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The significance of considering excited 0+ states is discussed in both an experimental and theoretical context. Experimental results on possible phase transitional nuclei are presented. New calculations on Yb and Hf nuclei in the framework of the IBA‐1 model are presented and compared to previous fits in this region.

It is shown that the simple IBA‐1, which acts in a single space, robustly predicts a sharp rise in ρ2(E0; 02+ → 01+) values in spherical‐deformed transition regions, in agreement with the data. These predictions are effectively parameter‐free and provide an alternative to the usual coexistence model for these transitions.

We discuss the empirical evolution of structure in the spherical‐deformed phase transition region in the context of the behavior of basic structural signatures in the IBA symmetry triangle. The main signatures of a phase/shape transition are a sharp increase in R4/2 ≡ E(41+)/E(21+) and minima in E(02+) and E(2γ+).

We present the first extensive test of the critical point symmetry X(5) for the $\ensuremath{\gamma}$ degree of freedom, based in part on recent measurements for the $\ensuremath{\gamma}$ band in $^{152}\mathrm{Sm}$. The agreement is good for some observables including the energies and most intraband and interband transitions, but there is also a serious discrepancy for one transition.

High spin states in 140Eu were populated following the reaction 92Mo(51V,2pn) at a beam energy of 205 MeV at Yale. A total of 5 bands and 69 transitions were assigned to 140Eu. The band assignments and structures are discussed in terms of the rotational model and interpreted following a series of cranked shell model calculations.

We show that, contrary to a recent paper, the new, analytic, critical point symmetry $\mathrm{X}(5)$, which is parameter-free (except for scale), reproduces the data in $^{152}\mathrm{Sm}$ and $^{150}\mathrm{Nd}$ quite well, and better than multiparameter models based on bandmixing of pure rotor states.

High-spin states of $^{187}\mathrm{Ir}$ have been populated in the $^{176}\mathrm{Yb}(^{15}\mathrm{N},4n)$ reaction and measured with the YRAST Ball spectrometer. The $\ensuremath{\pi}{h}_{9∕2}$ rotational band has been extended beyond the first alignment crossing, which was found at rotational frequency $\ensuremath{\hbar}{\ensuremath{\omega}}_{c}\ensuremath{\approx}0.39\phantom{\rule{0.3em}{0ex}}\text{MeV}$. Two different scenarios for describing this crossing are considered: the alignment of an ${h}_{9∕2}$ proton or ${i}_{13∕2}$ neutron pair and it is concluded that a proton band crossing is more likely. A systematic study of the rotational alignment crossings in the $\ensuremath{\pi}{h}_{9∕2}$ bands in the $N=104,106,108$ isotopes of $_{73}\mathrm{Ta},_{75}\mathrm{Re},_{77}\mathrm{Ir},$ and $_{79}\mathrm{Au}$ is presented.

Mean lifetimes of five levels in the S band and three levels in the ground-state band of ${}^{156}\mathrm{Dy},$ populated via the ${}^{124}\mathrm{Sn}{(}^{36}\mathrm{S},4n)$ reaction at $E=145\mathrm{MeV},$ were measured by the Doppler-shift attenuation technique using a line-shape analysis. The differential decay-curve method was applied for a lifetime determination. In contrast with earlier data, the present $B(E2)$ values in the yrast band do not indicate a reduction in the collectivity after the crossing between the S band and the ground-state band, and confirm the results of theoretical calculations using mean-field approaches.

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.

Lifetimes of the first ${4}^{+}$ and ${6}^{+}$ states in ${}^{104}\mathrm{Mo}$ and ${}^{106}\mathrm{Mo}$ have been measured using the recoil distance method following spontaneous fission of ${}^{252}\mathrm{Cf}.$ The experiment was performed at the 88-inch cyclotron of the Lawrence Berkeley National Laboratory employing the Gammasphere array and the New Yale Plunger Device. Reduced transition probabilities in the ground state band of ${}^{104}\mathrm{Mo}$ are compared with predictions of the critical point symmetry X(5) for phase transitional nuclei between rotational and vibrational shape. While known level energies of ${}^{104}\mathrm{Mo}$ are in good agreement with the X(5) predictions, the analysis of the measured $B(E2)$ values favors a rotor interpretation.

The Qec value for 80Y has been measured by beta-gamma coincidence spectroscopy. Combining this result with the adopted mass excess of the daughter 80Sr gives a mass excess of >-61376(83) keV. Results are compared with other measurements and predictions of mass formulas. Implications of this measurement are considered for the rp-process.

Recent developments in the description of the structural evolution of nuclei invoke the concepts of phase transitions and phase coexistence. New, analytic, parameter‐free symmetries have been developed that describe nuclei at the “critical points” of phase/shape transition regions. The complete nuclear phase diagram at low energy and low angular momentum can be elegantly described in terms of the Landau theory of second order phase transition points and the lines of first order phase transitions that intersect these points.

A staggering index for alternating parity bands in even-even nuclei is discussed. A study of parity-doublet structures shows that the critical angular momentum at which strong octupole correlations develop can be expressed by a universal relation in terms of the [ital P] factor, [ital P]=[ital N][sub [ital p]N[ital n]]/([ital N][sub [ital p]]+[ital N][sub [ital n]]).

states, and hence E1orE3 tran-sition rates, is schematic only. Nevertheless, the results high-light the importance of including the octupole degree of free-dom if one is studying deformed nuclei above the pairinggap. We interpret these results as being an existence proof~rather than quantitative predictions! that models including

The claim that the two-phonon gamma-vibrational configuration constitutes a major component for the I=4+ states in osmium nuclei is based on solid experimental evidence. A non-negligible two-quasiparticle or hexadecapole component must also exist in order to explain the data.

A study of the low-lying levels of ${}^{128}\mathrm{Ba}$ was performed using three clover detectors in a compact arrangement. The levels were populated by beta decay of ${}^{128}\mathrm{La}$ which was produced by the fusion evaporation reaction ${}^{116}{\mathrm{S}\mathrm{n}(}^{16}\mathrm{O},1p3n).$ $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ angular correlations and polarization measurements were performed. The decay properties of several low-lying states were investigated. Spin assignments were made for two states, and several $E2/M1$ mixing ratios were determined. The results are in good agreement with predictions of the O(6) limit of the interacting boson approximation. One of the states is unambiguously determined to be the hitherto unobserved member of the $\ensuremath{\tau}=4$ multiplet.

We present a simple method for discerning the evolution from vibrational to rotational structure in nuclei as a function of spin. The prescription is applied to the yrast cascades in the A approximately 110 region and a clear transition from vibrational to rotational motion is found.

Institut fu ¨r Kernphysik, UniversitatzuKoln, D-50937 Ko¨ln, Germany~Received 25 April 2002; published 13 August 2002!It is shown that the empirical transition region near neutron number N590 can be described in terms of thecrossing of configurations in a two-level system, as expected for a first order phase transition.DOI: 10.1103/PhysRevC.66.021304 PACS number~s!: 21.60.Fw, 21.10.Re, 27.70.1q, 64.90.1b

The near-yrast structure of the weakly deformed, ‘‘transitional,’’ nucleus 101 Ru has been investigated using the fusion-evaporation reaction 96 Zr( 9 Be,4n) 101 Ru at a beam energy of approximately 44 MeV. The experimental data are compared with theoretical calculations using the cranked Woods-Saxon-Strutinsky method. The yrast positive-parity structures are observed to undergo a backbend, consistent with the crossing of an aligned (nh11/2) 2 configuration. The h11/2(@550# 1 2 ) intruder band configuration is extended to a tentative spin/parity of ( 47 2 2 ) and excitation energy of more than 9 MeV. This structure exhibits properties which can be explained by the rotational alignment of a pair of midshell g9/2 protons, in contrast to the behavior observed in the heavier N557, odd-A isotones where the predicted proton crossing is delayed in favor of neutron alignments. The effect of static g deformation on the theoretically predicted alignment properties is investigated by means of the cranked shell model. The observed band crossings are found to be consistent with a significant triaxial rigidity, persistent into the medium-spin regime.

Excited states of ${}^{162}\mathrm{Er}$ were populated in \ensuremath{\beta} decay and studied through \ensuremath{\gamma}-ray spectroscopy at TRIUMF ISAC to assess the nature of low-lying ${K}^{\ensuremath{\pi}}{=0}^{+}$ instrinsic excitations. Improved measurements of the decay properties of the lowest ${K}^{\ensuremath{\pi}}{=0}^{+}$ excitation suggest a \ensuremath{\beta}-vibrational nature for its structure. Data were also obtained ruling out the spin assignment of a previously assigned ${K}^{\ensuremath{\pi}}{=(0}_{3}^{+})$ excitation.

Existing data for the ${3}_{1}^{+}$ state of ${}^{152}\mathrm{Sm}$ present serious uncertainties for any collective interpretation of this nucleus. In this work the lifetime of the ${3}_{1}^{+}$ state in ${}^{152}\mathrm{Sm}$ was remeasured, using the gamma ray induced Doppler technique in the $(n,\ensuremath{\gamma})$ capture reaction, and the $E2/M1$ mixing ratio of the ${3}_{1}^{+}\ensuremath{\rightarrow}{2}_{3}^{+}$ transition was obtained from linear polarization measurements of $\ensuremath{\gamma}$ rays following the $\ensuremath{\epsilon}$ decay of ${}^{152}\mathrm{Eu}.$ The results remove the previous potential discrepancies and are in agreement with the interpretation of ${}^{152}\mathrm{Sm}$ as exhibiting phase coexistence near the critical point of a spherical-deformed phase transition.

Lifetimes of states in 150Nd were measured using the recoil distance method following Coulomb excitation of 150Nd by a 132 MeV 32S beam. The experiment was performed at the Yale Tandem accelerator, employing the SPEEDY gamma-ray detector array and the New Yale Plunger Device. Reduced transition probabilities in 150Nd are compared to the predictions of the critical point symmetry X(5) of the phase/shape transition that occurs for the N = 90 rare earth isotones. Very good agreement was observed between the parameter-free (apart from scale) X(5) predictions and the low-spin level scheme of 150Nd, revealing this as the best case thus far for the realization of the X(5) symmetry.

In this paper states in ${}^{102}\mathrm{Pd}$ populated in the $\ensuremath{\epsilon}/{\ensuremath{\beta}}^{+}$ decay of ${}^{102}\mathrm{Ag},$ produced in the ${}^{89}\mathrm{Y}{(}^{16}\mathrm{O},3n)$ reaction, were studied with high efficiency Ge detectors. The level scheme of ${}^{102}\mathrm{Pd}$ is in good overall agreement with the predictions of the E(5) critical point symmetry, with the exception of the ${0}_{2}^{+}$ state, which may be of intruder character.

Lifetimes and $\ensuremath{\gamma}\ensuremath{\gamma}$ coincidences for low-spin states of the odd-odd nucleus ${}^{50}\mathrm{Mn}$ were measured in the ${}^{40}\mathrm{Ca}{(}^{12}\mathrm{C}{,np)}^{50}\mathrm{Mn}$ fusion-evaporation reaction at 27 MeV beam energy at the ESTU-tandem accelerator at Yale. The excitation energy of the ${J}^{\ensuremath{\pi}}{=5}^{+}$ isomer is established for the first time from high-resolution $\ensuremath{\gamma}$-ray spectroscopy. Comparison to simulations of the Doppler-shift attenuation processes as functions of the level lifetimes enables us to extract lifetime information for five states. The measurement of $B(M1)$ values agrees with the previous assignments of quasideuteron configurations in ${}^{50}\mathrm{Mn}$ done on the basis of $E2/M1$-multipole mixing ratios and $\ensuremath{\gamma}$-branching ratios. The observations verify the predictions of an earlier full $\mathrm{pf}$-shell model calculation for ${}^{50}\mathrm{Mn}.$

The g‐factor of the first excited state of 164Yb was measured by perturbed gamma‐gamma angular correlation in an external static magnetic field of 5.55 Tesla. The result, g(21+)=0.32(5), extends the systematics of g(21+) for Yb isotopes down to N=94, and is discussed in the framework of different models.

Radioactive Nuclear Beams (RNBs) are opening new regions of the nuclear landscape to nuclear structure studies. Early experiments with RNBs rely on reactions with large cross sections, inverse kinematics, and very efficient detector geometries in order to measure observables that are very sensitive to structural features. A Coulomb excitation experiment extracted the B(E2;01+ → 21+) values of the neutron rich RNBs 132,134Te at the HRIBF with the GRAFIK through‐well NaI(Tl) detector. In addition, other experiments with RNBs, such as Coulomb excitation of octupole states and reorientation experiments, inelastic scattering, and single‐particle transfer, will be discussed.

The Wright Nuclear Structure Laboratory has recently acquired a gas‐filled recoil separator previously used at Berkeley National Laboratory for heavy‐element synthesis. The separator will be used to separate reaction recoils from primary beam particles and fission products following target bombardment. Commisioning of the separator has recently been completed, and the structure of 203Rn investigated.

The opportunities for the study of exotic nuclei are discussed with emphasis on structural evolution. In particular, the concept of critical point nuclei in phase transitional regions, experimental evidence for them, their theoretical description, and the role of exotic nuclei in their further study will be discussed.

The concept of symmetries pervades much of our understanding of nature. In nuclear structure, the IBA embodies a framework with three dynamical symmetries U(5), O(6) and SU(3). Of course, most nuclei break these symmetries. Leviatan has discussed a concept of Partial Dynamical Symmetry (PDS) in which the states of the ground and gamma bands, only, are exactly described by SU(3) while all others are not. With an E2 operator which is not a generator of SU(3), this PDS gives a parameter-free description of γ to ground band relative B(E2) values in 168Er that is virtually identical to the best collective model (IBA) calculations with 2-3 parameters. We have carried out the first extensive study of this PDS, in 47 rare earth nuclei. Overall, the PDS works very well, and the deviations from the data are usually understandable in terms of specific kinds of mixing.

Using the high-resolution Q3D magnetic spectrograph at the Maier-Leibnitz Laboratory (MLL) Tandem accelerator in Munich, we studied 0+ excitations in the mercury isotopes 198 Hg, 200 Hg, and 202 Hg after two-neutron transfer. We only observed 4-6 excited 0+ states per nucleus up to about 3-MeV excitation energy, far fewer than in other experiments of this (p, t ) campaign. The results reveal a sharp drop in the number of low-lying 0+ states towards the 208 Pb shell closure. We discuss the low-energy 0+ state density as a function of the valence nucleon number N val . The 0+ excitation energies and the measured (p, t ) transfer cross sections indicate a structural change throughout the Hg isotopes, with the most notable result being the peaking in the cross section of the low-lying excited 02 + state in 200 Hg.

Lifetimes of states in 150Nd were measured using the recoil distance method following Coulomb excitation of 150Nd by a 132 MeV 32S beam. The experiment was performed at the Yale Tandem accelerator, employing the SPEEDY gamma-ray detector array and the New Yale Plunger Device. Reduced transition probabilities in 150Nd are compared to the predictions of the critical point symmetry X(5) of the phase/shape transition that occurs for the N = 90 rare earth isotones. Very good agreement was observed between the parameter-free (apart from scale) X(5) predictions and the low-spin level scheme of 150Nd, revealing this as the best case thus far for the realization of the X(5) symmetry.

A simple compact correlation of the energies of the lowest ${0}^{+}$ excitation with the yrast energy ratio ${R}_{4/2}(\mathrm{g}.\mathrm{s}.)\ensuremath{\equiv}{E(4}_{1}^{+}{)/E(2}_{1}^{+})$ is found to characterize all collective nuclei, regardless of structure. This correlation can be reproduced by interacting bosom approximation calculations. Collective signature observables for the states based on ${0}_{2}^{+}$ excitations indicate a different structure than for the ground state configuration but systematic inconsistencies in their global behavior and discrepancies with calculations prevent a definite interpretation.

We identify the ${J}^{\ensuremath{\pi}}{=2}_{3}^{+}$ state of ${}^{96}\mathrm{Ru}$ as the proton-neutron mixed-symmetry ${2}_{\mathrm{ms}}^{+}$ state of this nucleus. This identification is based on the measurement of the transition strengths ${B(M1,2}_{3}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})=0.78(23) {\ensuremath{\mu}}_{N}^{2}$ and ${B(E2;2}_{3}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})=1.6(3)$ W.u. These transition strengths were obtained from the Coulomb excitation yield for the population of the ${2}_{3}^{+}$ state relative to the yield of the ${2}_{1}^{+}$ state with known $E2$ excitation strength. The Coulomb excitation was done in inverse kinematics using the reaction ${}^{\mathrm{nat}}\mathrm{C}{(}^{96}\mathrm{Ru}{,}^{96}{\mathrm{Ru}}^{\ensuremath{\star}})$ at 280 MeV. This work demonstrates the accessibility of the isovector quadrupole excitation in the valence shell using experiments with an accelerated beam of the nuclei of interest.

We examine a quantum phase transition in gamma-soft nuclei, where the O(6) limit is simultaneously a dynamical symmetry of the U(6) group of the interacting boson model and a critical point of a prolate-oblate phase transition. This is the only example of phase transitional behavior that can be described analytically for a finite s,d boson system.

The high-spin structure of ${}^{203}\mathrm{Rn}$ has been investigated using two separate reactions. $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidences were measured for the ${}^{174}\mathrm{Yb}{(}^{34}\mathrm{S},5n)$ reaction at a beam energy of 167 MeV using the YRAST Ball array at the Wright Nuclear Structure Laboratory at Yale University. The ${}^{168}\mathrm{Er}{(}^{40}\mathrm{Ar},5n)$ reaction at an energy of 188 MeV was also employed. In this experiment \ensuremath{\gamma} rays were observed using the Gammasphere array in coincidence with the fragment mass analyzer at Argonne National Laboratory. The level scheme of ${}^{203}\mathrm{Rn}$ has been developed to spins of $\ensuremath{\sim}41/2\ensuremath{\Elzxh}$ and excitation energies of $\ensuremath{\sim}3 \mathrm{MeV}.$ The high-spin decay is dominated by three sequences of \ensuremath{\gamma} rays, and the possible configurations are discussed.

It is shown that ${}^{152}\mathrm{Sm}$ and other $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}90$ isotones are the first empirical manifestation of the newly predicted analytic description of nuclei at the critical point of a vibrator to axial rotor phase transition.

Lifetimes in the neutron-rich nuclei ${}^{104}\mathrm{Mo},$ ${}^{110}\mathrm{Ru},$ and ${}^{144}\mathrm{Ba}$ were measured using the differential recoil distance method. The experiment was performed with a ${}^{252}\mathrm{Cf}$ fission source inside the New Yale Plunger Device. $\ensuremath{\gamma}$ rays were detected by the SPEctrometer for Experiments with Doppler shifts at Yale (SPEEDY) while fission fragments with the appropriate kinematics were detected by an array of photocells.

In a study parallel to one recently carried out for the interacting boson model, the behavior of the geometric collective model (GCM) with (partially restricted) random interactions is studied. In particular, we study the frequency distribution of E(4{sub 1}{sup +})/E(2{sub 1}{sup +}) ratios. In addition, we characterize those GCM potentials giving E(5) spectra and distinguish them from others giving R{sub 4/2}{approx}2.3 but non-E(5) spectra.