Fine structure of strength functions for beta decays of atomic nuclei

The β transition strength function S _β(E) is the nuclear excitation energy distribution of moduli squared of the β-decay-type matrix elements. The function S _β(E) determines the characteristics of β decay, the spectra of accompanying radiation, and the probabilities of delayed processes following the β decay. Until recently, tools widely used for experimental investigation of the S _β(E) structure have been total absorption gamma spectrometers and total absorption gamma-ray spectroscopy (TAGS) which could not provide high energy resolution. Development of experimental techniques allows nuclear spectroscopy methods with high energy resolution to be used for studying the fine structure of S _β(E). A thorough investigation of this kind has been carried out for a number of nuclei produced at the YASNAPP-2 facility in Dubna. In this review, studies involving works on measuring the fine structure of S _β(E) in spherical and deformed nuclei are analyzed. Modern nuclear spectroscopy methods made it possible to identify the splitting of peaks from nuclear deformation in S _β(E) for Gamow-Teller (GT) transitions. The resonance nature of S _β(E) for first-forbidden (FF) transitions in both spherical and deformed nuclei is experimentally proven. It is shown that for some nuclear excitation energies, FF transitions can be comparable in intensity with GT transitions. Criteria for verifying the completeness of nuclear decay schemes are considered. The S _β(E) functions obtained by TAGS and by the high-resolution spectroscopy are compared.     

Nuclear β-decay and photoproduction of e + e − pairs in intense electromagnetic fields with a complex configuration

The effect of an intense electromagnetic field formed by the superposition of a constant magnetic field and a laser-type field on nuclear β-decay and on pair production by two g-rays with different polarizations is studied. Time integral representations are obtained for the total probabilities of these processes without restrictions on the strengths of the fields making up the configuration. Despite the different nature of these reactions, in the nonrelativistic limitthese expressions contain similar dependences on the field characteristics and the differences reduce to different power-law singularities in the behavior of the integrands at zero. At low fields, complete asymptotic expansions of the probabilities of these processes, including perturbation theory terms and oscillatory field contributions, are obtained in terms of parameters characterizing the fields. It is shown that the oscillatory corrections can be enhanced owing to the effect of a combination external field. The analysis of the probabilities of the various processes given here in terms of nonlinear functions of the field is illustrated by numerical calculations and graphs. Zh. éksp. Teor. Fiz. 113, 21–42 (January 1998)     

Theory of superfluidity of nuclear matter based on the Fermi-liquid approach

This paper discusses how an electromagnetic field consisting of a superposition of a constant magnetic field and a field of laser type can affect nuclear beta decay. In general it is not assumed that the intensities of the two types of fields are small compared to the characteristic field H _cr*=β ₁ H _cr, where H _cr=m ² c ³/eℏ and the quantity β ₁ depends on the energy liberated in the decay and the configuration of the electromagnetic field. For nonrelativistic decays the quantity β ₁ is found to be of the same order as the maximum kinetic energy of an electron referenced to its rest energy β ₁∼I≪1. It is assumed that the frequency of the wave field satisfies ℏω/mc ²⩽I. The behavior of the probability for the process is studied over a wide range of the fundamental parameters that characterize the fields. Corresponding asymptotic expressions are derived in the “weak”-and “strong”-field regimes. Also discussed are so-called interference corrections to the unperturbed decay probability, which cannot in principle be studied by the methods of perturbation theory. It is shown that the times and distances that are important in generating these contributions exceed the parameters of the unperturbed processes, just as in the case of a plane-wave field previously investigated in detail by Nikishov and Ritus. However, in contrast to the case of a pure wave field, when a system is simultaneously subjected to a constant magnetic field and a wave field, the degree to which these characteristic regions are enlarged can depend not only on the intensities of the electromagnetic fields but also on their rates of change, even in the limit in which the wave field is slowly varying. Zh. éksp. Teor. Fiz. 111, 3–24 (January 1997)     

Gauss law constraints on Debye-Hückel screening

The half-lives are calculated for the β ⁻ decay process for nuclei in the mass range ∼65–75 relevant for the core of a massive star at the late burning stage of stellar evolution and the collapse that leads to supernova explosion. These half-lives and rates are calculated by expressing the β ⁻ Gamow-Teller decay strengths in terms of smoothed bivariate strength densities. These strength densities are constructed in the framework of spectral averaging theory for two-body nuclear Hamiltonian in a large nuclear shell model space. The method has a natural extension to electron captures as well as weak interaction rates for r and rp-processes.      

Giant Gamow-Teller resonance in neutron-rich nuclei

The giant Gamow-Teller resonance and other branches of collective nuclear excitations are described on the basis of the theory of finite Fermi systems. A connection between the Gamow-Teller resonance and Wigner SU(4) symmetry is proven. The beta-decay strength function and processes accompanying the β ⁻ decay of neutron-rich nuclei are described. The effect of the satellites of the Gamow-Teller resonance on the decay properties of neutron-rich nuclei is analyzed.     

Nuclear deformation and the two-neutrino double- β decay in <Superscript>124, 126</Superscript>Xe , <Superscript>128, 130</Superscript>Te , <Superscript>130, 132</Superscript>Ba and <Superscript>150</Superscript>Nd isotopes

The two-neutrino double-beta decay of ^{124, 126}Xe , ^{128, 130}Te , ^{130, 132}Ba and ¹⁵⁰Nd isotopes is studied in the Projected Hartree-Fock-Bogoliubov (PHFB) model. Theoretical 2ν β^-β^- half-lives of ^{128, 130}Te , and ¹⁵⁰Nd isotopes, and 2ν β⁺β⁺ , 2ν β⁺ EC and 2ν ECEC for ^{124, 126}Xe and ^{130, 132}Ba nuclei are presented. Calculated quadrupolar transition probabilities B(E2 : 0⁺ → 2⁺) , static quadrupole moments and g -factors in the parent and daughter nuclei reproduce the experimental information, validating the reliability of the model wave functions. The anticorrelation between nuclear deformation and the nuclear transition matrix element M _2ν is confirmed.     

The investigation of 0<Superscript>+</Superscript> ↔ 0<Superscript>−</Superscript><Emphasis Type="Italic">β</Emphasis> decay in some spherical nuclei

The 0⁺ ↔ 0⁻ first-forbidden β decay transitions have been investigated for some spherical nuclei. The theoretical framework is based on a proton-neutron quasiparticle random phase approximation (pnQRPA). The Woods-Saxon potential basis has been used in our calculations. The transition probabilities have been calculated within the ξ approximation. The relativistic β moment matrix element has been calculated both directly without any assumption and assuming that it is proportional to the non-relativistic one.     

Beta-decay of nuclei near the neutron shell <Emphasis Type="Italic">N</Emphasis> = 126

A self-consistent approach to the weak interaction rates is presented. It is based on the generalized energy-density functional method and continuum QRPA. The study has been made of the β-decay total energy releases, half-lives and β-delayed neutron emission branchings for recently identified near-spherical nuclei with charge numbers Z = 76–79 approaching the closed neutron shell at N = 126. Together with our previous calculations near N = 28, 50, 82 this provides an important update to the standard set of weak rates for the r-process modeling, radioactive beam experiments and advanced reactor applications. Within the fully microscopic framework a significant competition is found of the Gamow-Teller and first-forbidden decay contributions to the total half-lives.     

Ion detection from beta decay and two-body decay experiments with laser-cooled atoms

Localized and cold samples of atoms produced with laser cooling and trapping techniques are a powerful tool for nuclear β-decay experiments. Recently we have concentrated on measurements of the momentum of the daughter ion produced, which leads to a variety of new observables. Angular distributions of the recoils with respect to the nuclear spin in β ⁺ decay are sensitive to non-standard model interactions. Measurements of the momentum of monoenergetic recoils from either electron capture or isomer γ decay would make it possible to search for particles with masses of 10s of keV.      

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.     

Relation between E2-transition probabilities for nuclei that are soft with respect to β vibrations

For collective even-even nuclei, a relation between the E2-transition probabilities, which characterize the decay properties of For collective even-even nuclei, a relation between the E2-transition probabilities, which characterize the decay properties of and 2 _γ ⁺ states, are obtained. This relation features no free parameters; it is applicable to describing nuclei that are soft with respect to β vibrations. The ¹⁵²Sm and ¹⁵⁴Gd nuclei are considered as examples illustrating the application of the aforementioned relation. __________ Translated from Yadernaya Fizika, Vol. 63, No. 4, 2000, pp. 633–637. Original Russian Text Copyright ? 2000 by Jolos, Palchikov.     

Microscopic three-body force for asymmetric nuclear matter

Brueckner calculations including a microscopic three-body force have been extended to isospin-asymmetric nuclear matter. The effects of the three-body force on the equation of state and on the single-particle properties of nuclear matter are discussed with a view to possible applications in nuclear physics and astrophysics. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs. isospin asymmetry β = (N - Z)/A is fulfilled in the whole asymmetry range 0≤β≤1 up to high densities. The three-body force provides a strong enhancement of the symmetry energy which increases with density in good agreement with the predictions of relativistic approaches. The Lane's assumption that proton and neutron mean fields linearly vary vs. the isospin parameter is violated at high density due to the three-body force, while the momentum dependence of the mean fields turns out to be only weakly affected. Consequently, a linear isospin split of the neutron and proton effective masses is found for both cases with and without the three-body force. The isospin effects on multifragmentation events and collective flows in heavy-ion collisions are briefly discussed along with the conditions for direct URCA processes to occur in the neutron star cooling. Received: 18 February 2002 / Accepted: 16 May 2002     

Low-Temperature Dynamics of the Curie-Weiss Model: Periodic Orbits,Multiple Histories,and Loss of Gibbsianness

We consider the Curie-Weiss model at initial temperature 0<β ⁻¹≤∞ in vanishing external field evolving under a Glauber spin-flip dynamics with temperature 0<β′⁻¹≤∞. We study the limiting conditional probabilities and their continuity properties and discuss their set of points of discontinuity (bad points). We provide a complete analysis of the transition between Gibbsian and non-Gibbsian behavior as a function of time, extending earlier work for the case of independent spin-flip dynamics.     

Double beta decays and Majorana neutrinos

Neutrino-less double beta decays (0νββ) are sensitive and realistic probes for studying the Majorana nature of neutrinos (ν), the ν-mass spectrum, the absolute ν-mass scale, the Majorana CP phases and other fundamental properties of neutrinos and weak interactions. Current 0νββ experiments, which use detectors with the mass sensitivity of the order of 300 meV, study the ν-mass in that mass region. Future experiments with higher sensitivities of the orders of 100meV and 30 meV, using different nuclei and methods (calorimetric, spectroscopic), are indispensable for establishing 0νββ in the quasi degenerate and the inverted hierarchy mass regions. R&D for ultra-high sensitivity detectors are encouraged for studying the normal hierarchy mass region. Theoretical and experimental studies for evaluating nuclear matrix elements are important for extracting the sensible ν-mass from the 0νββ rate. Charge exchange reactions by means of nuclear, electromagnetic and ν probes provide valuable data which are used to evaluate the nuclear matrix elenments. International collaborations for 0νββ experiments and for the matrix elements are crucial for next generation 0νββ studies.     

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.     

Intra- and intergroup azimuthal correlations of particles in the interaction of gold nuclei with silver and bromine nuclei of track emulsions at the projectile energy of 10.6 GeV per nucleon

Inter- and intragroup azimuthal correlations of target and projectile fragments and of shower particles in the interactions between gold nuclei of energy 10.6 GeV per nucleon and silver and bromine nuclei of a track emulsion are studied at intermediate values of the impact parameter. The asymmetry index β′₁ and the collinearity index β′₂ of groups’ asymmetry vectors are used to study azimuthal correlations between two and three groups of particles. The interplay of effects of intra- and intergroup azimuthal particle correlations is investigated.     

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.     

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.     

Beta decay of the proton-rich nuclei 102Sn and 104Sn

The β decays of ¹⁰²Sn and ¹⁰⁴Sn were studied by using high-resolution germanium detectors as well as a Total Absorption Spectrometer (TAS). For ¹⁰⁴Sn, with three new β-delayed γ-rays identified, the total Gamow-Teller strength (B_GT) value of 2.7(3) was obtained. For ¹⁰²Sn, the γ-γ coincidence data were collected for the first time, allowing us to considerably extend the decay scheme. This scheme was used to unfold the TAS data and to deduce a B_GT value of 4.2(8) for this decay. This result is compared to shell model predictions, yielding a hindrance factor of 3.6(7) in agreement with those obtained previously for ⁹⁸Cd and ¹⁰⁰In. Together with the latter two, ¹⁰²Sn completes the triplet of Z ⩽ 50, N ≥ 50 nuclei with two proton holes, one proton hole and one neutron particle, and two neutron particles with respect to the doubly magic ¹⁰⁰Sn core.     

Beta–neutrino correlation experiments on laser trapped 38mK, 37K

Laser trapping and cooling techniques are now being applied to the study of nuclear β-decay at several labs. A magneto-optical trap (MOT) provides a localized source of atoms suspended in space, so the low-energy recoiling nuclei can freely escape and be detected in coincidence with the β. This allows reconstruction of the neutrino momentum, and the deduction of the β-v correlation in a more direct fashion than previously possible. In addition, the nuclei can be polarized by atomic techniques, opening a new class of spin correlation measurements to test the degree to which parity is maximally violated in the weak interaction. Our present experiment has detected several hundred thousand recoil-β⁺ coincidences from the 0⁺ → 0⁺ pure Fermi decay of ^38mK, produced at the on-line isotope separators TISOL and ISAC at TRIUMF. Our goal is to set constraints on non-Standard Model scalar bosons competitive with high-energy colliders and more conventional β-v correlation experiments. This revised version was published online in August 2006 with corrections to the Cover Date.