Rotation-particle Coupling Research Articles

Nonadiabatic quasiparticle description of rotation-particle coupling in triaxial odd–odd nuclei

A large wealth of data and a variety of models led to significant progress in understanding the spectra of deformed nuclei. However, a robust theoretical approach, which is less reliant on adjustable parameters is still elusive. Due to the scarcity of data, this drawback gets more pronounced while studying the exotic nuclei. With the motive to overcome this difficulty, we have developed the nonadiabatic quasiparticle approach for the description of rotational states in triaxial deformed odd–odd nuclei. The rotation-particle coupling is carried out utilizing an appropriate basis transformation such that the matrix elements of the odd–odd system can be written in terms of the rotor energies. This provides the advantage of studying the role of core more efficiently as compared to the conventional particle rotor model. The residual interaction between the valence proton and neutron is incorporated in two reliable ways, namely, the constant potential form and the zero-range interaction.

Triaxiality in the odd-A nuclei 109−117I studied through a microscopic rotationparticle coupling

A systematic study of ground state spectrum with the triaxial deformation γ for odd-A Iodine isotopes 109−117I is carried out with the nonadiabatic quasiparticle approach. The rotation-particle coupling is accomplished microscopically such that the matrix elements of a particle-plus-rotor system are written in terms of the rotor energies. The 5/2+ state is confirmed as ground state for odd-A 111−117I and also coming out as lowest in energy for 109I.

Triaxiality in the proton emitter I109

We study the role of triaxial deformation in the proton-emitting nucleus $^{109}\mathrm{I}$. We analyze the rotational spectrum as well as the decay width within the nonadiabatic quasiparticle approach. The parent nuclear wave functions are calculated using a modified rotation-particle coupling where the matrix elements of the Hamiltonian representing the rotational states of the parent nucleus are written in terms of the rotational energies of the daughter nucleus. The measured spectrum of the daughter nucleus $^{108}\mathrm{Te}$ suggests a strong role of either triaxial or vibrational degrees of freedom which is applicable for $^{109}\mathrm{I}$ also. With these results we successfully explain the spectra of the parent and daughter and also the decay width in a unified way which enables us to establish the configuration of the rotational bands and the decaying state.

Nonadiabatic quasiparticle approach for rotation-particle coupling in triaxial odd-Anuclei

We discuss the formulation of a nonadiabatic approach to study the rotational states in triaxially deformed odd-$A$ nuclei. The rotation-particle coupling is treated microscopically by coupling the triaxial rotor states of the even-even core with the states of the valence particle in order to obtain the matrix elements of the odd-$A$ system. We arrive at a nonadiabatic quasiparticle approach where the rotational states can have contributions from various quasiparticle states near the Fermi level. We bring out the advantages of this approach over the conventional particle rotor model with a fixed or variable moment of inertia. One clear evidence favoring our approach is the rotation alignment phenomenon which is demonstrated in the case of $^{137}\mathrm{Pm}$. We discuss our results for $^{136}\mathrm{Nd}$ and $^{137}\mathrm{Pm}$, and justify that this approach is suitable also for studying nuclei away from stability.

Spectroscopy of 183W Measured magnetic moments and rotation-particle coupling

The gyromagnetic ratios of 6 excited levels in the lowest K = 12and23 bands of 183W were measured using the thin-foil transient-field technique. The level scheme was extended to spin 17−2 and multipole mixing ratios measured for several transitions. Detailed comparisons of the spectroscopic data on 183W with the rotation-particle coupling model show good agreement, but favour a Carlolis mixing strength much larger than predicted by previous Nilsson model calculations in which hexadecapole deformation was neglected.

Band structure in 95Ru.

The {sup 95}Ru nucleus has been studied through the {sup 94}Mo({alpha},3{ital n}){sup 95}Ru reaction. A level scheme has been proposed from {gamma}-{gamma} coincidence data and spin assignments are made on the basis of the results of angular distribution measurements. A rotation-particle coupling calculation has been performed and the proposed level scheme is discussed in the light of its predictions. The results obtained in the present work are also compared to those of previous investigations on this nucleus.

Deformed1h112neutron-hole states inSm147

A six band rotation-particle coupling calculation is done for the $\frac{11}{{2}^{\ensuremath{-}}}$ states in $^{147}\mathrm{Sm}$. An entirely different distribution of the band energies is found as compared with the recently reported results from ($^{3}\mathrm{He}$, $\ensuremath{\alpha}$) reactions.NUCLEAR STRUCTURE Rotation-particle calculation for $1{h}_{\frac{11}{2}}$ neutron-hole states in $^{147}\mathrm{Sm}$.

Investigation of the low-lying levels of 179Hf with the (n, γ) and (n, e) reactions

The excited levels of 179Hf are investigated using the thermal neutron capture γ-ray and conversion electron spectra measured with the bent crystal diffraction spectrometer in Risø and the β-spectrograph in Riga. The level scheme contains the odd parity rotational bands 7 2 −[514], 1 2 −[510], 5 2 −[512], 1 2 −[521], 3 2 −[512] and 7 2 −[503] . The energies of these levels and the intensity ratios of the transitions between them are calculated taking into account the rotation-particle coupling (RPC). The following even parity levels are proposed: 859.0 and 942.2 keV ( 7 2 + and 9 2 + of the 7 2 + [633] band) ; 1004.1 and 1079.2 keV ( 5 2 + and 7 2 + of the 9 2 +[624] + Q(22) band) ; 1186.0, 1199.2 and 1296.4 keV ( 1 2 +, 5 2 + and 3 2 + of the 1 2 +[651] band) . The levels at 1249.8, 1269.7, 1432.9, 1482.2 and 1755.5 keV, supported by the analysis of the γγ coincidence spectrum and Ge(Li) singles data, are discussed.

Rotation-particle coupling effects in low energy nuclear spectrum of183W

The deviations from I(I+1) rule for K=0 rotational bands are generally explained by writing a phenomenological expression with a power series in I(I+1). For K not=0 bands the rotation-particle coupling (RPC or Coriolis) term in the Hamiltonian introduces an additional series which alternates in sign with level spin. The leading term of this alternating series for K=1/2 rotational bands can be said to arise from the third order RPC perturbation effects of K=1/2 states. These third order Coriolis perturbation effects are calculated for the 3/2-(512) based band in 183W, by considering the mixing of all the possible Kpi =1/2- states in the same oscillator shell. The matrix elements are calculated using the modified Nilsson model potential. The effect of the deformed spin-orbit coupling term is also investigated. The calculated coefficient is compared with its 'experimental' value and the comparison is used to discuss the characterization of the non-adiabatic corrections.

Influence of the particle-number fluctuation on theE1ΔK=±1transitions in deformed odd-mass nuclei

Dipole electric transitions with $\ensuremath{\Delta}K=\ifmmode\pm\else\textpm\fi{}1$ are studied theoretically for odd-mass nuclei in the rare-earth region (i) in the frame work of an elaborated Nilsson model with rotation-particle coupling and with isospin-dependent parameters, (ii) with the usual BCS wave function, and (iii) with sharp particle-number-projected BCS wave functions. These projected wave functions are the limit of very speedily converging sequences of functions. General formulas for the pairing reduction factors with strict nucleon number conservation are established. The unphysical effects due to particle fluctuation in the usual BCS wave functions are found to be very important in the theoretical BCS evaluation of reduction factors and half-lives. In most of the analyzed $E1$ transitions, the hindrance factors are improved by the elimination of the unphysical effects due to particle fluctuation. The blocking effect is systematically taken into account. The importance and validity of the physical and mathematical approximations used is discussed.RADIOACTIVITY $^{153,155}\mathrm{Eu}$; $^{159,161}\mathrm{Tb}$; $^{175,177}\mathrm{Lu}$; $^{179,181}\mathrm{Ta}$; $^{155,157}\mathrm{Gd}$; $^{161}\mathrm{Dy}$; $^{169,171,173,177}\mathrm{Yb}$; $^{175,177,179}\mathrm{Hf}$; $E1$ $\ensuremath{\Delta}K=\ifmmode\pm\else\textpm\fi{}1$ particle-number-projected pairing reduction factor and ${T}_{\frac{1}{2}}$.

Effects of strong rotation-particle coupling on the energy levels of two-quasiparticle systems with possible application to 184Ir and 186Ir

The consequences of the availability of the [541↓] proton orbital in light even-mass Ir nuclei are examined. The structure of rotational bands in which the state of lowest energy is not the state of minimum angular momentum is described in terms of an effective decoupling parameter. The [541↓] assignment for the proton in the ground state configurations of 184Ir and 186Ir is seen to be plausible and the level ordering in these nuclei may be largely determined by the properties of the [541↓] orbital stemming from the j = 9 2 spherical state, while the perturbing effects of a low-Ω neutron partner ([510↑] or [512↑]) should be relatively insignificant. Other interesting consequences of this description are also discussed.

High-spin rotational states in 177, 173Lu and evidence for ΔK = 2 and ΔK = 4 mixings

The level schemes of the deformed odd-proton nuclei 171Lu and 173Lu have been studied by in-beam spectroscopy. Measurements of singles γ-ray spectra, angular distributions and γ-γ coincidences were performed in the 169Tm(α, 2nγ) 171Lu reaction at 27 MeV α-particle energy. In the reaction 173Yb(d, 2nγ) 173Lu singles spectra and γ-γ coincidences were measured. Additional γ-ray spectra were taken for the reactions 169Tm(α, 2nγ) 171Lu at E α = 23 MeV and 173Yb(p, nγ) 173Lu. The proposed level schemes of 171Lu and 173Lu involve rotational bands of the intrinsic states 7 2 +[404] , 1 2 +[411] , 5 2 +[402] , 1 2 −[541] and 9 2 −[514] up to spin 25 2 , 23 2 , 23 2 , 29 2 and 21 2 , respectively, in 171Lu and up to spin 23 2 , 17 2 , 19 2 , 25 2 , and 23 2 , respectively, in 173Lu. Transitions between some states of the 1 2 +[411] and 5 2 +[402] bands in 171Lu indicate a strong mixing of states with ΔK = 2. Similarly, a ΔK = 4 mixing between states of the 1 2 −[541] and 9 2 −[514] bands in 171Lu is indicated by interband transitions. These mixings are described in terms of the rotation-particle coupling, considering only the interaction between states with K and K±1. The dependence of the side feeding to the 1 2 −[541] and 7 2 +[404] bands on the level spins and energies was investigated.

High-spin states and rotation-particle coupling in 179W

The 178Hf(α, 3n) 179W and 181Ta(p, 3n) 179W reactions are used to populate rotational states in 179W. Particular attention is paid to the strongly perturbed positive-parity bands. The rotational energies within these bands are successfully explained within the unified model with pairing and Coriolis interactions included if the theoretical Coriolis matrix elements are reduced. The wave functions are calculated from a fit to the experimental energies and the theoretical and experimental transition probabilities are compared. Rotational bands built on the 7 2 −[514], 1 2 −[521] and 5 2 −[512] intrinsic states are also observed.

Abregung der [formula omitted] und [formula omitted] banden im 177Lu

The decay and the structure of the 1 2 − [541] and 1 2 + [411] bands in 177Lu have been studied in the (n, γ) reaction by means of prompt and delayed γ-γ coincidence measurements. Nanosecond lifetime investigations with Ge(Li) detectors provided the following results for the 177Lu excited levels: T 1 2 (761.6 keV, 5 2 1 2 − [541]) = 35 ± 5 ns; T 1 2 (573.6 keV, 3 2 1 2 + [411]) = 3.5±1 ns; T 1 2 (457.9 keV, 5 2 5 2 + [402]) ≦0.8 ns . The structure of the 1 2 − [541] band and the decay of the 35 ns isomer 5 2 1 2 − [541] to the 1 2 + [411], 5 2 + [402] and 7 2 + [404] bands are discussed in terms of the Nilsson theory by taking into consideration pairing correlations and the rotation-particle coupling (RFC).

Rotation-particle coupling in the ground state band of 161Dy

The 160Gd(α, 3n)161Dy reaction is used to populate the 5/2+ [642] ground state band in 161Dy up to the member with spin 33/2. The rotational energies within this strongly perturbed band are successfully explained within the unified model with the pairing, Coriolis and ΔN = 2 interactions included if the theoretical Coriolis matrix elements are reduced. This model can at the same time account for the relative electromagnetic transition probabilities and the static magnetic moment of the 5/2, 5/2+ [642] ground state only if the intraband M1 transition amplitudes with |Δ K| = 1 are also reduced. The same conclusion may be drawn from an analogous analysis of the 7/2+ [633] band in 167Er. These observations suggest that the longitudinal and the transverse spin polarisation is different or that the mechanism which is responsible for the reduction of the Coriolis force is also effective in preventing intra-band M1 transitions with |ΔK| = 1.

Rotational states and rotation-particle coupling in 155Tb and 157Tb

For the investigation of excited states of the odd-proton nuclei 155Tb and 157Tb, studies have been made of the γ-radiation emitted in the reactions 153Eu(α, 2n), 155Gd(d, 2n) and 155Gd(p, n) as well as 157Gd(d, 2n) and 157Gd(p, n), respectively. Measurements of coincidence relations were performed in the reactions with α-partieles and deuterons. Furthermore, in the reaction with α-partieles excitation functions and angular distributions γ-rays were measured. The level schemes proposed for 155Tb and 157Tb are very similar. They contain the band heads (energies are given in keV for 155Tb and 157Tb, respectively) 3 2 +[411] (ground state), 5 2 +[413] (271.3; 327.6), 7 2 +[404] (466.9; 658.6), 5 2 −[532] (227.0; 326.4) and 7 2 −[523] (545.3; 571.7), as well as several rotational states. In both nuclei the distorted rotational band built on the 5 2 −[532] band head has been analyzed in terms of the Coriolis coupling between the Nilsson orbitals based on the H 11 2 . shell-model state. In 155Tb the Coriolis coupling (mainly with the 7 2 +[404] orbital) gives rise to an energy difference of only 63.7 keV between the 7 2 and 5 2 members of the 5 2 +[413] band.

Calculated energies and branching ratios for the low-lying states in 23Mg

The low-lying positive parity states in 23Mg are investigated by means of the Nilsson model with rotation particle coupling. The energies are strongly affected by the coupling. The isospins as good quantum numbers are included in order to calculate the branching ratios.

Hexadecapole deformation and rotation-particle coupling in the rare earth nuclei

Calculations of the energy spectra for odd- A nuclei in the rare earth region have been made using a rotational model for deformed nuclei. Both pairing and band mixing have been included in detail. A hexadecapole ( P 4 ) deformation was considered in addition to the usual quadrupole ( P 2 ) deformation. In most cases, this additional hexadecapole deformation proved to be quite necessary to achieve a good fit to the experimental spectra. Thirty nuclei in this region were investigated. Good results were obtained for twenty-seven. With the parameters found in achieving a fit to the energy spectra, reduced transitions rates and spectroscopic factors were calculated. Band mixing made it possible to investigate K -for-bidden transitions. In most cases there was good agreement with experimental values.

Hexadecapole deformation and rotation-particle coupling in the rare earth nuclei

Calculations of the energy spectra for odd- A nuclei in the rare earth region have been made using a rotational model for deformed nuclei. Both pairing and band mixing have been included in detail. A hexadecapole ( P 4) deformation was considered in addition to the usual quadrupole ( P 2) deformation. In most cases, this additional hexadecapole deformation proved to be quite necessary to achieve a good fit to the experimental spectra. Thirty nuclei in this region were investigated. Good results were obtained for twenty-seven. With the parameters found in achieving a fit to the energy spectra, reduced transitions rates and spectroscopic factors were calculated. Band mixing made it possible to investigate K-forbidden transitions. In most cases there was good agreement with experimental values.

Spectroscopic factors for 19F from the 18( 3He, d) 19F reaction

Spectroscopic factors for states in 19F have been determined from the 18O ( 3He, d) 19F reaction. They are compared with recent independent-particle model and rotation-particle coupling model calculations for this nucleus.