Nucleon-Nucleon Correlations and Inelastic Electron Scattering on<sup>4</sup>He

Dementij, S. V.; Korchin, A. Yu.; Kuplennikov, E.L.; Ranyuk, Yu.N.; Sorokin, P.V.; Katayama, Toshiyuki; Akaishi, Yoshinori; Tanaka, Hajime

doi:10.1143/jpsj.57.2988

Cited by 2 publications

(4 citation statements)

References 15 publications

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“…The term "shrinking" implies that each of these densities, after being CM corrected, increases in its central but decreases in its peripheral region. As it has been shown in the past [22,46], such a simultaneous change of the onebody distributions plays an essential role in getting a fair treatment of the data on elastic and inelastic electron scattering off 4 He. Notice that the product r0 p0 = 1−1/A = 1, unlike the relation r 0 p 0 = 1.…”

Section: He and Discussionmentioning

confidence: 99%

The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion⋆

Papakonstantinou

Mavrommatis²

2006

Eur. Phys. J. A

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Abstract. The one-body and two-body density matrices in coordinate space and their Fourier transforms in momentum space are studied for a nucleus (a nonrelativistic, self-bound finite system). Unlike the usual procedure, suitable for infinite or externally bound systems, they are determined as expectation values of appropriate intrinsic operators, dependent on the relative coordinates and momenta (Jacobi variables) and acting on intrinsic wavefunctions of nuclear states. Thus, translational invariance (TI) is respected. When handling such intrinsic quantities, we use an algebraic technique based upon the Cartesian representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operatorsâ + andâ for oscillator quanta. Each of the relevant multiplicative operators can then be reduced to the form: one exponential of the set {â + } times other exponential of the set {â}. In the course of such a normal-ordering procedure we offer a fresh look at the appearance of "Tassie-Barker" factors, and point out other model-independent results. The intrinsic wavefunction of the nucleus in its ground state is constructed from a nontranslationally-invariant (nTI) one via existing projection techniques. As an illustration, the one-body and two-body momentum distributions (MDs) for the 4 He nucleus are calculated with the Slater determinant of the harmonic-oscillator model as the trial, nTI wavefunction. We find that the TI introduces important effects in the MDs.PACS. 21.60.-n Nuclear structure models and methods -21.45.+v Nuclear few-body systems -24.10.-i Nuclear reaction models and methods

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Section: He and Discussionmentioning

confidence: 99%

The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion⋆

Papakonstantinou

Mavrommatis²

2006

Eur. Phys. J. A

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“…An alternative evaluation [3]- [5], [15] of the intrinsic FF's, densities and momentum distributions, put forward in [3] to overcome some obstacles in describing the elastic and inclusive electron scattering off the 4 He nucleus, has brought a fresh look at the CM correction of these quantities. In particular, it turns out that ρ int (r) and η int (p) are shrunk (from the periphery of each of them to its central part) compared to ρ(r) and η(p).…”

Section: Introductionmentioning

confidence: 99%

“…Regarding the second aspect, we mean firstly a comparatively simple relation in the Born approximation to express the elastic electron scattering cross section through the charge form factor (FF) F ch (q) of the target-nucleus and its charge density ρ ch (r) being defined by the Fourier transform of F ch (q). In addition, in the so-called approximation of small interaction times (see [3]- [5]) the double differential (e, e ) reaction cross section becomes proportional to an integral of the momentum distribution (MD) η(p) over the momentum range that is a shebeko@kipt.kharkov.ua b grigorov@mail.ru c iurasov90@gmail.com fixed with certain combination (the y−scalling variable) of the momentum transfer q and the energy transfer ω (cf. [6]).…”

Section: Introductionmentioning

confidence: 99%

“…[15]) while the not intrinsic DM n(k) has been corrected (without any good reasons) via the renormalization b −→ A−1 A b of the corresponding oscillator parameter b (see, e.g., [28]), i.e., as in the case of ρ ch (r). An alternative evaluation [3]- [5], [15] of the intrinsic FF's, densities and momentum distributions, put forward in [3] to overcome some obstacles in describing the elastic and inclusive electron scattering off the 4 He nucleus, has brought a fresh look at the CM correction of these quantities. In particular, it turns out that ρ int (r) and η int (p) are shrunk (from the periphery of each of them to its central part) compared to ρ(r) and η(p).…”

Section: Introductionmentioning

confidence: 99%

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Translationally invariant calculations of form factors, nucleon densities and momentum distributions for finite nuclei with short-range correlations included

Grigorov

2012

Eur. Phys. J. A

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Relying upon our previous treatment of the density matrices for nuclei (in general, nonrelativistic self-bound finite systems) we are studying a combined effect of center-of-mass motion and short-range nucleon-nucleon correlations on the nucleon density and momentum distributions in light nuclei ( 4 He and 16 O). Their intrinsic ground-state wave functions are constructed in the so-called fixed center-ofmass approximation, starting with mean-field Slater determinants modified by some correlator (e.g., after Jastrow or Villars). We develop the formalism based upon the Cartesian or boson representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operators for oscillatory quanta in the three different space directions, and get the own "Tassie-Barker" factors for each distribution and point out other model-independent results. After this separation of the center-of-mass motion effects we propose additional analytic means in order to simplify the subsequent calculations (e.g., within the Jastrow approach or the unitary correlation operator method). The charge form factors, densities and momentum distributions of 4 He and 16 O evaluated by using the well known cluster expansions are compared with data, our exact (numerical) results and microscopic calculations.

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Nucleon-Nucleon Correlations and Inelastic Electron Scattering on⁴He

Cited by 2 publications

References 15 publications

The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion⋆

The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion⋆

Translationally invariant calculations of form factors, nucleon densities and momentum distributions for finite nuclei with short-range correlations included

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Nucleon-Nucleon Correlations and Inelastic Electron Scattering on4He

Cited by 2 publications

References 15 publications

The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion⋆

The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion⋆

Translationally invariant calculations of form factors, nucleon densities and momentum distributions for finite nuclei with short-range correlations included

Contact Info

Product

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Nucleon-Nucleon Correlations and Inelastic Electron Scattering on⁴He