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Isospin-Breaking Corrections to Superallowed Fermi Beta Decay in Isospin- and Angular-Momentum-Projected Nuclear Density Functional Theory
Background: Superallowed -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 decays and estimate theoretical uncertainties related to the basis truncation, to time-odd polarization effects related to the intrinsic symmetry of the underlying Slater determinants, and to the functional parametrization. Methods: We use the self-consistent isospin- and angular-momentum-projected nuclear density functional theory employing two density functionals derived from the density-independent Skyrme interaction. Pairing correlations are ignored. Our framework can simultaneously describe various effects that impact matrix elements of the Fermi decay: symmetry breaking, configuration mixing, and long-range Coulomb polarization. Results: Isospin-breaking corrections to the I=0+, T=1 I=0+, T=1 pure Fermi transitions are computed for nuclei from A=10 to A=98 and, for the first time, to the Fermi branch of the I,T=1/2 I, T=1/2 transitions in mirror nuclei from A=11 to A=49. We carefully analyze various model assumptions impacting theoretical uncertainties of our calculations and provide theoretical error bars on our predictions. Conclusions: The overall agreement with empirical isospin-breaking corrections is very satisfactory. Using computed isospin-breaking corrections we show that the unitarity of the CKM matrix is satisfied with a precision of better than 0.1%.
Isospin effects in N ≈ Z nuclei in extended density functional theory
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.
Isospin Splittings of Doubly Heavy Baryons
The SELEX Collaboration has reported a very large isospin splitting of doubly charmed baryons. We show that this effect would imply that the doubly charmed baryons are very compact. One intriguing possibility is that such baryons have a linear geometry Q-q-Q where the light quark q oscillates between the two heavy quarks Q, analogous to a linear molecule such as carbon dioxide. However, using conventional arguments, the size of a heavy-light hadron is expected to be around 0.5 fm, much larger than the size needed to explain the observed large isospin splitting. Assuming the distance between two heavy quarks is much smaller than that between the light quark and a heavy one, the doubly heavy baryons are related to the heavy mesons via heavy quark-diquark symmetry. Based on this symmetry, we predict the isospin splittings for doubly heavy baryons including {Xi}{sub cc}, {Xi}{sub bb} and {Xi}{sub bc}. The prediction for the {Xi}{sub cc} is much smaller than the SELEX value. On the other hand, the {Xi}{sub bb} baryons are predicted to have an isospin splitting as large as (6.3 {+-} 1.7) MeV. An experimental study of doubly bottomed baryons is therefore very important to better understand the structure of baryons with heavy quarks.
Spin- and isospin-polarized states of nuclear matter in the Dirac-Brueckner-Hartree-Fock model
Spin-polarized isospin asymmetric nuclear matter is studied within the Dirac-Brueckner-Hartree-Fock approach. After a brief review of the formalism, we present and discuss the self-consistent single-particle potentials at various levels of spin and isospin asymmetry. We then move to predictions of the energy per particle, also under different conditions of isospin and spin polarization. Comparison with the energy per particle in isospin symmetric or asymmetric unpolarized nuclear matter shows no evidence for a phase transition to a spin-ordered state, neither ferromagnetic nor antiferromagnetic.
Effects of isospin mixing in the A=32 quintet
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 in {sup 32}Cl, and a correction to the allowed Fermi {beta}{sup +} decay of {sup 32}Ar. We demonstrate 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.
Global investigation of odd-even mass differences and radii with isospin-dependent pairing interactions
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Isospin dependence of capture cross sections: The {sup 36}S+{sup 208}Pb reaction
The capture-fission cross section for the {sup 36}S+{sup 208}Pb reaction was measured for seven center-of-mass energies ranging from 147.5 to 210.2 MeV. A comparison of the deduced interaction barriers from ''distribution of barriers'' measurements and simple 1/E{sub c.m.} plots for 13 well-characterized systems shows the validity of the latter approach for deducing interaction barriers, especially for reaction systems involving radioactive beams where the former measurements are not currently feasible. Application of the 1/E{sub c.m.} plot technique for the {sup 36}S+{sup 208}Pb reaction gives an interaction barrier height of 140.4{+-}1.4 MeV. This value as well as the deduced interaction barriers for all known studies of capture cross sections with radioactive beams are in good agreement with recent predictions of an improved isospin-dependent quantum molecular dynamics model and a modified version of capture cross-section systematics by Swiatecki et al. The deduced barriers for these n-rich systems are lower than one would expect from semiempirical systematics based upon the Bass potential. In addition to the barrier lowering, there is an enhanced subbarrier cross section in these n-rich systems not predicted by the Bass potential systematics. These enhanced subbarrier cross sections may be important in the synthesis of the heaviest nuclei.
Probing the sensitivity of the total nucleus-nucleus reaction cross section at intermediate energies to medium effects and isospin asymmetries
This paper presents reaction cross-section predictions. These predictions are the result of a continuous pipeline that originates from a microscopic nuclear interaction. Density parameters and effective nucleon-nucleon cross sections (both involved in the reaction calculations) are by-products of the same equation of state. First, we perform tests of sensitivity to medium effects using reactions involving {sup 208}Pb, a stable but weakly isospin-asymmetric nucleus. We also show predictions for collisions of some neutron-rich isotopes of calcium and argon. We observe significant sensitivity of the reaction cross section to medium effects but very weak sensitivity to inclusion of isospin asymmetry in the effective nucleon-nucleon cross sections.
Microscopic Calculations of Isospin-Breaking Corrections to Superallowed Beta Decay
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Magnetoelectric effect in bilayer graphene controlled by valley-isospin density
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S - and D -wave phase shifts in isospin-2 π π scattering from lattice QCD
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α decay of the T = 1 , 2 + state in B 10 and isospin symmetry breaking in the A = 10 triplet
Here, the rate of the T =1, 2+ to T =1, 0 + transition in 10 B ( T =1, T z =0) is compared to the analog transitions in 10 Be ( T =1, T z =–1) and 10 C ( T =1, T z =+1) to provide constraints on ab initio calculations using realistic nuclear forces. The relevant state in 10 B, at E x =5.164 MeV, is particle unbound. Therefore, a determination of the B ( E 2) electromagnetic transition rate requires a precise and accurate determination of the width of the state, as well as the α-particle and γ-ray branching ratios. Previous measurements of the α-particle branching ratio are just barely in agreement. We report on a new study of the α-particle branch by studying the 10 B(p,p') 10 B* reaction in inverse kinematics with the HELIOS spectrometer. The α-particle branching ratio that we observe, 0.144±0.027, is in good agreement with the evaluated value and improves the associated uncertainty. The resulting experimental B ( E 2) value is 7.0±2.2 e 2 fm 4 and is more consistent with a flat trend across the A=10 triplet than previously reported. This is inconsistent with Green's function Monte Carlo predictions using realistic three-nucleon Hamiltonians, which overpredict the B ( E 2) value in 10 C and 10 B.