Description of the two-nucleon system on the basis of the Bargmann representation of the S matrix

For the effective-range function $k\cot \delta$, a pole approximation that involves a small number of parameters is derived on the basis of the Bargmann representation of the $S$ matrix. The parameters of this representation, which have a clear physical meaning, are related to the parameters of the Bargmann $S$ matrix by simple equations. By using a polynomial least-squares fit to the function $k\cot \delta$ at low energies, the triplet low-energy parameters of neutron-proton scattering are obtained for the latest experimental data of Arndt et al. on phase shifts. The results are $a_{t}=5.4030$fm, $r_{t}=1.7494$fm, and $v_{2}=0.163$fm$^{3}$. With allowance for the values found for the low-energy scattering parameters and for the pole parameter, the pole approximation of the function $k\cot \delta$ provides an excellent description of the triplet phase shift for neutron-proton scattering over a wide energy range ($T_{\text{lab}}\lesssim 1000$MeV), substantially improving the description at low energies as well. For the experimental phase shifts of Arndt et al., the triplet shape parameters $v_{n}$ of the effective-range expansion are obtained by using the pole approximation. The description of the phase shift by means of the effective-range expansion featuring values found for the low-energy scattering parameters proves to be fairly accurate over a broad energy region extending to energy values approximately equal to the energy at which this phase shift changes sign, this being indicative of a high accuracy and a considerable value of the effective-range expansion in describing experimental data on nucleon-nucleon scattering. The properties of the deuteron that were calculated by using various approximations of the effective-range function comply well with their experimental values.Comment: 39 pages, 3 figure

The Oldest Case of Decapitation in the New World (Lapa do Santo, East-Central Brazil)

We present here evidence for an early Holocene case of decapitation in the New World (Burial 26), found in the rock shelter of Lapa do Santo in 2007. Lapa do Santo is an archaeological site located in the Lagoa Santa karst in east-central Brazil with evidence of human occupation dating as far back as 11.7-12.7 cal kyBP (95.4% interval). An ultra-filtered AMS age determination on a fragment of the sphenoid provided an age range of 9.1-9.4 cal kyBP (95.4% interval) for Burial 26. The interment was composed of an articulated cranium, mandible and first six cervical vertebrae. Cut marks with a v-shaped profile were observed in the mandible and sixth cervical vertebra. The right hand was amputated and laid over the left side of the face with distal phalanges pointing to the chin and the left hand was amputated and laid over the right side of the face with distal phalanges pointing to the forehead. Strontium analysis comparing Burial 26's isotopic signature to other specimens from Lapa do Santo suggests this was a local member of the group. Therefore, we suggest a ritualized decapitation instead of trophy-taking, testifying for the sophistication of mortuary rituals among hunter-gatherers in the Americas during the early Archaic period. In the apparent absence of wealth goods or elaborated architecture, Lapa do Santo's inhabitants seemed to use the human body to express their cosmological principles regarding death