Beta-vibrational Band Research Articles

Nuclear phase transitions near the critical points: a study with the Relativistic Hartree-Bogoliubov model, the Interacting Boson Model and the Boson Coherent-State Framework

We present an analysis of the intensity of 2-particle transfer reactions in the Interacting Boson Model (IBM), and in the Boson Coherent-State framework, as a tool to study nuclear phase transitions. We study transfer reactions between two ground states, and between the ground state and the band head of the beta-vibrational band. We suggest characteristic fingerprints that should allow experimentalists to identify the critical points of the nuclear phase transition. Two analytical solutions, X(5) and E(5), have been proposed recently for two of the critical points. We present a study within the Relativistic Hartree-Bogoliubov model (RHB), using Potential-Energy Surfaces (PES), to test whether the initial approximations made in deriving the analytical solutions are valid.

Lifetime measurements in the transitional nucleus138Gd

Lifetime measurements have been made in the ground-state band of the transitional nucleus (138)Gd from coincidence recoil-distance Doppler-shift data. (138)Gdnuclei were produced using the (106)Cd ((36)Ar, 2p2n) reaction with a beam energy of 190 MeV. Reduced transition probabilities have been extracted from the lifetime data collected with the Koln plunger placed at the target position of the JUROGAM-II array. The B(E2) values have been compared with predictions from X(5) critical-point calculations, which describe the phase transition between vibrational and axially symmetric nuclear shapes, as well as with IBM-1 calculations at the critical point. While the excitation energies in (138)Gdare consistent with X(5) predictions, the large uncertainties associated with the measured B(E2) values cannot preclude vibrational and rotational contributions to the low-lying structure of (138)Gd. Although experimental knowledge for the low-lying gamma and beta-vibrational bands in (138)Gd is limited, potential-energy surface calculations suggest an increase in gamma softness in the ground-state band. In order to more fully account for the effects of gamma softness, the X(5) and IBM-1 calculations need to be extended to include the gamma degree of freedom for (138)Gd.

The mixing of ground-state rotational and gamma and beta vibrational bands in the regionA ≥ 228

The mixing of beta, gamma and ground-state bands has been investigated through the experimental determination of mixing parametersZ γ andZ βγ . TheseZ γ values have been compared with the theoretical calculations of this parameter from the solutions of time-dependent HFB equations on the adiabatic and nonadiabatic assumptions. The experimental values are in better agreement with the results obtained under the nonadiabatic assumption, valid for small deviations from the spherical symmetry.

The (t, p) reaction across the shape transitional Gd nuclei

The 152Gd(t, p) 154Gd reaction has been studied using 15 MeV tritons from the McMaster University tandem accelerator facility. The reaction products were analyzed with a magnetic spectrograph. Distinctive L = 0 angular distributions indicated that four 0 + states were populated, the first three with comparable strengths and the fourth with a cross section about an order of magnitude smaller. The 2 + 3 state at 1418 keV, previously interpreted as the 2 + member of the two-phonon beta-vibrational band, has been populated as strongly as the 2 + member of the ground-state band. The 0 + 3 and 2 + 3 states in 154Gd are analogous to the previously observed “spherical” states coexisting in the “deformed” 152Sm isotone.

Gamma-gamma directional correlations and coincidence studies in154Gd

The intensities, placements andE2/M1 mixing ratios of transitions in the decay of154Eu have been carefully studied to provide accurate data for microscopic calculations. Coincidence relationships in the decay of154Eu have been studied extensively with a multiparameterγ-γ coincidence system with two large volume Ge(Li) detectors. Spectra in coincidence with twenty energy gates were analyzed. Twenty-nine new coincidence relationships were established and confirmed most, but not all, of several levels previously assigned by energy fits only. From an analysis of coincidence spectra and singles spectra with a 18% efficiency Ge(Li) detector new information on the gamma-ray intensities were obtained. Precise values of theE2/M1 mixing ratios of transitions from the gamma- and beta-vibrational bands to the g.s. band have been determined fromγ-γ directional correlation measurements with a NaI(Tl)-Ge(Li) detector coincidence system. Mixing ratios were obtained for a number of other transitions including those fromKπ =0− and 2+ bands from direct and skipped cascade correlations.

Gamma vibrational band in160Dy

From the accurately measured gamma ray intensities following the decay of 160Tb (72.4 d), the properties of the gamma vibrational band in 160Dy have been critically examined. No unique value of the band-mixing parameter, Zgamma , could be obtained from the B(E2) ratios corresponding to different interband transitions. This inconsistency is also observed in the values of Zbeta gamma parameter arising from the mixing of the gamma vibrational band with a possible beta vibrational band. A comparison of the properties of 160Dy with those of the nuclei in the strongly deformed region and those in the beginning of this region indicates that the nucleus resembles transitional nuclei and hence a microscopic approach may be essential to understand its properties.

The decay of174Ta

Levels in174Hf excited in the decay of174Ta have been studied. Measurements of gamma-rays, conversion electrons and gamma-gamma-time coincidences were performed. The ground state band, the beta-vibrational band, the gamma-vibrational band with its head at 1226.81 keV, aK=3+ band at 1303.42 keV and aK=2− octupole band at 1308.67 keV were observed. Several 2+ levels withK=0 are excited. The mainβ+-branches proceed through allowed or first-forbidden transitions to the 2+ and 4+ levels of the ground state band. The character of theIπ=3(+) ground state of174Ta is discussed.

Anomalous moments of inertia for high-spin levels in the beta vibrational band of 154Gd

The levels of 154Gd populated by the 154Sm(α,4n) reaction have been studied with γ-γ coincidence techniques. The energy spacings of the β-band levels of spin > 8 are found to differ from the rotational picture in a manner similar to that recently observed in the ground-state bands of some other rare-earth nuclei. The ground-state band of 154Gd does not show the anomaly;

Levels in 153Sm

Abstract The nuclear levels of 153Sm have been investigated by Ge(Li) and Si(Li) detector measurements of both high- and low-energy γ-rays following thermal neutron capture in 152Sm, and by magnetic spectrograph measurements of the tritons from the 154Sm(d, t) reaction. The observed states are classified within the Nilsson scheme as follows: the mixed 3 2 + [651] + [402] ground state band up to the 13 2 + member, the 3 2 − [521] band to the 7 2 − member, the 3 2 − [532] band to the 11 2 − member, the 11 2 − [505] band head, the 3 2 + [402]+ [651] configuration up to 7 2 + , and the members up to 7 2 − of a K π = 1 2 − band that is partly 1 2 − [521] and partly vibrational. Also, tentative assignments have been made of the 5 2 + [642] , 1 2 − [530] and 1 2 + [400] bands, as well as a K π = 3 2 − beta-vibrational band. The K π = 3 2 + rotational bands are severely distorted, presumably due to Coriolis coupling. An estimate is made of the amount of mixing between the 3 2 + [651] and 3 2 + [402] orbitals. Comparisons are made with the level structure of other 91-neutron nuclei and with theoretical calculations.

Electric quadrupole transitions from high spin states in the beta-vibrational band of 154Gd

The interband E2 γ-ray transitions between the rotational levels of the γ-vibrational band and ground-state band in 154Gd were investigated for spins up to 10 + by studying the 154 Sm(α, 4 nγ) 154 Gd reaction. These transitions were analysed in terms of the rotation-vibration interaction.

Gamma rays from coulomb excitation of 151Eu and 153Eu

De-excitation gamma rays following Coulomb excitation of 151Eu and 153Eu by 4.5 MeV protons and 5 to 11 MeV alpha particles were studied with a 2 cm 3 and a 50 cm 3 Ge(Li) detector. Excitation curves and reduced transition probabilities were measured. Nineteen gamma-ray transitions found in 151Eu are interpreted as decay branches from levels of 195.8, 196.5, 243.0, 306.8, 500.0, 503.1, 578.0, 600.6, 719 and possibly 696, 781 and 906 keV. In 153Eu ten gamma rays were found and are interpreted as decays from levels of 83.3, 151.3, 192.3, 569.0, 617.5 and 711.0 keV. The level energies are consistent with recent inelastic scattering data. In 153Eu the level at 569.0 keV may be the gamma-vibrational band head with J = 9 2 . The levels at 617.5 and 711.0 keV may be the beta-vibrational band members with J = 5 2 and 7 2 respectively.

Electromagnetic transitions from levels in the beta-vibrational band of 174Hf

The E0, M1 and E2 matrix elements were obtained for the interband transitions between levels with spins up to 6 in the beta-vibrational and the ground-state bands of 174Hf by studying the following nuclear reactions: 174Hf(α, α') 174Hf, 175Lu(p, 2nγ) 174Hf, 172Yb(α, 2nγ) 174Hf and 172Yb(α, 2ne) 174Hf. The interband E2 transition matrix elements are well explained in terms of a coupling of the beta vibration with the rotation. The ratios of the E0 to E2 matrix elements for interband transitions between states of the same spin are fairly constant over spins I = 0–6. On the other hand, the M1 to E2 ratios for these transitions increase rapidly with the increase of spin. The observed transition matrix elements are discussed in the framework of the collective model including the rotation-vibration interaction.

The decay scheme of 1.3 h 174Ta

The decay of 174Ta (T½ =1.3 h) has been studied with Ge(Li) and Si(Li) detectors. Single, coincidence and sum γ-ray spectra, conversion lines and e-γ coincidence relations have been measured. The results are in good agreement with those of earlier investigations for the ground state and the beta-vibrational band. Above these bands 14 levels have been established having the following energies (in keV) spin values and parities : 1276.8 (3,4); 1318.9 (2+) ; 1394.4 (3, 4) ; 1448.9 (3- ) ; 1503.3 (4+) ; 1659.2 (4+); 2 030.1 (3, 4) ; 2124.5 (3,4) ; 2 145.5 (4+); 2198.2 (4-) ; 2 237.3 (5); 2 490.5 (3, 4) ; 2 590.7 (3, 4) and 3 023.7 (2). The level scheme accounts for 49 of the 60 transitions firmly assigned to the decay of 174Ta. The Q-value of the decay 174Ta → 174Hf was determined to be 3 845 ± 80 keV. The half life of the first 2+ level was remeasured and found to be 1.68 ± 0.08 ns. The structure of 174Ta and of the levels of 174Hf are discussed in terms of current nuclear models.

Coulomb excitation of rotational and vibrational states in 167Er, 163Dy and 155Gd

Low-lying states in deformed odd-neutron rare-earth nuclei have been studied by Coulomb excitation with 36–52 MeV 16O ions. The gamma rays from the reaction were observed as single spectra in Ge(Li) detectors. In 167Er, the K0−2 and K0+2 gamma-vibrational bands were observed at 532 and 711 keV with B(E2)↑ = 2.6 and 2.5 s. p. u., respectively. In 163Dy, the K0−2 gamma-vibrational band was observed at 351 keV with B(E2)↑ = 1.2 s. p. u. The 32−|521| Nilsson state was observed at 422 keV with B(E2)↑ = 0.5 s. p. u. due to its Coriolis coupling to the ground band. In 155Gd, the K0−2 gamma-vibrational band was observed at 556 keV with B(E2)↑ = 1.6 s. p. u. The excitation of the 12−|530| Nilsson state at 422 keV with B(E2)↑ = 1.2 s. p. u. seems to be due to Coriolis coupling to the ground band. In this nucleus, indications were found for a beta-vibrational band at 592 keV and a K0+2 gamma-vibrational band at 1028 keV corresponding to B(E2)↑ ≧ 1.3 and 0.8 s. p. u.

Energy levels of 237Np (I). The alpha decay of 241Am

The γ-ray spectrum of 241Am from 80 to 850 keV was studied with a high resolution semiconductor γ-ray spectrometer; α-γ- and α-electron-coincidence spectra were studied with semiconductor and scintillation detectors. From these data and previous results, a decay scheme is constructed. Theoretical α-intensity calculations aided in establishing the decay scheme. Nilsson assignments 5 + 2 [642], 5 − 2 [523] and 1 + 2 [400] for rotational bands based on levels at 0, 59.54 and 332.36 keV are confirmed. A new 1 − 2 [530] band, whose lowest member is the well-known 267.54 keV 3 − 2 level, is positively identified, and a K = 5 − 2 beta-vibrational band established. The latter band decays primarily by M1 transitions, in violation of the vibrational selection rule. A new level at 770 keV with a probable I π = 7 + 2 assignments is also of probable vibrational character. A brief study of 243Am decay reveals a similar structure for 239 Np.

Low-Lying Collective States ofSm152andSm154

The excited states up to 2 MeV in ${\mathrm{Sm}}^{152}$ and ${\mathrm{Sm}}^{154}$ have been studied by magnetic analysis of the inelastic protons from thin targets bombarded by a 12-MeV proton beam from the Florida State University tandem Van de Graaff accelerator. The results are compared with previous studies and with the predictions of collective nuclear models. The ground-state band levels up to spin 6 are excited in these experiments. The 2+, 3+, and 4+ states in the gamma vibrational band, the 0+ and 2+ states in the beta vibrational band, and the 1-, 3-, and 5- states in the octupole band have been observed in ${\mathrm{Sm}}^{152}$. In ${\mathrm{Sm}}^{154}$ the gamma band head is observed at 1443 keV and the octupole band head is observed at 927 keV. Additional levels in these bands and the beta band are suggested. Several other levels are observed above 1100 keV in these nuclei.

Nuclear structure studies with high energy heavy ions

Abstract With improved instrumentation it has become possible to examine a variety of otherwise inaccessible nuclear phenomena utilizing high energy beams from the Yale Heavy Ion Accelerator. Selected examples will be presented illustrating a number of the unique features of these high energy reactions and emphasizing the nuclear structure potential of the heavy ion beams from the Emperor accelerators. In Li6 induced interactions it has been demonstrated that dissociation of the projectile dominates at higher energies; characteristics of the dissociation mechanism have been studied supporting a pronounced binary cluster structure. Deuteron and nucleon transfer reactions to isolated final nuclear states have been examined; at high energies these show promise of providing a direct probe for determination of fractional parentage information, and of the location and character of two-particle states in nuclei. It has been demonstrated that inelastic scattering of heavy ions preferentially excites collective nuclear states; the deformations indicated by DWBA analyses of the inelastic scattering data are in reasonable accord with those obtained from electromagnetic studies. Multiple coulomb excitation measurements with O16 ions have included studies of interband mixing in even-even nuclei and of higher order Coriolis perturbations in odd A nuclei, in the rare earth region. In the former it has been demonstrated that mixing of the ground state and beta vibrational bands is dominant; in the latter, that third order perturbation effects are required to fit the higher excitations in the rotational bands.

Further studies on the decay of Eu 156

The beta decay of Eu 156 has been studied by means of an intermediate image magnetic spectrometer modified for the beta-gamma coincidence studies. An attempt has been made to detect the possible beta feeding to the lowest energy level of the beta vibrational band which is expected in the deformed Gd 156 nucleus. The present study does not give any definite indication of feeding of such a level in the decay of Eu 156 and if it exists it should be less than 0.1%. The energy and intensity of different beta groups and various gamma-rays in this decay are given.

Nuclear Levels in a Number of Even-Even Rare Earths (150≤A≤184)

To obtain more data on the system of levels in even-even nuclei, a number of such nuclei ($150\ensuremath{\le}A\ensuremath{\le}184$) were studied with electron-capturing sources in permanent magnet spectrogaphs. Some measurements were made with scintillation counters. Data confirming recently reported results on the decay of ${\mathrm{Tb}}^{152}$, ${\mathrm{Tb}}^{156}$, and ${\mathrm{Ho}}^{162}$ have been obtained. It was found that ${\mathrm{Eu}}^{150}$ has two isomeric states (${T}_{\frac{1}{2}}=14$ hr and > 5 yr). Levels at 740.7 (0+) and 773.3 (4+) kev in ${\mathrm{Sm}}^{150}$ are proposed. A study of the two isomeric activities of ${\mathrm{Tb}}^{154}$ indicated the existence of levels in ${\mathrm{Gd}}^{154}$ which may be described as a gamma-vibrational band (at 997.3 kev) and a beta-vibrational band (at 680.6 kev). The new data for ${\mathrm{Tm}}^{166}$ (7.7 hr) are consistent with levels in ${\mathrm{Er}}^{166}$ at 2137.3 and 2164.6 kev, both of which are probably 3 states and which exhibit considerably different branching ratios of the de-exciting transitions. The decay of ${\mathrm{Lu}}^{172}$ appears to populate a large number of even-parity levels in ${\mathrm{Yb}}^{172}$ which may be arranged in rotational bands corresponding to primary or base states at 1174.0 kev ($I=3+$), 1467.5 kev ($I=2+$), 1664.3 kev ($I=3+$), 1702.1 kev ($I=3+$), 2075.0 kev ($I=4+$), and 2287.3 kev ($I=4+$). The very complex decay of the two isomers of ${\mathrm{Re}}^{182}$ excite many odd-parity levels which may be arranged in seven or more bands. In addition, even-parity beta- and gamma-vibrational bands may be populated. Electron-capture decay of ${\mathrm{Re}}^{184}$ populates a gamma-vibrational band in ${\mathrm{W}}^{184}$ of spins 2, 3, and 4. Data relevant to the rotational energy parameters and ratios of gamma-ray transition probabilities from the various states are presented. As a corollary, data on the decay of ${\mathrm{Eu}}^{149}$ are presented since this activity was present in some of our composite sources.

The decay of neptunium-238

A study has been made of the energy levels of Pu 238 which are populated by Np 238 beta decay, by an examination of the Np 238 conversion electron spectrum in high-resolution beta spectrographs. The general features of the level scheme as previously given are unchanged but several new transitions are observed, with energies 119.8, 871, 943, 989 and 1034 keV, and two new levels are postulated at 915 and 1034 keV which accommodate all but the 943-keV transition. A possible assignment of the 943-keV transition to the (0+, 0) state of the beta vibrational band is discussed. In addition, the weak 885-keV transition from the 2+ state of the gamma-vibrational band to the 4+ state of the ground band is seen and its relative intensity determined. Comparisons are made of the experimental relative transition intensities of the three photons depopulating this band with those predicted from the rules of Alaga et al.; only fair agreement is noted. A discussion is given of the beta decay branchings and log ft values of Np 238 decay in terms of the postulated characters of the Pu 238 states and the measured spin of Np 238.