Quasi-elastic neutrino-nucleus reactions

The quasi-elastic contribution of the nuclear inclusive electron scattering model developed in [A. Gil, J. Nieves, and E. Oset: Nucl. Phys. A 627 (1997) 543] is extended to the study of electroweak charged current induced nuclear reactions at intermediate energies of interest for future neutrino oscillation experiments. The model accounts for long-range nuclear (RPA) correlations, final state interaction and Coulomb corrections. RPA correlations are shown to play a crucial role in the whole range of neutrino energies, up to 500 MeV, studied in this work. Predictions for inclusive muon capture for different nuclei, and for the reactions ¹²C(ν _μ , μ ₋)X and ¹²C(ν _e, e⁻)X near threshold are also given. Presented by M. Valverde at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

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.     

Uncertainties in the 0νββ-decay nuclear matrix elements

The nuclear matrix elements M ^0ν of the neutrinoless double-beta decay (0νβ β) of most nuclei with known 2νββ-decay rates are systematically evaluated using the Quasiparticle Random Phase Approximation (QRPA) and Renormalized QRPA (RQRPA). The experimental 2νβ β-decay rate is used to adjust the most relevant parameter, the strength of the particle-particle interaction. With such procedure the M ^0ν values become essentially independent of single-particle basis size, the axial vector quenching factor, etc. Theoretical arguments in favor of the adopted way of determining the interaction parameters are presented. It is suggested that most of the spread among the published M ^0ν ’s can be ascribed to the choices of implicit and explicit parameters, inherent to the QRPA method. Presented by V. Rodin at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

μCR42β: Muon capture rates for double-beta decay

Gamma-rays following nuclear capture of negative muons in enriched ⁴⁸Ti, ⁷⁶Se, ¹⁰⁶Cd, as well as natural Se and Cd targets were measured. Time evolution of several gamma-lines allowed to deduce the total μ-capture rates in Ti, Se and Cd isotopes, which are compared to the Primakoff estimate. The data on the partial μ-capture rates will be used for more precise calculation of the 2β-NMEs of ⁴⁸Ca, ⁷⁶Se and ¹⁰⁶Cd. Presented by V. Egorov at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005. Partly supported by the Russian Foundation for Basic Research (grant 06-02-16587).     

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.     

A study of neutrinoless double-beta decay in the framework of QRPA

A study concerning the valence space dependence of neutrinoless doubleβ ⁻ decay observables is performed for several nuclei in the framework of QRPA using the multiple commutator method (MCM). Calculations and comparison to earlier results show that at least for the ground state to ground state transition the dependence is much weaker than in the two neutrino doubleβ ⁻ decay. It is still a difficult task to extract the parameters of the neutrinoless doubleβ ⁻ decay since the half-life expression contains products of the parameters 〈m _ν 〉 〈η〉 and 〈λ〉. Presented by M. Aunola 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.     

The role of the continuum and the spurious 1− transitions in incoherent μ −−e− conversion rate calculations

By using the Continuum RPA (CRPA) method, the incoherent transition strength of the exotic μ ⁻−e⁻ conversion in nuclei is investigated. The question whether excited nuclear states lying high in the continuum give an important contribution to the incoherent rate is addressed. Results for ⁴⁰Ca are compared with those obtained previously for ²⁰⁸Pb. For both nuclei we then investigate in detail the admixture of spurious components in the rate coming from 1⁻ excitations, within the self-consistent CRPA with Skyrme interactions as well as within a less consistent version. We employ and compare two methods for removing the spurious strength: the use of effective operators, as done in a previous work for ²⁰⁸Pb, or simply the exclusion of the spurious state appearing close to zero energy. In all cases, the correction achieved is quite large. Presented by P. Papakonstantinou at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Issues and status of “basic divertor and SOL physics” from papers and discussions

⁴⁸Ca, the lightest double beta decay candidate, has been until now the only one simple enough to be treated exactly in the nuclear shell model. Thus, theββ(2ν) half-life measurement, reported here, provides a unique test of the nuclear physics involved in theββ matrix element calculation. Enriched⁴⁸Ca sources of two different thicknesses have been exposed in a time projection chamber, and yieldT ₁ ^2/2ν =(4.3 _−1.1 ^+2.4 [stat.] ± 1.4[syst.]) × 10¹⁹ years, compatible with the shell model calculations. The consequences of this result for the shell model calculation of theββ(2ν) rate are briefly discussed. Presented by P. Vogel at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. This work was funded by the US Department of Energy under contracts DE-FG03-01ER40679 and DE-FG03-88ER40397.     

Nuclear responses for double-beta decays by hadron, photon, and neutrino probes and MOON experiment

Neutrino-less double-beta decays (0νββ) with the mass sensitivities of the solar and atmospheric ν masses are of great interest for studying the Majorana nature of neutrinos and the absolute mass spectrum as suggested by recent ν oscillation experiments. Here nuclear responses (nuclear matrix elements) for 0νββ are crucial. They are well studied experimentally by using charge-exchange, photo-nuclear and neutrino reactions. MOON(Mo Observatory Of Neutrinos) is a high sensitivity 0νβ β experiment with the mass sensitivity of an order of 30 meV. Experimental studies of the nuclear responses and the present status of MOON are briefly discussed. Presented by the author at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Extension of the renormalized quasiparticle random phase approximation

The quasiparticle random phase approximation is extended in order to restore of the Pauli principle beyond the renormalized approach by treating the so-called scattering terms in the QRPA phonon operators. It has been shown that this new framework can be described in a case of a single nuclear shell occupied by both protons and neutrons in terms of the QRPA(14,3) algebra. An application of the formalism to the double beta decay of calcium⁴⁸Ca is discussed to some extent. Presented by W.A. Kamiński at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. This work has been supported in part by the State Committee for Scientific Research (Poland), Contract No. 2 P03B 189 09.     

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.     

Study of low-lying collective states using a Microscopic Anharmonic Vibrator Approach

Anharmonic features of the low-lying collective states in the ruthenium isotopes have been investigated systematically by using the Microscopic Anharmonic Vibrator Approach (MAVA). MAVA is based on a realistic microscopic G-matrix Hamiltonian, only slightly renormalized in the adopted large realistic single-particle spaces. This Hamiltonian is used to derive equations of motion for the mixing of one-and two-phonon degrees of freedom starting from collective phonons of the quasiparticle random-phase approximation. Interesting applications to analysis of double-beta-decay rates to excited collective states are foreseen. Presented by J. Suhonen at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

Counting nucleon pairs

A simple method is used to count average numbers of different kinds of nucleon pairs within the Sp(4) seniority-like model which describesT=1 pairing modes of protons and neutrons. These numbers as well as the total strengths of pair-transfer processes clearly indicate that pn configurations are preferred in theN _p=N _n odd-odd systems. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Beta decays and muon capture as probes of ββ matrix elements

Detection of the neutrinoless double-beta decay is essential in probing physics beyond the standard model of electroweak and strong interactions. At the moment there is a considerable uncertainty associated with the calculation of the involved nuclear matrix elements. This uncertainty can be diminished by suitably chosen nuclear probes, like beta decays and nuclear muon capture. The related experiments are urgently called for. Presented by J. Suhonen at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’05), Corfu, Greece, September 26–29, 2005.     

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.