0+ states and E0 and E2 transition rates in even Sn nuclei

0⁺ states and their depopulating E0 and E2 transitions have been studied in ^112–124Sn. Several methods of γ-ray and electron spectrometry have been employed, including special coincidence techniques for lifetime, conversion electron and double Coulomb excitation measurements. For ^114–118Sn the E2 transition probabilities from the first excited 0⁺states (0₂⁺) are about 20 W.u., which is compatible with a vibrational two-phonon character. Also the E0 transition probabilities from these states are within a factor of two from the vibrational values. For the second excited 0⁺ states (0₃⁺) the corresponding E2 and E0 transition probabilities are considerably smaller. A total of 12 E0 transitions have been observed. The 0₃⁺ → 0₂⁺ transition is observed in ^114–120Sn and has in ¹¹⁶Sn a reduced transition probability 1–2 orders of magnitude larger than those of the groundstate E0 transitions, which indicates that the 0₃⁺ and 0₂⁺ states are strong mixtures of components with different 〈r²〉. The 0⁺ states in ¹¹⁶Sn are discussed as possible rotational band heads associated with a deformation β₂ ≈ 0.2. The Coulomb excitation cross section of the 0₂⁺ state is found to be sensitive to an interference term including matrix elements with the 2₂⁺ state. The relative sign of this term has been determined.     

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.     

Quadrupole collective properties of 114Cd

The nucleus ¹¹⁴Cd has been Coulomb excited using beams of ¹⁶O, ⁴⁰Ca, ⁵⁸Ni and ²⁰⁸Pb. Several new states have been observed and an almost complete set of reduced E2 matrix elements for the lowest-lying positive-parity states in ¹¹⁴Cd have been measured. In total, about 40 E2 matrix elements have been determined in a model-independent way, including the static quadrupole moments of the 4⁺₁, 6⁺₁, 2⁺₂ and 2⁺₃ states. Large negative static quadrupole moments were found for the 4⁺₁ and 6⁺₁ states and a large positive quadrupole moment for the 2⁺₂ state. All E2 matrix elements involved in the deexcitation of the quintuplet of states at an energy of about 1.2 Me V were determined. The data are compared with predictions by various models, including a configuration mixing calculation within the framework of the IBA model, the harmonic vibrator and a model in which the states of a near-harmonic vibrator are mixed with those of a rotational intruder band with a large deformation. Although no perfect match is obtained, the data favour a vibration-like structure involving levels up to the four-quadrupole phonon multiplet.     

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.     

New states in heavy Cd isotopes and evidence for weakening of the N = 82 shell structure

A chemically selective laser ion source has been used in a β-decay study of heavy Ag isotopes into even-even Cd nuclides. Gamma-spectroscopic techniques in time-resolving event-by-event and multiscaling modes have permitted the identification of the first 2⁺ and 4⁺ levels in ¹²⁶Cd₇₈, ¹²⁸Cd₈₀, and tentatively the 2⁺ state in ¹³⁰Cd₈₂. From a comparison of these new states in ₄₈Cd with the E(2⁺) and E(4⁺)/E(2⁺) level systematics of ₄₆Pd and ₅₂Te isotopes and several recent model predictions, possible evidence for a weakening of the spherical N = 82 neutron-shell below double-magic ¹³²Sn is obtained. Received: 13 July 2000 / Accepted: 12 October 2000     

Present status and future aspects of nuclear structure close to 100Sn

The present status of experimental approach to ¹⁰⁰Sn in the spectroscopy of excited states is landmarked by the T_z=3/2 nuclei between ⁹⁵Pd and ¹⁰¹In and the T_z=1 nuclei ⁹⁴Pd and ⁹⁸Cd. The detection limits with Pre-EUROBALL γ-arrays and ancillary detectors are below the 10^?5 level of the total fusion- evaporation residue cross section. A large scale shell model analysis of the existing data reveals the shell structure at ¹⁰⁰Sn, which shows a remarkable similarity to ⁵⁶Ni. Evidence for an increasing proton-neutron interaction in approaching the N=Z line is deduced from high spin isomers and spherical yrast lines. The effective E2 operator for protons and neutrons and implications for a low lying particle-hole (ph) E2 excitation in ¹⁰⁰Sn are discussed.     

Electric transition strengths and (e,e') form factors for the first 2+ and 3− states in the even Sn isotopes

The Baranger formalism for the structure of spherical nuclei is applied to the first 2⁺ and 3^? states in the even Sn isotopes. Reduced electric transition strengths and (e, e') form factors for these states are calculated. The results compare satisfactorily with recently measured data.     

IBA-2 model calculation on even mass tellurium isotopes compared with results of recent nuclear orientation experiments

Calculations using the IBA-2 model code are presented for even-even tellurium isotopes¹¹⁸Te to¹²⁴Te. Three parameter sets are used, two from previous work and a third chosen to give optimum fit to experimental positive parity energy levels and B(E2) ratios. With only two additional parameters, each with simple physical interpretation, the three parameter sets are shown to give excellent fits to the known collective negative parity states in these isotopes. Failure to fit the O ₂ ⁺ ,O ₃ ⁺ and 2 ₃ ⁺ levels suggests these may be 4p-2h intruder states, although their Behaviour with varying neutron number is not as clearly characteristic of such configurations as is found for the 2p-4h states in Cd isotopes.     

Low-lying dipole excitations in the stable Cd isotopes: A systematics

Low-lying dipole excitations in the medium-weight vibrational nuclei of the Cd isotopic chain were investigated by means of nuclear resonance fluorescence experiments performed at the bremsstrahlung beam of the Stuttgart Dynamitron accelerator (endpoint energy 4.1 MeV). Detailed information has been obtained on excitation energies, spins, decay widths, and transition probabilities of numerous excited states in ^{110–114,116}Cd. Additionally, the use of two Compton polarimeters enabled model-independent parity assignments for excitations in the even-even isotopes. Strongly excited J ^π = 1^? states are found in all even-even Cd nuclei at excitation energies near the sumof the energies of the first 2⁺ and 3^? states. These excitations are interpreted as the 1^? member of the quadrupole-octupole coupled quintuplet (2+?3^?). The fragmented strength observed in the odd isotopes ^111,113Cd is compared with the strength distributions in the neighboring even-even Cd isotopes.     

E0 transitions in 70Ge and shape-coexistence interpretation of even-mass Ge isotopes

The branching ratios of E0 and E2 transitions depopulating the 0⁺₂ and 0⁺₃ states in ⁷⁰Ge have been studied using conversion-electron and γ-ray spectroscopy, as well as a new internal-pair measurement technique. A value of 3.7 (2) ns has been obtained in a remeasurement of the half-life of the 0⁺₂ state. Two new E0 transitions, 0⁺₃ → 0⁺₂ and 0⁺₃ → 0⁺₁, have been observed. A comparison of the measured X(E0/E2), ρ²(E0) and B(E2) values for the excited 0⁺ states in ⁷⁰Ge with the corresponding ¹⁵⁰Sm data supports a recent shape-coexistence interpretation of the even-mass Ge isotopes.     

Application of a microscopic interacting boson model to single-closed-shell nuclei

The microscopic treatment of an extended IBM including the pairing vibrational modes is applied to single-closed-shell nuclei with N = 50 or Z = 50. The low-lying spectra in the N = 50 isotones are well described in terms of the quadrupole phonon and the pairing vibration. The Sn isotopes roughly resemble the N = 50 isotones. The behavior of the 0₂⁺, 0₃⁺ and 2₁⁺ levels can be explained fairly well by the present model. Introduction of the pairing-vibrational modes into the IBM is essential for describing the single-closed-shell nuclei.     

Excited 0+ states in 156,158,160,162 Gd

Excited K^π = 0⁺ states in ^{156,158,160,162} Gd isotopes are studied by using the pairing plus quadrupole model (PPQ). To determine the nature and the general trend of the properties of these states depending on the neutron number, B(E2), ρ²(E0) values and two‐nucleon transfer strengths are calculated. We observe that by means of the PPQ model, approximately 13‐14 0⁺ states can be obtained up to 3.3 MeV for the nuclei in question, where most of them are two‐quasiparticle (2qp) in character.     

Collective bands in even mass Sn isotopes

Positive parity bands in ^{112, 114, 116, 118}Sn have been excited up to levels with spin and parity J^π = 12⁺ using Cd(α, 2nγ)Sn reactions. The experiments consisted of γ-ray excitation function, γ-γ coincidence, lifetime, γ-ray angular distribution, γ-ray linear polarization and conversion electron measurements. The observed bands show strong resemblances with ground-state bands of transitional nuclei in this mass region. It is pointed out that the J^π = 0⁺ band-heads originate from 2p-2h excitations in the Z = 50 proton shell. The excitation energies of the band-heads are calculated by means of the macroscopic-microscopic renormalization method. Pair correlations between the 2h and 2p configurations are included separately in a phenomenological way by taking into account the pairing energies of the Cd and Te ground states with respect to the Sn ground state.     

New features in the systematics of low-spin states in170–178W

Excited states in the range of even tungsten isotopes, from¹⁷⁰W to¹⁷⁸W, populated in the β-decay of^170–178Re parents have been identified using γ-ray singles and coincidence techniques, utilising the high efficiency of a Compton-suppressed array, and conversion electron systems. Many new states at low excitation energies have been identified, complementing the level schemes previously established from in-beam studies. The new states include excited O⁺ states in¹⁷⁰W,¹⁷²W,¹⁷⁴W,¹⁷⁶W and¹⁷⁸W. A large body of data on decay properties, spins and parities, and relative E2 and E0 matrix elements has been obtained. The properties of theK ^π=0⁺ (quasi-β) bands are compared with similar bands observed in light osmium, platinum and mercury isotopes, which have been attributed to shape coexistence.     

Collective bands in doubly even Sn nuclei

Starting from a simplified picture treating proton two-particle two-hole excitations coupled with spherical quadrupole vibrations, in interaction with the low-lying quadrupole vibrational states in the doubly even Sn nuclei, we are able to account for a regular ΔJ = 2 band structure on top of excited J^π = 0⁺ states. We compare in some detail results for ¹¹⁶Sn concering energy spectra and E2 transition rates.     

Two-neutrino double- β decay of 94 ⩽ A ⩽ 110 nuclei for the 0<Superscript>+</Superscript> → 0<Superscript>+</Superscript> transition

The two-neutrino double-beta decay of ^{94, 96}Zr,^98,100Mo,¹⁰⁴Ru and ¹¹⁰Pd nuclei for the 0⁺0⁺ transition is studied in the PHFB model in conjunction with the summation method. In the first step, the reliability of the intrinsic wave functions has been established by obtaining an overall agreement between a number of theoretically calculated spectroscopic properties and the available experimental data for ^{94, 96}Zr,^94,96,98,100Mo, ^98,100,104Ru, ^104,110Pd and ¹¹⁰Cd isotopes. Subsequently, the PHFB wave functions of the above-mentioned nuclei are employed to calculate the nuclear transition matrix elements M₂ as well as half-lives T_1/2². Furthermore, we have studied the effects of deformation on the M₂.