Influence of an enlargement of the model space on number projected quasiparticle calculations

Results of number projected quasiparticle calculations for Sn isotopes in large and in small model spaces are compared when the force strengths and single-particle energies are determined consistently within each model space. When extending the model space, one observes that the model parameters extracted from the odd nuclei become more satisfactory. For even nuclei the collective states are not lowered in energy although electromagnetic transition rates increase considerably. Spectroscopic factors for one-nucleon transfer reactions change noticeably only for shells close to the Fermi level. Two-nucleon transfer cross-sections are strongly increased for ground state to ground state transitions only. We criticize a usual approximation formula for theL=0 two-nucleon transfer cross-section.     

Influence of an enlargement of the model space on number projected quasiparticle calculations

Results of number projected quasiparticle calculations for Sn isotopes in large and in small model spaces are compared when the force strengths and single-particle energies are determined consistently within each model space. When extending the model space, one observes that the model parameters extracted from the odd nuclei become more satisfactory. For even nuclei the collective states are not lowered in energy although electromagnetic transition rates increase considerably. Spectroscopic factors for one-nucleon transfer reactions change noticeably only for shells close to the Fermi level. Two-nucleon transfer cross-sections are strongly increased for ground state to ground state transitions only. We criticize a usual approximation formula for theL=0 two-nucleon transfer cross-section.     

New BCS and renormalized QRPA formalism with application to double beta decay

A new analysis of the renormalized proton–neutron quasiparticle random phase approximation based on simultaneous recalculation of the one-body density matrix and the pairing tensor has been used to study the double beta decay. We demonstrated that inclusion of the quasiparticle correlations at the BCS level reduces ground state correlations in the particle–particle channel of the proton–neutron interaction. We also simplified the RQRPA equations significantly obtaining a low-dimensioned set of linear equations for the quasiparticle densities. The formalism was applied to the double beta decay of ⁷⁶Ge. Received: 4 January 1999 / Revised version: 29 March 1999     

Ground state correlations and structure of odd spherical nuclei

It is well known that the Pauli principle plays a substantial role at low energies because the phonon operators are not ideal boson operators. Calculating the exact commutators between the quasiparticle and phonon operators, one can take into account the Pauli principle corrections. Besides, the ground state correlations due to the quasiparticle interaction in the ground state influence the single-particle fragmentation as well. In this paper, we generalize the basic equations of the quasiparticle-phonon nuclear model to account for both effects mentioned. As an illustration of our approach, calculations on the structure of the low-lying states in ¹³³Ba have been performed. The text was submitted by the authors in English.     

Looking for an Optimal Ground State Within Quasiparticle Random Phase Approximation

A new ansatz for the correlated ground state of the many-nucleon system is proposed which results in obtaining a modified Quasiparticle Random Phase Approximation (QRPA). An additional degree of freedom is introduced which allows to determine variationally the ground state simultaneously with solving the QRPA equations. This new approach, QRPA with an optimal ground state, is studied within the proton-neutron Lipkin model. New solutions have been found, in the range of the interaction strength where the standard QRPA formalism does not work. A relation between one of them and the solution obtained within a semi-classical approach is established. A detailed study of the expectation value of the quasiparticle number operator in the ground state and the transition amplitude for the two-neutrino double beta Fermi decay, is also presented.     

A large Hilbert space QRPA and RQRPA calculation of neutrinoless double beta decay

A large Hilbert space is used for the calculation of the nuclear matrix elements governing the light neutrino mass mediated mode of neutrinoless double beta decay (Ovββ-decay) of⁷⁶ Ge,¹⁰⁰ Mo,¹¹⁶ Cd,¹²⁸ Te, and¹³⁶ Xe within the proton-neutron quasiparticle random phase approximation (pn-QRPA) and the renormalized QRPA with proton-neutron pairing (full-RQRPA) methods. We have found that the nuclear matrix elements obtained with the standard pn-QRPA for several nuclear transitions are extremely sensitive to the renormalization of the particle-particle component of the residual interaction of the nuclear hamiltonian. Therefore the standard pn-QRPA does not guarantee the necessary accuracy to allow us to extract a reliable limit on the effective neutrino mass. This behavior already known from the calculation of the two-neutrino double beta decay matrix elements, manifests itself in the neutrinoless double-beta decay but only if a large model space is used. The full-RQRPA, which takes into account proton-neutron pairing and considers the Pauli principle in an approximate way, offers a stable solution in the physically acceptable region of the particle-particle strength. In this way more accurate values on the effective neutrino mass have been deduced from the experimental lower limits of the half-lifes of neutrinoless double beta decay.     

Systematic study of the single-state dominance in 2νββ decay transitions

The single-state-dominance hypothesis (SSDH) states that the decay rates of the two-neutrino double-beta decay are governed by a virtual two-step transition connecting the initial and final ground states through the first 1⁺ state, 1_l⁺, of the intermediate odd-odd nucleus, for those odd-odd nuclei where the 1_l⁺ state is the ground state. To investigate the validity of the SSDH we have performed a systematical theoretical analysis of all known double-beta-decay transitions where the SSDH conditions are fulfilled. the calculations are based on the quasiparticle random-phase approximation (QRPA) and the results have been obtained by using realistic single-particle bases and realistic interactions. We have studied the double β⁻ decays of ¹⁰⁰Mo, ¹¹⁰Pd, ¹¹⁴Cd, ¹¹⁶Cd and ¹²⁸Te and the double electron-capture transitions in ¹⁰⁶Cd and ¹³⁶Ce. The analysis shows that the SSDH is realized either through a true dominance of the first intermediate 1⁺ state or by cancellations among the contributions of higher lying 1⁺ states of the intermediate nucleus.     

Influence of pairing on the nuclear matrix elements of the neutrinoless betabeta decays

We study in this Letter the neutrinoless double beta decay nuclear matrix elements (NME's) in the framework of the interacting shell model. We analyze them in terms of the total angular momentum of the decaying neutron pair and as a function of the seniority truncations in the nuclear wave functions. This point of view turns out to be very adequate to gauge the accuracy of the NME's predicted by different nuclear models. In addition, it gives back the protagonist role in this process to the pairing interaction, the one which is responsible for the very existence of double beta decay emitters. We show that low seniority approximations, comparable to those implicit in the quasiparticle RPA in a spherical basis, tend to overestimate the NME's in several decays.     

超重核的球形和变形壳结构

应用宏观 微观模型系统研究了超重核的形状和结构性质.其中,宏观能是由基于核子密度泛函的连续介质模型计算得到.计算结果很好地再现了超重核的结合能、α衰变能和寿命的实验数据.对单粒子能级的计算和分析表明超重核的壳结构是形变和同位旋相关的.位能曲面的计算结果显示,与其它区域的核相比,超重核的形状不易变化. The structure of superheavy nuclei has been studied by using the macroscopic-microscopic model. The macroscopic energy was calculated with the continuous medium model in which the energy is expressed as a functional of nucleon densities. The deformations and structures of superheavy nuclei were investigated systematically. Calculations reproduce well the available data of experimental α decay energies and half-lifes. The investigation of single-particle levels shows that the shell structure is deformed a...     

Non-collapsing QRPA for neutrinoless double beta decay

The standard quasiparticle random phase approximation(QRPA) is widely used to describe the neutrinoless double beta decay process. Although it has been quite successful in many cases of interest, it has some shortcomings. The most important one is that its solutions collapse for physical values of the particle-particle strength. We shall show that modifications can be done which can extend the validity of this standard QRPA beyond the point of collapse. Such modifications are: The introduction of proton-neutron pairing, the inclusion of the Pauli principle and the extension of the Hilbert space. If all these modifications are introduced into the standard QRPA then the collapse does not occur for physical values of the particle-particle strengths. Thus, one might be able to extract more accurate values on the effective neutrino mass by using the best available experimental limits on the half life of neutrinoless double beta decay. Presented by G. Pantis at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Nature of quasiparticles in itinerant correlated electron systems with geometrical frustration

Using the exact diagonalization technique, we study the effect of geometrical frustration on single-particle, spin and charge excitations in the Hubbard model in a metallic state close to half-filling. As the frustration increases, the magnetic order in the system is suppressed and the peak in the single-particle spectrum becomes sharper, indicating enhanced quasiparticle formation. Careful examination of spin and charge excitations shows that increasing frustration also leads to the merge of spin and charge excitation energies to that of the single-particle excitation. This is consistent with a Fermi liquid having well-defined quasiparticles with both spin and charge characteristics. The calculated results show that geometrical frustration plays an important role in defining the nature of quasiparticles in itinerant correlated electron systems.     

Muon capture on nickel and tin isotopes

We calculate total and differential muon capture rates on nickel and tin isotopes ranging from the proton dripline to the neutron dripline. The total rates decrease as the neutron number increases due to the combined effect of gradual blocking of available final-state neutron levels and of decreased phase space. The ordering of single-particle levels determines when blocking becomes important. We show that the total capture rates thereby are sensitive to the evolution of nuclear structure along an isotope chain.Received: 28 January 2003, Revised: 7 March 2003, Published online: 4 June 2003PACS: 24.30.Cz Giant resonances - 23.40.-s Beta decay; double beta decay; electron and muon capture - 23.40.Hc Relation with nuclear matrix elements and nuclear structure     

Spin-flipβ − decay of even-even deformed nuclei110Ru and112Ru

Neutron-rich nuclides¹¹⁰Ru and¹¹²Ru produced in symmetric fission of²³⁸U by 20 MeV protons have been studied at the IGISOL facility by means ofβ-ray,γ-ray and conversion electron spectroscopy. A total of 12 and 6γ-transitions were observed in the decays of¹¹⁰Ru and¹¹²Ru, respectively. Multipolarities were determined for a few transitions. The beta decay half-life was determined to be 11.6±0.6 s for¹¹⁰Ru and 1.75±0.07 s for¹¹²Ru. As a side product, a new value of 2.1±0.3 s for theβ half-life of the¹¹²Rh 1⁺ state was obtained. The decay energy measured with the plastic scintillator was 2.81 ±0.05 MeV for¹¹⁰Ru and 4.52 ±0.08 MeV for¹¹²Ru. The beta decay schemes of¹¹⁰Ru and¹¹²Ru isotopes indicate that the main fraction of their beta strength resides in two 0⁺→1⁺ spin-flip transitions with their logf t values between 4.4 and 4.7. The decay energies and the energies of the 1⁺ GT states are compared with the macroscopic-microscopic model calculations. The observed GT-strengths are discussed in the framework of the deformed single-particle model.     

Neutrino-antineutrino pair emission from thermally excited nuclei in stellar collapse

We examine the rate of neutrino-antineutrino pair emission by hot nuclei in collapsing stellar cores. The rates are calculated assuming that only allowed charge-neutral Gamow-Teller (GT₀) transitions contribute to the decay of thermally excited nuclear states. To obtain the GT₀ transition matrix elements, we employ the quasiparticle random phase approximation extended to finite temperatures within the thermo field dynamics formalism. The decay rates and the energy emission rates are calculated for the sample nuclei ⁵⁶Fe and ⁸²Ge at temperatures relevant to core collapse supernovae.     

Double core hole creation and subsequent Auger decay in NH3 and CH4 molecules

Energies of the hollow molecules CH(4)(2+) and NH(3)(2+) with double vacancies in the 1s shells have been measured using an efficient coincidence technique combined with synchrotron radiation. The energies of these states have been determined accurately by high level electronic structure calculations and can be well understood on the basis of a simple theoretical model. Their major decay pathway, successive Auger emissions, leads first to a new form of triply charged ion with a core hole and two valence vacancies; experimental evidence for such a state is presented with its theoretical interpretation. Preedge 2-hole-1-particle (2h-1p) states at energies below the double core-hole states are located in the same experiments and their decay pathways are also identified.     

A New Mechanism for Low Energy Pion Induced Double Charge Exchange Reaction

Using a method developed in theory of double beta decay[1], we propose a new mechanism, namely the two-nucleon pion absorption-emission mechanism for pion double charge exchange reaction at low energies. The calculations are compared with the experimental data of the angular distribution at 50 MeV and the 0° excitation functions of the DCX reactions on ¹⁴C, ¹⁸O with energies < 130 MeV. It is found that the contribution of this new mechanism is very important at low energies.     

The 208Pb(n,p)208Tl reaction at En = 97 MeV

Double-differential cross sections of the ²⁰⁸Pb(n,p) reaction have been measured at 97 MeV in the angular range 0°–30° for excitation energies up to 40 MeV. The experimental proton spectra have been compared with calculated spectra obtained with a statistical multistep direct reaction theory, in which charge exchange and inelastic response functions are described microscopically in the quasiparticle random phase approximation. The direct parts of the spectra have also been distributed on different multipole components by using a decomposition technique, based on sample angular distributions calculated within the distorted-wave Born approximation.     

Calculation of double beta decay rates and the neutrino mass

Predictions for 2v and 0v double beta decay rates are given for all nuclei with A ⩾ 70, for which double beta decay is energetically allowed. These predictions are based on detailed nuclear structure studies of the beta strength distribution and replace earlier estimates basing mostly on phase space considerations. New and more stringent limits on the Majorana neutrino mass are deduced from existing double beta decay experiments. Since the collective effects arising from spin-isospin as well as quadrupole-quadrupole forces are found to lead to a strong reduction of the nuclear matrix elements for two-neutrino double beta decay, but to have only minor influence on the matrix elements M^0v for the neutrinoless decay mode, the smaller limits for m_v result mainly from the fact that the widely used scaling procedure underestimates the 0_v matrix elements. It is further discussed to what extent interference between different neutrinos affects the obtained mass limits.     

Shell model structures in the N = 46 isotones 86Zr, 87Nb, 88Mo, 89Tc, 90Ru and 91Rh

The known level energies, electromagnetic moments and decay probabilities of high-spin states in the N = 46 isotones ⁸⁶Zr, ⁸⁷Nb, ⁸⁸Mo, ⁸⁹Tc, and ⁹⁰Ru are interpreted within the shell model. The single-particle space was truncated to the p _1/2 and g _9/2 orbits (relative to the ⁸⁸Sr core) and the single-particle energies and empirical two-body matrix elements derived by Gross and Frenkel were used in the calculations. Based on the generally good success of this approach, energies and decay properties of the yrast spectra in ⁹⁰Ru and ⁹¹Rh are predicted. Received: 31 July 2000 / Accepted: 18 December 2000