Symmetry-restoring interactions for Kπ = 1+ isovector vibrations

The low-lying isovector 1⁺ states are studied by a symmetry-restoring RPA approach in some rare-earth nuclei. A new velocity-dependent residual interaction is proposed in order to restore the rotational invariance of the hamiltonian in the quasiparticle random-phase approximation with an axially-symmetric Woods-Saxon potential. A new quadrupole interaction is introduced with a self-consistently determined coupling strength. Calculations for six rare-earth nuclei (¹⁵⁴Sm, ^156,158Gd,¹⁶⁴Dy,¹⁶⁸Er,¹⁷⁴Yb) show a good agreement with the experimental energies and B(M1) values. The M1 transitions, corresponding to the experimental strong magnetic dipole states, have in all apart from one case a predominant orbital contribution. The largest orbital contribution (90%) is found in ¹⁵⁴Sm. About half of the low-energy (E < 5MeV, B(M1)↑>0.1μ_N²) states in each nucleus have an orbital character with a (10–40)% spin admixture. The M1 strength is concentrated in the region 2–9 MeV with a maximum around 5 MeV and corresponds to ΔN_osc = 0 transitions.     

High-spin states in154Er

High-spin states in¹⁵⁴Er have been populated by bombarding¹⁴⁷Sm and¹⁴⁸Sm with¹²C particles. Excitation functions, lifetimes, angular distributions andγ-γ coincidences were measured. AT _1/2=35ns isomeric state atE _x～3 MeV has been found and is interpreted as a two-quasi-particle state with aligned angular momenta. A cascade of intense individual lines from states with spin up to at least 26 (excitation energy up to 8.543 MeV) was found to feed the isomeric state. The level sequence above this yrast trap exhibits an irregular pattern which cannot be easily interpreted in terms of collective modes.     

Evidence of non-statistical structures in the elastic and inelastic scattering of58Ni+58Ni and58Ni+62Ni and intermediate dinuclear states

Excitation functions and angular distributions of⁵⁸Ni+⁵⁸Ni and⁵⁸Ni+⁶²Ni scattering at energies just above the Coulomb barrier have been measured aroundθ _cm=90° in energy stepsΔE _cm=0.25 MeV fromE _cm ? 110 MeV toE _cm ? 120 MeV for⁵⁸Ni+⁵⁸Ni and fromE _cm ? 110 MeV toE _cm ? 118 MeV for⁵⁸Ni+⁶²Ni. Evidence for structure of non-statistical character has been found in the angle-summed excitation functions; this evidence is corroborated by the analysis of the angular distributions. This is the first time that non-statistical structure in elastic and inelastic scattering is reported with high confidence level for this mass and excitation energy ranges. Attempts are presented to understand the nature of this structure, including the presence of intermediate dinuclear states and virtual states in a potential well.     

Fission time in the 28Si + natPt reaction

The experimental fission times are analyzed for excited nuclei produced in the ²⁸Si + ^natPt reaction. Experimental lifetimes obtained by the crystal-blocking technique range between 10^?17 and 10^?18 s at bombarding energies between 140 and 170 MeV, respectively. Experimental data are analyzed within the statistical theory of nuclear reactions and the double-humped-fission-barrier model with allowance for preequilibrium processes and the nuclear-dissipation phenomenon. It is shown that fission barriers retain their double-humped structure for nuclear temperatures up to about 1.7–1.8 MeV and that the lifetimes of excited strongly deformed states in the second potential well contribute substantially to the observed delay times in the fission decay channel.     

Valence and inner proton hole states in119in via the (d,3He) reaction

Proton holes states have been studied up toE _x=17 MeV andE _x=3.5 MeV in the¹¹⁹In nucleus via the¹²⁰Sn(d,³He)¹¹⁹In reaction respectively atE _d=108.4 MeV andE _d=51 MeV. DWBA analysis of angular distributions has allowedl attributions for a large number of new levels and the determination of valence and inner hole strength distributions. The first 1g _9/2, 2p _1/2 and 2p _3/2 levels only exhaust 40%, 60% and 32% of their respective sum rule limits. The missing strengths are shared among several low lying levels and significant higher lying contributions. The 1f strength, not identified in the previous experiments is spread fromE _x=1 MeV to about 17 MeV. The low lying levels aroundE _x=2.4 MeV could exhaust some 40% of the 1f _5/2 sum rule. The higher lying strength with a flat maximum aroundE _x=7.5 MeV could account for the 1f _7/2inner hole strength and the missing 1f _5/2 valence strength. The experimental strength functions compare rather well with the predictions of the quasiparticle-phonon model.     

Decay properties of very-high-spin states in transitional Er nuclei aroundA=154

Theγ ray continuum structures of the transitional Er isotopes withA～154 are studied using the reaction⁷⁴Ge(⁸⁴Kr,xn)^158?xEr atE _lab=340 MeV. The measurements include energy spectra, total energies, multiplicities, angular distributions and lifetimes using the DSAM method. The analysis of data confirms the previously observed two-bump structure of the continuum radiation. A meticulous subtraction of discrete contributions proves the persistence of the low-energy bump even at high spins, i.e.I>40?. The angular-distribution measurements assign predominant dipole structure to the bump atE _γ=0.65 MeV, whereas the bump atE _γ=1.3 MeV is of almost pure quadrupole character at high spins. The lifetime measurements give evidence for a strong enhancement of theB(E2) values of the upper bump,B(E2)/B _sp>130. Spin-selection studies reveal, in the spin rangeI=30?50? an almost constant energy for the 1.3 MeV bump,ΔE<60 keV.     

The phenomenon of nucleon emission at high angular momentum states of fused compound systems

Nucleon emission from high spin fused compound systems is analyzed in the framework of the statistical theory of hot rotating (STHR) nuclei. This is an elaborate version of our earlier work and we present our results for¹⁵⁶Er,¹⁶⁶Er,¹⁶⁸ Yb and¹⁸⁸Hg. We predict an increase in neutron emission for¹⁶⁶Er due to the abrupt decrease in neutron separation energy aroundI ≈55ℏ. Since the drop in the separation energy is closely associated with the structural changes in the rotating nuclei, relative increase in neutron emission probability around certain values of angular momentum may be construed as evidence for the shape transition. A similar effect is predicted for¹⁶⁸Yb aroundI ≈55ℏ. We also extend the microscopic cranked Nilsson method (CNM) to hot nuclear systems and compare the results with that of the STHR method. The two methods yield different results for triaxially deformed nuclei although for biaxial deformations the results are identical. This is illustrated for¹⁸⁶Hg.     

High spin states in153Er

High spin states in¹⁵³Er have been populated in the¹⁴⁴Sm(¹²C, 3n)¹³³Er reaction. Excitation functions, lifetimes, angular distributions,γ-γ coincidences and internal conversion coefficients were measured. Three isomeric states at 2.75 MeV (T _1/2=400 ns), 2.95 MeV (T _1/2～10 ns) and 5.2 MeV (T _1/2=200 ns) have been observed. A fourth isomer seems to be weakly excited above 6.8 MeV. The level scheme proposed is discussed in term of the nuclear shell model.     

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.     

The rotational quasi-continuum in specific configurations: high-K states and superdeformation

The analysis of the fluctuations of the counts of unresolved γ-γ energy spectra can extend our knowledge of the rotational motion at high angular momentum and excitation energy above the yrast band. Detailed studies of the rotational quasi-continuum built on specific intrinsic nuclear configurations are here discussed. First, the validity of the K-selection rules in the quasi-continuum region is investigated in the case of the normal deformed nucleus ¹⁶³Er. The γ cascades feeding into low-K and high-K bands are analyzed studying variance and covariance of the spectrum fluctuations. Low-K bands are found to be fed by a much larger effective number of cascades than high-K bands, while the covariance between pairs of gated spectra shows that the cascades feeding into low-K bands are different from those feeding into high-K bands. These findings suggest a persistence of K-selection rules in the region of excitation energy and angular momentum probed by the rotational decay of ¹⁶³Er. As a second case, the existence of a rotational quasi-continuum in the super deformed well of ¹⁴³Eu is discussed. An intense bump of rotationally correlated transitions is observed to develop as function of fold in the high spin region of gated spectra. Fold distribution, angular anisotropies, moment of inertia and life time show that the bump consists of fully damped super deformed transitions. This gives experimental evidence of damped rotational motion up to several MeV excitation energy above the super deformed yrast line.     

High-spin structure of 190–194Hg and the cranked shell model

High-spin states in ^190–194Hg, populated in the ¹⁷⁰Er (^{24, 26}Mg, xn) and ^{184, 186}W(¹³C, xn) reactions, were investigated by in-beam γ-ray spectroscopic techniques. The level schemes in all five nuclei were extended to considerably higher spins and new band intersections were found. The band structure is interpreted within the framework of the cranked shell model. Remarkable agreement is obtained between the predictions of the model and the experimental data for these weakly oblate deformed nuclei. In ^{192, 194}Hg irregular sequences were found which could be examples of “ terminating bands”.     

Investigation of high spin states in23Na and23Mg and the12C+12C resonance atE c.m.=19.3 MeV

The resonance in the¹²C+¹²C system atE _c.m.=19.3 MeV has been studied in the neutron and proton decay channels. From(p, γ), (n, p) and (n, γ) coincidence measurements high spin states could be localized inA=23 nuclei, in²³Mg up to possibly 21/2⁺. These states were resonantly populated. The present data favorJ ^π=17/2⁺ for the 9.61 MeV state in²³Mg and therefore also for the probable parent state at 9.81 MeV in²³Na. AJ ^π=12⁺ assignment to the resonance is supported and evidence was found that the resonant excitation of the lowest 15/2⁺ and 17/2⁺ states in mass 23 nuclei is caused by a change of the intrinsic structure of the Yrast levels aroundJ ^π=15/2⁺ towards larger deformation.     

Properties of isovector 1+ states in A=28 nuclei and nuclear muon capture

A method is proposed for taking into account, in a calculation of partial rates of muon capture by nuclei, experimental information about strength functions for Gamow-Teller and isovector M1 transitions. The method, which amounts to choosing an orthogonal transformation that acts in the subspace of wave functions for excited states, requires neither modifying transition operators nor introducing effective charges. The matrix of the above transformation is constructed as a product of the matrices of reflection in a plane. All calculations are performed on the basis of the multiparticle shell model. Numerical results are obtained for isovector states in A=28 nuclei. Strength functions for Gamow-Teller and isovector M1 transitions in ²⁸Si are considered, and the lifetimes of 1⁺ states in ²⁸Al and the branching fractions for gamma decays of this state are calculated. Owing to taking into account experimental information about the properties of isovector states, the branching fractions for the γ decays of the 1⁺ state at 2.201 MeV in ²⁸Al are successfully described for the first time. The above transformation of the wave functions changes substantially the distribution of partial rates of allowed muon capture by a ²⁸Si nucleus among the 1⁺ states of the final nucleus ²⁸Al in relation to the results of the calculations with the eigenfunctions of the Hamiltonian of the multiparticle shell model. The muon-capture rates calculated with the transformed functions agree well with experimental data.     

Description of low-lying vibrationalK π≠0+ states of deformed nuclei in the quasiparticle-phonon nuclear model

The QPNM equations are derived taking account of p-h and p-p interactions. The calculated quadrupole, octupole and hexadecapole vibrational states in¹⁶⁸Er,¹⁷²Yb and¹⁷⁸Hf are found to be in reasonable agreement with experimental data. It is shown that distribution of theEλ strength in some deformed nuclei differs from the standard one. There are cases when for a givenK ^π theEλ strength is concentrated not on the first but on higher-lying states. The assertion made earlier about the absence of collective two-phonon states in deformed nuclei is confirmed.     

High-resolution (e,e') study of isovector M1 and M2 transitions in the oxygen isotopes: (III). 18O

The excitation energy region in ¹⁸O from about E_x = 11–27 MeV has been studied with low-momentum transfer, but high-resolution inelastic electron scattering. Two sharp lines are prominent in the spectra, corresponding to the excitation of T = 2 levels at 16.399 ± 0.005 MeV and 18.871 ± 0.005 MeV of J^π = 2^? and 1⁺, respectively. In contradiction to theoretical predictions no more strong M2 transitions could be found. Broad peaks were observed at 18.5, 19.7, 20.2, 22.5 and 23.8 MeV, the latter two are due to the giant dipole resonance as known from photonuclear reactions. The spectra show in addition considerable fine structure and the application of a cross correlation function technique for its analysis resulted in the location of twelve more low multipolarity weak transitions in the excitation energy range between 16 and 19 MeV. Tentative J^π assignments are given for these levels. The spectra of isospin T = 2 states of A = 18 nuclei are discussed in view of the existing experimental and theoretical work. Finally, the pattern of the isovector M1 and M2 strength distributions of all the three oxygen isotopes ^16,17,18O is discussed.     

Density of high-spin states in38Ar and42Ca

Theγ-decay modes of³⁸Ar levels withE _x ≦11,630keV and of⁴²Ca levels withE _x ≦10,036keV have been studied using the³⁵Cl(α, pγ) reaction at 16MeV and the³⁹K(α, pγ) reaction at 15.14 MeV, respectively. In both nuclei the number of states withJ≧6 exceeds fifty. Weak coupling calculations of the Bansal and French type reproduce the density of high-spin states. The success of the model implies that the excitations of up to four particles from thed _3/2 into thef _7/2 shell play a role in both nuclei. The structure of deformed states was found to be predominantly 4p/s 6h in³⁸Ar and 4p/s 2h in⁴²Ca, respectively.     

The structure of 26Mg investigated with the (d,p) reaction

Angular distributions have been measured for the ²⁵Mg(d, p)²⁶Mg reaction at 13 MeV leading to excited states between E_x = 0 and 8 MeV. Experimental cross sections are compared with DWBA calculations and extended shell-model calculations in the full sd shell. Spin and parity restrictions are obtained for several levels in the region E_x = 6?;8 MeV. Spectroseopic factors for transitions to the lowest four positive-parity states of each spin are well reproduced by the shell-model calculations; however, in mixed configurations the largest component is systematically underestimated by the shell model. Only 60% of the strength for $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ transfer is observed.     

Lifetime measurements of spherical and deformed states in 1f7/2 nuclei

Lifetimes have been determined using the Doppler Shift Attenuation Method in the N ≈ Z nuclei ⁴⁶V and ⁴⁸V, populated with the reaction ²⁸Si on ²⁴Mg at 115 MeV and ²⁴Mg on ²⁸Si at 100 MeV using Au and Pb backed targets. The coexistence of spherical and deformed states in the middle of the 1f_7/2 shell is discussed. The B(E2) and B(M1) reduced rates agree very well with large scale shell model predictions.     

<Emphasis Type="Italic">J</Emphasis><Superscript>π</Superscript>0<Superscript>−</Superscript> levels in <Superscript>156</Superscript>Gd and <Superscript>158</Superscript>Gd

The 0^? states in the ¹⁵⁶Gd nucleus at E = 1952.38 keV and in the ¹⁵⁸Gd nucleus at E = 2269.16 keV are established on the basis of an analysis of available data on even-even deformed nuclei. From data on the deexcitation of the levels and on the probability of their population by beta transitions, it is found that these states have a two-particle proton structure. A comparison of our data with information about the 0^? levels in the ¹⁷⁰Yb and ¹⁷⁶Hf nuclei makes it possible to conclude that J^π0^? two-particle states exist at an excitation energy of about 2 MeV and higher.