Structure of even-even actinides in the interacting boson model and the N = 152 subshell closure

We show that a wide range of deformed actinides can be described in terms of an interacting boson model hamiltonian with three parameters, two of them [including the coefficient of the only SU(3) symmetry breaking term] remaining almost constant over the whole region. In addition to ground γ₁ and β₁ spectra, B(E2:0_g⁺ → 2_g⁺) values are well reproduced with no extra adjustable parameters for nuclei with 136⩽N⩽146, while for nuclei beyond N = 146 an effective boson number has to be considered in order to fit the observed in the B(E2:0⁺_g → 2⁺_g) values, which is due to the presensce of a subshell closure at N = 152. The sensitive dependence of the B(E2:0_g⁺→2_g⁺) values on the effective boson numbers is emphasized. β₁ → ground and β₁ → ground transitions are fitted by breaking the SU(3) symmetry of the E2 transition operator.     

Mixed-symmetry states in the neutron-proton interacting boson model

States of mixed proton-neutron symmetry are investigated in different dynamical symmetries of the interacting boson model. We discuss in each of the limits the energy spectrum, the wave functions and the B(M1; 0₁⁺ → 1 _1⁺) values. We also study three classes of transitional nuclei namely the Pd nuclei [U(5) → O(6)], the Sm nuclei [U(5) → SU(3)] and the Pt nuclei [O(6) → SU(3)] with respect to the energy of the lowest non-symmetric J^π = 1⁺, 3⁺ levels as well as the M1 and M3 strengths for exciting these levels from the ground state. For ⁹⁸Pd we compare this calculation with a shell-model calculation. Finally, we adress the problem of the mixing of the non-symmetric J^π = 1⁺ state with nearby hexadecapole (g-boson) configurations.     

IsoscalarE2 transition strengths in 10≦A≦48 nuclei

Electric quadrupole transition strengths for the 2 ₁ ⁺ ,T=1→0 ₁ ⁺ ,T=1γ-decay branches are summarized for 10≦A≦42 nuclei. In¹⁰B the corresponding branch has been remeasured by use of the⁹Be(p, γ)¹⁰B resonance reaction atE _p =320 keV; an upper limit of 0.6% is found. The variation of theE2 strengths within each individualT=1 isobaric multiplet reveals the particleor hole-character of the levels involved. The isoscalar 2 ₁ ⁺ →0 ₁ ⁺ transition strengths in 10≦A≦48 nuclei vary between 2 and 20 Weißkopf units showing drastic shell effects. Results for the ratio of neutron and proton matrix elements deduced from analogγ-decay studies and from inelastic pion scattering are compared.     

Core polarization and 5/2+ states in91Nb

The energies and spectroscopic factors ofJ ^π=5/2⁺ states of nucleus⁹¹Nb excited via a reaction transferring a proton to the 2d _5/2 orbit of⁹⁰Zr target state have been calculated. Effective two-body interaction used has been extracted from the experimentally observed two-body energies of (1g ₉ ^2/?1 (n) 2d _5/2(n)), (1g ₉ ^2/?1 (n) 1g _9/2(p)) and (1g _9/2(p)-2d _9/2(n)) multiplets in⁹⁰Zr,⁹⁰Nb and⁹²Nb nuclei respectively. Most of the calculated energies and the strengths ofJ ^π=5/2⁺ levels have reasonably good counterparts in the experimental spectrum, however the calculation shows about 17% strength lying at 6.8 MeV, without having a confirmed counterpart in the observed level scheme. The reduced transition strengthsB(M1) forM l transitions from 5/2^? T>(11/2) state to the various components of 5/2⁺ T<(=9/2) state have also been reported; but the corresponding experimental values are not available. The main feature of the reduced transition strengths is that theM1 transition to the state at 3.69 MeV is inhibited whereas that to the state at 6.79 MeV is enhanced, the relevant core-configuration, interfering destructively in the former case and constructively in the latter.     

Collective states in even Sn nuclei

0⁺, 2⁺, 4⁴ and 3^? states in ^112–124Sn have been studied with the (p, p′γ) reaction and in Coulomb excitation. Absolute E2 transition rates between these levels have been extracted with the aid of the Winther-de Boer code. For ^116,118Sn, B(E2; 4₁⁺ → 2₁⁺) ≈ 20 W.u., suggesting a two-phonon character of the 4₁⁺ states. For the lighter and heavier isotopes, this value is significantly smaller. All observed values of B(E2; 2₂⁺ → 2₁⁺) and B(E2; 2₃⁺→ 2₁⁺) are about 5 W.u. Also. values of B(E3; 0₁⁺ → 3^?₁) have been measured for all stable even Sn nuclei. In ¹¹⁶Sn the branching ratio (3₁^? → 0₁⁺)/(3₁^? → 2₁⁺) has been measured. From this we obtain a half-life of 0.34±0.07 ps for the first 3^? level in ¹¹⁶Sn and B(E1; 3₁^? → 2₁⁺) = (1.4±0.3) × 10^?5'e² · b, corresponding to a hindrance factor of 10³.     

Magnetic dipole transitions and proton-neutron degrees of freedom in nuclear deformation

The M1 transitions between low-lying collective states are discussed from the viewpoint of the Proton-Neutron Interacting Boson Model, with particular emphasis on the mixed-symmetry states. Mixed-symmetry 2⁺ states are studied for⁵⁶Fe and⁵⁴Cr in terms of realistic and large-scale shell-model calculations, including M1 properties. The Doorway-state character of the mixed-symmetry 2⁺ state is proposed with examples in these nuclei. The possible candidate of the mixed-symmetry 2⁺ state in¹³⁴Ba is analyzed based on recent experiment by Molnaret al. on M1 transitions. The M1 transitions from the quasi-γ to quasi-g bands in γ-unstable or O(6) nuclei are discussed next, by taking Ba isotopes as an example. It is suggested that such M1 transitions are enhanced compared to axially symmetric nuclei as an indication of softness towards proton-neutron incoherent motion in γ-unstable nuclei,i.e., mixture of mixed-symmetry states. A new mirror-type symmetry is introduced for γ-unstable nuclei, and the M1 selection rule due to this symmetry is presented, making 4 ₂ ⁺ →4 ₁ ⁺ transition allowed but 3 ₁ ⁺ →2 ₁ ⁺ forbidden, for instance.     

Fragmented 2d 5/2, 1g 7/2 and 1g 9/2 deep proton-hole states of207TI

The three proton-hole states ?2d_5/2, 1g_7/2 and 1g_9/2 are found to be fragmented as a result of coupling of these states with the 3^?, 5^?, 2⁺, 4⁺ and 6⁺ collective states of²⁰⁸Pb. The excited states in²⁰⁸Pb (t,α) reaction can be quantitatively explained in terms of altered 2d_5/2, 1g_7/2 and 1g_9/2 states with the hole-core coupling model.     

Decay of three-particle high spin states in85Y

High spin states in⁸⁵Y have been excited in the reaction⁷²Ge(¹⁶O,p2n) at 48–60 MeV beam energy. From measurements ofnγ andγγ coincidences, excitation functions and angular distributions, the high spin spectrum of⁸⁵Y has been established up to 5.4 MeV excitation energy and spinI≦29/2. Lifetimes or limits of lifetimes have been determined for 14 levels via the recoil distance and Doppler shift attenuation method. Theg _9/2 decoupled proton band is found to backbend atI ^π=17/2⁺ as also seen in the reduction of the 17/2⁺→13/2⁺ and 21/2⁺→17/2⁺ E2 transition strengths. The lowest (3qp) positive parity band has predominantly aν ² g _9/2×πg _9/2 structure. The observed negative parity yrast states in the spin range 15/2^?≦I≦29/2^? are most probably of (g _9/2)² ×(f _5/2,p _1/2) (3qp) nature as suggested by a comparison of the⁸⁴Sr and⁸⁵Y level structures and electromagnetic transition strengths.     

The ΔTz = + 1 Gamow-Teller excitation of N = 28 isotones

Results of shell-model calculations of Gamow-Teller strength distributions are presented for ⁵⁰Ti → ⁵⁰Sc, ⁵²Cr → ⁵²V and ⁵⁴Fe → ⁵⁴Mn. The results support the previous shell-model estimates that a large fraction of Gamow-Teller strength is concentrated at low excitation energy in the daughter nuclei. The strength distributions are in fairly good agreement with those of forward-angle cross sections of T₀ + 1 isospin states of the intermediate-energy (p, p') reaction on N = 28 isotones. An estimate of quenching in the T₀ → T₀ + 1 τσ mode transition is attempted. Calculations are performed also for the first 2⁺ and 4⁺ parent states in the context of electron capture at the late stages of stellar evolution.     

CW Optical-Optical Double Resonance studies of the 23Πg, 33Πg, 43Πg+, and 13Δg Rydberg states of Na2

The 2³Π_g, 3³Π_g, 4³Σ_g⁺, and 1³Δ_g states of the Na₂ molecule are observed by sub-Doppler Perturbation Facilitated Optical-Optical Double Resonance (PFOODR) spectroscopy. Absolute vibrational assignments and molecular constants are obtained for two of these states (3³Π_g, v = 0–25 observed, and 4³Σ_g⁺, v = 3–5, 13, 14 observed). Tentative vibrational assignments and provisional molecular constants are obtained for the 2³Π_g (v = 43–89 observed) and 1³Δ_g (v = 31–35, 40, 46–51 observed) states. Spin-orbit, spin-spin, and hyperfine splittings are observed. The direct ³Λ_g⁺ → a³Σ_u, 2³Π_g ∼ 3³Π_g perturbation-induced, and collision-induced contributions of these four ³Λ_g states to the ubiquitous Na-vapor violet and ultraviolet emission bands are discussed.     

Excitation energies and intensities of λπ=0−, 2− charge exchange modes in spherical nuclei

Theβ ^?, (n→p) and (p→n), transition strengths and excitation energies for first forbidden resonances with λ^π=0^? and 2^? in spherical nuclei are calculated in the framework of the linear response theory. The results show that the intensities associated with these modes are strongly fragmented, particularly, for the λ^π=2^? states.     

Electronic transition moments between excited singlet states of the H2 molecule

The twelve transition moments which connect each of the three ¹Σ_g⁺ states EF, GK, and $\text{H}\text{H}$ with the three ¹Σ_u⁺ states B,B′, $\text{B″}\text{B}$ and with the state C¹Π_u were computed in the range of internuclear distances 1.25 ≤ R ≤ 15 a.u. using accurate electronic wavefunctions. The relative phases of the wavefunctions, which determine the signs of the transition moments, were consistently defined at all R values. The strong R dependences of the transition moments reflect the R-dependent changes in electronic character of the states involved in these transitions. At large R values the ¹Σ_g⁺-¹Σ_u⁺ transition moments are dominated by the two-electron charge resonance in the ionic configuration H⁺ + H^? whose transition moment is $\text{M(R) ? R}$.     

Description of spectrum and electromagnetic transitions in <Superscript>94</Superscript>Mo through the proton-neutron interacting boson model

We investigated the properties of low-lying states in ⁹⁴Mo within the framework of the proton-neutron interacting boson model (IBM-2), with special focus on the characteristics of mixed-symmetry states. We calculated level energies and M1 and E2 transition strengths. The IBM-2 results agree with the available quantitative and qualitative experimental data on ⁹⁴Mo. The properties of mixed-symmetry states can be well described by IBM-2 given that the energy of the d proton boson is different from that of the neutron boson, especially for the transition of B(M1; 4 ₂ ⁺ → 4 ₁ ⁺ ).     

The deformation of the ground and excited states in the Ag and Sn nuclei

The microscopic calculation of the potential energies in the ground and excited states of Ag and Sn nuclei has been performed. The single particle Nilsson potential and the shell correction Strutinski method have been used. The weak sensitivness to nonaxial deformation has been found for even neighbours of these nuclei. The small tendency towards prolate deformation of the ground and excited one-quasiparticle states originating from theg _9/2 proton subshell in^101–105Ag odd isotopes has been noticed. The behaviour with quadrupole e and hexadecapole ε₄ deformation of the ground and two-quasiparticle excited 0⁺ states originating from thed _5/2,g _9/2 andg _7/2 proton subshells andh _11/2 neutron subshell in^112–118Sn has been investigated. The small quadrupole deformation of the excited 0⁺ states has been found what is in agreement with the experimental data concerning the rotational bands build on the first excited 0⁺ states in Sn isotopes.     

Shape coexistence close to N=50 in the neutron-rich isotope ~(80)Ge investigated by IBM-2

The properties of the low-lying states,especially the relevant shape coexistence in~(80)Ge,close to one of most neutron-rich doubly magic nuclei at N=50 and Z=28,have been investigated within the framework of the proton-neutron interacting model(IBM-2).Based on the fact that the relative energy of the d neutron boson is different from that of the proton boson,the calculated energy levels of low-lying states and E2 transition strengths can reproduce the experimental data very well.Particularly,the first excited state 0_2~+,which is intimately related to the shape coexistence phenomenon,is reproduced quite nicely.Theρ~2(E0,0_2~+→0_1~+)transition strength is also predicted.The experimental data and theoretical results indicate that both collective spherical andγ-soft vibration structures coexist in~(80)Ge.     

Description of mixed symmetry states in <Superscript>96</Superscript>Ru using IBM-2

We have investigated the properties of low-lying states in ⁹⁶Ru within the framework of the neutron-proton interacting boson model (IBM-2), with special attention paid to the characteristics of the mixed symmetry states. By considering the relative energy of d proton boson to be different from that of neutron boson, the level energies and M1, E2 transition strengths have been calculated. The IBM-2 calculation is consistent with the experimental data of ⁹⁶Ru both quantitatively and qualitatively. Particularly, the strong M1 transition between the 4₂ ⁺ and 4₁ ⁺ states has been reproduced nicely. The calculated results show that the M1 transition strength of B(M1; 4₂ ⁺ → 4₁ ⁺) in ⁹⁶Ru can be described successfully by the IBM-2.