Nuclear Response Functions Research Articles

Role of color neutrality in nuclear physics: Modifications of nucleonic wave functions.

The influence of the nuclear medium upon the internal structure of a composite nucleon is examined. The interaction with the medium is assumed to depend on the relative distances between the quarks in the nucleon consistent with the notion of color neutrality, and to be proportional to the nucleon density. In the resulting description the nucleon in matter is a superposition of the ground state (free nucleon) and radial excitations. The effects of the nuclear medium on the electromagnetic and weak nucleon form factors and the nucleon structure function are computed using a light-front constituent quark model. Further experimental consequences are examined by considering the electromagnetic nuclear response functions. The effects of color neutrality supply small but significant corrections to predictions of observables. {copyright} {ital 1996 The American Physical Society.}

Two-body and many-body final state interaction corrections in the nuclear matter response function around the quasielastic peak

Abstract The inclusive scattering response function of nuclear matter is studied in the regime of large but non-relativistic momentum transfer q . We review the derivation leading to the complete two-particle final state interaction corrections to the impulse approximation. These are calculated with an eikonal approach and using models that we develop for the two-particle density matrix, which account for spin and isospin degrees of freedom. The two-body part gives comparable results to a many-body approximation with a sizable reduced strength in the response at values q = 550 MeV, and energy transfers ω around and beyond the quasielastic peak, and, with a finite-size approximation involving the nucleus scale, it produces oscillations. These behaviours are in accordance with data from nuclei. Our results resemble those with a hard-core interaction for which strength in the response is shifted to large values of the energy transfer ω.

Investigation of the neutron form factors by inclusive quasielastic scattering of polarized electrons off polarized 3He: A theoretical overview.

The theory of quasielastic inclusive scattering of polarized leptons off polarized $^{3}\mathrm{He}$ is critically reviewed and the origin of different expressions for the polarized nuclear response function appearing in the literature is explained. The sensitivity of the longitudinal asymmetry upon the neutron form factors is thoroughly investigated and the role played by the polarization angle for minimizing the proton contribution is illustrated.

Relativistic treatment of spin-transfer observables in quasielastic (p

We calculate all spin-transfer observables for the quasielastic (p\ensuremath{\rightarrow},n\ensuremath{\rightarrow}) reaction in a relativistic plane-wave impulse approximation. The nuclear structure information is contained in a large set of nuclear response functions that are computed in nuclear matter using a relativistic random-phase approximation to the Walecka model. A reduced value of the nucleon mass in the medium induces important dynamical changes in the residual isovector interaction relative to its nonrelativistic counterpart. As a result, good agreement is found for all spin observables---including the spin-longitudinal to spin-transverse ratio---when compared to the original (q=1.72 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$) NTOF (neutron time-of-flight facility) experiment. In contrast, the spin-longitudinal to spin-transverse ratio is underpredicted at q=1.2 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$ and overpredicted at q=2.5 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. We comment on the role of distortions as a possible solution to this discrepancy.

Subthreshold response function in the Delta -resonance region.

Nuclear response functions for quasielastic electron scattering are studied in the \ensuremath{\Delta}-resonance region below threshold. We find that the slow falloff below threshold required by the data in the dip region can be understood in a general way that depends only on kinematics and the approximate mass and width of the \ensuremath{\Delta}.

Nuclear response in the Δ - region and spin observable in charge exchange reactions

The cross-section of the charge exchange ( 3He,t) reaction in a Δ-isobar region was calculated for a finite nucleus in terms of a relativistic nuclear response function. The medium effects modifying a Δ and a pion propagation were considered for a finite size nucleus. The Glauber approach was used for distortion treatment of a 3He and a triton in the initial and the final states. The influence of the distortion on a spin transfer coefficient has been studied for ( p, n) and ( 3 He, t) reactions on nuclei for a pure longitudinal OPE amplitude of the Δ production.

The quasifree (p

The ratio of unnatural to natural parity exchange in quasifree excitation of nuclei is calculated in the eikonal scattering limit. Calculations with and without random phase approximation (RPA) correlations in the nuclear response function are compared with the ratio deduced from a recent (p\ensuremath{\rightarrow},n\ensuremath{\rightarrow}) experiment at LAMPF at 495 MeV bombarding energy and 1.7 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$ momentum transfer. At small energy transfers the cross section is well described both with and without correlations. In this region, the RPA calculation predicts a strong enhancement of the spin-longitudinal reaction channel which reflects itself in an enhanced ratio of unnatural to natural parity exchange. The spin-transfer data from LAMPF provide no support for the hypothesis of correlations in the spin-longitudinal channel as implied by the RPA calculations.

The pion in electromagnetic and weak neutral-current nuclear response functions

The impact of pionic correlations and meson-exchange currents in determining the (vector) response functions for electroweak quasielastic lepton scattering from nuclei is discussed. The approach taken builds on previous work where the Fermi gas model is used to maintain consistency in treating forces and currents (gauge invariance) and to provide a Lorentz covariant framework. Results obtained in first-order perturbation theory are compared with infinite-order summation schemes (HF and RPA) and found to provide quite successful approximations for the quasielastic response functions. The role of pionic correlations in hardening the responses R L and R T is investigated in some detail, including studies of the relative importance of central and tensor pieces of the force and of exchange and self-energy diagrams; in addition, their role in significantly modifying the longitudinal parity-violating response R AV L is explored. The MEC are shown to provide a small, but non-negligible, contribution in determining the vector responses.

Nuclear response in delta-isobar region in the (3He,t) reaction.

The excitation of a $\Delta$-isobar in a finite nucleus in charge--exchange ($^3\!$He,t) reaction is discussed in terms of a nuclear response function. The medium effects modifying a $\Delta$- and a pion propagation were considered for a finite size nucleus. The Glauber approach has been used for distortion of a $^3\!$He and a triton in the initial and the final states. The effects determining the peak positions and its width are discussed. Large displacement width for the $\Delta$ - h excitations and considerable contribution of coherent pion production were found for the reaction on $^{12}$C.

Parity-violating experiments using the quasi-elastic electron and positron scattering

The advantage of performing in parallel parity-violating experiments of electrons and positrons on nuclei for disentangling the nuclear (and nucleonic) axial response function and the isoscalar nucleon-nucleon correlations in nuclei is shown. The difficulties of carrying out this type of experiments are addressed. In order to be meaningful they indeed require intense and polarized (to a substantial degree) positron beams, which are presently not available.

Nucleon Electromagnetic Properties Modified in Nuclear Medium

Introducing effective masses of mesons and nucleons in the framework of the cloudy bag model, we calculated the bound nucleon form factors, magnetic moments, rms radii and axial coupling constant. These form factors have been applied to evaluate the dynamical charge longitudinal structure factors and the sum rules of nuclear response functions.

Extraction of nuclear spin response functions from spin observables of nucleon quasifree scattering.

Extraction of spin-longitudinal and -transverse response functions from polarization transfer measurements of nucleon-nucleus quasifree scatterings is discussed. The method proposed by Carey et al. is reconsidered and more general formulas are presented. Spin-longitudinal and -transverse interactions are well defined in the nucleon-nucleon scattering t matrix in the nucleon-nucleon center-of-mass frame. However, observed data are given in the nucleon-nucleus laboratory frame and theoretical analysis based on the distorted-wave and plane-wave impulse approximations is carried out in the nucleon-nucleus center-of-mass system, in which the t matrix in a certain optimum frame of the nucleon-nucleon system is used. Careful consideration is paid for transformations among these reference frames relativistically.

Quasielastic electron scattering in quasiparticle approach.

A quasiparticle Hamiltonian, which includes the effects of Hartree-Fock and correlations, has been introduced through a parametrization of the radial shape of the effective mass ${\mathit{m}}^{\mathrm{*}}$(r)/m. Within this phenomenological quasiparticle approach the longitudinal and transverse response functions of quasielastic electron scatterings are studied. It is found that the quasiparticle effective mass plays an important role on the nuclear response functions. The correlations of a nucleon coupling to the nuclear surface excitations have little effects at the momentum transfer qg400 MeV/c. Though this model could improve the agreement with experiments, the discrepancy on the longitudinal response remains to be solved.

Polarized Deuteron Scattering as a Probe for Spin-Dependent Response Functions in Nuclei

Inelastic scattering of polarized deuterons is considered as a probe to study nuclear spin·. dependent response functions. Partial spin-transfer cross sections are defined and are expressed in terms of polarization transfer coefficients. Relationship between spin observables and nuclear response functions is studied in the plane wave impulse approximation. Intensive studies of isovector spin-dependent excitation modes in nuclei have been performed using such reactions as (p, -;) or (p, p'). In particular, polarization transfer measurements have been done to extract information on spin-dependent response functions in nuclei. 1 ),2) Up to now a certain amount of knowledge on isovector spin-dependent excitations has thus accumulated, while that for isoscalar ones is still scarce. This is partly due to the lack of efficient probes for the latter mode, and may also be due to weakness of the effective interaction in the isoscalar spin-dependent channel, although a possibility still remains to develop collective nuclear states. 3 ) Recently a first attempt was made at Saturne 4 ) to measure polarization transfer coefficients in inelastic deuteron scattering, and to search for a combination of spin observables which would give a clear signature for isoscalar spin-dependent excita­ tions. The discussion there has been restricted to the spin-transfer of the projectile (deuteron), and therefore no clear statement on target structure could be made without the previous knowledge obtained from other probes. The purpose of the present paper is to consider a relationship between the polarization observables' in intermediate-energy deuteron soattering and nuclear response functions, within the plane-wave impluse approximation (PWIA), assuming a simple model for the deuteron-nucleon t-matrix. Within this approximation it is shown that a number of simple relations can be obtained among spin observables. It is known that even for a nucleon projectile distortion effect on the polarization­ transfer coefficients is important. 5 ) Nevertheless the present study is expected to give a suggestion on the possible use of polarized deuterons in detecting spin-dependent excitations, especially those not accessible with other probe~.

Second order effects in the nuclear response functions

A detailed calculation of the polarization propagator up to second order in perturbation theory is presented, involving 2p-2h states. The relevance of the latter is felt both at low and at high energies, in a variety of processes which might thus be described in a consistent framework. In particular the nonleptonic decay of Lambda -hypernuclei and the nuclear response to an electromagnetic probe are discussed in connection with second order effects.

Quasiparticle Effects in Quasielastic Electron Scattering

The quasiparticle effect on the nuclear response in the quasielastic electron scattering is studied in a phenomenological quasiparticle model. The quasiparticle Hamiltonian which includes correlations has been introduced through a parameterization of the effective mass m*(r)/m. It is found that the quasiparticle effective mass plays an important role on the nuclear response functions. Though this model could give better agreement with experiments, the discrepancy in the longitudinal response remains to be eliminated.

Nuclear response function at finite temperature.

The static-path approximation is applied to the real-time response function of a nucleus at finite temperature. This approximation is shown to become accurate in the high-temperature limit for an appropriately energy-smoothed strength function. An additional local approximation to overlap integrals yields the familiar adiabatic approximation. These two approximations are compared with exact results for the Lipkin model. For a sufficiently large ratio of two-body interaction to single-particle energy, the static-path approximation accurately describes the exact strength function. For parameters characteristic of nuclear shape transitions, the static-path approximation is not reliable and the adiabatic approximation is qualitatively in error.

Separation of the interference response function RLT in the 16O(e,e'p)15N reaction.

In one of the first measurements of its type, the nuclear response function ${\mathit{R}}_{\mathit{L}\mathit{T}}$ has been determined in the $^{16}\mathrm{O}$(e,e'p${)}^{15}$N reaction in quasielastic kinematics for the ground state (1/${2}^{\mathrm{\ensuremath{-}}}$) and the first excited state (6.32 MeV, 3/${2}^{\mathrm{\ensuremath{-}}}$). Extracted momentum distributions for these two states exhibit asymmetric behavior. Spectroscopic factors show significant depletion of strength, consistent with previous results. ${\mathit{R}}_{\mathit{L}\mathit{T}}$ agrees better with relativistic distorted-wave impulse-approximation calculations in magnitude than does the total cross section.

Second-order effects in the nuclear-response functions

Second-order effects in the nuclear-response functions

Gross-shell effects in nuclear response functions

We study nuclear collective vibrations and try to separate contributions from quasi-particle excitations close to the Fermi level from statistically averaged quantities. In this paper we concentrate on the variation coming from the quasi-particle component. As theoretical means we use linear response functions and their semiclassical expansions over trajectories. We study gross-shell effects in vibrating spherical nuclei and evaluate these expansions for the case of an infinitely deep square well, and thus for surface peaked interactions. We calculate strength functions for monopole and quadrupole vibrations. Restricting to only a few dominating terms in the semiclassical expansion we obtain simple expressions which can easily be evaluated numerically. For the case of the quadrupole we find good agreement with available data and with previous computations in the frame of conventional RPA, both for the excitation energies itself as well as their distribution within an energy-weighted sum. The resonance behaviour of the strength function, or its quasi-particle component rather, is determined by the distance between gross shells. The latter is related to the mean period of the shortest periodic orbits.