Tensor correlation in nuclei and its high momentum behavior

R. F. Bishop, R. Guardiola, I. Moliner +4 more

Takayuki Myo

Takayuki Myo

T. L. Ainsworth, E. Krotscheck

Massimiliano Alvioli, C. Ciofi degli Atti, L. P. Kaptari +2 more

The nucleon momentum distribution ${n}_{A}(k)$ for $A=2$, 3, 4, 16, and 40 nuclei is systematically analyzed in terms of wave functions resulting from advanced solutions of the nonrelativistic Schr\"odinger equation, obtained within different many-body approaches based upon different realistic bare nucleon-nucleon ($NN$) interactions featuring similar short-range repulsion and tensor interactions. Particular attention is paid to the separation of the momentum distributions into the mean-field and short-range correlation (SRC) contributions. It is shown that although at high values of the momentum $k$ different approaches lead to some quantitative differences, these do not hinder the general conclusion that the high-momentum behavior ($k\ensuremath{\gtrsim}1.5--2$ fm${}^{\ensuremath{-}1}$) of all nuclei considered are very similar, exhibiting the well-known scaling behavior with the mass number $A$, independently of the used many-body approach and the details of the bare $NN$ interaction. To analyze and understand the frequently addressed question concerning the relationships between the nucleus, ${n}_{A}(k)$, and the deuteron, ${n}_{D}(k)$, momentum distributions, the spin ($S$)-isospin ($T$) structure of few-nucleon systems and complex nuclei is analyzed in terms of realistic $NN$ interactions and many-body approaches. To this end, the number of $NN$ pairs in a given ($ST$) state, viz., $(ST)=(10)$, (00), (01), and (11), and the contribution of these states to the nucleon momentum distributions are calculated. It is shown that, apart from the (00) state, which has very small effects, all other spin-isospin states contribute to the momentum distribution in a wide range of momenta. It is shown that for all nuclei considered the momentum distributions in the states $T=0$ and $T=1$ exhibit at $k\ensuremath{\gtrsim}1.5--2$ fm${}^{\ensuremath{-}1}$ very similar behaviors, which represents strong evidence of the $A$-independent character of SRCs. The ratio ${n}_{A}(k)/{n}_{D}(k)$ is analyzed in detail, stressing that in the SRC region it always increases with the momentum and the origin of such an increase is discussed and elucidated. The relationships between the one- and two-body momentum distributions, considered in a previous paper, are discussed and clarified, pointing out the relevant role played by the center-of-mass motion of a correlated pair in the (10) state. Eventually, the values of the the probability of high-momentum components in nuclei and the per nucleon probability ${a}_{2}$ of deuteronlike configurations in nuclei are calculated, and the relationship of the present approach with the many-body methods based upon low-momentum effective interactions is briefly discussed.

O. Hen, L. B. Weinstein, E. I. Piasetzky +3 more

Background: The high-momentum distribution of atoms in two spin-state ultracold atomic gases with strong short-range interactions between atoms with different spins, which can be described by using Tan's contact, are dominated by short-range pairs of different fermions and decreases as ${k}^{\ensuremath{-}4}$. In atomic nuclei the momentum distribution of nucleons above the Fermi momentum ($k>{k}_{F}\ensuremath{\approx}250$ MeV/$c$) is also dominated by short-range-correlated different-fermion (neutron-proton) pairs.Purpose: Compare high-momentum unlike-fermion momentum distributions in atomic and nuclear systems.Methods: We show that, for $k>{k}_{F}$ MeV/$c$, nuclear momentum distributions are proportional to that of the deuteron. We then examine the deuteron momentum distributions derived from a wide variety of modern nucleon-nucleon potentials that are consistent with $NN$-scattering data.Results: The high-momentum tail of the deuteron momentum distribution, and hence of the nuclear momentum distributions, appears to decrease as ${k}^{\ensuremath{-}4}$. This behavior is shown to arise from the effects of the tensor part of the nucleon-nucleon potential. In addition, when the dimensionless interaction strength for the atomic system is chosen to be similar to that of atomic nuclei, the probability for finding a short-range different-fermion pair in both systems is the same.Conclusions: Although nuclei do not satisfy all of the conditions for Tan's contact, the observed similarity of the magnitude and ${k}^{\ensuremath{-}4}$ shape of nuclear and atomic momentum distributions is remarkable because these systems differ by about 20 orders of magnitude in density. This similarity may lead to a greater understanding of nuclei and the density dependence of nuclear systems.