Odd-spin States Research Articles

Spectroscopy and second hyperpolarizability of odd spin states of acetonitrile: Theoretical study

The present study reports the spectroscopic characterization and second hyperpolarizability of odd spin states of acetonitrile in gas phase and water solvent. The odd spin states of acetonitrile are singlet, triplet and quintet spin state of acetonitrile have been considered for the study. The spectroscopic characterization viz. energy, geometrical parameters, infrared and electronic absorption spectra, molecular orbitals (MOs) their energies and natural transitions orbitals (NTOs) in gas phase and water solvent state reported at B3LYP/aug-cc-pVDZ level of theory. The second hyperpolarizability values are obtained using various methods and basis sets for comparison. It has been observed that the second hyperpolarizability values for the odd spin states of acetonitrile are more positive than the first hyperpolarizability. It is clearly seen that the effect of spin on spectroscopic parameters except on energy. The singlet gas phase acetonitrile calculations are well matching with the available experimental determinations. The TDDFT approach has been used to study electronic absorption spectra of all spin states of acetonitrile in gas phase and in water solvent. The IEFPCM model implemented in studying acetonitrile in water solvent at B3LYP/aug-cc-pVDZ level of theory. It is observed that HOMO to LUMO gap is larger for singlet than the triplet and quintet spin state and it decrease with an increase in strength of an applied field. All these calculations performed using Gaussian 16 program package.

Multiple octupole-type band structures inTh220: Reflection-asymmetric tidal waves?

The $^{220}\mathrm{Th}$ level scheme has been considerably extended from an experiment using the $^{26}\mathrm{Mg}+^{198}\mathrm{Pt}$ reaction at 128 MeV. The evaporation residues from this very fissile system were selected with the HERCULES detector system and residue-gated $\ensuremath{\gamma}$ rays were measured with Gammasphere. The simplex feature (alternating-parity levels) persists up to the highest spins observed ($23\ensuremath{\hbar}$), but the nucleus exhibits a more vibrational-like behavior than the heavier Th isotopes. In addition, a doubling of the negative-parity, odd-spin states is seen as well as a staggering of the $B(E1)/B(E2)$ ratios. A new interpretation based on a picture of tidal waves on a reflection-asymmetric nuclear surface is proposed.

Symmetries in nuclear structure

The symmetries of the rotating mean field and their consequences for rotational bands are discussed. Chirality of rotating triaxial nuclei differs from the chirality of molecules and mass-less particles, because the roles of space inversion and time reversal are exchanged. The experimental consequences of chirality and mass regions where it is expected are discussed. Rotational bands of the predicted shapes with tetrahedral symmetry are Δ I = 2 sequences with alternating parity. Breaking of the isospin rotational symmetry by the isovector pair field leads to isorotational bands. The low spin spectra of N = Z nuclei can be explained combining mean-field calculations that take only isovector pairing into account with the concept of isorotational bands. The possible appearance of an isoscalar pair field at high spin would manifest as a pair-rotational band consisting of even-spin states in the even-even and odd-spin states in odd-odd N = Z nuclei.

Wobbling motion: Aγ-rigid orγ-soft mode?

For even-even nuclei, it is shown that the predicted B(E2) values from the odd spin states of the quasi-gamma band in a gamma-soft nucleus to the yrast band are quite similar to those predicted for the one-phonon wobbling mode of a rigidly triaxial nucleus. This suggests that the observation of wobbling points to axial asymmetry but not necessairly to rigid triaxiality.

In-band and inter-band B(E2) values within the Triaxial Projected Shell Model

The Triaxial Projected Shell Model (TPSM) has been successful in providing a microscopic description of the energies of multi-phonon vibrational bands in deformed nuclei. We report here on an extension of the TPSM to allow, for the first time, calculations of B(E2) values connecting γ- and γγ-vibrational bands and the ground-state band. The method is applied to 166,168Er. It is shown that most of the existing B(E2) data can be reproduced rather well, thus strongly supporting the classification of these states as γ-vibrational states. However, significant differences between the data and the calculation are seen in those B(E2) values which involve odd-spin states of the γ-band. Understanding these discrepancies requires accurate experimental measurements and perhaps further improvements of the TPSM.

Crossings of the g-, s- and t-bands in 184Os

In-beam γ-ray spectroscopic studies for high-spin states in 184Os have been performed. The favoured and unfavoured extensions of the g- and s-bands are observed. In addition, rotational levels built on the K π =10 + isomer are identified up to I=20 ℏ for the even-spin states and I=(25) ℏ for the odd-spin states, showing a large signature splitting. A three-band-mixing calculation involving the g-, s- and t-bands has been carried out to analyze the backbending in the yrast sequence and the signature splitting of the K π =10 + band. The extracted interaction strengths are compared with those deduced in the neighbouring nuclei.

Negative-parity yrast band in 170Yb: Rotation-aligned neutrons with deformation-coupled bandhead?

A sideband in 170Yb has been identified up to I π =17 −. It has an isomeric I=4 bandhead, yet the odd-spin states have prompt branches to the ground-state band. The contrasting properties are explained by the Coriolis effects on the quasi-particle configuration.

Multiple high-spin band structure inEr164

$^{164}\mathrm{Er}$ high-spin states were studied via the $^{160}\mathrm{Gd}(^{9}\mathrm{Be},5n)$ reaction at 59-MeV beam energy. We find significant population of three new rotational bands in addition to higher-spin levels of the previously known $\ensuremath{\gamma}$-vibrational band. In most cases the spins of the levels were established by angular distribution measurements, and some parities were established by linear polarization measurements on interband transitions. Two odd-parity bands with both even- and odd-spin states begin with the previously reported ${5}^{\ensuremath{-}}$ (1664 keV) and ${7}^{\ensuremath{-}}$ (1985 keV) levels and extend to levels of spin 22 (5350 keV) and 13 (3351 keV), respectively. These two bands exhibit markedly different moments of inertia. The third band is of unknown parity and has a likely even-spin sequence extending from a level of spin 8 (2091 keV) to a possible spin-22 level (5678 keV). The even-spin sequence of the $\ensuremath{\gamma}$ band extends to a spin-14 level (3267 keV) and exhibits a backbend at the ${10}^{+}$ level to a new ${12}^{+}$' level of the previously established even-spin even-parity yrast band. The odd-spin sequence backbends at spin 13, and extends to a possible spin-19 level at 4588 keV, thereby providing evidence for an odd-spin even-parity yrast band some 500 keV higher in energy than its even-spin counterpart.NUCLEAR STRUCTURE $^{160}\mathrm{Gd}(^{9}\mathrm{Be},5n\ensuremath{\gamma})$, $E=59$ MeV; measured ${I}_{\ensuremath{\gamma}}$, $W{(\ensuremath{\theta})}_{\ensuremath{\gamma}}$, linear $P$; deduced $\ensuremath{\Lambda}$, levels, $J$, $\ensuremath{\pi}$.

Staggering of even and odd spin states in196, 198Tl nuclei

Recent experimental results for 81 196 Tl115 along with that of 81 198 Tl115 are analysed. It is shown that staggering observed in the excitation energy of the even and odd spin states in these odd-odd mass transitional nuclei is due to the residual interaction between the two odd particles.

Decoupled and strongly coupled particles system in odd-odd mass nuclei

An odd-odd mass system in which a particle and a hole occupy high angular momentum states like π h 9 2 and v i 13 2 , respectively, is studied in terms of two quasi particles and the triaxial rotor model. It is pointed out that π h 9 2 particle which is strongly coupled to the deformed core at a low core angular momentum state changes gradually its direction towards the core angular momentum as the total spin of the system increases. Furthermore, the effect of the residual interaction is shown to be responsible for the staggering of the even and odd spin states in the excitation energy observed in recent experiments.

Negative parity bands in 100Ru observed in the 100Mo(α, 4n)100Ru reaction

In the study of the 100Mo(α, 4n)100Ru reaction at Eα = 45 MeV the ground state band of 100Ru was excited up to Jπ = 10+ and a negative parity band up to Jπ = (15)−. In addition, two negative parity bands were observed, one of which probably has even and the other odd spin states. The experiments encompassed γ-ray angular distribution, coincidence, linear polarization and conversion electron measurements. New levels are reported at Ex = 5130, 5165 (Jπ = (13)−), 5280, 5717 and at 6201 keV (Jπ = (15)−). In addition spin or parity assignments were made for the Ex = 2529, 2953, 2965, 3141, 3356, 3505 and 4233 keV levels as Jπ = 5−, 7−, (6)−, 7−, (8)−, 9− and (11)−, respectively. A 3− state is for the first time observed at Ex = 2180 ± 20 keV in the 100Ru(α, α') reaction at Eα = 104 MeV. Multipolarities, conversion coefficients, branching and quadrupole/dipole amplitude mixing ratios have been determined for many transitions in 100Ru. From a detailed comparison of excitation energies and of the properties of many, even weak, transitions with the results of the interacting boson approximation model, it appears that this simple model provides a good overall parametrization. This supports the description of 100Ru as an anharmonic vibrator with quadrupole and octupole bosons as independent but interacting basic excitation modes. A negative parity band in 101Ru, of which a new level at Ex = 3474 keV is a candidate for the 272− member, is well described by coupling the h112 single particle to the 100Ru quadrupole excitation.

Analysis of the ( 3He, t) reaction on some 1p shell nuclei

Differential cross sections for the ( 3H, t) charge-exchange reactions have been measured on 9Be, 10B, 11B and 12C targets with 217 MeV 3He particles. The data on 9Be, 10B, 11B are compared with microscopic calculations using an appropriate central or central+tensor force. This analysis has been carried out for 12C and reported in a previous paper. The results indicate that the tensor force is quite important for exciting the odd-spin states at 217 MeV. Discrepancies with the theoretical description for even-spin transltions suggest that other complicated mechanisms are involved. Two-step processes involving a pickup-stripping mechanism or proceeding through an intermediate inelastic state, are also investigated. Both are found to be quite important at 217 MeV.

The [formula omitted] excitations in the odd nucleus 172Tm

The decay of 50 h 172Er has been investigated by electron and gamma-ray spectrometry and coincidence techniques. Excited levels, characterized by the quantum numbers ( K, I π ), have been established at the following energies in keV: 61(2, 3 −), 407(1, 1 −), 446(1, 2 −), 475(0, 0 −), 535(0, 1 −) and 610(1, 1 +). The levels can be interpreted in terms of the Nilsson orbitals expected in this region. Thus the four states from 407 to 535 keV are taken to belong to the configuration p 1 2 +[411]± n 1 2 −[521] , which gives rise to bands with K = 0 and K = 1. These two bands have an anomalous structure, partly because of the even-odd splitting in the K = 0 band, partly because of the Coriolis coupling between the two bands. By an analysis of the beta-transition probabilities in the decay of 172Er and of 170Tm it is shown that the Coriolis coupling vanishes in the odd-spin states in agreement with expectations. However, an analysis based on the level spacings in 170Tm and 172Tm indicates that the appreciable rotational perturbations of the even-spin states deviate from the theoretical value.