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Register a new userShort range correlations and the isospin dependence of nuclear correlation functions
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Pair densities and associated correlation functions provide a critical tool for introducing many-body correlations into a wide-range of effective theories. Ab initio calculations show that two-nucleon pair-densities exhibit strong spin and isospin dependence. However, such calculations are not available for all nuclei of current interest. We therefore provide a simple model, which involves combining the short and long separation distance behavior using a single blending function, to accurately describe the two-nucleon correlations inherent in existing ab initio calculations. We show that the salient features of the correlation function arise from the features of the two-body short-range nuclear interaction, and that the suppression of the pp and nn pair-densities caused by the Pauli principle is important. Our procedure for obtaining pair-density functions and correlation functions can be applied to heavy nuclei which lack ab initio calculations.
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The target-mass number dependence of nucleon-nucleon pairs with short-range correlations is explored in a physically transparent geometrical model within a zero-range approximation. The observed $A$ dependence of 2-nucleon ejection cross sections in $(e,e)$ reactions is found to reflect the mass dependence of nuclear density distributions. A parametrization of this $A$ dependence is given. The $A$ dependence of proton-proton vs. proton-neutron pairs relative to $^{12}$C is also analyzed in this model. It can be understood using simple combinatorics without any additional isospin dependence.
We develop a theoretical approach for nuclear spectral functions at high missing momenta and removal energies based on the multi-nucleon short-range correlation~(SRC) model. The approach is based on the effective Feynman diagrammatic method which allows to account for the relativistic effects important in the SRC domain. In addition to two-nucleon SRC with center of mass motion we derive also the contribution of three-nucleon SRCs to the nuclear spectral functions. The latter is modeled based on the assumption that 3N SRCs are a product of two sequential short range NN interactions. This approach allowed us to express the 3N SRC part of the nuclear spectral function as a convolution of two NN SRCs. Thus the knowledge of 2N SRCs allows us to model both two- and three-nucleon SRC contributions to the spectral function. The derivations of the spectral functions are based on the two theoretical frameworks in evaluating covariant Feynman diagrams: In the first, referred as virtual nucleon approximation, we reduce Feynman diagrams to the time ordered noncovariant diagrams by evaluating nucleon spectators in the SRC at their positive energy poles, neglecting explicitly the contribution from vacuum diagrams. In the second approach, referred as light-front approximation, we formulate the boost invariant nuclear spectral function in the light-front reference frame in which case the vacuum diagrams are generally suppressed and the bound nucleon is described by its light-cone variables such as momentum fraction, transverse momentum and invariant mass.
The recent x>1 (e,e) and correlation experiments at momentum transfer Q^2 ge 2 GeV^2 confirm presence of short-range correlations (SRC) in nuclei mostly build of nucleons. Recently we evaluated in a model independent way the dominant photon contribution to the nuclear structure. Taking into account this effect and using definition of x consistent with the exact kinematics of eA scattering (with exact sum rules) results in the significant reduction of R_A(x,Q^2)=F_{2A}(x,Q^2)/F_{2N}(x,Q^2) ratio which explains sim 50% of the EMC effect for xle 0.55 where Fermi motion effects are small. The remaining part of the EMC effect at $xge 0.5$ is consistent with dominance of the contribution of SRCs. Implications for extraction of the F_{2n}/F_{2p} ratio are discussed. Smallness of the non-nucleonic degrees of freedom in nuclei matches well the recent observation of a two-solar mass neutron star, and while large pn SRCs lead to enhancement of the neutron star cooling rate for kTle 0.01 MeV.
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 ($kgtrsim 1.5-2$ 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 $kgtrsim 1.5-2$ 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.
Ab-initio Quantum Monte Carlo (QMC) calculations of nuclei from deuterium to 40Ca, obtained using four different phenomenological and local chiral nuclear potentials, are analyzed using the Generalized Contact Formalism (GCF). We extract spin- and isospin-dependent nuclear contact terms for each interaction in both coordinate and momentum space. The extracted contact terms, that count the number of short-range correlated (SRC) pairs with different quantum numbers, are dependent on the nuclear interaction model used in the QMC calculation. However, the ratios of contact terms for a nucleus A to deuterium (for spin-1 pn pairs) or to 4He (for all NN pairs) are independent of the nuclear interaction model and are the same for both short-distance and high-momentum pairs. This implies that the relative abundance of short-range pairs in the nucleus is a long-range (mean-field) quantity that is insensitive to the short-distance nature of the nuclear force. Measurements of exclusive (e,eNN) pair breakup processes are instead more sensitive to short-range dynamics
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