Electromagnetic transitions in some doubly odd deformed nuclei

Nanosecond lifetimes of excited states in doubly odd deformed nuclei have been determined by in-beam measurements applying the method of delayed γ-γ coincidences as well as by experiments in the radioactive decay with the method of delayed γ-ce coincidences, respectively. Analysing the time distributions and delayed γ-ray spectra, the following half-lives of isomeric states could be obtained for the first time: $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(63.7}\text{keV in}{}^{160}\text{Tb}\text{) = 60 ± 5}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(138.7}\text{keV in}{}^{160}\text{Tb}\text{) = 5.7 ± 0.5}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(82.0}\text{keV in}{}^{156}\text{Ho}\text{) = 1.25 ± 0.20}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(87.2}\text{keV in}{}^{156}\text{Ho}\text{) = 58.5 ± 3.5}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(139.2}\text{keV in}{}^{158}\text{Ho}\text{) = 1.85 ± 0.10}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(38.3}\text{keV in}{}^{162}\text{Ho}\text{) = 1.2 ± 0.2}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(179.9}\text{keV in}{}^{162}\text{Ho}\text{) = 8.7 ± 0.2}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(342.8}\text{keV in}{}^{164}\text{Ho}\text{) = 2.6 ± 0.2}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(295.1}\text{keV in}{}^{166}\text{Ho}\text{) = 1.10±0.15}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(44.6}\text{keV in}{}^{162}\text{Tm}\text{) = 1.40±0.15}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{,(163.4}\text{keV in}{}^{162}\text{Tm}\text{) = 1.1 ± 0.1}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(220.1}\text{keV in}{}^{178}\text{Ta}\text{) = 8.5 ± 1.0}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(289.5}\text{keV in}{}^{178}\text{Ta}\text{) = 2.0 ± 0.5}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(392.8}\text{keV in}{}^{178}\text{Ta) ≈ 1 ns, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(316.5}\text{keV in}{}^{186}\text{Re}\text{) = 0.20 ± 0.10}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(300.2}\text{keV in}{}^{188}\text{Re}\text{) = 1.5 ± 0.2}\text{ns and}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(482.2}\text{keV in}{}^{188}\text{Re}\text{) = 0.26 ± 0.10}\text{ns}$. Furthermore, upper limits for the half-lives of fifteen excited states in ¹⁶⁰Tb, ^{164, 166}Ho and ^{186, 188}Re have been estimated. For eight isomeric levels in ^{186, 188}Re, the lifetimes earlier determined have been remeasured. Unlike previous studies, the existence of isomeric states at 87.2 keV in ¹⁵⁶Ho and at 179.9 keV in ¹⁶²Ho is suggested. Absolute γ-ray transition probabilities are deduced and compared with single-particle estimates according to Weisskopf and Nilsson, the latter also including pairing correlations. The K-, Ω- and f-forbidden transitions can qualitatively be explained in terms of configuration mixings. Experimental El, ΔK= 1 transition matrix elements in odd-odd deformed nuclei are supposed to be appreciably influenced by higher-order vibrational admixtures coupled via RPC and p-n interaction mixings.     

Electromagnetic transitions in some odd-proton deformed nuclei

In-beam measurements of nanosecond lifetimes applying the method of delayed γ-γ coincidences were performed in the (p, n) reaction. Analysing the time spectra with the centroid shift method, the following half-lives of excited nuclear states in the subnanosecond region could be found: $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(353.2}\text{keV in}{}^{161}\text{Ho}\text{) = 0.52±0.15}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(252.7}\text{keV in}{}^{161}\text{Ho}\text{) ≦ 0.2}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(579.4}\text{keV in}{}^{161}\text{Ho}\text{) ≦ 0.2}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(431.2}\text{keV in}{}^{163}\text{Ho}\text{) = 0.37±0.15}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(439.9}\text{keV in}{}^{163}\text{Ho}\text{) = 0.35±0.15}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(471.3}\text{keV in}{}^{163}\text{Ho}\text{) ? 0.2}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(612.8}\text{keV in}{}^{163}\text{Ho}\text{) ? 0.3}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(295.6}\text{keV in}{}^{171}\text{Lu}\text{) = 0.85±0.20}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(469.2}\text{keV in}{}^{171}\text{Lu}\text{) ≦ 0.2}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(357.0}\text{keV in}{}^{173}\text{Lu}\text{) = 0.40±0.08}\text{ns and}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(449.0}\text{keV in}{}^{173}\text{Lu}\text{) = 0.58±0.12}\text{ns}$. Following half-lives in ¹⁷³Lu have been remeasured: $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(425.3}\text{keV}\text{) = 0.84±0.20}\text{ns and}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(434.9}\text{keV}\text{) = 0.38±0.10}\text{ns}$. Absolute γ-ray transition probabilities are deduced and compared with Nilsson model predictions including pairing correlations. Coriolis mixing calculations are performed for K-allowed as well as for K-forbidden transitions.     

One-nucleon transfer reactions in deformed nuclei

The one-nucleon transfer reaction on deformed nuclei has been computed with the inclusion of indirect inelastic transitions that go through intermediate rotational states. The specific examples considered are¹⁷¹Yb(d, p), ¹⁷²Yb(p, d) and ¹⁸⁶W(p, d). Anomalies in the shapes of of experimental angular distributions with respect to predictions of the distorted-wave Born approximation are shown to be reproduced when these higher-order inelastic processes are taken into account. Consideration is also given to the deuteron optical potential needed for these studies.     

Rotation-induced shape transitions in Dy nuclei

Lifetimes of states with spins up to 30? have been measured in the nuclei ¹⁵⁶Dy, ¹⁵⁷Dy, and ^ll58Dy using the recoil-distance technique together with inverse reactions of the type $\text{Mg}\text{(}{}^{136}\text{Xe}\text{, x}\text{n}\text{)}$. The applied method, which benefited from the high velocities of the fusion residues as well as from improvements of the recoil-distance technique, allowed us to determine lifetimes and feeding times down to 0.1 ps. Below the first backbending the resultant B(E2) values in the ground-state band of ^{156, 158}Dy increase faster with increasing rotational frequency than expected for rigid rotors, reaching values similar to those observed for the well-deformed neutron-rich Dy isotopes. In contrast to this, the E2-transition probabilities between high-spin states are clearly retarded. The retardation gradually evolves from the rotation alignment of nucléons and indicates deformation changes most likely towards a triaxial shape. From the analysis of the side-feeding times of the high-spin yrast states it could be furthermore deduced that the E2 component of the preyrast γ-decay stems from transitions along highly collective bands.     

Heavy-ion excitation of 3− states in deformed nuclei

Previously measured data for 70.4 MeV ¹²C excitation of 3^? states in ^{148, 150}Nd are reanalyzed using a third-order rotational-vibrational model. Calculations using 3^? quadrupole moments which are expected if they are K = 0 states are in reasonable agreement with the magnitude of the large-angle data, but the quality of the fit in the Coulomb-nuclear interference region is only fair. It is found that the matrix element 〈2⁺∥M(E3)∥3^?〉 plays an important role in the calculations making the “measurement” of the 3^? quadrupole moments very difficult, if not impossible.     

Electromagnetic transitions in 42Ti

Levels in ⁴²Ti up to 4 MeV have been investigated using the ⁴⁰Ca(³He, n)⁴²Ti reaction and a neutron time-of-flight method. Using the DSA method, lifetimes of 750±300, > 200, 350±250, > 2000 and < 250 fs have been measured for levels at E_x = 1.56, 1.85, 2.40, 2.68 and 3.74 MeV respectively. The level at E_x = 3043.0±1.5 keV is tentatively identified as the 6⁺ member of the $\text{(f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{)}{}^2$ configuration, and its mean life has been measured as 26±5 ns by a direct timing method. Using isospin formalism, transition strengths are compared with theoretical and experimental values for ⁴²Ca and ⁴²Sc.     

Electromagnetic transitions in 51Mn

The nuclear structure of ⁵¹₂₅Mn was studied by γ-ray spectroscopy in the ⁵⁴Fe(p, α)⁵¹ Mn reaction (E_p = 9.0–13.2 MeV) and the ¹⁴N+³⁹K, ¹⁶O+⁴⁰Ca and ¹⁴N+⁴⁰Ca fusion-evaporation reactions (E_beam = 36 MeV). In the ⁵⁴Fe(p, αγ)⁵¹Mn reaction γ-rays were detected in coincidence with α-particles emitted near 180°; mean lifetimes and γ-ray mixing and branching ratios were deduced from Doppler shift attenuation and α-γ angular correlation measurements, respectively. Definite spin assignments are: 237 and 2416 keV, $\text{J}{}^{\mathrm{\pi }}\text{=}\text{7}\text{2}{}^{\mathrm{?}}$; 1140 keV, $\text{9}\text{2}$^?; 1488 keV, $\text{11}\text{2}$^?; 1825 and 2140 keV, $\text{3}\text{2}$^?. The results for other states below 3 MeV are consistent with the existence of rotational bands (/kh²/2/OI/t~ 95 keV) built on the ($\text{3}\text{2}$⁺) 1817 keV and $\text{1}\text{2}$⁺ 2276 keV hole states. The various measurements together with an earlier value for the lifetime of the first-excited state determine unambiguously the B(M1) and B(E2) values for all of the decay branches of the $\text{7}\text{2}$^?, $\text{9}\text{2}$^? and $\text{11}\text{2}$^? lowest three excited states. From the γ-singles and γ-γ coincidence observations with fusion-evaporation reactions, the yrast cascade proceeds through these three states and higher states at 2957, 3250,3680 and 4139 keV which are suggested to have $\text{J}{}^{\mathrm{\pi }}\text{=}\text{13}\text{2}{}^{\mathrm{?}}$, $\text{15}\text{2}$^?,$\text{15}\text{2}$^? and $\text{19}\text{2}$^?, respectively. The various experimental results for the $\text{5}\text{2}$^? → ($\text{19}\text{2}$^?) yrast states are in good overall agreement with shell-model calculations in the (f_{$\text{7}\text{2}$}¹ space.     

Structure of 186Ir and decoupling phenomena in doubly-odd deformed nuclei

States of ¹⁸⁶Ir, excited through several (HI, xn) reactions, were studied using in-beam γ-ray spectroscopy techniques. A completely new high-spin level scheme, comprising several rotational bands, is presented. The positive-parity ΔI = 2 ground-state band is possibly a first example of a hitherto unreported scheme called double decoupling associated with a proton and neutron both occupying $\text{Ω =}\text{1}\text{2}$ orbits of decoupling parameters larger than unity. A prominent ΔI = 1 negative-parity structure is interpreted as the $\text{π}\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{?}\text{ν}\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ band known in Tl isotopes but in a prolate-deformed situation.     

Landau-Ginzburg theory of phase transitions in heated rotating nuclei

The Landau-Ginzburg theory is applied to heated rotating superfluid systems. It is demonstrated that the free energy F' is an even function of the order parameter Δ even when external fields are present. The energy surfaces F'(Δ) are calculated for various rotational frequencies and temperatures. These surfaces provide clear illustrations of first-order and second-order phase transitions, as well as a critical point.     

Partial transitions in radiative pion capture on light atomic nuclei

The partial transitions in radiative pion capture on light nuclei are studied within the shell model with intermediate coupling. The probabilities of capture from s- and p-states of a mesoatom and the total yield of γ-quanta have been calculated and compared with experimental data.     

An approximate projection technique for the calculation of electromagnetic properties of deformed nuclei

A three-dimensional angular momentum projection is carried out for cranking model wave functions. The projected matrix elements of electromagnetic operators are evaluated using a method originally developed by Kamlah for the case of projected energy, which is valid for large deformations and weakly triaxial nuclei. The calculated spectroscopic quadrupole moments deviate substantially from the predictions of a rigid rotor model with axial symmetry. For E2 transitions the deviations are small. Projected values of the magnetic moments are almost identical with those of a semiclassical calculation. Cranking model wave functions are decomposed into its components having good angular momentum.     

On the moment of inertia in deformed Ba-Xe nuclei as deduced from gamma-gamma energy correlation experiments

The γ-rays following reactions induced by bombarding targets of ^{114, 116, 118, 120, 122}Sn with 118 MeV ¹²C ions were investigated using six NaI(Tl) detectors in a two-dimensional coincidence arrangement. Experimental energy-correlation spectra were extracted from the original coincidence matrices. The energy-correlation spectra exhibit the features expected for rotational nuclei and were used to deduce information on the moment of inertia $\text{I}{}^{\mathrm{(2)}}\text{= ΔI/Δω}$. The gross properties of the behaviour of $\text{I}$⁽²⁾ in the Ba-Xe region are discussed together with their interpretation within the cranked shell model (CSM).     

E1 isobaric analogue resonances of strongly deformed nuclei in (e,e′p) reactions

The cross sections of the (e, e′p) reaction on the deformed nuclei ¹⁵⁹Tb, ¹⁶⁵Ho, ¹⁶⁹Tm, ¹⁷⁵Lu and ¹⁸¹Ta have been measured in the vicinity of the ground isobaric analogue state. Resonances corresponding to the E1 isobaric analogue states are found and displacement energies are calculated from these resonances. These energies are smaller than those obtained from proton scattering, which shows their dependence on the reaction type. The radiative widths of the E1 transitions of the isobaric analogue resonances were obtained. The ratio of these to the single-particle width calculated with the Nilsson model is order of 0.1–1 for non-spin-flip transitions and more than 10² for spin-flip transitions. These results are similar to those of the spherical nuclei ¹³⁹La, ¹⁴¹Pr, ²⁰⁷Pb and ²⁰⁹Bi.     

Total reaction cross sections of deformed nuclei: A study of the 233, 238U + α systems

The cross sections for α-particle scattering and α-particle induced fission of ^{233, 238}U were measured at bombarding energies of 15 to 27 MeV. For these fissionable systems, the fission cross sections are very nearly equal to the total reaction cross sections. These experimental reaction cross sections are compared with various theories based on spherical and deformed potentials in order to investigate the effect of static target deformation on the reaction cross sections. From such comparisons no effect of target deformation is established. An interaction barrier (defined by the condition of 22.34 MeV is obtained from a spherical optical model fit to the experimental reaction cross-section data of uranium. This value agrees within 2.3 % with values deduced by a number of other methods.     

(3He, 2n) excitation functions for some light nuclei

Excitation functions have been measured for the reaction ⁹Be(³He, 2n)¹⁰C over the range $\text{E(}{}^3\text{He}\text{) = 10–41}\text{MeV}$ and for the reaction ²⁷Al(³He, 2n)²⁸P over the range $\text{E(}{}^3\text{He}\text{) = 14–41}$ MeV by detecting β-delayed γ-rays. An excitation function has also been measured for the reaction ²⁴Mg(³He, 2n)²⁵Si over the range $\text{E(}{}^3\text{He}\text{) = 21–43}\text{MeV}$ by detecting β-delayed protons.     

Total cross sections for some (α, n) and (α, p) reactions in medium-weight nuclei

Total cross sections have been measured for the ⁴⁵Sc(α, n), ⁴⁶Ti(α, n), ⁵⁰Cr(α, n), ⁵¹V(α, n), ⁵⁴Fe(α, n) and ⁵⁸Ni(α, p) reactions, and stellar reaction rates have been calculated from them. These have been compared to recent theoretical calculations which used compound nuclear theory. The calculated values are generally higher than the experimental values by factors ranging from 2 to 10.     

Heavy-ion inelastic scattering from deformed nuclei

Theoretical and experimental methods for studying heavy-ion inelastic scattering from deformed nuclei are described. The theoretical methods involve classical-limit approximations, while particle- γ-spectroseopy techniques are employed experimentally. With these approaches, heavy-ion excitation in the Coulomb-nuclear interference region acquires a transparent interpretation, despite the apparent complexity of the multistep excitation processes involved. The examples discussed provide a good illustration of the relationship between classical and quantum physics. The sensitivity of the inelastic scattering to details of the surface ion-ion potential due to radial and angular localization is exploited to provide a method of determining the equipotential contours in a direct manner which bypasses particular model-dependent parametrizations. The method is used to construct ion-ion potentials from inelastic scattering data for the systems ⁴⁰Ar + ¹⁶⁰Gd, ¹⁵⁶Gd, ¹⁶²Dy, ¹⁶⁴Dy, and¹⁸⁰Hf. The contribution of adiabatic giant resonance polarization to this potential is discussed. The relation between the deformed ion-ion potential and nuclear shapes is illustrated by comparing the experimental potentials to deformed double-folding and deformed proximity-potential calculations.     

Evidence for deformed states in 75Br

The excited states in ⁷⁵Br have been studied via the reactions ⁷⁴Se(p, γ), ⁷⁴Se(d, n), ⁷⁴Se(³He, pn) and ⁷⁴Se(α, p2n) by using in-beam γ-ray spectroscopy. In addition to measurements of γ-γ coincidences, excitation functions and angular distributions of γ-rays, ns lifetime measurements have also been carried out. As a result 19 levels have been identified up to spin ($\text{17}\text{2}$) and excitation energies up to 2.6 MeV. The B(E2) value of 88 W.u. derived for the 88.4 keV γ-ray indicates strong collectivity within a positive-parity band. A comparison of the excitation energies of the unique-parity states in ⁷⁵Br and ⁷⁷Br with those in ¹⁵³Tb and ¹⁵⁵Tb reveals that the average deformation increases when going from ⁷⁷Br (N = 42) to ⁷⁵Br (N = 40).