Low-momentum Effective Interaction Research Articles

Four-body bound state calculations using three-dimensional low-momentum effective interaction Vlow-k

In this paper, we solve the coupled Yakubovsky integral equations for four-body (4B) bound state using the low-momentum effective two-body interaction [Formula: see text] in a three-dimensional (3D) approach, without using a partial wave (PW) decomposition. The renormalization group (RG) evolved interaction is constructed from spin-independent Malfliet–Tjon potential using the Lee–Suzuki method. The cutoff dependence of the 4B binding energy and wave function is investigated for a wide range of the momentum cutoff [Formula: see text] of [Formula: see text] interaction from 1.0 to 8.0[Formula: see text][Formula: see text].

Nucleon momentum distributions, their spin-isospin dependence, and short-range correlations

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\"{o}dinger equation, obtained within different many-body approaches. Particular attention is paid to the separation of the momentum distributions into the mean-field and short-range correlations (SRC) contributions. It is shown that at high values of the momentum $k$ the high-momentum components ($k\gtrsim 1.5-2$ fm$^{-1}$) 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. 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 that for all nuclei considered the momentum distributions in the states T=0 and T=1 exhibit at $k\gtrsim 1.5-2$ fm$^{-1}$ 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. The relationship of the present approach with the many-body methods based upon low-momentum effective interactions is briefly discussed.

Tensor force in effective interaction of nuclear force

The tensor force in effective interactions is discussed. We show that the tensor force in low-momentum effective interactions Vlowk and effective interactions for shell model studies are almost identical to that of the bare nucleon-nucleon interaction. We use realistic nuclear forces and microscopic theories of effective interactions. We calculate Vlowk by the technique of similarity transformation. The effective interaction for the nuclear shell model is calculated by folded diagram theory. The monopole contribution from the tensor force is analyzed by a spin-tensor decomposition.

Fermionic-bosonic couplings in a weakly deformed odd-mass nucleus,4193Nb

A comprehensive decay scheme of $^{93}$Nb below 2 MeV has been constructed from information obtained with the $^{93}$Nb(n,n$^\prime$$\gamma$) and $^{94}$Zr(p,2n$\gamma$$\gamma$)$^{93}$Nb reactions. Branching ratios, lifetimes, transition multipolarities and spin assignments have been determined. From $M1$ and $E2$ strengths, fermionic-bosonic excitations of isoscalar and isovector character have been identified from the weak coupling $\pi1g_{9/2}$$\otimes$$^{92}_{40}$Zr and $\pi2p_{1/2}^{-1}$$\otimes$$^{94}_{42}$Mo configurations. A microscopic interpretation of such excitations is attained from shell-model calculations using low-momentum effective interactions.

Realistic low-momentum effective interactions and nuclear structure near double closed shells

We report on a shell-model study of nuclei with four valence nucleons in the 132Sn and 208Pb regions. This aims at investigating to what extent the striking similarity existing between the low-energy properties of 134Sb and 210Bi persists when adding a pair of identical particles. We employ realistic low-momentum effective interactions derived from the CD-Bonn nucleon-nucleon potential through use of the Vlow-k approach. The calculated results are in very good agreement with the available experimental data and emphasize the persistence of a close resemblance between the spectroscopy of the two regions when moving away from the one proton-one neutron systems.

A realistic formalism for low-momentum effective interaction in three-dimensional approach

The low-momentum effective interaction V low k has been formulated in the three-dimensional momentum-helicity representation as a function of the magnitude of momentum vectors and the angle between them. As an application, AV18 potential has been used in the model space of Lee–Suzuki method and it has been shown that the low-momentum effective interaction, V low k reproduces the same two-body observables obtained by the bare potential V NN .

Low-momentum effective interaction in the three-dimensional approach

The formulation of the low-momentum effective interaction in the model space Lee–Suzuki and the renormalization group methods is implemented in the three-dimensional approach. In this approach the low-momentum effective interaction V low k has been formulated as a function of the magnitude of momentum vectors and the angle between them. As an application the spin–isospin independent Malfliet–Tjon potential has been used into the model space Lee–Suzuki method and it has been shown that the low-momentum effective interaction V low k reproduces the same two-body observables obtained by the bare potential V N N .