Spectral Functions In Nuclear Matter Research Articles

Three-body force effect on off-shell mass operator and spectral functions in nuclear matter

Within the framework of the Brueckner theory, the off-shell behaviors of the mass operator $M(k,\omega)=V(k,\omega)+iW(k,\omega)$, i.e., its dependence upon the momentum $k$ and upon the nucleon frequency $\omega$, are investigated by including nuclear three-body force (TBF). The first two terms of the hole-line expansion of the mass operator are taken into account. The TBF effects on their off-shell properties are discussed. A comparison is made between the on-shell and off-shell values of $M_{1}$. The nucleon spectral function and nucleon momentum distribution are also calculated, and the calculation shows that they are hardly affected by the TBF effect at the saturation density. At a high density two times greater than the saturation density, inclusion of the TBF may lead to a visible effect on the spectral function and may enhance the depletion of the hole states.

Hadronic spectral functions in nuclear matter

We study the in-medium properties of mesons ( π, η, ρ) and baryon resonances in cold nuclear matter within a coupled-channel analysis. The meson self energies are generated by particle–hole excitations. Thus multi-peak spectra are obtained for the mesonic spectral functions. In turn this leads to medium-modifications of the baryon resonances. Special care is taken to respect the analyticity of the spectral functions and to take into account effects from short-range correlations both for positive and negative parity states. Our model produces sensible results for pion and Δ dynamics in nuclear matter. We find a strong interplay of the ρ meson and the D 13(1520), which moves spectral strength of the ρ spectrum to smaller invariant masses and leads to a broadening of the baryon resonance. The optical potential for the η meson resulting from our model is rather attractive whereas the in-medium properties modifications of the S 11(1535) are found to be quite small.

Sum rules and short-range correlations in nuclear matter at finite temperature

The nucleon spectral function in nuclear matter fulfills an energy weighted sum rule. Comparing two different realistic potentials, these sum rules are studied for Green's functions that are derived self-consistently within the $T$ matrix approximation at finite temperature.

Vector Mesons in Nuclear Matter

We present a relativistic and unitary approach to pion- and photonnucleon scattering taking into account the πN, ρN, щN, хN, πΔ, KΛ and KΣ channels. Our scheme dynamically generates the s- and d-wave baryon resonances N (1535), N (1650), N (1520) and N (1700) and as well as Δ (1620) and Δ (1700) in terms of quasi-local two-body interaction terms. We obtain a fair description of the experimental data relevant for the properties of slow vector mesons in nuclear matter. The resulting s-wave ρ- and ω-meson nucleon scattering amplitudes, which define the leading density modification of the ρ-and ω-meson spectral functions in nuclear matter, are presented.

From Meson– and Photon–Nucleon Scattering to Vector Mesons in Nuclear Matter

We present a relativistic and unitary approach to pion- and photon-nucleon scattering taking into account the $\pi N$, $\rho N$, $\omega N$, $\eta N$, $\pi\Delta$, $K \Lambda$ and $K \Sigma$ channels. Our scheme dynamically generates the s- and d-wave nucleon resonances N(1535), N(1650), N(1520) and N(1700) and isobar resonances $\Delta(1620)$ and $\Delta(1700)$ in terms of quasi-local two-body interaction terms. We obtain a fair description of the experimental data relevant for slow vector-meson propagation in nuclear matter. The s-wave $\rho $- and $\omega $-meson nucleon scattering amplitudes, which define the leading density modification of the $\rho$- and $\omega $-meson spectral functions in nuclear matter, are predicted.

From Meson- and Photon-Nucleon Scattering to Vector Mesons in Nuclear Matter

We present a relativistic and unitary approach to pion- and photon-nucleon scattering taking into account the πN, ρN, ωN, ηN, πΔ, KΛ and KΣ channels. Our scheme dynamically generates the s- and d-wave baryon resonances N(1535), N(1650), N(1520) and N(1700) and as well as Δ(1620) and Δ(1700) in terms of quasi-local two-body interaction terms. We obtain a fair description of the experimental data relevant to the properties of slow vector mesons in nuclear matter. The resulting s-wave ρ- and ω-meson-nucleon scattering amplitudes which define the leading density modification of the ρ- and ω-meson spectral functions in nuclear matter, are presented.

Two-nucleon spectral function in infinite nuclear matter

The two-nucleon spectral function in nuclear matter is studied using Correlated Basis Function perturbation theory, including central and tensor correlations produceded by a realistic hamiltonian. The factorization property of the two-nucleon momentum distribution into the product of the two single nucleon distributions shows up in an analogous property of the spectral function. The correlated model yields a two-hole contribution quenched whith respect to Fermi gas model, while the peaks acquire a quasiparticle width that vanishes as the two momenta approach $k_F$. In addition, three-hole one-particle and more complicated intermediate states give rise to a background, spread out in energy and absent in the uncorrelated models. The possible connections with one- and two-nucleon emission processes are briefly discussed.

Transport theoretical approach to the nucleon spectral function in nuclear matter

The nucleon spectral function in infinite nuclear matter is calculated in a quantum transport theoretical approach. Exploiting the known relation between collision rates and correlation functions the spectral function is derived self-consistently. By re-inserting the spectral functions into the collision integrals the description of hard processes from the high-momentum components of wave functions and interactions is improved iteratively until convergence is achieved. The momentum and energy distributions and the nuclear matter occupation probabilities are in very good agreement with the results obtained from many-body theory.

Vector mesons in nuclear matter

We present novel results for the ϱ and ω spectral functions in nuclear matter, deduced from a coupled channel analysis of pion-nucleon scattering data.

Nucleon self-energies and spectral functions in nuclear matter at finite temperature with a realistic potential

We use a separable form of the Paris nucleon-nucleon interaction to calculate nucleon self-energies and spectral functions at the saturation density of symmetric nuclear matter at finite temperature. The behaviour of these quantities at temperatures above and close to the critical temperature for the superfluid phase transition in nuclear matter is investigated. From the self-energy the spectral function and occupation numbers at finite temperature are calculated. The sensitivity of the results for the realistic nucleon-nucleon potential to details of the interaction potential is studied by a comparison to an exploratory calculation previously done for the purely attractive Yamaguchi potential.

SOME CONSEQUENCES OF DRESSING NUCLEONS

A representation of nucleon spectral functions in nuclear matter is developed. Various contributions are identified including a quasiparticle term, broad background contributions below and above the Fermi energy, and a high-energy tail which has no significant momentum dependence. A convenient analytical energy dependence supplemented by a numerical dependence on momentum allows computationally tractable studies of the consequences associated with the considerable dressing of the nucleons. Applications are presented for high-momentum components as a function of energy, density of states, dressed particle-hole response, and the dressed particle-particle/hole-hole propagator.

Two-nucleon correlations and the nucleon spectral function in nuclear matter at finite temperature: low-density region

The nucleon spectral function is calculated in low-density nuclear matter at finite temperature. Using Matsubara Green's functions the nucleon selfenergy is evaluated in the ladder approximation for the thermodynamic two-particle T-matrix. In addition to the contribution from the continuum part of the T-matrix special attention is paid to its pole contribution reflecting the two-particle bound state (deuteron) in the medium. The consequences of the formation of two-particle bound states for the selfenergy and the one-particle spectral function are shown.

Energy weighted sum rules for spectral functions in nuclear matter.

The energy weighted sum rule of single-particle spectral functions in nuclear matter is studied. The spectral functions include the influence of short-range correlations as generated by the Reid potential in the framework of the self-consistent Green's function method. For the range of momenta studied, the sum rule is rather accurately fulfilled numerically (within 5%). It is observed that the high-energy tail of the particle part of the spectral function exhausts most of the sum rule, which confirms the need for the appearance of single-particle strength at very high energies.

Spectral functions in nuclear matter.

Spectral functions are calculated from mean fields calculated both by Brueckner and by Botermans-Malfliet Green's function methods. Similarities and differences between the two methods are illustrated. Results are shown at normal nuclear matter density and zero temperature. Calculations are made by the separable phase-shift technique that was introduced earlier including the single-particle strength up to \ensuremath{\sim}1700 MeV with (usually) less than 1% of the total strength missing. It is found that \ensuremath{\sim}5% of the single particle strength lies above 500 MeV. Mean removal (centroid) energies of nucleons and occupation numbers are calculated by energy averaging over the spectral functions. The averages are also done in the extended quasiparticle approximation for the spectral function discussed in an earlier paper showing good agreement with the ``exact'' results. It is in fact shown that this approximation yields the same result for centroid energies as does Koltun's work which was based on an analysis of the linked cluster expansion. The total energy is calculated by Koltun's sum rule which involves an integration over the calculated (correlated) occupation numbers. The result compares favorably with the Brueckner energy which involves an integration over model (uncorrelated) occupation numbers.

Off-the-energy-shell properties of the mass operator and spectral functions in nuclear matter

We investigate the off-the-energy-shell properties of the mass operator M( k; ω) = V( k; ω) + iW( k; ω), i.e., its dependence upon the nucleon momentum k and upon the nucleon frequency ω, separately. Particular attention is paid to the dispersion relation which connects its real and imaginary parts. We limit ourselves to the first two terms of the hole-line expansion of the mass operator, namely to the Brueckner-Hartree-Fock field M 1( k; ω) and to the second-order “rearrangement” term M 2( k; ω). Most previous works only dealt with “on-shell values” obtained by setting ω equal to the root e( k) of an energy-momentum relation, or equivalently by setting k equal to the root k( e) of this energy-momentum relation. We use as input a finite-rank representation of the realistic Argonne v 14 nucleon-nucleon interaction. The Fermi momentum is set equal to 1.36 fm −1. For momenta larger than the Fermi momentum, the calculated k-dependence of the on-shell depth V 1( k; e( k)) can be approximated by a gaussian. The corresponding nonlocality range is close to that assumed by Perey and Buck in their phenomenological analysis of scattering cross sections; it is somewhat smaller than that associated with the k-dependence of the off-shell potential V 1( k; ω) for fixed ω. The calculated ω-dependence of V 2( k; ω) is in excellent agreement with the dispersion relation which connects V 2( k; ω) to the values of W 2( k; ω′) for all ω′< e( k 1). The dispersion relation between V 1( k; ω) and W 1( k; ω′) is also investigated; in that case, caution must be exercised because the values of W 1( k; ω′) for ω′ larger than 500 MeV still play a sizeable role, and also because the dispersion relation involves a large ω-independent “background”; it is proved that the latter is equal to the Hartree-Fock potential. More generally, the dispersion relation between the real and imaginary parts of the exact mass operator involves an ω-independent background for which we derive a closede xpression analogous to but different from the Hartree-Fock potential. The ω-dependence of the spectral function S( k; ω) is calculated for two typical values of k, namely 3 4 k F and 5 4 k F . Its integral over all values of ω differs from unity by only a few percent, which provides an estimate of the reliability of our approximation scheme. We study the dependence upon E A + 1 ∗ of the integrated “particle” strength located below the excitation energy E A + 1 ∗ in the system formed by adding a nucleon with momentum k to the nuclear-matter ground state. We also calculated the dependence upon E A − 1 ∗ of the integrated “hole” strength located below the excitation energy E A − 1 ∗ in the system formed by taking out a nucleon with momentum k from the nuclear-matter ground state. In the limit E A − 1 ∗ → ∞ , this integrated hole strength yields an approximation of the occupation probability of the momentum k in the ground state. We compare this result with estimates obtained from other approximate expressions which involve the partial derivative of V 1( k; ω) with respect to ω. We also evaluate the “mean removal energies” and compare them to the “quasiparticle energies,” i.e., to the energies at which the spectral function presents a maximum.

Mean field, occupation numbers and spectral functions in nuclear matter

Using the experimental free-scattering phase shifts as input, properties of nuclear matter are calculated by Brueckner many-body techniques. Previously reported calculations are extended to include second-order “rearrangement” contributions to the mean field, occupation numbers and spectral functions. Results are in close agreement with potential model calculations.