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 ⁺ ).     

New algebraic solutions for SO(6) ↔ U(5) transitional nuclei in the interacting boson model

Exact solutions for energy eigenvalues and eigenstates for SO(6) ↔ U(5) transitional (Class C) nuclei in IBM-1 and one case in IBM-2 are found by using an infinite dimensional algebraic method. As examples, the energy spectra and some E2 transition rates and quadrupole moments of the ^100–108Ru and ^102–112Pd isotopes are calculated in IBM-1 and compared with experimental results.     

Matrix elements of Yale potential and level properties of light nuclei

Shell model calculations using bare and renormalized matrix elements of the Yale potential are reported for the normal-parity states ofA=6–9 nuclei. Renormalization of the two-body matrix elements using second-order perturbation theory is not found to improve the agreements with the experimental data. Inclusion of the energy shifts of ground state rotational bands in⁸Be and⁹Be are, however, found to improve the agreements with the excitation energies of nuclear levels. The need for carrying out more calculations of these nuclei with realistic forces is pointed out.     

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.     

Interplay of valence-shell clusters and the vibrational field in94Mo and95Mo

The properties of⁹⁴Mo and⁹⁵Mo nuclei, which are typical representatives of N=52 and N=53 nuclei, respectively, are described in the cluster-vibrational field coupling model in natural representation (without parameter fitting). The interplay of few valenceshell neutrons and vibrational degree of freedom gives rise to the coexistence of quasivibrational, quasirotational, and clustering phenomena.     

Properties of electromagnetic transitions from high-spin states in94Mo

The multipole mixing ratios of transitions from 6⁺ and 8⁺ states in⁹⁴Mo, following the decay of⁹⁴Tc, have been measured by means ofγγ angular correlations. The spin of the 2423.4 keV state, being important for the interpretation ofγ cascades feeding this level, has been firmly established as 6⁺ by a method in which the angular correlation data are utilized in a non-conventional way. Furthermore, properties of electromagnetic transitions in⁹⁴Mo have been calculated in the shell model framework and are compared with the corresponding experimental quantities.     

Correspondence between phenomenological and IBM-1 models of even isotopes of Yb

Energy levels and the reduced probability of E2–transitions for ytterbium isotopes with proton number Z=70 and neutron numbers between 100 and 106 have been calculated through phenomenological(Ph M)and interacting boson(IBM-1)models.The predicted low-lying levels(energies,spins and parities)and the reduced probability for E2–transitions results are reasonably consistent with the available experimental data.The predicted low-lying levels(gr–,β1–andγ1–band)produced in the Ph M are in good agreement with the experimental data compared with those by IBM-1 for all nuclei of interest.In addition,the phenomenological model was successful in predicting theβ2–,β3–,β4–,γ+2–and 1+–band while it was a failure with IBM-1.Also,the 3–band is predicted by the IBM-1 model for172Yb and174Yb nuclei.All calculations are compared with the available experimental data.     

Nuclear structure effects on the neutrinoless double beta decay

The nuclear matrix elements of the 0ν ββ decay of⁷⁶Ge,⁸²Se,¹⁰⁰Mo,^128,130Te,¹³⁶Xe and¹⁵⁰Nd are calculated in the proton-neutron quasiparticle RPA with theG-matrix of the Paris potential. It is shown that the matrix elements are not sensitive to details of nuclear structure, in contrast to the 2ν ββ decay. We investigate effects of ground-state correlations and those of short-range correlations on the suppression of the nuclear matrix elements. We also discuss effective values of the neutrino mass which are deduced from experimental 0ν ββ decay half-lives.     

E0 transition and coupling between quadrupole and pairing-vibrational modes

Using a theory of mode-mode coupling between the two-phonon 0⁺ mode and the pairing-vibrational mode, we have extensively investigated the first excited 0⁺(0₂²) states in spherical and transitional nuclei. The results tell us that the 0₂⁺ states in a wide range of nuclei are strongly mixed states of both the modes. By making use of these results, the matrix elements for the E0 transitions from the 0₂⁺ states to the ground states are calculated for the Zn, Ge, Se, Kr, Sr, Zr, Mo, Ru, Pd, Cd and Sn isotopes. For some of the Cd and Sn isotopes, the matrix elements between the 0₂⁺ and 0₂⁺ states are also obtained. These numerical calculations make a rather good fit to the E0 experiments.     

The nilsson-potential parameters for neutrons at A≃-100 and new deformation values for103Mo and105Mo

The half-lives of the first excited levels in odd-neutron nuclei¹⁰³Mo and¹⁰⁵Mo have been measured. From these data, values of the deformation parameter of?=0.31±0.05 and 0.29±0.06 for¹⁰³Mo and¹⁰⁵Mo, respectively, have been deduced assuming prolate spheroidal shapes. The present results in combination with previously determined properties of the ground-state bands of these nuclei are used to determineμ, the magnitude of the coefficient of the 1² term, in the Nilsson Hamiltonian, for the new region of deformation atA～-100.     

Deformation and shape coexistence in medium mass nuclei

Emerging evidence for deformed structures in medium mass nuclei is reviewed. Included in this review are both nuclei that are ground state symmetric rotors and vibrational nuclei where there are deformed structures at excited energies (shape coexistence). For the first time. Nilsson configurations in odd-odd nuclei within the region of deformation are identified. Shape coexistence in nuclei that abut the medium mass region of deformation is also examined. Recent establishment of a four-particle, four-hole intruder band in the doublesubshell closure nucleus⁹⁶Zr₅₆ is presented and its relation to the Nuclear Vibron Model is discussed. Special attention is given to the N=59 nuclei where new data have led to the reanalysis of⁹⁷Sr and⁹⁹Zr and the presence of the [404 9/2] hole intruder state as isomers in these nuclei. The low energy levels of the N=59 nuclei from Z=38 to 50 are compared with recent quadrupole-phonon model calculations that can describe their transition from near-rotational to single closed shell nuclei. The odd-odd N=59 nuclei are discussed in the context of coexisting shape isomers based on the (p[303 5/2]n[404 9/2])2^– configuration. Ongoing in-beam (t.p conversion-electron) multiparameter measurements that have led to the determination of monopole matrix elements for even-even₄₂Mo nuclei are presented, and these are compared with initial estimates using lBA-2 calculations that allow mixing of normal and cross subshell excitations. Lastly, evidence for the neutron-proton³S₁ force's influence on the level structure of these nuclei is discussed within the context of recent quadrupole-phonon model calculations.Work supported by USDOE contract Nr.W-7405-Eng-48 and NATO Grant Nr.RGO565/82.     

Role of thermal and photobeta decays in processes of nucleosynthesis of problematic p nuclei of 113In, 115Sn, 92,94Mo, and 96,98Ru in massive stars

The temperature dependence of the rates of ¹¹³Cd →¹¹³In, ¹¹⁵In →¹¹⁵Sn, ⁹²Zr→⁹²Nb →⁹²Mo, ⁹⁴Zr→⁹⁴Nb →⁹⁴Mo, ⁹⁶Mo →⁹⁶Tc→⁹⁶Ru, and ⁹⁸Mo→⁹⁸Tc→⁹⁸Ru thermal beta transitions was studied at temperatures of massive-star matter in the range of 1 × 10⁸–6 × 10⁹ K. These decays are the possible channel of synthesis of the p nuclei of ¹¹³In, ¹¹⁵Sn, ⁹²,⁹⁴Mo, and ⁹⁶,⁹⁸Ru. The abundances of these nuclei present a challenge for models that study the explosivemechanism of synthesis. The contribution of photobeta decay to the synthesis of the aforementioned p nuclei was estimated. It was shown that the channel of thermal beta decay for ¹¹³In, ¹¹⁵Sn, ⁹⁴Mo, and ⁹⁸Ru p nuclei and the channel of photobeta decay for the ⁹⁶Mo p nucleus could be efficient at the high-temperature quasiequilibrium stage of massive-star evolution.     

Construction of microscopic boson states and their relevance for IBM-2

We investigate four methods for the construction of collective shell model states which may be mapped onto boson states of the IBM-2. These methods use, as building blocks for the wave functions, particle-particle pair operators, particle-hole operators, pair operators with seniority projection and energy-weighted quadrupole operators. It is demonstrated that one obtains stronger collectivity with the energy-weighted quadrupole operator than with the other methods.On the basis of a comparison of calculated and empirical IBM-2 interaction parameters we can rule out the seniority projection method. This implies that particle-particle and particle-hole approaches difler.The ratios between quadrupole matrix elements of the microscopic boson states appear to be similar to the IBM predictions. For states corresponding to those with two d-bosons coupled to J = 0 there is a smaller quadrupole matrix element when subshells with small angular momenta dominate near the Fermi level. Especially for this type of states the collective quadrupole space will be larger than represented in the IBM, however, which may compensate the smaller proton-neutron quadrupole coupling.The calculated bare quadrupole interaction between like bosons is found to be weak.     

Comparing some predictions between Davidson-like potentials and interacting boson model: <Emphasis Type="Italic">X</Emphasis>(5) behavior of even-even <Superscript>128–140</Superscript>Nd isotopes

We denote that the level scheme of the transitional nuclei ^128–140Nd also presents the characteristic X(5) pattern, not only in the ground-state band, but also in some low-lying bands. An adequate point of the model leading to the X(5) symmetry is therefore confirmed. We also carry out calculations of positive-parity states of even-mass Nd nuclei within the framework of the interacting-boson model, and then the calculated energy values are compared with the experimental data along with the Davidson potential predictions. By comparing transitional behavior in the Nd nuclei with the predictions of an X(5) critical symmetry, we investigate an achievable degree of agreement between the predictions of the model leading to this symmetry and the interacting-boson model (IBM-1 and IBM-2). They agree well with the predictions of the experimental data. The text was submitted by the authors in English.     

Theβ + decay of the new isotope86Mo and the first observation of86m Nb

Theβ ⁺ decay of⁸⁶Mo has been firstly investigated by means ofβγ spectroscopy. The⁸⁶Mo nuclei were produced by fusion-evaporation reactions of⁵⁴ Fe (³⁵Cl, 1 p2n) and⁵⁸Ni (³²S,2p 2n) at beam energies of 103 and 120 MeV, respectively. Threeγ rays of 47.3, 49.8 and 187.0 keV were unambiguously identified to follow theβ ⁺ decay of⁸⁶Mo by results ofXγ andβγ coincidence and cross-bombardment. A half life and a maximumβ ⁺-ray energy of⁸⁶Mo were determined to be 19.6±1.1 s and 3.9±0.4 MeV, respectively. A decay scheme of⁸⁶Mo is proposed in this article. Furthermore, a decay of⁸⁶Nb has been studied using the same combinations of projectiles and targets, and a newβ-decaying isomer^86m Nb was observed with a half life of 56.3±8.3 s.     

Improved description of M1 transitions by special hamiltonians of the proton-neutron interacting boson model

The proton-neutron interacting boson model (IBM-2) describes energies, B(E2) and B(M1) values of nuclei. In order to reduce the great number of free IBM-2 parameters two special IBM-2 hamiltonians are proposed which allow a decoupling of the energy and B(E2) fit from the determination of the B(M1) values and the energy of the lowest mixed symmetry 1⁺ state. This property allows a simple fit procedure of the IBM-2 parameters in both cases.     

The 0+ → 0+ positron double- β decay with emission of two neutrinos in the nuclei 96Ru, 102Pd, 106Cd and 108Cd

Theoretical results for two neutrinos in the nuclei ⁹⁶Ru, ¹⁰²Pd, ¹⁰⁶Cd and ¹⁰⁸Cd are presented. The study employs the Hartree-Fock-Bogoliubov model to obtain the wave functions of the parent and daughter nuclei, in conjunction with the summation method to estimate the double-beta decay nuclear matrix elements. The reliability of the intrinsic wave functions of ^{96, 102}Ru, ⁹⁶Mo, ^{102, 106, 108}Pd and ^{106, 108}Cd nuclei is tested by comparing the theoretically calculated spectroscopic properties with the available experimental data. The calculated half-lives T_1/2^2ν of ⁹⁶Ru, ¹⁰²Pd, ¹⁰⁶Cd and ¹⁰⁸Cd nuclei for 2ν β⁺β⁺, 2ν β⁺EC and 2ν ECEC modes are presented. The effect of deformation on the nuclear transition matrix element M_2ν is also studied.     

Multi-band spectra of odd and even nuclei of the s-d shell

The energy levels of^{21, 23}Na,^{22, 23}Ne,^{24, 28}Mg and^{25, 29}Al are obtained by mixing various bands using the projected deformed Hartree-Fock (DHF) method. Solutions having minimum energies are found to be prolate for all the nuclei considered here. Higher bands are obtained either by considering particle-hole excitations or oblate solutions. These various bands are mixed using the projection method and care has been taken to orthogonalize the bands. The interactions used in this study are those given by Kuo, Preedom-Wildenthal (PW) and WHMK interactions. The last one seems to give good results for most of the nuclei considered here. Not only are the lowest bands well-reproduced but the second lowest bands agree reasonably well in most nuclei. The third lowest ones obtained in some nuclei are not yet observed as complete bands. However, K obtained for the third band seems to be correct. A comparison with shell model calculations—which are numerically exhausting—shows similar results for the lowest band. However, the agreement of the second band varies from nucleus to nucleus. A comparison between matrix elements of the interactions is made to analyze the results.     

Nuclear level structure of99Tc

The gamma rays of⁹⁹Tc excited through negatron decay of⁹⁹Mo have been studied by internal conversion spectroscopy, using a high resolution double focusing beta-ray spectrometer. Conversion electrons were observed for all transitions reported before. In addition a new gamma ray of energy 989.37±1.02 keV could be identified and ascribed for the first time to the decay of⁹⁹Mo. Gamma-ray energies have been determined with high precision. Multipolarity data, obtained from the measurements of absolute or ratio of conversion coefficients of gamma rays, were utilized for assigning possible spins and parities to the levels of⁹⁹Tc. From our present data combined with other studies spins and parities; 7/2+, 1/2?, 5/2+, 3/2?, 3/2+ and 5/2? have been given to the 140, 142, 181, 514, 922 and 1131 keV levels respectively. The experimental level scheme is discussed in terms of theoretical predictions.     

Nuclear resonance fluorescence in94Mo,95Mo and96Mo

Using gaseous sources of Tc₂O₇ containing the radioactive isotopes⁹⁴Tc,⁹⁵Tc and⁹⁶Tc, levels at 871.0keV (⁹⁴Mo), 765.8, 820.6, 947.8, 1074.0keV (⁹⁵Mo) and 778.3keV (⁹⁶Mo) have been excited. From the effective cross sections for nuclear resonance scattering and from the lifetimes of the 947.8, 1074.0 and 778.3keV levels known from Coulomb excitation experiments the profiles of theγ-lines have been determined. A broadening of theγ-lines due to Coulomb explosion of the molecules has been observed. Making use of the line profiles, lifetimes ofΤ=(6.4±1.0) ps andΤ=(0.90 ± 0.20) ps have been determined for the 765.8 and 820.6keV levels, respectively. The angular distribution of the resonantly scattered radiation yields an amplitude ratioδ for the mixed M1 E2 765.8keV transition ofδ=0.14 _?0.009 ^+0.08 . TheB(E2) from a Coulomb excitation experiment and the lifetimeΤ from the present experiment yield ¦δ¦=0.07±0.01 for the 820.6keV transition.