Multinucleon short-range correlation model for nuclear spectral functions: Theoretical framework

We develop a theoretical approach for nuclear spectral functions at high missing momenta and removal energies based on the multinucleon short-range correlation (SRC) model. The approach is based on the effective Feynman diagrammatic method which allows us to account for the relativistic effects important in the SRC domain. In addition to two-nucleon (2N) SRC with center of mass motion we also derive 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 nucleon-nucleon (NN) interactions. This approach allows 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 two theoretical frameworks for evaluating covariant Feynman diagrams: In the first, referred to 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 to 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-front variables such as momentum fraction, transverse momentum, and invariant mass.

Figure 1

Representation of the covariant Feynman amplitude through the sum of the time ordered amplitudes. Panel (b) corresponds to the scenario in which first, the bound nucleon is resolved in the nucleus which interacts with the incoming probe $h$. In panel (c), initially, the incoming probe produces $\overline{N}N$ pair with $\overline{N}$ being subsequently absorbed in the nucleus.

Figure 2

Expansion of the nuclear spectral function into the contributions of mean field (a), 2N (b), and 3N (c) SRCs. For each case the initial nuclear transition vertices are different, corresponding to transition of $A\to N,A-1;A\to NN,A-1$; and $A\to NNN,A-3$ for the mean field, 2N, and 3N SRCs respectively. The NN (b) and NNN (c) labels identify 2N and 3N SRCs with effective NN and NNN vertices elaborated in the text.

Figure 3

Diagram corresponding to 3N SRC contribution to the spectral function.