Low-momentum Nucleon-nucleon Interaction Research Articles

Nucleon-pair approximation with particle-hole excitations

In this paper, the formalism for the nucleon-pair approximation (NPA) with particle-hole excitations is developed. By using this approach, one is able to perform multiple-major-shell calculations. In this formulation, we use a particle-hole mixed representation, i.e., the particle-hole conjugate transformation is used for operators of the lower major shells, while operators of the upper major shells remain unchanged. We consider collective valence-particle pairs in the upper major shells, collective valence-hole pairs in the lower major shells, and collective pairs consisting of one valence particle in the upper shells and one valence hole in the lower shells to construct our model space. Matrix elements for the shell-model Hamiltonian, both for effective interactions and for phenomenological pairing plus multipole-multipole interactions, are derived in the nucleon-pair basis. As a special case, analytical formulas for doubly magic nuclei with excitations up to two-particle--two-hole are presented. To exemplify this approach, we calculate $^{100}\mathrm{Sn}$ considering both proton and neutron up to four-particle--four-hole excitations, where valence particles are in the 50-82 major shell and valence holes in the 28-50 major shell, with the low-momentum nucleon-nucleon interaction derived from the CD-Bonn potential.

Three-Dimensional Low-Momentum Interaction in Two-Body Bound State Calculations

The deuteron binding energy and wave function are calculated by using the recently developed three-dimensional form of low-momentum nucleon-nucleon ( NN ) interaction. The homogeneous Lippmann- Schwinger equation is solved in momentum space by using the low-momentum two-body interaction, which is constructed from Malfliet-Tjon potential. The results for both, deuteron binding energy and wave function, obtained with low-momentum interaction, are compared with the corresponding results obtained with bare potential.

Second-order quasiparticle interaction in nuclear matter with chiral two-nucleon interactions

We employ Landau's theory of normal Fermi liquids to study the quasiparticle interaction in nuclear matter in the vicinity of saturation density. Realistic low-momentum nucleon-nucleon interactions evolved from the Idaho N3LO chiral two-body potential are used as input potentials. We derive for the first time exact results for the central part of the quasiparticle interaction computed to second order in perturbation theory, from which we extract the L=0 and L=1 Landau parameters as well as some relevant bulk equilibrium properties of nuclear matter. The accuracy of the intricate numerical calculations is tested with analytical results derived for scalar-isoscalar boson exchange and (modified) pion exchange at second order. The explicit dependence of the Fermi liquid parameters on the low-momentum cutoff scale is studied, which provides important insight into the scale variation of phase-shift equivalent two-body potentials. This leads naturally to explore the role that three-nucleon forces must play in the effective interaction between two quasiparticles.

Gamow shell-model calculations of drip-line oxygen isotopes

We employ the Gamow shell model (GSM) to describe low-lying states of the oxygen isotopes $^{24}\mathrm{O}$ and $^{25}\mathrm{O}$. The many-body Schr\odinger equation is solved starting from a two-body Hamiltonian defined by a renormalized low-momentum nucleon-nucleon ($\mathit{NN}$) interaction and a spherical Berggren basis. The Berggren basis treats bound, resonant, and continuum states on an equal footing and is therefore an appropriate representation of loosely bound and unbound nuclear states near threshold. We show that the inclusion of continuum effects has a significant effect on the low-lying ${1}^{+}$ and ${2}^{+}$ excited states in $^{24}\mathrm{O}$. On the other hand, we find that a correct description of binding energy systematics of the ground states is driven by the proper treatment and inclusion of many-body correlation effects. This is supported by the fact that we get $^{25}\mathrm{O}$ unstable with respect to $^{24}\mathrm{O}$ in both oscillator and Berggren representations starting from a $^{22}\mathrm{O}$ core. Furthermore, we show that the structure of these loosely bound or unbound isotopes is strongly influenced by the ${}^{1}{S}_{0}$ component of the $\mathit{NN}$ interaction. This has important consequences for our understanding of nuclear stability.

Nuclear saturation with low momentum interactions

Relativistic effects are investigated in nuclear matter calculations employing renormalized low-momentum nucleon-nucleon ($\mathit{NN}$) interactions. It is demonstrated that the relativistic effects cure a problem of nonrelativistic low-momentum interactions, which fail to reproduce saturation of nuclear matter. Including relativistic effects, one already obtains saturation in a Hartree-Fock calculation. Brueckner-Hartree-Fock calculations lead to a further improvement of the saturation properties. The results are rather insensitive to the realistic $\mathit{NN}$ interaction on which they are based.

Low-momentumNNinteractions and all-order summation of ring diagrams of symmetric nuclear matter

We study the equation of state for symmetric nuclear matter using a ring-diagram approach in which the particle-particle hole-hole (pphh) ring diagrams within a momentum model space of decimation scale \ensuremath{\Lambda} are summed to all orders. The calculation is carried out using the renormalized low-momentum nucleon-nucleon ($\mathit{NN}$) interaction ${V}_{\mathrm{low}\text{\ensuremath{-}}k}$, which is obtained from a bare $\mathit{NN}$ potential by integrating out the high-momentum components beyond \ensuremath{\Lambda}. The bare $\mathit{NN}$ potentials of CD-Bonn, Nijmegen, and Idaho have been employed. The choice of \ensuremath{\Lambda} and its influence on the single particle spectrum are discussed. Ring-diagram correlations at intermediate momenta ($k\ensuremath{\simeq}2 {\mathrm{fm}}^{\ensuremath{-}1}$) are found to be particularly important for nuclear saturation, suggesting the necessity of using a sufficiently large decimation scale so that the above momentum region is not integrated out. Using ${V}_{\mathrm{low}\text{\ensuremath{-}}k}$ with $\ensuremath{\Lambda}~3 {\mathrm{fm}}^{\ensuremath{-}1}$, we perform a ring-diagram computation with the above potentials, which all yield saturation energies $E/A$ and Fermi momenta ${k}_{F}^{(0)}$ considerably larger than the empirical values. On the other hand, similar computations with the medium-dependent Brown-Rho scaled $\mathit{NN}$ potentials give satisfactory results of $E/A\ensuremath{\simeq}\ensuremath{-}15$ MeV and ${k}_{F}^{(0)}\ensuremath{\simeq}1.4 {\mathrm{fm}}^{\ensuremath{-}1}$. The effect of this medium dependence is well reproduced by an empirical three-body force of the Skyrme type.

Shell Model Description of theC14DatingβDecay with Brown-Rho-ScaledNNInteractions

We present shell model calculations for the beta decay of 14C to the 14N ground state, treating the states of the A=14 multiplet as two 0p holes in an 16O core. We employ low-momentum nucleon-nucleon (NN) interactions derived from the realistic Bonn-B potential and find that the Gamow-Teller (GT) matrix element is too large to describe the known lifetime. By using a modified version of this potential that incorporates the effects of Brown-Rho scaling medium modifications, we find that the GT matrix element vanishes for a nuclear density around 85% that of nuclear matter. We find that the splitting between the (J(pi),T)=(1(+),0) and (J(pi),T)=(0(+),1) states in 14N is improved using the medium-modified Bonn-B potential and that the transition strengths from excited states of 14C to the 14N ground state are compatible with recent experiments.

Microscopic restoration of proton-neutron mixed symmetry in weakly collective nuclei

Starting from the microscopic low-momentum nucleon-nucleon interaction ${V}_{\mathrm{low}k}$, we present a systematic shell-model study of magnetic moments and magnetic dipole transition strengths of the basic low-energy one-quadrupole phonon excitations in nearly spherical nuclei. Studying in particular the even-even $N=52$ isotones from $^{92}\mathrm{Zr}$ to $^{100}\mathrm{Cd}$, we find the predicted evolution of the predominantly proton-neutron nonsymmetric state reveals a restoration of collective proton-neutron mixed-symmetry structure near midshell. This provides a quantitative explanation for the existence of pronounced collective mixed-symmetry structures in weakly collective nuclei.

Low-momentum nucleon-nucleon interactions and shell-model calculations

In the last few years, the low-momentum nucleon-nucleon (NN) interaction V{sub low-k} derived from free-space NN potentials has been successfully used in shell-model calculations. V{sub low-k} is a smooth potential which preserves the deuteron binding energy as well as the half-on-shell T matrix of the original NN potential up to a momentum cutoff {lambda}. In this paper, we test a new low-momentum NN potential derived from chiral perturbation theory at next-to-next-to-next-to-leading order with a sharp low-momentum cutoff at 2.1 fm{sup -1}. Shell-model calculations for the oxygen isotopes using effective Hamiltonians derived from both types of low-momentum potential are performed. We find that the two potentials show the same perturbative behavior and yield very similar results.

Low momentum shell model effective interactions with all-order core polarizations

An all-order summation of core-polarization diagrams using the low-momentum nucleon-nucleon interaction ${V}_{\mathrm{low}\ensuremath{-}k}$ is presented. The summation is based on the Kirson-Babu-Brown (KBB) induced interaction approach in which the vertex functions are obtained self-consistently by solving a set of nonlinear coupled equations. It is found that the solution of these equations is simplified using ${V}_{\mathrm{low}\ensuremath{-}k}$, which is energy independent, and using the Green's functions in the particle-particle and particle-hole channels. We have applied this approach to the sd-shell effective interactions and find that the results we calculated to all orders by using the KBB summation technique are remarkably similar to those of second-order perturbation theory, the average differences being less than 10%.

Low-momentum nucleon-nucleon interaction and its application to few-nucleon systems

Low-momentum nucleon-nucleon interactions are derived within the framework of a unitary-transformation theory, starting with realistic nucleon-nucleon interactions. A cutoff momentum $\ensuremath{\Lambda}$ is introduced to specify a border between the low- and high-momentum spaces. By Faddeev-Yakubovsky calculations the low-momentum interactions are investigated with respect to the dependence of ground-state energies of $^{3}\mathrm{H}$ and $^{4}\mathrm{He}$ on the parameter $\ensuremath{\Lambda}$. It is found that we need the momentum cutoff parameter $\ensuremath{\Lambda}\ensuremath{\geqslant}5\phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$ in order to reproduce satisfactorily the exact values of the binding energies for $^{3}\mathrm{H}$ and $^{4}\mathrm{He}$. The calculation with $\ensuremath{\Lambda}=2\phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$ recommended by Bogner et al. leads to considerable overbinding at least for few-nucleon systems.

EFFECTIVE NUCLEON-NUCLEON INTERACTION AND FERMI LIQUID THEORY

We present two novel relations between the quasiparticle interaction in nuclear matter and the unique low momentum nucleon-nucleon interaction in vacuum. These relations provide two independent constraints on the Fermi liquid parameters of nuclear matter. Moreover, the new constraints define two combinations of Fermi liquid parameters, which are invariant under the renormalisation group flow in the particle-hole channels. Using empirical values for the spin-independent Fermi liquid parameters, we are able to compute the major spin-dependent ones by imposing the new constraints as well as the Pauli principle sum rules.