(1) with the experimental ones extracted from different spin assignments, the spin 17/2~-→13/2~- is assigned to the lowest-lying 196.6(5) ke V transition of the 1/2~-[521] band, and 15/2~-→11/2~- to the 189(1) ke V transition of the 7/2~-[514] band, respectively. The proton N = 7 major shell is included in the calculations. The intruder of the high- j low-? 1 j_((15)/2)(1/2~-[770]) orbital at the high spin leads to band-crossings at ω≈0.20( ω≈0.25) Me V for the 7/2~-[514] α =-1/2(α = +1/2) band, and at ω≈0.175 Me V for the1/2~-[521] α =-1/2 band, respectively. Further investigations show that the band-crossing frequencies are quadrupole deformation dependent.     

Crossing of negative parity bands in even-even nuclei around A≈150

Level energies of negative parity yrast bands (NPB) have been studied with a recently proposed, sensitive method. The irregular behaviour of the NPB's in theN=88 nuclei around spin 9–11 and the smooth behaviour in¹⁵⁶Dy (up toI=13) and in²³⁸U (up to I=19) support calculations by Vogel, where NPB's are described as aligned octupole bands up to a critical spin where intersection with two-quasiparticle bands takes place. Considering the NPB levels (I≦13) in¹⁵⁶Dy as members of an aligned octupole band, we obtain a remarkably good reproduction of their decay properties and energies using the VMI model.     

Microscopic study of neutron-rich dysprosium isotopes

Microscopic studies in heavy nuclei are very scarce due to large valence spaces involved. This computational problem can be avoided by means of the use of symmetry-based models. Ground-state, γ and β bands, and their B(E2) transition strengths in ^160–168Dy isotopes, are studied in the framework of the pseudo-SU(3) model which includes the preserving symmetry Q · Q term and the symmetry-breaking Nilsson and pairing terms, systematically parametrized. Additionally, three rotor-like terms are considered, whose free parameters, fixed for all members of the chain, are used to fine tune the moment of inertia of rotational bands and the band head of γ and β bands. The model succesfully describes in a systematic way rotational features in these nuclei and allows to extrapolate toward the midshell nucleus ¹⁷⁰Dy. The results presented show that it is possible to study a full chain of isotopes or isotones in the region with the present model.