Fermi Beta Decay Research Articles

Coulomb corrections to Fermi beta decay in nuclei

We study the influence of the Coulomb force on the Fermi beta-decays in nuclei. This work is composed of two main parts. In the first part, we calculate the Coulomb corrections to super-allowed beta decay. We use the notion of the isovector monopole state and the self-consistent charge-exchange Random Phase Approximation to compute the correction. In the second part of this work, we examine the influence of the anti-analog state on isospin mixing in the isobaric analog state and the correction to the beta-decay Fermi transition.

Beta decay logft values for zinc isotopes by using pn-QRPA

Allowed Fermi (F), Gamow-Teller (GT), and first forbidden (FF) transitions were simulated using Pyatov Method (PM) and Schematic Model (SM) for even-even neutron rich isotopes of Zinc. The Fermi beta-decay calculations were obtained by the pure the Pyatov Method without introducing effective values of coupling constants using the proton-neutron quasi-particle random phase approximation (pn-QRPA). The pn-QRPA was utilized in the particle-hole (ph) and particle-particle (pp) channels in the PM and SM for the GT transitions. For FF transitions, only the corresponding ph channel in the SM was considered in the calculations. We solved the secular equations of Fermi, Gamow-Teller, and first forbidden transitions for eigenvalues and eigenfunctions of corresponding Hamiltonians. A spherical shape was assigned for each Zn nuclei throughout all simulations. Compared to the experimental studies, in general, the calculated logft values of the allowed F and GT transitions of PM and SM simulations were found to be closer to the experimental values. Alongside logft values, simulated half-lives obtained in this work are also in excellent agreement with experimental counterparts for the FF excitations.

Exotic phenomena in medium mass N ≃ Z nuclei within the beyond-mean-field approach

Recent studies on properties of proton-rich nuclei in the A = 70 mass region brought insights into fundamental symmetries and interactions and produced characteristics required by the astrophysical scenarios on the rp-process path revealing coexistence phenomena which dominate the structure and dynamics of these exotic nuclei. Isospin mixing and related phenomena like Coulomb energy differences, mirror energy differences, triplet energy differences as well as superallowed Fermi beta decay in isovector triplets have been investigated. The interplay between isospin-symmetry-breaking and shape-coexistence effects on isospin-related phenomena in nuclei as well as weak interaction processes under terrestrial and stellar x-ray burst environment have been explored in the frame of the beyond-mean-field complex Excited Vampir variational model. We used an adequate model space and the effective interaction was derived from a G-matrix starting from the charge-dependent Bonn CD potential. Results concerning the influence of shape coexistence and mixing on the structure and β-decay properties of exotic nuclei will be reviewed.

Nuclear Structure Studied with Direct Reactions for Fundamental Symmetry Tests

Direct reaction studies provide crucial information on nuclear structure for nuclei that are used in weak interaction and fundamental symmetry tests. Motivated by the superallowed Fermi beta-decay studies, we have investigated the structure of Cr-50 and Zn-62, the daughters of the superallowed beta(+)/EC emitters Mn-50 and Ga-62, with (p,t) reactions. For both nuclei, we reassigned the location of the first excited 0(+) state. The data for these reassignments are reviewed and limits on the possible L = 0 transfer to the previously assigned 0(2)(+) states are determined. For Cr-50, we find no evidence for the presence of a 0(+) state at 3695 keV. For Zn-62, the data allow for a possible contribution of L = 0 and L = 2, indicating a possible 0(+)/2(+) doublet of states at 2342 keV. However, this relies on an enhanced cross section at only one data point, and thus the existence of a 0(+) state at this energy is not clear. A preliminary result from a gamma-gamma angular correlation measurement following the beta(+)/EC decay of Ga-62 weakly favours the existence of a 0(+) state, but requires further study with increased statistics.

No-core configuration-interaction model for the isospin- and angular-momentum-projected states

[Background] Single-reference density functional theory is very successful in reproducing bulk nuclear properties like binding energies, radii, or quadrupole moments throughout the entire periodic table. Its extension to the multi-reference level allows for restoring symmetries and, in turn, for calculating transition rates. [Purpose] We propose a new no-core-configuration-interaction (NCCI) model treating properly isospin and rotational symmetries. The model is applicable to any nucleus irrespective of its mass and neutron- and proton-number parity. It properly includes polarization effects caused by an interplay between the long- and short-range forces acting in the atomic nucleus. [Methods] The method is based on solving the Hill-Wheeler-Griffin equation within a model space built of linearly-dependent states having good angular momentum and properly treated isobaric spin. The states are generated by means of the isospin and angular-momentum projection applied to a set of low-lying (multi)particle-(multi)hole deformed Slater determinants calculated using the self-consistent Skyrme-Hartree-Fock approach. [Results] The theory is applied to calculate energy spectra in N~Z nuclei that are relevant from the point of view of a study of superallowed Fermi beta-decays. In particular, a new set of the isospin-symmetry-breaking corrections to these decays is given. [Conclusions] It is demonstrated that the NCCI model is capable to capture main features of low-lying energy spectra in light and medium-mass nuclei using relatively small model space and without any local readjustment of its low-energy coupling constants. Its flexibility and a range of applicability makes it an interesting alternative to the conventional nuclear shell model.

The influence of pairing correlations on the isospin symmetry breaking corrections of superallowed Fermi beta decays

Within the framework of quasi-particle random phase approximation, the isospin breaking correction of superallowed 0+ → 0+ beta decay and unitarity of Cabibbo-Kobayashi-Maskawa mixing matrix have been investigated. The broken isotopic symmetry of nuclear part of Hamiltonian has been restored by Pyatov’s method. The isospin symmetry breaking correction with pairing correlations has been compared with the previous results without pairing. The effect of pairing interactions has been examined for nine superallowed Fermi beta decays; their parent nuclei are 26Al, 34Cl, 38K, 42Sc, 46V, 50Mn, 54Co, 62Ga, 74Rb.

The ft values of the superallowed Fermi beta decays

In this work, the ft values of the 0+→0+ superallowed Fermi beta decays have been investigated. In the calculations, the shell model has been modified by Pyatov’s restoration method because of the isospin breaking and the transition matrix elements have been found by means of the quasi-particle random phase approximation (QRPA).

The Influence of Pairing Correlations on the Isospin Symmetry Breaking Corrections of Superallowed Fermi Beta Decays

The Influence of Pairing Correlations on the Isospin Symmetry Breaking Corrections of Superallowed Fermi Beta Decays

The isospin mixing and the superallowed Fermi beta decay

In the present work, the isospin admixtures in the nuclear ground states of the parent nuclei and isospin structure of the isobar analog resonance (IAR) states have been investigated by studying the 0 + →0 + superallowed Fermi β decays using Pyatov’s restoration method. Within the random phase approximation (RPA), in this method, the effect of isospin breaking due to the Coulomb forces has been evaluated, taking into account the effect of pairing correlations between nucleons.

Effects of isospin mixing in theA=32quintet

For the A=32 T=2 quintet we provide a unified theoretical description for three related aspects of isospin mixing: the necessity of more than three terms in the isobaric mass multiplet equation, isospin-forbidden proton decay, and a correction to the allowed Fermi beta decay. We demonstrate for the first time that all three effects observed in experiment can be traced to a common origin related to isospin mixing of the T=2 states with T=1 states.

Super-allowed Fermi beta-decay: CKM unitarity

Analysis of the super-allowed Fermi beta-decay of nine bodies from 10C through 54Co yields |Vud|2 = 0.9514 ± 0.0014 and a unitarity test of the first row of the Cabibbo–Kobayashi–Maskawa matrix of |Vud|2 + |Vus|2 + |Vub|2 = 0.9996 ± 0.0017 in agreement with the standard model but in disagreement with alternative analyses of such data and with a study of the beta-decay of the free neutron.

Precise half-life measurement for the superallowed 0(+)-->0(+) beta emitter (74)Rb: first results from the new radioactive beam facility (ISAC) at TRIUMF.

Presently, the world data for superallowed beta decay leads to a result in disagreement (at the 98% confidence level) with the predictions of the minimal standard model for the unitarity of the Cabibbo-Kobayashi-Maskawa matrix. Precise data for the superallowed 0(+)-->0(+) beta decay of (74)Rb would provide a critical test of the nucleus-dependent isospin symmetry-breaking corrections that must be calculated for these superallowed Fermi beta decays. The present work reports the first precise measurement of the half-life for (74)Rb ( t(1/2) = 64.761+/-0.031 ms). The data were obtained at the radioactive beam facility (ISAC) at TRIUMF using a beam of approximately 4000 (74)Rb ions s(-1).

Large-basis no-core shell-model calculations and their application to 10 C → 10 B fermi beta decay

We use a 4ħΩ shell-model calculation with a two-body effective interaction derived microscopically from the Reid93 potential to calculate the isospin-mixing correction for the10C→10B superallowed Fermi transition. The effective interaction takes into account the Coulomb potential as well as the charge dependence ofT=1 partial waves. Our results suggest the isospin-mixing correctionδ c ≈ 0.1%, which is compatible with previous calculations obtained by other methods. The obtainedδ C correction is about a factor of four too small to obtain unitarity of the Cabibbo-Kobayashi-Maskawa matrix with the present experimental data.

Restoration of the Ikeda sum rule in self-consistent quasiparticle random-phase approximation

The so-called self-consistent quasiparticle random phase approximation, accounting for a better treatment of ground-state correlations, is applied to a schematic Hamiltonian, describing the Fermi beta decay process. The self-consistent procedure coupling the BCS minimum with the quantum fluctuations yields an exact fulfillment of the Ikeda sum rule. The role of the ground-state correlations is analyzed in the case of the double beta decay process.

Effect of nucleon structure variation in super-allowed Fermi beta-decay

There is a well known anomaly between the value of the Fermi decay constant extracted from super-allowed Fermi beta-decay of nuclear isotriplets and that required by unitarity of the Cabibbo-Kobayashi-Maskawa matrix. This discrepancy remains at the level of a few tenths of a percent after the most rigorous investigation of conventional nuclear and radiative corrections. Within the framework of the quark-meson coupling model of nuclear matter, which has been previously applied successfully to phenomena such as nuclear saturation and nuclear charge symmetry violation, we show that it is possible to understand a significant fraction of the observed anomaly.

Nuclear mismatch in super-allowed Fermi beta-decay

Abstract If super-allowed Fermi beta-decay is to be consistent with the conserved vector current and with unitarity of the Cabibbo-Kobayashi-Maskawa matrix it is necessary to understand a mismatch, as between the parent and daughter members of the isotriplets involved, that is worth several tenths of a percent in the transition rates. Present theoretical estimates of this mismatch fall short of what is needed by a factor of order 2 or more. It has been suggested that this shortfall is due to inadequate allowance for the effects of the spectator nucleons, but the present study shows that such effects are worth only a few hundredths of one percent.

G v , CKM unitarity, neutron decay; WR?

Superallowed Fermi beta-decay is analyzed in the light of new experimental data, new methodology and new treatment of the radiative and charge-dependent corrections. The following values are recommended:G v /(ħc) 3=(1.13769±0.00091)×10−5 GeV−2;G * /(ħc) 3 =(1.15128±0.00084) × 10−5GeV−2 whereG v is purged of radiative corrections suitably for combining withG μ to gain: ¦V ud ¦=0.97539±0.00080 which leads to:¦V ud ¦ 2 +¦V us ¦ 2 +¦V ub ¦2=1.0000+0.0017 and whereG * is the operational constant, incorporating the inner radiative correction, suitable for use in ordinary nuclear physics. It is noted that present results on the beta-decay of the neutron, when confronted by the above values, are inconclusive as to possible conflict with the minimal standard model and that judgement as to, for example, the intervention of a right-handed sector, should be suspended. The valueG * =1.2657±0.0030 is also recommended.

Nuclear deformation and super-allowed Fermi beta-decay

The Q EC values for the eight bodies from whose super-allowed Fermi beta-decay we derive our most accurate knowledge of the vector coupling constant are now determined with such precision that the associated uncertainties in the phase-space factor amount, on that account, to an average of only 0.030%; we must therefore consider all possible influences at the 0.01% level. Although the bodies in question are of J = 0 they possess, or may possess, large intrinsic deformations that: (i) affect the radial distribution of the charge whose field operates upon the emitted positron; (ii) affect the leptonic-nucleonic convolution of the shape factor. These effects are evaluated in an approximation that exaggerates their influence on the phase-space factor; using for the nuclear deformation values deriving from Q 2+-values measured by the re-orientation effect in Coulomb excitation the resultant magnitude of the change in the phase-space factor due to the deformation is found to be everywhere less than 0.01% although approaching that figure in some cases.

Methodology for superallowed Fermi beta-decay Part. I. Preliminaries and data

The group of papers, of which this is the first, discusses superallowed Fermi beta-decay in the context of the eight accurately-measured examples: 14O, 26Al m, 34Cl, 38K m, 42Sc, 46V, 50Mn and 54Co. The present paper, following a general introduction, considers the best current figures for the Q EC-values and t-values of the eight bodies of concern. It is pointed out that we are here interested not so much in the individual Q EC-values and t-values of the individual members of the set of eight as with the way in which all those values jointly determine a single final number, namely the vector coupling constant G V. In this case a single statistical criterion, based on the total number of input data involved for the entire set (at present 69), should be adopted when considering the admissibility, on statistical grounds, of any single measurement of any single quantity rather than a criterion relating just to the measurements of that single quantity. It is shown that this overall group criterion results in a very satisfactory statistical pattern for all the data relating to the eight bodies taken as a whole. A critical discussion is presented of the role of atomic excitations in the determination of Q EC-values and beta-decay rates.

Isospin conservation and the neutron halo

Isospin breaking is studied in nuclei which are isobaric to light neutron-halo nuclei with the 1s single-neutron case 11Be as an example. For this the total mixing probability into the daughter state increases with decreasing binding energy asymptotically reaching about 2 × 10 −4. The admixed intensity of the analogue state, which determine the rate of the Fermi beta decay, increases at first with decreasing binding and then passes through a rather flat maximum of about (1–2) × 10 −4 before it converges towards zero.