Muon-capture rates and their relation with the double-beta decay

We discuss the non-radiative μ ⁻ capture (i.e. ordinary muon capture, OMC) in light nuclei in terms of the nuclear shell model, and in the medium-and heavy-mass nuclei in terms of the quasiparticle random-phase approximation. A new probe of the double-beta-decay matrix elements, namely the use of the OMC to states of the intermediate nucleus of the double beta decay, is also addressed. Presented by J. Suhonen at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Theoretical LSP detection rates for dark-matter detectors

Low-energy structure of the dark-matter detector nuclei ⁷¹Ga, ⁷³Ge and ¹²⁷I has been studied by using the nuclear shell model. The calculations have been done in realistic model spaces by using renormalized microscopic two-body interactions. The resulting ground states have been used to calculate theoretical predictions for detection rates of the lightest supersymmetric particle (LSP) in experiments studying elastic scattering of the LSP’s from atomic nuclei. Presented by T.S. Kosmas at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Symmetry violations in nuclear Hamiltonians and their consequences for electroweak decays

We discuss the results of the treatment of nuclear Hamiltonians in terms of collective and intrinsic variables. The BRST method is adapted to identify spurious and physical sectors of the wave functions and operators. Counterterms are added to the Hamiltonian to enforce the symmetries broken by the single-particle field and/or by the residual two-body interactions. We focus on the study of Fermi and Gamow-Teller transitions, with reference to the nuclear double-beta-decay processes, and on the study of vector operators (λ^π = 1^?) with reference to (μ, e^?) conversion processes. We address the following aspects of the problem: (a) Isospin symmetry and the calculation of 0₊ and 1⁺ states; sensitivity of the Fermi and Gamow-Teller response in double-beta-decay processes; (b) Restoration of the translational and Galilean invariance of the nuclear Hamiltonians and the calculation of I^π = 1^? states; sensitivity of the nuclear response to the spurious center-of-mass motion and μ-electron lepton-flavor-violation processes.     

Intrinsic frame inverse mass tensor as a function of <Emphasis Type="Italic">β</Emphasis> and <Emphasis Type="Italic">γ</Emphasis> in the Bohr Hamiltonian

Analytical expressions are derived for the components of the intrinsic frame inverse mass tensor of the Bohr Hamiltonian. These expressions contain parameters which are determined by the experimental data on the B(E2)’s and the excitation energies of the low-lying collective states. It is shown that the nondiagonal component of the intrinsic frame mass tensor has a small effect on the collective motion. It is shown also that the values of the B _ββ , B _γγ and the rotational mass coefficientB ₁ differ in the well-deformed nuclei by factor 3 or more.     

Microscopic structure of <Superscript>126</Superscript>Ba in IBM terms

The yrast band of the nonaxially deformed ¹²⁶Ba nucleus is described by the Hamiltonian of the interaction boson model. Its parameters are calculated on the basis of a microscopic theory within a spherical mean field, and residual interactions that include pairing and multipole factorized forces. Each state of the yrast band is considered independently of others, allowing us to study variations in the superfluid properties of the nucleus and the quasiparticle structure of collective D phonons with spin. The calculations are performed in an expanded configuration space that includes the collective D phonon states, and noncollective states in which an additional phonon of positive parity whose spin assumes values of 0 to 6 is present along with the D phonons. It is shown that the collective Hamiltonian parameters cannot be reproduced without considering the effect of the noncollective states.     

Dooble beta decay: Operator expasion method revisited

The Operator Expansion Method (OEM) for the calculation of two-neutrino double beta decay (2ν2β-decay) is reconsidered. The assumed two-body Hamiltonian, in contrast to the ones considered previously, allows a consistent derivation of the OEM transition operators. The OEM is combined with the renormalized proton-neutron QRPA (pn-RQRPA) ground state wave functions and the 2ν2β-decay of⁷⁶Ge is calculated. The influence and relative importance of the central, tensor and Coulomb interactions are investigated. We have found that the strong suppression of the nuclear matrix elementM _GT has its origin in the choice of the pn-RQRPA ground state wave functions of the initial and final nuclei. Presented by M. Veselsky at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Two-neutrino double beta decay to excited states

Both doubleβ ⁻ and doubleβ ⁺/EC decay transitions to excited final states in the two-neutrino mode are discussed, their gross properties reviewed and a compilation of recent calculations presented. A brief presentation of the involved nuclear models is given. The close connection between the single and double beta decays is discussed. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Considering collective degrees of freedom in the β decay of odd nuclei

The β decay of around 30 odd nuclei was calculated within the dynamic collective model using expressions for the reduced matrix elements of the weak-interaction Hamiltonian for U-type and V-type β decay obtained earlier by the authors. All of the many-phonon states of the yrast band of an even-even core contributing to the formation of the excited states of nuclei were taken into account. For β transitions with an intensity of >1%, the calculated logft values differ from the experimental values by no more than 0.2.     

Operator expansion method and beyond

Nuclear structure problems ofββ decay are discussed, focusing on methods to deal with a number of nuclear intermediate states, the operator expansion method and the resolvent operator expansion based on Lanczos algorithm, and on extensions of quasiparticle RPA toward a self-consistent formulation. Also, preliminary results are shown for electron-inducedββ transitions which might be feasible for investigations of second-order weak processes. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. Numerical calculations were performed by using the VP2100 computer system at Institute for Nuclear Study, University of Tokyo.     

Shape mixing dynamics in the low-lying states of proton-rich Kr isotopes

We study the oblate–prolate shape mixing in the low-lying states of proton-rich Kr isotopes using the five-dimensional quadrupole collective Hamiltonian. The collective Hamiltonian is derived microscopically by means of the CHFB (constrained Hartree–Fock–Bogoliubov) + Local QRPA (quasiparticle random phase approximation) method, which we have developed recently on the basis of the adiabatic self-consistent collective coordinate method. The results of the numerical calculation show the importance of large-amplitude collective vibrations in the triaxial shape degree of freedom and rotational effects on the oblate–prolate shape mixing dynamics in the low-lying states of these isotopes.     

Model with uniquely deducible parameters for the combined analysis of two resonating vibrational states. Anharmonic resonances in molecules of asymmetric-gyroscope type

A model of an effective Hamiltonian with parameters that are uniquely deducible from the spectrum for the combined analysis of the rotational structure of two resonating vibrational states is proposed and validated. Anharmonic resonances in molecules of asymmetric-gyroscope type are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 108–112, February, 1982.     

Neutron-proton pairing and double-beta decay in algebraic models

Nuclear models based on Lie algebras provide insight into collective phenomena. Here neutron-proton pairing, which plays an important role in double beta decay, is discussed in two such models, one based on SO(5) and the second on SO(8). The latter model is used to test the accuracy of the Quasiparticle Random Phase Approximation and improvements to it. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. This work was supported in part by the U.S. Department of Energy under Grant DE-FG02-97ER41019.     

pn-QRPA and higher-order approximations

The proton-neutron Quasi-particle Random Phase Approximation (pn-QRPA) is reviewed and higher-order approximations discussed with reference to the beta decay physics. The approach is fully developed in a boson formalism. Working within a schematic model, we first illustrate a fermion-boson mapping procedure and apply it to construct boson images of the fermion Hamiltonian at different levels of approximation. The quality of these images is tested through a comparison between approximate and exact spectra. Standard QRPA equations are derived in correspondence with the quasi-boson limit of the boson Hamiltonian. The use of higher-order Hamiltonians is seen to improve considerably the stability of the approximate solutions. The mapping procedure is also applied to Fermi beta operators and transition amplitudes are discussed. The range of applicability of the QRPA formalism is examined. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Calculation of double beta decay matrix elements: Third day moderator’s report

The talks presented on the third day of theWorkshop on Calculation of Double Beta Decay Matrix Elements and the ensuing round table discussion are summarized. Presented by the moderator at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Calculation of double beta decay matrix elements: A status report

The current status of efforts to calculate double beta decay matrix elements is summarized. Particular focus is put on the two most popular theoretical approaches in use for such calculations, the nuclear shell model and the proton-neutron Quasi Particle Random Phase Approximation. Some brief comments regarding double beta decay to excited states are also made. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. My participation in the workshop was supported in part by the National Science Foundation under grant # PHY-9600445.     

Electromagnetic Few-Body Response Functions with the Lorentz IntegralTransform Method

 The inclusive reactions and are studied with the Lorentz integral transform method. The method allows the inclusion of the full final-state interaction without explicit knowledge of the continuum states. Features of the inversion procedure are discussed in this work. The technique for the calculation of the matrix elements of the Hamiltonian is described. The total photoabsorption cross section of ³H is calculated with a realistic super-soft-core NN force. In the threshold region the cross section is rather similar to that obtained with central forces only, while in the peak the realistic NN interaction leads to more strength. For the longitudinal (e, e′) response we extend our calculation with a semirealistic force to MeV/c. Rather good agreement with experimental data is found. The accuracy of the quasielastic response approximation is discussed. Received August 15, 1998; revised February 22, 1999; accepted for publication March 9, 1999