Quartet N-d Scattering Lengths

Quartet n-d scattering lengths are calculated using second-generation nucleon-nucleon potential models. These results are compared to the corresponding quantity recently calculated using chiral perturbation theory. 1 Accurate calculations of n-d quartet scattering lengths were first performed 10 years ago[1]. This quantity is known to be insensitive to most physics, such as ℓ > 0 partial waves of the nucleon-nucleon (NN) potential and three-nucleon forces, because of constraints arising from the Pauli principle. The low (actually, zero) energy of the incoming neutron emphasizes s-waves, while the quartet spin emphasizes S = 1 between the two neutrons, which combination is Pauli forbidden. This reaction at zero energy depends only on details of the deuteron s-wave for an accurate calculation. The potentials of a decade ago (sometimes called " first-generation " potentials) were not particularly accurate fits to the NN data base (or even to the data bases in use when those potentials were constructed). Deuteron properties, such as binding energies and asymptotic normalization constants, had considerable variations. Thus, it is not surprising that three-nucleon properties showed considerable spread due to these indifferent fits, although it was never clear in advance which properties were suspect. One such property was a 4 , the n-d quartet scattering length, where values of 6.304 fm and 6.380 fm were obtained[1] for the RSC[2] and AV14[3] potential models, respectively. Variations of these numbers due to partial-wave limitations or three-nucleon forces are of the order of 10 −3 a 4 (or less), which is much smaller than the potential-model difference. Recently, a new class of potentials has been developed (sometimes called " second-generation ") that provides greatly improved fits to the NN data base[4, 5]. Only a single calculation[6] of a 4 exists for a single second-generation potential model (AV18)[5], and that result lies between the RSC and AV14 results listed above. Until very recently , no particular motivation existed for revisiting the a 4 calculations. Chiral perturbation theory[7] (χPT) provides an alternative path (to conventional potentials) for calculating few-nucleon observables. Scattering amplitudes are constructed directly from a field theory, employing one or another scheme of regulariza-tion and renormalization. In this fashion the first three-nucleon calculation exploiting chiral perturbation theory was recently performed[8] for the observable a 4. The result, 6.33(10) fm, lies between the RSC and AV14 results quoted above, which motivates this brief update of the theoretical situation. Table 1: Quartet n-d scattering lengths (a 4 …