Renormalization of the Axial-Vector Coupling Constant in NuclearβDecay

Abstract

to one's convenience. For small A, the wave function does not seem to be so nearly factorable and solving Eq. (2V) should lead to an improvement in both the energy and the wave function.In summary, we point out that a continuous class of transformations (for generating a state which is an eigenstate of the total momentum from a state which is not) have been presented. Of this class, the transformation which minimizes the energy is the transformation characterized by the function G which sa'tisf led Eq. (2V). This transformation yieMs the variationally "best" intrinsic wave function (t"~4 ). Thus quantities which may be sensitive to how the center of mass is treated" ' should be calculated using the transformation characterized by G as shown above.The isoscalar magnetic moments and Gamer-Teller p decay of the systems A~11, 13, 15, 17, 19, and 21 are analyzed in an attempt to extract, in a largely model-independent way, the effective nuclear renormalization of the axial coupling constant: gz g", . We find: gz~/g~= 0.920 + 0.047.Conservation of the vector current, which, for the purposes of this paper, we take to be absolute, assures us, in effect, that the Fermi p decay of nucleons bound 1nto a nucleus 18 ldentlcal 1Q 1Qtrinsic strength with that for nucleons in the free state; The strong interactions that clothe the bare nucleon in the free state and that, additionally, bind nucleons together into complex systems do not renormalize the effective intrinsic vector coupling constant; we do Qot have to ask how the overall nuclear Fermi P-decay strength ls divided between baryonic and mesonic components, since an exact compensation exists and the differing mesonic currents as between one nucleus and another merely rearrange the seat of the vector P decay as between baryons and mesons but do not change its total strength. The situation with axial decay is quite otherwise; the axial current is not conserved; the strong interactions renormalize the axial coupling constant of the bare nucleon so that, for free nucleons,~g "(~1 . 23~g"( and must effect an additional renormalization when they bind nucleons together into nuclei, The intrinsic Gamovr-Teller p-decay strength is therefore not constant from nucleus to nucleus nor from transition to transition within a single nuclear system nor can it be associated in a unique way with baryons and arith mesons; the effect of meson currents on the axial decay, the division of the strength between single nucleon and many-body terms and so on must be expected to vary smith every circumstance but without the overriding compensation between

Orbital electron capture by the nucleus

“…Thus, X is in principle not a constant over the whole range of nuclei. For light nuclei, a deviation of X from the free-nucleon value by 17% has been found Szybisz, 1975;(Wilkinson, 1973a, 1974aAEricson et al,, 1973Ohta and Wakamatsu, 1974), Under these assumptions, we develop the relation between form-factor coefficients and nuclear matrix elements for a pure V-A nucleon current of the form given in Eq. (2-4).…”

Nuclear matrix elements for double-βdecay

“…The first type of quenching depends strongly on the size of the model space used in the calculation and is thus model dependent. It was extensively investigated in light nuclei, A ∼ 20, in the 1970s [65][66][67] within the framework of the ISM where it was found that g A,ef f ∼ = 1.0, q ∼ = 0.75. In heavy nuclei, of particular interest in this paper, the ques-tion of quenching was first discussed by Fujita and Ikeda [68] in 1965.…”

On the asymmetry of Gamow–Teller β-decay rates in mirror nuclei in relation with second-class currents

“…However, it is also well established [30,43] that in the shell model, up to a good approximation, the phenomenon can be taken into account by an empirical multiplicative factor, (g A /g V ) eff = λ (g A /g V ) bare with a bare value for the ratio of 1.26 as obtained from neutron decay (see Ref. [44] for certain cautions).…”