Beta Decay ofC14and Nuclear Forces

Abstract

The anomalously long lifetime of C 14 is interpreted as being due to an accidental cancellation in the /3-decay matrix element which is complete to about one part in 160. In the shell model with oscillator wave functions, general two-nucleon interactions are introduced which are linear in the velocities and which satisfy various invariance requirements. As many of the force parameters are determined from low-energy experimental nuclear data as possible. The strength of the spin-orbit force is fixed by the P$~Ph splitting in N 15 , while the tensor force is taken from meson theory. The conditions for cancellation are then shown to be satisfied, although uncertainties in the central force prevent an exact calculation of the wave functions. These uncertainties are therefore eliminated by requiring cancellation, in addition to fitting the three lowest energy levels of N 14 . The resulting N 14 ground state wave function is mainly Z>-state, containing only 13% P-and 3% ^-component, and checks satisfactorily against various experimental properties of N 14 . In addition, the /? decay of O 14 is investigated and it is shown that the C 14 -O 14 difference in //-values is not adequately accounted for by the Coulomb repulsion theory of Jancovici and Talmi. The discrepancy is removed by including the slight difference in spin-orbit coupling strength for protons and neutrons, due to electromagnetic interaction with their magnetic moments. It is also pointed out that a nonlinearity of about 10% should be expected in the O 14 FermiKurie plot. In the appendices are a treatment of nucleon hole conjugation, an extension of a proof by Inglis on the impossibility of cancellation without the tensor force, a calculation of the n-a spin-orbit splitting, and an approximate treatment of the binding energy of the a particle.

Allowed Gamow–Teller excitations from the ground state of 14N

“…In Table IV, we present the values of the coefficients C As mentioned in the introduction, it has been noted in the past [6,7,10,11] to a similar conclusion in their study of M1 excitation rates in the 0p and 1d − 0d shells [20]. It is useful to note here, as pointed out by Wong [21], that the tensor interaction in an open-shell acts to some extent like a spin-orbit interaction of the opposite sign of the basic spin-orbit interaction, so that these two types of adjustments to the N − N interaction are really equivalent for our purpose.…”

“…Thus, the A = 14 system affords us one of the few instances where one can study the elusive effects of the tensor interaction in nuclear structure [4,5]. Visscher and Ferrel [6] plotted the strength parameters of the spin-orbit and tensor interactions for which one could get the GT matrix element to vanish. They noted that if the spin-orbit interaction is too weak then they cannot get the GT matrix element to vanish for any value of the tensor interaction strength parameter.…”

Measurement of the shape factor for theβdecay ofO14

“…More than 99% of the decays proceed by a 0 + → 0 + Fermi transition from the 14 O ground state to the isobaric analog 2.313 MeV first excited state of 14 N. The ground state branch, which is the subject of the present work, is an allowed 0 + → 1 + Gamow-Teller (GT) transition with an endpoint energy of 4.12 MeV, and a log f t value of roughly 7.3. The unusually large f t is thought to be the result of an accidental cancellation between various nuclear wave function components that contribute to the axial vector matrix element [2,3].…”

Nucleon Charge-Exchange Reactions at Intermediate Energy

“…Initial results have been reported for a number of targets ranging from 9 Be to 154 Sm, which again demonstrate the strong excitation ofGT transitions [63]. In addition, the good energy resolution in these measurements (210 keV) has revealed fine structure in the GTGR of medium mass nuclei such as 58 Ni, which permits interesting comparisons with the M1 strength distributions observed in high resolution (e,e') measurements [64].…”

“…A possible connection between nuclear beta decay rates and (p , n) reactions was noted at least as early as 1957 [9], but the first paper to really investigate the potential of charge-exchange reactions for studies of the effective interaction in nuclei was that of Bloom, Glendenning and Mozkowski [ 10] entitled "The proto-neutron interaction and the (p , n) reaction in mirror nuclei." In it they assumed that the effective interaction could be expressed as an isoscalar and an isovector part v = v a + v b -.…”