We present a test with which to evaluate the calculated isospin-symmetry-breaking corrections to superallowed 0+-to-0+ nuclear beta decay. The test is based on the corrected experimental Ft values being required to satisfy conservation of the vector current (CVC). When applied to six sets of published calculations, the test demonstrates quantitatively that only one set -- the one based on the shell model with Saxon-Woods radial wave functions -- provides satisfactory agreement with CVC. This test can easily be applied to any sets of calculated correction terms that are produced in future.
A precision measurement of the gamma yields following the beta decay of 32Cl has determined its isobaric analogue branch to be (22.47^{+0.21}_{-0.19})%. Since it is an almost pure Fermi decay, we can also determine the amount of isospin-symmetry breaking in this superallowed transition. We find a very large value, delta_C=5.3(9)%, in agreement with a shell-model calculation. This result sets a benchmark for isospin-symmetry-breaking calculations and lends support for similarly-calculated, yet smaller, corrections that are currently applied to 0+ -> 0+ transitions for tests of the Standard Mode…
Background: The superallowed beta-decay rates provide stringent constraints on physics beyond the Standard Model of particle physics. To extract crucial information about the electroweak force, small isospin-breaking corrections to the Fermi matrix element of superallowed transitions must be applied. Purpose: We perform systematic calculations of isospin-breaking corrections to superallowed beta-decays and estimate theoretical uncertainties related to the basis truncation, time-odd polarization effects related to the intrinsic symmetry of the underlying Slater determinants, and to the function…
We study the formalism to include isospin-symmetry-breaking corrections when extracting the up-down Cabibbo-Kobayashi-Maskawa matrix element from superallowed 0+ -> 0+ nuclear beta decay. We show that there are no first order isospin-symmetry-breaking corrections to the relevant nuclear matrix elements. We find corrections to the treatment of Towner and Hardy, and assess these using schematic models of increasing complexity.
Based on an exact formalism, we study the effects of isospin-symmetry-breaking interactions on superallowed 0+ -> 0+ transitions. We calculate the second-order renormalization of the Fermi matrix element due to radial contributions and show that radial excitations neglected in the treatment of Towner and Hardy are significant. These are estimated to decrease the isospin-symmetry-breaking corrections. Our results provide a correction term that can be included in existing approaches.
We report the first branching-ratio measurement of the superallowed 0+-to-0+ beta transition from 38Ca. The result, 0.7728(16), leads to an ft value of 3062.3(68)s with a relative precision of +/-0.2%. This makes possible a high-precision comparison of the ft values for the mirror superallowed transitions, 38Ca-to-38mK and 38mK-to-38Ar, which sensitively tests the isospin symmetry-breaking corrections required to extract Vud, the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, from superallowed beta decay. The result supports the corrections currently used, and poin…
Theoretical approaches that use one-body densities as dynamical variables, such as Hartree-Fock or the density functional theory (DFT), break isospin symmetry both explicitly, by virtue of charge-dependent interactions, and spontaneously. To restore the spontaneously broken isospin symmetry, we implemented the isospin-projection scheme on top of the Skyrme-DFT approach. This development allows for consistent treatment of isospin mixing in both ground and exited nuclear states. In this study, we apply this method to evaluate the isospin impurities in ground states of even-even and odd-odd N~Z n…
Recently, we have applied for the first time the angular momentum and isospin projected nuclear density functional theory to calculate the isospin-symmetry breaking (ISB) corrections to the superallowed beta-decay. With the calculated set of the ISB corrections we found |V_{ud}|=0.97447(23) for the leading element of the Cabibbo-Kobayashi-Maskawa matrix. This is in nice agreement with both the recent result of Towner and Hardy [Phys. Rev. {\bf C77}, 025501 (2008)] and the central value deduced from the neutron decay. In this work we extend our calculations of the ISB corrections covering all s…
The superallowed beta-decay rates that provide stringent constraints on physics beyond the Standard Model of particle physics are affected by nuclear structure effects through isospin-breaking corrections. The self-consistent isospin- and angular-momentum-projected nuclear density functional theory is used for the first time to compute those corrections for a number of Fermi transitions in nuclei from A=10 to A=74. The resulting leading element of the CKM matrix, |V_{ud}|= 0.97447(23), agrees well with the recent result by Towner and Hardy [Phys. Rev. C {\bf 77}, 025501 (2008)].
We investigate isospin-symmetry breaking effects in the sd-shell region with large-scale shell-model calculations, aiming to understand the recent anomalies observed in superallowed Fermi beta-decay. We begin with calculations of Coulomb displacement energies (CDE's) and triplet displacement energies (TDE's) by adding the T=1,J=0 isospin nonconserving (INC) interaction into the usual isospin-invariant Hamiltonian. It is found that CDE's and TDE's can be systematically described with high accuracy. A total number of 122 one- and two-proton separation energies are predicted accordingly, and loca…
Self-consistent random phase approximation (RPA) approaches in the relativistic framework are applied to calculate the isospin symmetry-breaking corrections $δ_c$ for the $0^+\to0^+$ superallowed transitions. It is found that the corrections $δ_c$ are sensitive to the proper treatments of the Coulomb mean field, but not so much to specific effective interactions. With these corrections $δ_c$, the nucleus-independent $\mathcal{F}t$ values are obtained in combination with the experimental $ft$ values in the most recent survey and the improved radiative corrections. It is found that the constancy…
After application of an analytical transformation, a new exact representation for the nuclear isospin-symmetry breaking correction $δ_C$ to superallowed beta decay is obtained. The correction is shown to be essentially the reciprocal of the square of an energy parameter $Ω_M$ which characterizes the charge-exchange monopole strength distribution. The proportionality coefficient in this relation is determined by basic properties of the ground state of the even-even parent nucleus, and should be reliably calculable in any realistic nuclear model. Therefore, the single parameter $Ω_M$ contains al…
We report new shell-model calculations of the isospin-symmetry-breaking correction to superallowed nuclear beta decay. The most important improvement is the inclusion of core orbitals, which are demonstrated to have a significant impact on the mismatch in the radial wave functions of the parent and daughter states. We determine which core orbitals are important to include from an examination of measured spectroscopic factors in single-nucleon pick-up reactions. We also examine the new radiative-correction calculation by Marciano and Sirlin and, by a simple reorganization, show that it is possi…
We investigate the radial-overlap part of the isospin-symmetry breaking correction to superallowed $0^+\to 0^+$-decay using the shell-model approach similar to that of Refs. [1, 2]. The 8 sd-shell emitters with masses between $A=22$ and $A=38$ have been re-examined. The Fermi matrix element is evaluated with realistic spherical single-particle wave functions, obtained from spherical Woods-Saxon (WS) or Hartree-Fock (HF) potentials, fine-tuned to reproduce the experimental data on charge radii and separation energies for nuclei of interest. The elaborated adjustment procedure removes any sensit…
Influence of configuration-interaction on isospin impurities and isospin symmetry breaking corrections to superallowed $0^+\rightarrow 0^+$ beta decays
University of Warsaw（华沙大学）；The University of Manchester（曼彻斯特大学）；Akal University（阿卡尔大学）；Osaka University（大阪大学）
Superallowed $β$-decay studies provide some of the best constraints on the possibility of additional quark generations, as well as limits on exotic currents in the weak interaction. The three experimental quantities that are required for performing these tests using $0^+\rightarrow0^+$ nuclear decays (branching ratio, half-life, and $Q$-value) can all be measured to high-precision with rare-isotope beams at the TRIUMF-ISAC facility in Vancouver, Canada. This proceeding presents a brief outline of the general experimental techniques used at TRIUMF over the past 15 years, as well as recent theor…
We study the shell-model formalism to include the isospin-symmetry-breaking correction ($δ_{C}$) to nuclear matrix element of superallowed $0^+\to 0^+$ Fermi $β$ decays of $T=1$ nuclei. Based on a perturbation expansion in a small quantity, such as the deviation of the overlap integral between proton and neutron radial wave functions from unity or of the transition density from its isospin-symmetry value, we derive that $δ_C$ can be obtained as a sum of six terms, including two leading order (LO) terms, two next-to-leading order (NLO) terms, one next-to-next-to-leading order (NNLO) term and on…
Prompted by recent measurements, we have surveyed world data and calculated radiative and isospin-symmetry breaking corrections for the superallowed 0+ -to- 0+ Fermi transitions from 42Ti, 46Cr, 50Fe and 54Ni. This increases the number of such transition with a complete set of calculated corrections from 20 to 23. The results are compared with their equivalents for the mirror superallowed transitions from 42Sc, 46V, 50Mn and 54Co. The predicted ft-value asymmetries of these mirror pairs are sensitive to the correction terms and provide motivation for improving measurement precision so as to be…
In this work we present the first steps towards benchmarking isospin symmetry breaking in ab initio nuclear theory for calculations of superallowed Fermi $β$-decay. Using the valence-space in-medium similarity renormalization group, we calculate b and c coefficients of the isobaric multiplet mass equation, starting from two different Hamiltonians constructed from chiral effective field theory. We compare results to experimental measurements for all T=1 isobaric analogue triplets of relevance to superallowed $β$-decay for masses A=10 to A=74 and find an overall agreement within approximately 25…
Background: Models to calculate small isospin-symmetry-breaking effects in superallowed Fermi decays have been placed under scrutiny in recent years. A stringent test of these models is to measure transitions for which the correction is predicted to be large. The decay of 32Cl decay provides such a test case. Purpose: To improve the gamma yields following the beta decay of 32Cl and to determine the ft values of the the beta branches, particularly the one to the isobaric-analogue state in 32S. Method: Reaction-produced and recoil-spectrometer-separated 32Cl is collected in tape and transported …
This paper overviews various phenomena related to the concept of isospin symmetry. The focus is on N~Z nuclei, which are excellent laboratories of isospin physics. The theoretical framework applied is nuclear Density Functional Theory and its isospin- and angular-momentum projected extensions, as well as symmetry-projected multi-reference models. The topics covered include: isospin impurities, superallowed beta decays, beta-transitions in mirror nuclei, isospin breaking hadronic interactions, mirror and triplet binding energy differences, and isoscalar pairing.
We lay out a novel formalism to connect the isospin-symmetry breaking correction to the rates of superallowed nuclear beta decays, $δ_\text{C}$, to the isospin-breaking sensitive combinations of electroweak nuclear radii that can be accessed experimentally. We individuate transitions in the superallowed decay chart where a measurement of the neutron skin of a stable daughter even at a moderate precision could already help discriminating between models used to compute $δ_\text{C}$. We review the existing experimental situation and make connection to the existing and future experimental programs…
A direct $Q_{EC}$-value measurement of the superallowed $β^+$ emitter $^{22}$Mg was performed using TRIUMF's Ion Trap for Atomic and Nuclear science (TITAN). The direct ground-state to ground-state atomic mass difference between $^{22}$Mg and $^{22}$Na was determined to be $Q_{EC}=4781.40(22)$~keV, representing the most precise single measurement of this quantity to date. In a continued push towards calculating superallowed isospin-symmetry-breaking (ISB) corrections from first principles, ab-initio shell-model calculations of the $A=22$ IMME are also presented for the first time using the val…
The self-consistent random phase approximation (RPA) approach with the residual interaction derived from a relativistic point-coupling energy functional is applied to evaluate the isospin symmetry-breaking corrections δc for the 0+\to0+ superallowed Fermi transitions. With these δc values, together with the available experimental ft values and the improved radiative corrections, the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is examined. Even with the consideration of uncertainty, the sum of squared top-row elements has been shown to deviate from the unitarity condition by 0.1% fo…
We present the isospin- and angular-momentum-projected nuclear density functional theory (DFT) and its applications to the isospin-breaking corrections to the superallowed beta-decay rates in the vicinity of the N=Z line. A preliminary value obtained for the Cabbibo-Kobayashi-Maskawa matrix element, |V_{ud}|=0.97463(24), agrees well with the recent estimate by Towner and Hardy [Phys. Rev. C{\bf 77}, 025501 (2008)]. We also discuss new opportunities to study the symmetry energy by using the isospin-projected DFT.
The measured $ft$-values for superallowed $0^{+} \to 0^{+}$ nuclear $β$-decay can be used to obtain the value of the vector coupling constant and thus to test the unitarity of the Cabibbo-Kobayashi-Maskawa matrix. An essential requirement for this test is accurate calculations for the radiative and isospin symmetry-breaking corrections that must be applied to the experimental data. We present a new and consistent set of calculations for the nuclear-structure-dependent components of these corrections. These new results do not alter the current status of the unitarity test -- it still fails by m…
\textbf{Background}: Superallowed $0^+ \rightarrow 0^+$ $β$ decays of isospin $T=2$ nuclides can be used to test theoretical isospin symmetry breaking corrections applied to extract the CKM matrix element $V_{ud}$ from $T = 0,1$ decays by measuring precise $ft$ values and also to search for scalar currents using the $β-ν$ angular correlation. Key ingredients include the $Q_{\textrm{EC}}$ value and branching of the superallowed transition and the half life of the parent. \textbf{Purpose}: To determine a precise experimental $Q_{\textrm{EC}}$ value for the superallowed $0^+ \rightarrow 0^+$ $β$ …
A $^{52}$Cr$(p,t)$$^{50}$Cr two-neutron pickup reaction was performed using the Q3D magnetic spectrograph at the Maier-Leibnitz-Laboratorium in Garching, Germany. Excited states in $^{50}$Cr were observed up to an excitation energy of 5.3 MeV. Despite significantly increased sensitivity and resolution over previous work, no evidence of the previously assigned first excited $0^+$ state was found. As a result, the $0^+_2$ state is reassigned at an excitation energy of $E_x=3895.0(5)$ keV in $^{50}$Cr. This reassignment directly impacts direct searches for a non-analogue Fermi $β^+$ decay branch …
The results of systematic calculations of isospin-symmetry-breaking corrections to superallowed beta-decays based on the self-consistent isospin- and angular-momentum-projected nuclear density functional theory (DFT) are reviewed with an emphasis on theoretical uncertainties of the model. Extensions of the formalism towards no core shell model approach with basis cutoff scheme dictated by the self-consistent particle-hole DFT solutions will be also discussed.
A new critical survey is presented of all half-life, decay-energy and branching-ratio measurements related to 20 superallowed 0+ --> 0+ beta decays. Included are 222 individual measurements of comparable precision obtained from 177 published references. Compared with our last review in 2008, we have added results from 24 new publications and eliminated 9 references, the results from which having been superseded by much more precise modern data. We obtain world-average ft-values for each of the eighteen transitions that have a complete set of data, then apply radiative and isospin-symmetry-brea…
Isospin-mixing corrections for superallowed Fermi transitions in {\it fp}-shell nuclei are computed within the framework of the shell model. The study includes three nuclei that are part of the set of nine accurately measured transitions as well as five cases that are expected to be measured in the future at radioactive-beam facilities. We also include some new calculations for $^{10}$C. With the isospin-mixing corrections applied to the nine accurately measured $ft$ values, the conserved-vector-current hypothesis and the unitarity condition of the Cabbibo-Kobayashi-Maskawa (CKM) matrix are te…
Spin and isospin are essential degrees of freedom in nuclear systems, and the relevant studies on their properties play important roles not only in nuclear physics but also in nuclear astrophysics, particle physics, and so on. In this presentation for the IUPAP Young Scientist Prize 2016, I would like to introduce the microscopic studies on nuclear spin-isospin properties in the framework of covariant density functional theory (DFT), by taking a few works that I have been joining in as examples. It is seen that the covariant scheme plays an important role in describing the spin properties in a…
The no-core configuration-interaction model based on the isospin- and angular-momentum projected density functional formalism is introduced. Two applications of the model are presented: (i) determination of spectra of 0+ states in 62Zn and (ii) determination of isospin-symmetry-breaking corrections to superallowed beta-decay between isobaric-analogue 0+ states in 38Ca and 38K. It is shown that, without readjusting a single parameter of the underlying Skyrme interaction, in all three nuclei, the model reproduces the 0+ spectra surprisingly well.
The radial overlap correction, $δ_{RO}$ is re-examined for 30 superallowed $β$ decays using the shell model with Hartree-Fock (HF) radial wave functions. Our calculation is based on the Skyrme interaction including Coulomb, Charge-Symmetry-Breaking (CSB) and Charge-Independence-Breaking (CIB) terms. The corrections due to the gradient of charge density, vacuum polarization, Coulomb spin-orbit and finite size of nucleons are also considered. To avoid the spurious isospin mixing, the local equivalent potential is constructed from the solution of a HF calculation for the $Z=N$ nucleus without cha…
A new critical survey is presented of all half-life, decay-energy and branching-ratio measurements related to 20 0+ to 0+ beta decays. Compared with our last review, there are numerous improvements: First, we have added 27 recently published measurements and eliminated 9 references; of particular importance, the new data include a number of high-precision Penning-trap measurements of decay energies. Second, we have used the recently improved isospin symmetry-breaking corrections. Third, our calculation of the statistical rate function now accounts for possible excitation in the daughter atom. …
We present the self-consistent, non-perturbative analysis of isospin mixing using the nuclear density functional approach and the rediagonalization of the Coulomb interaction in the good-isospin basis. The largest isospin-breaking effects are predicted for N = Z nuclei and they quickly fall with the neutron excess. The unphysical isospin violation on the mean-field level, caused by the neutron excess, is eliminated by the proposed method. We find a significant dependence of the magnitude of isospin breaking on the parametrization of the nuclear interaction term. A rough correlation has been fo…
Quantum Monte Carlo calculation of $δ_C$ in the superallowed beta decay of $^{10}$C
Washington University in Saint Louis（圣路易斯华盛顿大学）；Argonne National Laboratory（阿贡国家实验室）；INFN-TIFPA Trento Institute for Fundamental Physics and Applications（特伦托基础物理与应用研究所 (INFN-TIFPA)）；Instituto de Física Corpuscular (IFIC), Consejo Superior de Investigaciones Científicas (CSIC) and Universidad de Valencia（瓦伦西亚大学与西班牙高等科学研究理事会联合粒子物理研究所 (IFIC)）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
We present results of systematic calculations of the isospin-symmetry-breaking corrections to the superallowed I=$0+,T=1 --> I=0+,T=1 beta-decays, based on the self-consistent isospin- and angular-momentum-projected nuclear density functional theory (DFT). We discuss theoretical uncertainties of the formalism related to the basis truncation, parametrization of the underlying energy density functional, and ambiguities related to determination of Slater determinants in odd-odd nuclei. A generalization of the double-projected DFT model towards a no core shell-model-like configuration-mixing appro…
The question of isospin-symmetry breaking in nuclei of the $sd$ shell is addressed. We propose a new global parameterization of the isospin-nonconserving (INC) shell-model Hamiltonian which accurately describes experimentally known isobaric mass splittings. The isospin-symmetry violating part of the Hamiltonian consists of the Coulomb interaction and effective charge-dependent forces of nuclear origin. Particular attention has been paid to the effect of the short-range correlations. The behavior of $b$ and $c$ coefficients of the isobaric-mass-multiplet equation (IMME) is explored in detail. I…
[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 c…
We present the full description of a measurement of the branching ratios for the beta-decay of 38Ca. This decay includes five allowed 0+ --> 1+ branches and a superallowed 0+ --> 0+ one. With our new result for the latter, we determine its ft value to be 3062.3(68) s, a result whose precision (0.2%) is comparable to the precision of the thirteen well known 0+ --> 0+ transitions used up till now for the determination of Vud, the up-down quark-mixing element of the CKM matrix. The 38Ca superallowed transition thus becomes the first addition to this set of transitions in nearly a decade and the f…
The current value of Vud is determined from superallowed beta-decay experiments. Other methods, briefly summarised here, have to overcome specific experimental hurdles before they are competitive. However, the nuclear results do depend on a nuclear-structure calculation of isospin-symmetry breaking, which is often a cause of some concern. We show here, by adopting the Conserved Vector Current (CVC) hypothesis, that these theoretical corrections can be tested for consistency. In this test, calculations based on the shell model with Saxon-Woods radial functions perform the best.
We present systematic study of isospin impurities ($α_{\rm ISB}$) to the wave functions of $T=1/2$, $11\leq A \leq 47$ mirror nuclei and the isospin-symmetry-breaking (ISB) corrections ($δ_{\rm ISB}^{\rm V}$) to their ground state vector $β$-decays using, for the first time, multi-reference charge-dependent density functional theory (MR-DFT) that includes strong-force-rooted class-III interaction adjusted to correct for the Nolen-Schiffer anomaly in nuclear masses. We demonstrate that, unexpectedly, the strong-force-rooted isovector force gives rise to a large systematic increase of $α_{\rm IS…
The assumption of an exact isospin symmetry would imply equal strengths for mirror E1 transitions (at least, in the long-wavelength limit). Actually, large violations of this symmetry rule have been indicated by a number of experimental results, the last of which is the 67As - 67Se doublet investigated at GAMMASPHERE. Here, we examine in detail various possible origins of the observed asymmetry. The coherent effect of Coulomb-induced mixing with the high-lying Giant Isovector Monopole Resonance is proposed as the most probable process to produce a large asymmetry in the E1 transitions, with co…
We use a $4\hbarΩ$ shell-model calculation with a two-body effective interaction derived microscopically from the Reid93 potential to calculate the isospin-mixing correction for the 10C->10B superallowed Fermi transition. The effective interaction takes into account the Coulomb potential as well as the charge dependence of T=1 partial waves. Our results suggest the isospin- mixing correction $δ_{C}\approx 0.1 %$, which is compatible with previous calculations. The correction obtained in those calculations, performed in a $0\hbarΩ$ space, was dominated by deviation from unity of the radial over…
Within an isospin-dependent transport model for nuclear reactions induced by neutron-rich nuclei, we perform a comparative study of $^{100}Sn+^{124}Sn$ and $^{100}Zn+^{124}Sn$ reactions at beam energies of 30 MeV/A and 400 MeV/A to identify optimal experimental conditions and observables for investigating the equation of state (EOS) of neutron-rich matter at RIA. Several observables known to be sensitive to the density-dependence of the symmetry energy are examined as a function of impact parameter for both reaction systems. In particular, the strength of isospin transport/diffusion is studied…
We analyze the axial $γW$-box diagram for $I(J^P)=1(0^+)$ nuclei and provide a dispersion representation of the nuclear-structure correction $δ_\text{NS}$ including its energy-dependent part. We also summarize useful isospin rotation formula and representations in nuclear theory that could facilitate the calculation of the parity-odd nuclear structure function $F_3(ν,Q^2)$. They provide a rigorous theory framework for the future, high-precision calculation of the nuclear structure correction $δ_\text{NS}$ necessary for the extraction of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{ud}|$ f…
We investigate the contribution to the angular correlation coefficients of the neutron beta decay within the R-parity violating (RPV) minimal supersymmetric standard model (MSSM). The RPV effects contribute to the scalar interaction at the tree level. The effective scalar interaction of the neutron beta decay is constructed by making use of the relation between isospin asymmetries and the proton-neutron mass difference. On the basis of the recent update of the analyses of the superallowed Fermi transitions and the recent measurement of transverse polarization of the emitted electrons at PSI, w…
We propose a novel dispersive treatment of the so-called inner radiative correction to the neutron and nuclear $β$-decay. We show that it requires knowledge of the parity-violating structure function $F_3^{(0)}$ that arises from the interference of the axial vector charged current and the isoscalar part of the electromagnetic current. By isospin symmetry, we relate this structure function to the charged current inelastic scattering of neutrinos and antineutrinos. Applying this new data-driven analysis we obtain a new, more precise evaluation for the universal radiative correction $Δ_{R}^{V,\,n…
