Calculation of a narrow resonance with the LIT method

Leidemann, Winfried

doi:10.1007/s00601-008-0199-5

Cited by 13 publications

(32 citation statements)

References 18 publications

(29 reference statements)

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“…Such a calculation requires a considerable additional computational effort and thus the threshold region is excluded from our present work. Allowing a narrow resonance in the inversion [27], we have checked that our results are stable for energies above E r + 2σ I .…”

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confidence: 99%

“…We should mention that we do not show the low-energy isoscalar response, where a narrow 0 + resonance with a width of a few hundred keV is present at E r very close to threshold [23]. To get accurate results for such a resonance a convergent LIT calculation with a σ I much smaller than the presently used values (smallest value σ I = 5 MeV) should be carried out, which then leads to a very slow asymptotically fall off of the solution | Ψ ρ σ,q (see [27]). Such a calculation requires a considerable additional computational effort and thus the threshold region is excluded from our present work.…”

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confidence: 99%

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Role of the Final-State Interaction and Three-Body Force on the Longitudinal Response Function ofHe4

et al. 2009

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We present an ab-initio calculation of the longitudinal electron scattering response function off 4 He with two-and three-nucleon forces and compare to experimental data. The full four-body continuum dynamics is considered via the Lorentz integral transform method. The importance of the final state interaction is shown at various energies and momentum transfers q. The three-nucleon force reduces the quasi-elastic peak by 10% for q between 300 and 500 MeV/c. Its effect increases significantly at lower q, up to about 40% at q=100 MeV/c. At very low q, however, data are missing.PACS numbers: 25.30.Fj, 27.10.+h, 31.15.xj Inelastic electron scattering off nuclei provides important informations on nuclear dynamics. Varying the momentum q, transferred by the electron to the nucleus, one can focus on different dynamical regimes. At lower q the collective behavior of nucleons is studied. As q increases one probes properties of the single nucleon in the nuclear medium and its correlations to other nucleons from longto short-range. Thus the inclusive longitudinal R L and transverse R T response functions are of particular importance. Different from R T , in a non-relativistic framework R L does not require the knowledge of implicit degrees of freedom (exchange currents), providing a clean leptonic probe of the nuclear Hamiltonian. In addition, the theoretical study of inclusive processes is important to help planning further investigations, for selected kinematics, via exclusive scattering experiments.In the '80 and '90's an intense experimental activity has been devoted to inclusive electron scattering, (e, e ′ ), in the so called quasi-elastic (q.e.) regime, corresponding to q-values of several hundred MeV/c and energy transfers ω around the q.e. peak (ω ≃ q 2 /2m). Here one can envisage that the electron has scattered elastically with a single nucleon of mass m. Various nuclear targets have been considered, from very light to heavy ones [1]. At these q one enters a very challenging regime, where nuclear and subnuclear degrees of freedom interwine. A very alive debate has taken place about the interpretation of those data. The two most discussed topics have been: (i) short-range correlations, i.e. the dynamical properties of nucleons at short distances; (ii) in medium modifications of the nucleon form factor. To date the debate is still open. More experiments are planned at Jefferson Laboratory (E05.110 at Hall A) which will contribute to those issues and a theoretical effort is needed to help interpreting old and new experimental results.The reason for concentrating on the q.e. regime has been the conviction that for such a kinematics the plane wave impulse approximation (PWIA) might be a reliable framework to describe the reaction. The neglect of the final state interaction (FSI) has the advantage to allow a simple interpretation of the cross section in terms of the dynamical properties of the nucleons in the ground state. Thus it is important to clarify the reliability of the PWIA (as well as of further refinements...

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Role of the Final-State Interaction and Three-Body Force on the Longitudinal Response Function ofHe4

et al. 2009

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“…This is the cause of the ill-posed problem and also the reason why the LIT approach is a method with a controlled resolution. That the LIT approach works in an excellent way has been shown in various benchmark calculations for two-and three-nucleon electromagnetic reactions [23,24,26,27,66,67]. The LIT results illustrated in the following are calculated using CHH and EIHH expansions (see section 2) for three-and four-nucleon systems, respectively.…”

Section: Inelastic Inclusive Electromagnetic Reactionsmentioning

confidence: 99%

“…In case that a single resonance with a width much smaller than σ I is present this will be realized in the inversion process even if it cannot be completely resolved (see discussion of Coulomb monopole resonance in [64,65]). If one wants to resolve such structures precisely one has to further reduce σ I (see [67]). Note that one has to make more and more accurate calculations for a smaller and smaller σ I in order to obtain a sufficiently converged LIT result.…”

Section: Inelastic Inclusive Electromagnetic Reactionsmentioning

confidence: 99%

Few-nucleon physics

Leidemann¹

2009

J. Phys.: Conf. Ser.

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Abstract. Recent progress in few-nucleon physics achieved by Italian research groups is described. Results for relativistic effects in elastic three-nucleon form factors (Rome group), hadronic and electromagnetic observables in three-and four-nucleon systems with special emphasis on three-nucleon force effects (Pisa and Trento groups), and spectra of nuclei with more than 4 nucleons (Padua group) are presented. IntroductionThe field of few-nucleon physics constitutes an essential part of nuclear physics. It consists of ab initio calculations of hadronic and electromagnetic observables with a given well-defined Hamiltonian of an A-nucleon system, where exact solutions of the quantum mechanical A-body system are requested for bound and/or scattering states. In particular one can consider boundstate spectra and observables from hadronic reactions like scattering lengths, phase shifts, total and differential cross sections. A polarization of beam, target, and/or final particles leads to many other hadronic polarization observables. In addition reactions with electroweak probes (photons, electrons, neutrinos) without and with polarization degrees of freedom give further information on the nuclear dynamics and electroweak structure of few-nucleon systems. For the latter one has to consider a further important aspect, namely the consistency of the electroweak currents with the nuclear Hamiltonian.Few-nucleon physics has many objectives: development of nuclear force models (nucleonnucleon (NN) and three-nucleon (3N) forces) and check whether even higher many-body forces are necessary, test of nuclear force models via two-and three-nucleon hadronic observables with possible feedback on force model, further test of nuclear dynamics in electromagnetic reactions with two-and three-nucleon systems; the study of the electroweak structure of few-nucleon systems; the investigation of the importance of relativistic effects; the extension of nuclear force models beyond pion threshold; the determination of neutron electroweak properties in twoand three-nucleon electroweak observables; the determination of observables with astrophysical relevance.Here follows a very brief summary on the state of the art for some selected aspects of fewnucleon physics. NN potential models have a long history (see e.g. [1] [5,6,7]. The potentials [2,3,4,5] all lead to a perfect or almost perfect description of various thousands of NN scattering data for energies up to pion threshold, while the chiral potential [6,7] is constructed more in the original spirit of effective field theory where open parameters are fitted to low-energy data only. The history of 3N forces started with

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“…This makes the inversion very reliable. For a discussion of the inversion procedure itself the reader is referred to [2,10], but it should be pointed out, that even resonances with a width as small as 300 keV can be reliably resolved with the LIT method [11].…”

Section: Lit Approach: a Simple Examplementioning

confidence: 99%

Do light nuclei exhibit “collective” motions?

Leidemann

2014

EPJ Web of Conferences

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Abstract. The Lorentz integral transform (LIT) method has allowed to perform ab initio calculations of the response function of 4,6 He, and 6,7 Li to the isoscalar monopole and isovector dipole operators in a wide range of energies. In this work we discuss some of these results and focus in particular on the 4 He case, where one has a 0 + resonance close to the 3+1 thresholds. In fact, in inelastic electron scattering off 4 He one finds a pronounced resonant structure in the isoscalar monopole strength. The knowledge of this strength as a function of energy makes possible calculations of the corresponding nonenergy weighted and energy-weighted sum rules. Comparing the sum rules with their contribution from the resonance region hints to the degree of collectivity of the resonant structure.

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Calculation of a narrow resonance with the LIT method

Cited by 13 publications

References 18 publications

Role of the Final-State Interaction and Three-Body Force on the Longitudinal Response Function ofHe4

Role of the Final-State Interaction and Three-Body Force on the Longitudinal Response Function ofHe4

Few-nucleon physics

Do light nuclei exhibit “collective” motions?

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